An Overview on Resource Allocation Techniques for Multi-User MIMO Systems
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paper_title: An overview of scheduling algorithms in MIMO-based fourth-generation wireless systems

paper_content:

In this article an overview of the scheduling algorithms proposed for fourth-generation multiuser wireless networks based on multiple-input multiple-output technology is presented. In MIMO systems a multi-user diversity gain can be extracted by tracking the channel fluctuations between each user and the base station, and scheduling transmission for the "best" user. Based on this idea, several opportunistic scheduling schemes that attempt to improve global capacity or satisfy users with different QoS requirements have been proposed. Transmit beamforming procedures aimed at increasing the channel fluctuations have been proposed. The simultaneous exploitation of both spatial and multi-user diversity is not straightforward; however, it may be achieved by a refined selection of the "best" user. In addition, a multiple access gain can be obtained from a simple SDMA/TOMA system. Finally, several resource allocation schemes are discussed for this hybrid multiple access system.
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paper_title: Call admission control in wireless networks: a comprehensive survey

paper_content:

Radio resource management (RRM) plays a major role in Quality of Service (QoS) provisioning for wireless communication systems. The performance of RRM techniques has a direct impact on each user's individual performance and on the overall network performance. Arriving (new and handoff) calls are granted/denied access to the network by the call admission scheme (CAC) based on predefined criteria, taking the network loading conditions into consideration. CAC in wireless networks has been receiving a great deal of attention during the last two decades due to the growing popularity of wireless communications and the central role that CAC plays in QoS provisioning in terms of the signal quality, call blocking and dropping probabilities, packet delay and loss rate, and transmission rate. In the first and second generation of wireless systems, CAC has been developed for a single service environment. In the third generation and beyond wireless systems, multimedia services such as voice, video, data, and audio are to be offered with various QoS profiles. Hence, more sophisticated CAC schemes are developed to cope with these changes. This article provides a comprehensive survey of CAC schemes in modern wireless networks.
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paper_title: 5G Network Capacity: Key Elements and Technologies

paper_content:

It has been projected that, in the next decade, a mobile traffic increase on the order of 1,000 times is expected compared to what we experience today. To meet that dramatic traffic growth, next-generation mobile networks are also expected to achieve a 1,000-fold capacity increase compared to the current generation of wireless network deployments. In this article, we discuss how such capacity growth could be achieved in a ten-year time frame. We discuss the techniques that we expect to have the highest opportunity for increasing the system capacity and estimate their gains based on analysis and simulation. We observe that the main driver of capacity growth is expected to come from network architecture advancements, with heterogeneous networks and convergence of information and communication technology being two of the key techniques. We also estimate that the air-interface evolution would focus not only on improving the link and system spectrum efficiency but also on facilitating the required network efficiency improvements. This article provides insights into the communication technology evolution and can be used as a guideline for technology development toward the fifth generation (5G).
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paper_title: A Survey on Opportunistic Scheduling in Wireless Communications

paper_content:

Wireless technology advancements made opportunistic scheduling a popular topic in recent times. However, opportunistic schedulers for wireless systems have been studied since nearly twenty years, but not implemented in real systems due to their high complexity and hardly achievable requirements. In contrast, today's popularity of opportunistic schedulers extends to implementation proposals for next generation cellular technologies. Motivated by such a novel interest towards opportunistic scheduling, we provide a taxonomy for opportunistic schedulers, which is based on scheduling design's objectives; accordingly, we provide an extensive review of opportunistic scheduling proposals which have appeared in the literature during nearly two decades. The huge number of papers available in the literature propose different techniques to perform opportunistic scheduling, ranging from simple heuristic algorithms to complex mathematical models. Some proposals are only designed to increase the total network capacity, while others enhance QoS objectives such as throughput and fairness. Interestingly, our survey helps to unveil two major issues: (i) the research in opportunistic is mature enough to jump from pure theory to implementation, and (ii) there are still under-explored and interesting research areas in opportunistic scheduling, e.g., opportunistic offloading of cellular traffic to 802.11-like networks, or cooperative/distributed opportunistic scheduling.
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paper_title: An Overview of Massive MIMO: Benefits and Challenges

paper_content:

Massive multiple-input multiple-output (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of state-of-the-art research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of non-orthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient single-carrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.
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paper_title: Survey of Large-Scale MIMO Systems

paper_content:

The escalating teletraffic growth imposed by the proliferation of smartphones and tablet computers outstrips the capacity increase of wireless communications networks. Furthermore, it results in substantially increased carbon dioxide emissions. As a powerful countermeasure, in the case of full-rank channel matrices, MIMO techniques are potentially capable of linearly increasing the capacity or decreasing the transmit power upon commensurately increasing the number of antennas. Hence, the recent concept of large-scale MIMO (LS-MIMO) systems has attracted substantial research attention and been regarded as a promising technique for next-generation wireless communications networks. Therefore, this paper surveys the state of the art of LS-MIMO systems. First, we discuss the measurement and modeling of LS-MIMO channels. Then, some typical application scenarios are classified and analyzed. Key techniques of both the physical and network layers are also detailed. Finally, we conclude with a range of challenges and future research topics.
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paper_title: 802.11 WLAN: history and new enabling MIMO techniques for next generation standards

paper_content:

IEEE 802.11, which designs wireless local area networks (WLAN), is one of the most successful standards in wireless communication systems. In this article, we review the history of WLAN standards, and provide technical overviews of the recent development of WLAN systems. Especially, as the original inventor and the proposer, we focus on beamforming and compressed feedback schemes, which have been adopted in 802.11 WLAN standards, to improve the throughput for a multiple-input multiple-output (MIMO) system. These techniques are essential to maximize the downlink system throughput for multiple user transmission as well as for single user transmission. Also, we present discussions on new technologies to further enhance user throughput, which are currently considered for future WLAN systems.
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paper_title: Five Disruptive Technology Directions for 5G

paper_content:

New research directions will lead to fundamental changes in the design of future 5th generation (5G) cellular networks. This paper describes five technologies that could lead to both architectural and component disruptive design changes: device-centric architectures, millimeter Wave, Massive-MIMO, smarter devices, and native support to machine-2-machine. The key ideas for each technology are described, along with their potential impact on 5G and the research challenges that remain.
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paper_title: Recent Advances in Radio Resource Management for Heterogeneous LTE/LTE-A Networks

paper_content:

As heterogeneous networks (HetNets) emerge as one of the most promising developments toward realizing the target specifications of Long Term Evolution (LTE) and LTE-Advanced (LTE-A) networks, radio resource management (RRM) research for such networks has, in recent times, been intensively pursued. Clearly, recent research mainly concentrates on the aspect of interference mitigation. Other RRM aspects, such as radio resource utilization, fairness, complexity, and QoS, have not been given much attention. In this paper, we aim to provide an overview of the key challenges arising from HetNets and highlight their importance. Subsequently, we present a comprehensive survey of the RRM schemes that have been studied in recent years for LTE/LTE-A HetNets, with a particular focus on those for femtocells and relay nodes. Furthermore, we classify these RRM schemes according to their underlying approaches. In addition, these RRM schemes are qualitatively analyzed and compared to each other. We also identify a number of potential research directions for future RRM development. Finally, we discuss the lack of current RRM research and the importance of multi-objective RRM studies.
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paper_title: A Unified Approach to QoS-Guaranteed Scheduling for Channel-Adaptive Wireless Networks

paper_content:

Scheduling amounts to allocating optimally channel, rate and power resources to multiple connections with diverse quality-of-service (QoS) requirements. It consti- tutes a throughput-critical task at the medium access control layer of today's wireless networks that has been tackled by seemingly unrelated information-theoretic and protocol design approaches. Capitalizing on convex optimization and stochastic approximation tools, the present paper develops a unified framework for channel-aware QoS-guaranteed scheduling protocols for use in adaptive wireless networks whereby multiple terminals are linked through orthogonal fading channels to an access point, and transmissions are (opportu- nistically) adjusted to the intended channel. The unification encompasses downlink and uplink with time-division or frequency-division duplex operation; full and quantized chan- nel state information comprising a few bits communicated over a limited-rate feedback channel; different types of traffic (best effort, non-real-time, real-time); uniform and optimal power loading; off-line optimal scheduling schemes benchmarking fundamentally achievable rate limits; as well as on-line scheduling algorithms capable of dynamically learning the intended channel statistics and converging to the optimal benchmarks from any initial value. The take-home message offers an important cross-layer design guideline: judiciously developed, yet surprisingly simple, channel-adaptive, on-line schedulers can approach information-theoretic rate limits with QoS guarantees.
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

paper_content:

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: What Will 5G Be?

paper_content:

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
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paper_title: An overview of scheduling algorithms in MIMO-based fourth-generation wireless systems

paper_content:

In this article an overview of the scheduling algorithms proposed for fourth-generation multiuser wireless networks based on multiple-input multiple-output technology is presented. In MIMO systems a multi-user diversity gain can be extracted by tracking the channel fluctuations between each user and the base station, and scheduling transmission for the "best" user. Based on this idea, several opportunistic scheduling schemes that attempt to improve global capacity or satisfy users with different QoS requirements have been proposed. Transmit beamforming procedures aimed at increasing the channel fluctuations have been proposed. The simultaneous exploitation of both spatial and multi-user diversity is not straightforward; however, it may be achieved by a refined selection of the "best" user. In addition, a multiple access gain can be obtained from a simple SDMA/TOMA system. Finally, several resource allocation schemes are discussed for this hybrid multiple access system.
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paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

paper_content:

This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
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paper_title: A Survey on Opportunistic Scheduling in Wireless Communications

paper_content:

Wireless technology advancements made opportunistic scheduling a popular topic in recent times. However, opportunistic schedulers for wireless systems have been studied since nearly twenty years, but not implemented in real systems due to their high complexity and hardly achievable requirements. In contrast, today's popularity of opportunistic schedulers extends to implementation proposals for next generation cellular technologies. Motivated by such a novel interest towards opportunistic scheduling, we provide a taxonomy for opportunistic schedulers, which is based on scheduling design's objectives; accordingly, we provide an extensive review of opportunistic scheduling proposals which have appeared in the literature during nearly two decades. The huge number of papers available in the literature propose different techniques to perform opportunistic scheduling, ranging from simple heuristic algorithms to complex mathematical models. Some proposals are only designed to increase the total network capacity, while others enhance QoS objectives such as throughput and fairness. Interestingly, our survey helps to unveil two major issues: (i) the research in opportunistic is mature enough to jump from pure theory to implementation, and (ii) there are still under-explored and interesting research areas in opportunistic scheduling, e.g., opportunistic offloading of cellular traffic to 802.11-like networks, or cooperative/distributed opportunistic scheduling.
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paper_title: Downlink Packet Scheduling in LTE Cellular Networks: Key Design Issues and a Survey

paper_content:

Future generation cellular networks are expected to provide ubiquitous broadband access to a continuously growing number of mobile users. In this context, LTE systems represent an important milestone towards the so called 4G cellular networks. A key feature of LTE is the adoption of advanced Radio Resource Management procedures in order to increase the system performance up to the Shannon limit. Packet scheduling mechanisms, in particular, play a fundamental role, because they are responsible for choosing, with fine time and frequency resolutions, how to distribute radio resources among different stations, taking into account channel condition and QoS requirements. This goal should be accomplished by providing, at the same time, an optimal trade-off between spectral efficiency and fairness. In this context, this paper provides an overview on the key issues that arise in the design of a resource allocation algorithm for LTE networks. It is intended for a wide range of readers as it covers the topic from basics to advanced aspects. The downlink channel under frequency division duplex configuration is considered as object of our study, but most of the considerations are valid for other configurations as well. Moreover, a survey on the most recent techniques is reported, including a classification of the different approaches presented in literature. Performance comparisons of the most well-known schemes, with particular focus on QoS provisioning capabilities, are also provided for complementing the described concepts. Thus, this survey would be useful for readers interested in learning the basic concepts before going into the details of a particular scheduling strategy, as well as for researchers aiming at deepening more specific aspects.
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paper_title: A Unified Approach to QoS-Guaranteed Scheduling for Channel-Adaptive Wireless Networks

paper_content:

Scheduling amounts to allocating optimally channel, rate and power resources to multiple connections with diverse quality-of-service (QoS) requirements. It consti- tutes a throughput-critical task at the medium access control layer of today's wireless networks that has been tackled by seemingly unrelated information-theoretic and protocol design approaches. Capitalizing on convex optimization and stochastic approximation tools, the present paper develops a unified framework for channel-aware QoS-guaranteed scheduling protocols for use in adaptive wireless networks whereby multiple terminals are linked through orthogonal fading channels to an access point, and transmissions are (opportu- nistically) adjusted to the intended channel. The unification encompasses downlink and uplink with time-division or frequency-division duplex operation; full and quantized chan- nel state information comprising a few bits communicated over a limited-rate feedback channel; different types of traffic (best effort, non-real-time, real-time); uniform and optimal power loading; off-line optimal scheduling schemes benchmarking fundamentally achievable rate limits; as well as on-line scheduling algorithms capable of dynamically learning the intended channel statistics and converging to the optimal benchmarks from any initial value. The take-home message offers an important cross-layer design guideline: judiciously developed, yet surprisingly simple, channel-adaptive, on-line schedulers can approach information-theoretic rate limits with QoS guarantees.
---
paper_title: An overview of scheduling algorithms in MIMO-based fourth-generation wireless systems

paper_content:

In this article an overview of the scheduling algorithms proposed for fourth-generation multiuser wireless networks based on multiple-input multiple-output technology is presented. In MIMO systems a multi-user diversity gain can be extracted by tracking the channel fluctuations between each user and the base station, and scheduling transmission for the "best" user. Based on this idea, several opportunistic scheduling schemes that attempt to improve global capacity or satisfy users with different QoS requirements have been proposed. Transmit beamforming procedures aimed at increasing the channel fluctuations have been proposed. The simultaneous exploitation of both spatial and multi-user diversity is not straightforward; however, it may be achieved by a refined selection of the "best" user. In addition, a multiple access gain can be obtained from a simple SDMA/TOMA system. Finally, several resource allocation schemes are discussed for this hybrid multiple access system.
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paper_title: On limits of wireless communications in a fading environment when using multiple antennas

paper_content:

This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. ::: ::: We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.
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paper_title: Multiple-antenna techniques for wireless communications - a comprehensive literature survey

paper_content:

The use of multiple antennas for wireless communication systems has gained overwhelming interest during the last decade - both in academia and industry. Multiple antennas can be utilized in order to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. With an enormous amount of yearly publications, the field of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly. To date, there are numerous papers on the performance limits of MIMO systems, and an abundance of transmitter and receiver concepts has been proposed. The objective of this literature survey is to provide non-specialists working in the general area of digital communications with a comprehensive overview of this exciting research field. To this end, the last ten years of research efforts are recapitulated, with focus on spatial multiplexing and spatial diversity techniques. In particular, topics such as transmitter and receiver structures, channel coding, MIMO techniques for frequency-selective fading channels, diversity reception and space-time coding techniques, differential and non-coherent schemes, beamforming techniques and closed-loop MIMO techniques, cooperative diversity schemes, as well as practical aspects influencing the performance of multiple-antenna systems are addressed. Although the list of references is certainly not intended to be exhaustive, the publications cited will serve as a good starting point for further reading.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: Degrees of freedom in wireless multiuser spatial multiplex systems with multiple antennas

paper_content:

This letter investigates the structure of the optimal spatial multiplex scheme in a multiuser multiantenna wireless fading environment. Based on a sum-capacity criterion, this letter shows that the optimal transmission strategy in an uplink or downlink channel with n antennas at the base-station involves more than n users at the same time. In particular, when remote users are equipped with m antennas each, the maximum number of data streams is shown to be upper bounded by n2, with each user transmitting or receiving up to m2 data streams. This gives a dimension-counting interpretation for multiuser diversity. Multiple antennas at the base-station increases the total number of dimensions, thus allowing more users to transmit and receive at the same time. By contrast, multiple antennas at the remote terminal allow a single user to occupy multiple dimensions, which increases its transmission rate, but also has the potential effect of precluding simultaneous transmission by other users
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paper_title: Solution of the multiuser downlink beamforming problem with individual SINR constraints

paper_content:

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.
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paper_title: Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels

paper_content:

Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. We propose the point of view that both types of gains can be simultaneously obtained for a given multiple-antenna channel, but there is a fundamental tradeoff between how much of each any coding scheme can get. For the richly scattered Rayleigh-fading channel, we give a simple characterization of the optimal tradeoff curve and use it to evaluate the performance of existing multiple antenna schemes.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: Adaptive Modulation in PU2RC Systems with Finite Rate Feedback

paper_content:

This paper addresses a per user unitary precoding and rate control (PU 2 RC) system with adaptive multi-level quadrature amplitude modulation (QAM) modulation, where both the PU 2 RC operation and adaptive modulation are based on finite rate feedback. The system supports two transmission modes (single user transmit beamforming and multiuser transmission with orthogonal beamforming), and switches between the two modes to maximize the average throughput. We first study single user transmit beamforming, and derive closed-form expressions for the average throughput and bit-error rate (BER) with outdated channel information. Then, multiuser transmission with orthogonal beamforming is investigated. We analyze the throughput and BER performance without feedback delay in the normal signal noise ratio (SNR) regime, and the performance with feedback delay in the interference-limited regime. Simulation results demonstrate the effect of time delay, and the preferred regions of the single user transmission mode and multiuser transmission mode.
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paper_title: Opportunistic beamforming using dumb antennas

paper_content:

An important means to cope with fading in wireless channels is the use of diversity. Diversity can be obtained over time (interleaving of coded bits), frequency (combining of multipaths in CDMA systems) and space (multiple antennas). The basic idea is to improve performance by creating several independent signal paths between the transmitter and the receiver. In this paper, we propose a scheme that induces random fading when the environment has little scattering and/or the fading is slow. We focus on the downlink of a cellular system. We use multiple antennas at the base-station to transmit the same signal from each antenna modulated by a gain whose phase and magnitude is changing in time in a controlled but pseudo random fashion.
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paper_title: An overview of scheduling algorithms in MIMO-based fourth-generation wireless systems

paper_content:

In this article an overview of the scheduling algorithms proposed for fourth-generation multiuser wireless networks based on multiple-input multiple-output technology is presented. In MIMO systems a multi-user diversity gain can be extracted by tracking the channel fluctuations between each user and the base station, and scheduling transmission for the "best" user. Based on this idea, several opportunistic scheduling schemes that attempt to improve global capacity or satisfy users with different QoS requirements have been proposed. Transmit beamforming procedures aimed at increasing the channel fluctuations have been proposed. The simultaneous exploitation of both spatial and multi-user diversity is not straightforward; however, it may be achieved by a refined selection of the "best" user. In addition, a multiple access gain can be obtained from a simple SDMA/TOMA system. Finally, several resource allocation schemes are discussed for this hybrid multiple access system.
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paper_title: Artificial Intelligence in Wireless Communications

paper_content:

This cutting-edge resource offers practical overview of cognitive radio - a paradigm for wireless communications in which a network or a wireless node changes its transmission or reception parameters. The alteration of parameters is based on the active monitoring of several factors in the external and internal radio environment. This book offers a detailed description of cognitive radio and its individual parts. Practitioners learn how the basic processing elements and their capabilities are implemented as modular components. Moreover, the book explains how each component can be developed and tested independently, before integration with the rest of the engine. Practitioners discover how cognitive radio uses artificial intelligence to achieve radio optimization. The book also provides an in-depth working example of the developed cognitive engine and an experimental scenario to help engineers understand its performance and behavior.
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paper_title: The Design of Approximation Algorithms

paper_content:

Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
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paper_title: Order Statistics in Wireless Communications: Diversity, Adaptation, and Scheduling in MIMO and OFDM Systems

paper_content:

Covering fundamental principles through to practical applications, this self-contained guide describes indispensable mathematical tools for the analysis and design of advanced wireless transmission and reception techniques in MIMO and OFDM systems. The analysis-oriented approach develops a thorough understanding of core concepts and discussion of various example schemes shows how to apply these concepts in practice. The book focuses on techniques for advanced diversity combining, channel adaptive transmission and multiuser scheduling, the foundations of future wireless systems for the delivery of highly spectrum-efficient wireless multimedia services. Bringing together conventional and novel results from a wide variety of sources, it will teach you to accurately quantify trade-offs between performance and complexity for different design options so that you can determine the most suitable design choice based on your specific practical implementation constraints.
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paper_title: Degrees of freedom in wireless multiuser spatial multiplex systems with multiple antennas

paper_content:

This letter investigates the structure of the optimal spatial multiplex scheme in a multiuser multiantenna wireless fading environment. Based on a sum-capacity criterion, this letter shows that the optimal transmission strategy in an uplink or downlink channel with n antennas at the base-station involves more than n users at the same time. In particular, when remote users are equipped with m antennas each, the maximum number of data streams is shown to be upper bounded by n2, with each user transmitting or receiving up to m2 data streams. This gives a dimension-counting interpretation for multiuser diversity. Multiple antennas at the base-station increases the total number of dimensions, thus allowing more users to transmit and receive at the same time. By contrast, multiple antennas at the remote terminal allow a single user to occupy multiple dimensions, which increases its transmission rate, but also has the potential effect of precluding simultaneous transmission by other users
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: Efficient Margin Adaptive Scheduling for MIMO-OFDMA Systems

paper_content:

In this paper we address the problem of margin adaptive scheduling in the downlink of an orthogonal frequency division multiple access (OFDMA) multiple-input multiple-output (MIMO) system. Optimal resource allocation in MIMO systems requires the joint optimization of: a) linear transmit and receive spatial filters, b) channel assignment and c) power allocation. This problem is not convex and its complexity becomes thus intractable already for small sets of users and subcarriers. To reduce the complexity of the problem at hand, we propose a novel heuristic strategy that partitions the users in different groups according to their average channel quality and addresses the original problem by solving a succession of lower-complexity allocation problems. The spatial dimension is employed to prevent multiple access interference from hindering the performance of the sequential allocation. To further reduce the complexity burden we introduce a linear programming formulation in combination with a waterfilling-based strategy to allocate channels and power to the groups of users. Numerical results and evaluation of the computational complexity show that, though suboptimal, in most cases the proposed algorithm manages to exploit in an original way the inherent multi-user diversity of multi-carrier systems to ease the task of resource allocation with a very limited performance loss from the theoretic optimum.
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paper_title: On the Capacity of MIMO Broadcast Channels With Partial Side Information

paper_content:

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.
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paper_title: Enhancing coverage and capacity for multiuser MIMO systems by utilizing scheduling

paper_content:

Recent studies have revealed that the remarkable capacity improvement resulting from an open-loop multiple-input-multiple-output (MIMO) spatial multiplexing system may come at the sacrifice of degrading link reliability. This tradeoff between antenna multiplexing gain against antenna diversity gain may translate into smaller coverage areas. In this paper, we suggest using the multiuser diversity to replenish the diversity-deficient spatial multiplexing MIMO system. Specifically, we propose a fair scheduling scheme, called the strongest-weakest-normalized-subchannel-first (SWNSF) scheduling, which requires only limited amount of feedback. Our analysis and results indicate that the SWNSF scheduling can significantly increase the coverage of the multiuser MIMO system while further improving the system capacity.
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paper_title: Switching between diversity and multiplexing in MIMO systems

paper_content:

Multiple-input multiple-output (MIMO) wireless communication systems can offer high data rates through spatial multiplexing or substantial diversity using transmit diversity. In this letter, switching between spatial multiplexing and transmit diversity is proposed as a simple way to improve the diversity performance of spatial multiplexing. In the proposed approach, for a fixed rate, either multiplexing or diversity is chosen based on the instantaneous channel state and the decision is conveyed to the transmitter via a low-rate feedback channel. The minimum Euclidean distance at the receiver is computed for spatial multiplexing and transmit diversity and is used to derive the selection criterion. Additionally, the Demmel condition number of the matrix channel is shown to provide a sufficient condition for multiplexing to outperform diversity. Monte Carlo simulations demonstrate improvement over either multiplexing or diversity individually in terms of bit error rate.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

paper_content:

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: Capacity Maximization for Zero-Forcing MIMO-OFDMA Downlink Systems with Multiuser Diversity

paper_content:

This paper considers the optimal resource allocation for a multiuser MIMO-OFDMA downlink system using zero-forcing SDMA, with the objective of maximizing the system capacity. We provide the general mathematical formulation of the capacity maximization problem whose resource allocation includes user selection, power allocation and receive signal subspace selection. While the optimal solution of this problem is difficult to obtain, we consider two special cases: user selection based only and antenna selection based only optimization, and develop the optimal solution by reformulating the combinatorial optimization problem into a convex problem. Our proposed algorithms for these special cases can be extended to develop a suboptimal algorithm for the original general optimization problem which allows subspace selection. Moreover, we develop reduced-complexity algorithms for these problems which incur negligible capacity loss. Numerical results and analysis are provided to evaluate the system capacity and to study the effect of the number of users and the receive antennas per user on the performance. Comparisons on the capacity achieved by user selection only, antenna selection only and suboptimal subspace selection are discussed
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paper_title: Novel scheduling strategy for downlink multiuser MIMO system: Particle swarm optimization

paper_content:

In this paper the scheduling problem in downlink multiuser MIMO system is described as an optimization problem and particle swarm optimization (PSO) algorithm is introduced to address such problem. Two PSO scheduling methods with different objective functions applicable to different requirements on capacity and complexity are investigated. One is the capacity based PSO(C-PSO) scheduling method aiming at achieving the near optimal capacity; and the other is the lower bound of eigenvalue based PSO (LBE-PSO) scheduling method with the purpose of reducing computational complexity and at the same time achieving as large as possible capacity gain. Furthermore, convergence analysis of PSO from both the particle and the velocity aspects is also presented to derive the convergent condition, which is validated by several examples of different parameter values. Simulation results reveal that the C-PSO can obtain nearly the same capacity as the exhaustive search method with lower complexity, while the LBE-PSO provides a viable approach by striking a better tradeoff between capacity and computational complexity.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: Asymptotically optimal simple user scheduling for massive MIMO downlink with two-stage beamforming

paper_content:

In this paper, a simple user-scheduling-and-beamforming method is proposed for massive multi-user multiple-input multiple-output (MU-MIMO) downlink adopting two-stage beamforming. The key ideas of the proposed scheduling-and-beamforming method are to divide users into several candidate subsets according to the level of alignment of user channels to the dominant directions of the channel covariance matrix and select the user in each candidate subset based on a certain channel quality indicator (CQI) and to apply post-selection zero-forcing beamforming (ZFBF) to the selected users based on their channel state information (CSI). It is proved that the proposed scheduling-and-beamformingmethod is asymptotically optimal as the number of users increases. Furthermore, the proposed method significantly reduces the feedback overhead and shows superior sum rate performance compared to existing scheduling methods for MU-MIMO downlink.
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paper_title: Subchannel allocation in multiuser multiple input multiple output systems

paper_content:

Assuming perfect channel state information at the transmitter of a Gaussian broadcast channel, strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel. For the general sum capacity maximizing solution, which has recently been found, a method is proposed that transforms each of the resulting vector channels into a set of scalar channels. This makes possible to achieve capacity by simply using scalar coding and detection techniques. The high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero-forcing allocation strategy that directly results in a set of virtually decoupled scalar channels. Simulation results show that this technique tightly approaches the performance of the optimum solution, i.e., complexity reduction comes at almost no cost in terms of sum capacity. As the optimum solution, the zero-forcing allocation strategy applies to any number of transmit antennas, receive antennas and users
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paper_title: Eigen-Based Transceivers for the MIMO Broadcast Channel with Semi-Orthogonal User Selection

paper_content:

This paper studies the sum rate performance of two low complexity eigenmode-based transmission techniques for the MIMO broadcast channel, employing greedy semi-orthogonal user selection (SUS). The first approach, termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first employ new analytical methods to prove that as the number of users K grows large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that the average sum rates of both techniques converge to the average sum capacity of the MIMO broadcast channel for large K. In addition to the asymptotic analysis, we investigate the sum rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS has significant performance advantages. Our results also provide key insights into the benefit of multiple receive antennas, and the effect of the SUS algorithm. In particular, we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second-order behavior of the multi-user diversity gain; for finite K, the benefit can be very significant. We also show the interesting result that the semi-orthogonality constraint imposed by SUS, whilst facilitating a very low complexity user selection procedure, asymptotically does not reduce the multi-user diversity gain in either first (log K) or second-order (loglog K) terms.
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paper_title: Efficient MAC protocol for JT CoMP in small cells

paper_content:

In this paper, we investigate an efficient MAC protocol for interference coordination in small cells embedded in a macro-cell mobile network. We perform joint transmission (JT)-coordinated multi-point (CoMP), where cells in the cluster include adjacent macro-cells as suggested by the small-cell terminal. Most gains compared to uncoordinated transmission come from selecting the right users in these macro-cells. For minimizing the feedback overhead, we propose successive channel state information (CSI) requests. Thereby we replace users in the set until all of them experience consistently enhanced performance when using JT-CoMP. Gains can be further increased by MIMO mode switching in each cell and frequency-selective scheduling. We tested our algorithms over coherently measured multi-cell channels in the LTE-Advanced testbed in Berlin where small cells were embedded at several places. Using these algorithms, performance becomes comparable to a popular bound assuming no more intra-cluster interference while feedback overhead and complexity are substantially reduced.
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paper_title: MIMO Downlink Scheduling with Non-Perfect Channel State Knowledge

paper_content:

Downlink scheduling schemes are well-known and widely investigated under the assumption that the channel state is perfectly known to the scheduler. In the multiuser MIMO (broadcast) case, downlink scheduling in the presence of non-perfect channel state information (CSI) is only scantly treated. In this paper we provide a general framework that addresses the problem systematically. Also, we illuminate the key role played by the channel state prediction error: our scheme treats in a fundamentally different way users with small channel prediction error ("predictable" users) and users with large channel prediction error ("non-predictable" users), and can be interpreted as a near-optimal opportunistic time-sharing strategy between MIMO downlink beamforming to predictable users and space-time coding to non-predictable users. Our results, based on a realistic MIMO channel model used in 3GPP standardization, show that the proposed algorithms can significantly outperform a conventional "mismatched" scheduling scheme that treats the available CSI as if it was perfect.
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paper_title: Learning-Based Adaptive Transmission for Limited Feedback Multiuser MIMO-OFDM

paper_content:

Performing link adaptation in a multiantenna and multiuser system is challenging because of the coupling between precoding, user selection, spatial mode selection and use of limited feedback about the channel. The problem is exacerbated by the difficulty of selecting the proper modulation and coding scheme when using orthogonal frequency division multiplexing (OFDM). This paper presents a data-driven approach to link adaptation for multiuser multiple input mulitple output (MIMO) OFDM systems. A machine learning classifier is used to select the modulation and coding scheme, taking as input the SNR values in the different subcarriers and spatial streams. A new approximation is developed to estimate the unknown interuser interference due to the use of limited feedback. This approximation allows to obtain SNR information at the transmitter with a minimum communication overhead. A greedy algorithm is used to perform spatial mode and user selection with affordable complexity, without resorting to an exhaustive search. The proposed adaptation is studied in the context of the IEEE 802.11ac standard, and is shown to schedule users and adjust the transmission parameters to the channel conditions as well as to the rate of the feedback channel.
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paper_title: User scheduling for massive MIMO OFDMA systems with hybrid analog-digital beamforming

paper_content:

This paper proposes a new user scheduling and sub-carrier allocation algorithm for multiuser downlink massive multiple input multiple output (MIMO) orthogonal frequency division multiple access (OFDMA) systems with hybrid analogdigital beamforming (HB). We assume that the transmitter having N antennas is serving K i decentralized single antenna receivers by sub-carrier i. The scheduling algorithm leverages the solutions of the digital beamforming (DB) result and is designed to maximize the total sum rate of all sub-carriers under per carrier power constraint. For this system and problem setup, the proposed algorithm is explained as follows: First, we express the HB matrix of sub-carrier i as a product of AB i , where the high dimensional matrix A ∈ CN×Na is common to all subcarriers whereas, B i ∈ CNa×Ki is a low dimensional matrix which is designed for sub-carrier i, and Na is the number of RF chains satisfying N ≥ Na ≥ K i . Second, we compute A as the first Na eigenvectors of the left singular value decomposition of the combined DB precoder matrices of sub-carriers having the highest sum rate. Finally, for fixed A, we compute Bi and its corresponding users such that the total sum rate of all sub-carriers is maximized. The performance of the proposed scheduling is studied analytically. Furthermore, the superiority of the proposed algorithm over that of the existing one is quantified analytically and demonstrated by computer simulations.
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paper_title: Order Statistics in Wireless Communications: Diversity, Adaptation, and Scheduling in MIMO and OFDM Systems

paper_content:

Covering fundamental principles through to practical applications, this self-contained guide describes indispensable mathematical tools for the analysis and design of advanced wireless transmission and reception techniques in MIMO and OFDM systems. The analysis-oriented approach develops a thorough understanding of core concepts and discussion of various example schemes shows how to apply these concepts in practice. The book focuses on techniques for advanced diversity combining, channel adaptive transmission and multiuser scheduling, the foundations of future wireless systems for the delivery of highly spectrum-efficient wireless multimedia services. Bringing together conventional and novel results from a wide variety of sources, it will teach you to accurately quantify trade-offs between performance and complexity for different design options so that you can determine the most suitable design choice based on your specific practical implementation constraints.
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paper_title: Enhanced multiuser random beamforming: dealing with the not so large number of users case

paper_content:

We consider the downlink of a wireless system with an M-antenna base station and K single-antenna users. A limited feedback-based scheduling and precoding scenario is considered that builds on the multiuser random beamforming (RBF). Such a scheme was shown to yield the same capacity scaling, in terms of multiplexing and multiuser diversity gain, as the optimal full CSIT-based (channel state information at transmitter) precoding scheme, in the large number of users K regime. Unfortunately, for more practically relevant (low to moderate) K values, RBF yields degraded performance. In this work, we investigate solutions to this problem. We introduce a two-stage framework that decouples the scheduling and beamforming problems. In our scenario, RBF is exploited to identify good, spatially separable, users in a first stage. In the second stage, the initial random beams are refined based on the available feedback to offer improved performance toward the selected users. Specifically, we propose beam power control techniques that do not change the direction of the second-stage beams, offering feedback reduction and performance tradeoffs. The common feature of these schemes is to restore robustness of RBF with respect to sparse network settings (low K), at the cost of moderate complexity increase.
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paper_title: User Selection With Zero-Forcing Beamforming Achieves the Asymptotically Optimal Sum Rate

paper_content:

In this paper, we propose a generalized greedy (G-greedy) algorithm based on zero-forcing beamforming (ZFBF) for the multiple-input multiple-output (MIMO) broadcast channel. This algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations. As previous results only give the scaling law of the sum rate of dirty paper coding (DPC), with the help of the G-greedy structure, we are able to obtain the exact limit of the DPC sum rate for a large number of users. We also prove that the difference between the sum rates obtained by G-greedy user selection and by DPC goes to zero as the number of users increases. In addition to this, we investigate one particular greedy user selection scheme called sequential water-filling (SWF). For this algorithm, a complexity reduction is achieved by an iterative procedure based on an LQ decomposition, which converts the calculation of the Moore-Penrose matrix inverse to one vector-matrix multiplication. A sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction. With the help of the G-greedy algorithm, we prove that SWF achieves the full DPC sum rate for a large number of users. For a moderate number of users, simulation demonstrates that, compared with other user selection algorithms, SWF achieves a higher sum rate that is close to the maximal sum rate achievable by ZFBF with the same order of complexity.
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paper_title: A New Approach to User Scheduling in Massive Multi-User MIMO Broadcast Channels

paper_content:

In this paper, a new user-scheduling-and-beamforming method is proposed for multi-user massive multiple-input multiple-output (massive MIMO) broadcast channels in the context of two-stage beamforming. The key ideas of the proposed scheduling method are 1) to use a set of orthogonal reference beams and construct a double cone around each reference beam to select `nearly-optimal' semi-orthogonal users based only on channel quality indicator (CQI) feedback and 2) to apply post-user-selection beam refinement with zero-forcing beamforming (ZFBF) based on channel state information (CSI) feedback only from the selected users. It is proved that the proposed scheduling-and-beamforming method is asymptotically optimal as the number of users increases. Furthermore, the proposed scheduling-and-beamforming method almost achieves the performance of the existing semi-orthogonal user selection with ZFBF (SUS-ZFBF) that requires full CSI feedback from all users, with significantly reduced feedback overhead which is even less than that required by random beamforming.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: On the achievable throughput of a multiantenna Gaussian broadcast channel

paper_content:

A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j<i is taken into account by coding for noncausally known interference. Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR). We conclude by providing some numerical results for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.
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paper_title: Networked MIMO with clustered linear precoding

paper_content:

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination to enhance the sum rate and limited inter-cluster coordination to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.
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paper_title: Adaptive radio resource allocation for downlink OFDMA/SDMA systems with multimedia traffic

paper_content:

This paper proposes an adaptive radio resource allocation (ARRA) algorithm for downlink OFDMA/SDMA systems with multimedia traffic. Considering multiple service classes and diverse QoS requirements of multimedia traffic, the ARRA algorithm is designed with the goal to maximize spectrum efficiency and to fulfill quality of service (QoS) requirements. It is composed of two parts, a dynamic priority adjustment (DPA) scheme and a priority-based greedy (PBG) scheme. The DPA adopts a type of time-to-expiration to indicate the degree of user's urgency, and dynamically gives high priorities to urgent users. The PBG allocates the radio resource iteratively, based on a cost value, to maximize the system throughput while allocating enough resource to high-priority users. Simulation results show that the ARRA algorithm outperforms conventional algorithms in terms of system throughput and satisfaction extent of QoS requirements; it can sustain users' QoS requirements up till a traffic load of 0.8, while the conventional algorithms cannot guarantee QoS requirements after a traffic load of 0.3.
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paper_title: Multiuser diversity for a dirty paper approach

paper_content:

Multiuser diversity has attracted significant attention recently. In this letter, we propose a greedy algorithm based on QR decomposition of the channel and dirty paper precoding to exploit the multiuser diversity of the Gaussian vector broadcast channel. Simulations show the approach provides performance which is extremely close to a well-known upper bound on the sum rate. Further, exploiting multiuser diversity can provide large gain over approaches ignoring this resource.
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paper_title: Greedy scheduling performance for a zero-forcing dirty-paper coded system

paper_content:

This letter presents two results for multiuser wireless systems employing dirty-paper coding strategies along with greedy scheduling over the broadcast multiple-input multiple-output channel. Specifically, an efficient and suboptimal downlink scheduler is proposed to approximate the maximum sum rate using equal power allocation, and it is shown to approach the maximum sum rate of optimal power allocation for a large number of users under optimal scheduling. The second result demonstrates that the average maximum sum rate can be tightly upper bounded when spatial multiplexing is maximized.
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paper_title: On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm

paper_content:

This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple "beams" directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of the same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum's scheme and, thus, offers an attractive alternative to DP-based schemes.
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paper_title: Opportunistic Two-Stage Feedback and Scheduling for MIMO Downlink Systems

paper_content:

We propose an opportunistic two-stage feedback and scheduling algorithm that is based upon zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) to reduce its feedback load. In an SUS algorithm, a base station schedules semi-orthogonal users using the feedback of all users' channel information. However, such feedback overhead significantly increases with the number of users. To reduce the feedback load of ZFBF-SUS systems, the proposed two-stage feedback scheme opportunistically and separately exploits the signal-to-interference-plus-noise ratio and orthogonality in each stage such that only a fraction of users feed back their channel information. Based on this opportunistic feedback scheme, we decouple the entire process of the SUS into two sub-processes. The proposed two-stage feedback and scheduling scheme effectively exclude the inappropriate users for ZFBF transmission in both feedback and scheduling periods, and thus save the scarce resources consumed for the feedback process. We derive an analytical expression for the average number of feedback bits of the proposed system and optimize it in an averaged sense. Further, the sum-rate of the proposed system is theoretically investigated. Both analytical and simulation results show that the proposed algorithm achieves the performance of conventional ZFBF-SUS systems with a significantly reduced number of feedback bits.
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paper_title: Training and Feedback Optimization for Multiuser MIMO Downlink

paper_content:

We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over time-frequency blocks that span a coherent time x a coherence bandwidth. In closed-loop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In open-loop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use closed-form lower bounds and tight approximations of the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three time-frequency block models inspired by actual systems, we provide useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.
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paper_title: Acquiring Partial CSI for Spatially Selective Transmission by Instantaneous Channel Norm Feedback

paper_content:

In the design of next-generation multiuser communication systems, multiple-antenna transmission is an essential part providing additional spatial degrees of freedom and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. Herein, we show that the Euclidean norm of the instantaneous channel, when combined with long-term channel statistics provides sufficient information for the transmitter to efficiently utilize multiuser diversity in time, frequency, and space. We consider the downlink of a communication system where the base station has multiple transmit antennas whereas each user terminal has a single receive antenna. The CSI provided by channel statistics and feedback of the norm of the instantaneous channel vector is studied in depth for correlated Rayleigh and Ricean fading channels, within a minimum mean-square error (MMSE) estimation framework. An asymptotic analysis (high instantaneous SNR) is presented which shows that channel realizations with large channel norm provide additional spatial CSI at the transmitter. This makes the proposed scheme ideal for multiuser diversity transmission schemes, where resources are only allocated to users experiencing favorable channel conditions.
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paper_title: User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming

paper_content:

In this paper, we propose a greedy user selection with swap (GUSS) algorithm based on zero-forcing beamforming for multiuser multiple-input-multiple-output (MIMO) downlink channels. Existing user selection algorithms such as zero forcing with selection (ZFS) have the flaws of “redundant users” and “local optimum,” which compromise the achieved sum rate. GUSS improves the performance by adding the “delete” and “swap” operations to the user selection procedure of ZFS to eliminate “redundant users” and escape from “local optimum,” respectively. In addition, an effective-channel-vector-based effective-channel-gain-updating scheme is proposed to reduce the complexity of GUSS. With the help of this updating scheme, GUSS has the same order of complexity as ZFS with only a linear increment. Simulation results indicate that over the range of transmit signal-to-noise ratios (SNRs) considered, on average, the sum rate of GUSS reaches 99.3% of the upper bound that is achieved by exhaustive search, with only 1.51 to 2.29 times the complexity of ZFS.
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paper_title: Multiuser MIMO Scheduling for LTE-A Downlink Cellular Networks

paper_content:

In this paper, we investigate multiuser MIMO scheduling in LTE downlink cellular networks. We formulate the downlink LTE-A MIMO scheduling as a weighted sum rate maximization problem by allocating the RBs to users or user pairs subject to some constraints in LTE-A. We develop a low-complexity MU-MIMO scheduling and resource allocation algorithm and propose an adaptive switching approach between SU-MIMO and MU-MIMO to improve network performance. System-level simulation results demonstrate significantly performance improvement of the proposed MU-MIMO scheduling algorithm and the adaptive switching algorithm.
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paper_title: Optimizing multi-cell massive MIMO for spectral efficiency: How Many users should be scheduled?

paper_content:

Massive MIMO is a promising technique to increase the spectral efficiency of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent beamforming. A common rule-of-thumb is that these systems should have an order of magnitude more antennas, N, than scheduled users, K, because the users' channels are then likely to be quasi-orthogonal. However, it has not been proved that this rule-of-thumb actually maximizes the spectral efficiency. In this paper, we analyze how the optimal number of scheduled users, K∗, depends on N and other system parameters. The value of K∗ in the large-N regime is derived in closed form, while simulations are used to show what happens at finite N, in different interference scenarios, and for different beamforming.
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paper_title: Hierarchical Interference Mitigation for Massive MIMO Cellular Networks

paper_content:

We propose a hierarchical interference mitigation scheme for massive MIMO cellular networks. The MIMO precoder at each base station (BS) is partitioned into an inner precoder and an outer precoder. The inner precoder controls the intra-cell interference and is adaptive to local channel state information (CSI) at each BS (CSIT). The outer precoder controls the inter-cell interference and is adaptive to channel statistics. Such hierarchical precoding structure reduces the number of pilot symbols required for CSI estimation in massive MIMO downlink and is robust to the backhaul latency. We study joint optimization of the outer precoders, the user selection, and the power allocation to maximize a general concave utility which has no closed-form expression. We first apply random matrix theory to obtain an approximated problem with closed-form objective. We show that the solution of the approximated problem is asymptotically optimal with respect to the original problem as the number of antennas per BS grows large. Then using the hidden convexity of the problem, we propose an iterative algorithm to find the optimal solution for the approximated problem. We also obtain a low complexity algorithm with provable convergence. Simulations show that the proposed design has significant gain over various state-of-the-art baselines.
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paper_title: Low complexity greedy, genetic and hybrid user scheduling algorithms for multiuser MIMO systems with successive zero‐forcing

paper_content:

In this paper, we consider low complexity user scheduling algorithms for multiuser multiple-input multiple-output systems employing successive zero-forcing precoding. Optimal scheduling involves an exhaustive search (ES), which is prohibitively complex. Greedy algorithms (GrAs) with heuristic scheduling metrics achieve performance close to that of the ES. Meanwhile, genetic algorithms (GAs) are a rapid suboptimal option of optimising utility (e.g. scheduling) metrics. Herein, we evaluate the performance and complexity of greedy and genetic scheduling algorithms for successive zero-forcing. We also propose and evaluate two hybrid algorithms combining the traits of the GrA and GA. The algorithms' performance is assessed through a series of computer simulations. We demonstrate both the GrA and GA achieve a near-optimal sum rate with low complexity, whereas the hybrid algorithms further enhance the GrA and GA performance without an increase in the order of complexity.Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: Optimizing User Selection Schemes in Vector Broadcast Channels

paper_content:

In this paper, we focus on the ergodic downlink sum-rate performance of a system consisting of a set of heterogeneous users. We study three user selection schemes to group near-orthogonal users for simultaneous transmission. The first scheme is a random selection policy that achieves fairness, but does not exploit multi-user diversity. The second scheme is a greedy selection policy that fully exploits multi-user diversity, but does not achieve fairness, and the third scheme achieves fairness while partially exploiting multi-user diversity. We also consider two beamforming methods for data transmission, namely, maximum-ratio transmission and zero-forcing beamforming. In all scheduling schemes studied in the paper, there is a key parameter that controls the degrees of orthogonality of channel directions between co-scheduled users. We focus on optimally setting this parameter for each scheduling scheme such that the ergodic downlink sum-rate is maximized. To this end, we derive analytical expressions for the ergodic downlink sum-rate considering each scheduling scheme. Numerical results are also presented to provide further insights.
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paper_title: Isotropic fading vector broadcast Channels:The scalar upper bound and loss in degrees of freedom

paper_content:

We propose a scalar upper bound on the capacity region of the isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel. The scalar upper bound is applicable to the broad class of isotropic fading broadcast channels regardless of the distribution of the users' channel magnitudes, the distribution of the additive noise experienced by each user, or the amount of channel knowledge available at the receiver. Using this upper bound, we prove the optimality of the Alamouti scheme in a broadcast setting, extend the recent results on the capacity of nondegraded, fading scalar broadcast channels to nondegraded fading vector broadcast channels, and determine the capacity region of a fading vector Gaussian broadcast channel with channel magnitude feedback. We also provide an example of a Rayleigh-fading broadcast channel with no channel state information available to the receiver (CSIR), where the bound on the capacity region obtained by a naive application of the scalar upper bound is provably loose, because it fails to account for the additional loss in degrees of freedom due to lack of channel knowledge at the receiver. A tighter upper bound is obtained by separately accounting for the loss in degrees of freedom due to lack of CSIR before applying the scalar upper bound.
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paper_title: Scheduling Methods with MIMO Interference Alignment for Mutually Interfering Broadcast Channels

paper_content:

In this paper, we investigate an interference alignment (IA) technique introduced by Cadambe and Jafar in mutually interfering broadcast channels (IFBCs). First, we study the spatial multiplexing gain (SMG) for the 3-cell IFBC where all base stations and mobile users are equipped with multiple antennas. To achieve the derived optimal SMG, we extend the IA algorithm designed for K-user multi-input multi-output (MIMO) interference channels (IFCs) to the IFBC. In this paper, we present the IA scheme in conjunction with user selection which outperforms the time division multiple access (TDMA) technique in the IFBC environment. The optimal scheduling method capitalizes on multiuser diversity to achieve a significant fraction of sum capacity by using an exhaustive search algorithm. Since the computational complexity of the optimal scheduling method is prohibitive, a reduced complexity suboptimal scheduling method is proposed based on a coordinate ascent approach. Simulation results confirm that the reduced complexity scheduling algorithm achieves the sum rate close to the optimal algorithm with much reduced complexity.
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paper_title: Multicell Cooperative Scheduling for Two-Tier Cellular Networks

paper_content:

Cellular wireless network architectures employing a tiered structure, consisting of traditional macro-cells and small-cells, have attracted much attention recently because of their potential to dramatically increase network capacity. These architectures can reduce the distances of transmit-receiver pairs, thus enhancing radio link qualities. However, a tiered cell deployment could incur severe cochannel interference. Prior work for single-tier networks has proposed coordinated multi-point (CoMP) transmission, which includes joint transmission, as a possible solution for overcoming the rate limitations induced by cochannel interference. Because users in each cell experience various interference conditions, each cell needs to support single transmission (in which only one cell transmits to a single user) and joint transmission. In a conventional implementation, a particular combination of transmissions over the entire network is fixed in advance for each time slot and opportunistic scheduling chooses one of the users supported by each transmission. However, when the number of users to be scheduled is small, the throughput improvement from opportunistic scheduling becomes limited. To overcome this problem, we propose a cumulative distribution function-based scheduling scheme which jointly chooses the transmitter set and the corresponding scheduled users in a two-tier network. It is shown that the throughput performance can be improved compared to those of the fixed slot resource allocation scheme because more users "compete" for slot resources.
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paper_title: Scheduling for Multiuser MIMO Broadcast Systems: Transmit or Receive Beamforming?

paper_content:

In this paper, we present an approximation formula and the close-form expression for the sum rate of the transmit and the receive zero-forcing (ZF) multiple-input multiple-output (MIMO) broadcast systems with user selection, respectively. Instead of assuming a large number of users to obtain a scaling law as most current work, we derive the sum rate formulas of the ZF MIMO broadcast systems with a small number of scheduled users. By analysis and simulations, we find that when taking the variations of feedback channel into account, the receive ZF MIMO broadcast system is more robust to feedback errors and can deliver equal or even higher sum rate than the transmit ZF MIMO broadcast system. We discuss whether a feedback channel is suitable to send channel state information (CSI) for calculating transmit antenna beamforming weights, or suitable to send CSI for selecting users in the receive ZF MIMO broadcast system. Our results show that as the variation of feedback channel errors increases from 0.5 to 1.5, the receive ZF 3 × 3 MIMO broadcast system can provide 36% to 116% higher sum rate than the transmit ZF 3 × 3 MIMO broadcast system in the case of 20 users at signal to noise ratio (SNR) equal to 20 dB. Providing that more feedback bandwidth and an error-free feedback channel are available, the transmit ZF MIMO broadcast system can achieve higher sum rate than the receive ZF MIMO broadcast system.
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paper_title: Decremental User Selection for Large-Scale Multi-User MIMO Downlink with Zero-Forcing Beamforming

paper_content:

This paper proposes a decremental user selection algorithm based on zero-forcing beamforming when the number of users K in the network is smaller than the number of antennas M at a base station. The algorithm is specifically designed for large-scale multi-user multiple-input multiple-output (MIMO) downlink channels. While previous user selection algorithms are based on incremental search that starts from an empty user set, our proposed delete the minimum lambda (DML) algorithm starts by selecting all users and then deleting one user per iteration. DML substantially reduces the computational complexity as the cardinality of the final user set is close to K. Simulation results indicate that on average DML achieves an equal or higher sum rate performance than previous algorithms with greatly reduced complexity of O(MK2).
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paper_title: Beamforming and User Selection in SDMA Systems Utilizing Channel Statistics and Instantaneous SNR Feedback

paper_content:

Spatial division multiple access (SDMA) systems efficiently take advantage of the spatial dimensions of the channel to increase the performance of the system. A major difficulty, common to all SDMA systems, is the requirement of channel knowledge at the transmitter to enable transmission of multiple streams without catastrophic interference. Herein we show that, in wide area scenarios, statistical channel information combined with the Euclidean norm of the channel realization, fed back from the users, provide sufficient information for SDMA systems to efficiently allocate users in time and space. A joint beamforming and scheduling algorithm is proposed for the downlink, which extends the proportional fair scheduling criterion to an SDMA setting, resulting in a weighted sum rate maximization.
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paper_title: Transmit correlation-aided opportunistic beamforming and scheduling

paper_content:

The problem of multiuser scheduling and beamforming with partial channel state information at the transmitter (CSIT) is considered here in the particular context of opportunistic beamforming. We consider a random multiuser beamforming scheme and show how long-term statistical information of users' channels can be efficiently combined with short-term SINR feedback to increase system performance substantially over a conventional opportunistic beamforming scheme. We propose a channel estimation method to be used by the transmitter which exploits the second-order channel statistics, the fading statistics and the information contained in the instantaneous SINR feedback of random opportunistic beamforming. This coarse (low feedback-based) channel estimate is shown to be particularly valuable for the purpose of user selection, as well as for the precoding matrix design.
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paper_title: Round-Robin Scheduling for Orthogonal Beamforming with Limited Feedback

paper_content:

We propose a round-robin scheduling algorithm for orthogonal beamforming with a strict signal to interference-plus-noise ratio (SINR) constraint and limited feedback. The presented algorithm aims at scheduling the users at identical slots over different blocks, in order to reduce the necessary scheduling overhead, and to minimize the maximum delay between serving the same user. Thus, the presented algorithm is especially suited for real-time multimedia traffic. The algorithm allocates the users using orthogonal beamforming based on the quantized feedback provided by the users. The quantized feedback consists of the estimated power that is necessary to fulfill a predefined SINR constraint. Further, we propose an algorithm to design codebooks to quantize the estimated power. Using the feedback, the base station redistributes power from users with spare power to users that lack power so that they fulfill their SINR constraints. The performance of the algorithm is demonstrated through simulations.
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paper_title: Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

paper_content:

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.
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paper_title: Packet Scheduling and Fairness for Multiuser MIMO Systems

paper_content:

This paper investigates the network resource allocation in multiuser downlink wireless systems where the base station and the mobile stations are equipped with multiple antennas to provide fair and efficient transmission services to the mobile users. We focus on packet scheduling, given that it has a significant impact on the overall performance of a multiple-input-multiple-output (MIMO) system. Most previous schedulers designed at the packet level do not take into account the traffic characteristics (different packet lengths and the arrival process parameters); consequently, they fall short of simultaneously providing fairness and a low average packet transmission delay. We are making use of a flexible packet transmission algorithm at the medium access control (MAC) layer to develop and propose a novel scheduler, which is referred to as MIMO packet-based proportional fairness (MP-PF). The new scheduler is designed with the goal of providing high performance in terms of a low average packet transmission delay and time and service fairness among the users based on the concept of proportional fairness. The scheduler also conserves work and takes into consideration the packet length, the user queue length, the user transmission rate (related to its channel quality), and the service guarantees for heterogeneous users. The well-known ideal service fair scheduler called max-min can also significantly be improved using our framework by taking into consideration the traffic characteristics. We also provide an analysis for the fairness of the new scheduler in terms of time and service allocation, which is the key contribution of this paper. Simulations that consider the traffic characteristics and the mobility of users show the relatively low average packet transmission delay and demonstrate the time and service fairness capabilities of MP-PF, compared with other well-known MIMO schedulers.
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paper_title: Simplified Semi-Orthogonal User Selection for MU-MIMO Systems with ZFBF

paper_content:

In this letter, we simplify the well-known semi-orthogonal user selection (SUS) algorithm for the multi-user multiple-input multiple-output (MU-MIMO) system with zero-forcing beamforming (ZFBF). Compared with the original SUS algorithm, the proposed user selection algorithm achieves the same performance, but with significantly less complexity. Simulation results show that the proposed algorithm can make a good tradeoff between performance and complexity for the MU-MIMO system with ZFBF.
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paper_title: Design Guidelines for Limited Feedback in the Spatially Correlated Broadcast Channel

paper_content:

A linear beamformer design for the broadcast channel where the base station is equipped with $N_t$ antennas and signals to $M = 2$ users (each with a single antenna)and where the vector channels are spatially correlated is considered. This problem is of relevance in wireless standardization efforts where two users are simultaneously scheduled (instead of the theoretically feasible $N_t$ user scheduling)to minimize signaling overhead. The users are assumed to have perfect channel state information (CSI), whereas the base station has statistical information of the channels. In the first part of this work, the role of the relevance of feedback is studied via the quantification of the gap in ergodic sum-rate between the perfect CSI and statistics-only extremes. In this direction, the importance of orthogonality of the dominant eigenmodes of the two users in maximizing the gap is established. In the second part of this work, in scenarios with a large gap, limited feedback beamforming codebooks and a codeword selection metric are designed for the low-rate feedback setting. The main contribution here is the proposal of a generalized eigenvector codebook and feedback of the codeword index that maximizes an estimate of the signal-to-interference-and-noise ratio $(\textsf{SINR})$ of each user. Extensions of this scheme are also proposed for the general $N_t$ antenna case with $M$ users, where $M \le N_t$ . It is shown via numerical studies that this scheme leads to significant performance improvement across a large family of channels over schemes such as Grassmannian/Random Vector Quantization/single-user codebooks with the channel projection metric for codeword selection.
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paper_title: The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel

paper_content:

The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the nondegraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints
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paper_title: Robust multi-user opportunistic beamforming for sparse networks

paper_content:

A scheme exploiting reduced feedback for the purpose of opportunistic multi-user beamforming is proposed. The scheme builds on recent promising advances realized in the area of multi-user downlink precoding and scheduling based on partial transmitter channel state information (CSIT) using random beamforming-based SDMA. Although random precoding followed by SDMA scheduling is optimal within the set of unitary precoders, it is only so in the asymptotic number of users K. For-practically relevant-sparse networks (i.e., with low to moderate number of users) random beam-forming SDMA yields severely degraded performance. In this work we present a scheme allowing to restore robustness with respect to cell sparsity. The core idea here is to preserve the low complexity low feedback advantage of random opportunistic beamforming in selecting a target group of users, while much more efficient beamforming schemes can be used to serve the group of users once it has been identified. We propose different designs, optimal and suboptimal, based upon variable levels of feedback requirement. We show substantial gain over opportunistic beamforming for a range of K.
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paper_title: Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels

paper_content:

In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total system-wide feedback load, is it preferable to get low-rate/coarse channel feedback from a large number of receivers or high-rate/high-quality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multi-user diversity to be exploited, while high-rate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining high-quality feedback, and that obtaining near-perfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users.
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paper_title: CoMP-CSB for ICI Nulling with User Selection

paper_content:

The capacity of downlink multiple-input multiple-output (MIMO) cellular networks is significantly limited by inter-cell interference (ICI), particularly at cell boundaries. Recently, two types of coordinated multiple point transmission (CoMP) technologies, joint processing and transmission (JPT) and coordinated scheduling and beamforming (CSB), were proposed. These technologies are intended for the latest cellular communication standard in order to improve the performance of cell-edge users who suffer from significant ICI. In this paper, we propose an ICI cancellation technique based on a user selection algorithm for CoMP-CSB. Under partial channel state information (CSI) and no data sharing condition, each base station (BS) concentrates more on the direction of interference to the adjacent cell's users, during the user selection process. Unlike prior concepts for a single-cell environment, in which each BS generates a precoding matrix for selected users to be served, the proposed technique considers the effects of interference to users located in adjacent cells. Although there are obvious trade-offs between ICI mitigation and the number of simultaneous scheduled users in terms of system capacity, the simulation results demonstrate that our proposed algorithm achieves higher sector throughput and is more robust against ICI if the system is limited by interference. Furthermore, through simulation we are able to obtain the preferred option for the coordination distance (R) and the number of degrees of freedom for ICI nulling (ξ).
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels

paper_content:

We investigate multiple-input multiple-output (MIMO) eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.
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paper_title: Spatial Transmission Mode Switching in Multiuser MIMO-OFDM Systems With User Fairness

paper_content:

Multiantenna radio systems allow accessing the channel in diversity or spatial multiplexing (SMUX) mode. Adequate switching between these modes according to current channel conditions was shown to yield significant performance improvements while requiring little feedback from the receiving side. We present a transmission concept for the downlink of a multiuser multiple-input-multiple-output orthogonal frequency-division-multiplexing (MU-MIMO-OFDM) system aiming at high user rates with limited feedback demands. An extended score-based scheduling (SB) approach ensures fair-resource allocation to the users, whereas transmission mode switching is used to guarantee high user rates. The degree of fairness of the scheduler can be adapted by adequately configuring a weighting function for the scores. Comparison with single-mode schemes reveals substantial throughput gains of the adaptive switching concept. Furthermore, targeting maximum throughput, we show that a considerable proportion of the capacity of the MIMO broadcast channel (BC) can be achieved with a comparatively low amount of required feedback.
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paper_title: Sum Rates, Rate Allocation, and User Scheduling for Multi-User MIMO Vector Perturbation Precoding

paper_content:

This paper considers the multiuser multiple-input multiple-output (MIMO) broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via vector perturbation. We derive expressions for the sum rate in terms of the average energy of the precoded vector, and use this to derive a high signal-to-noise ratio (SNR) closed-form upper bound, which we show to be tight via simulation. We also propose a modification to vector perturbation where different rates can be allocated to different users. We conclude that for vector perturbation precoding most of the sum rate gains can be achieved by reducing the rate allocation problem to the user selection problem. We then propose a low-complexity user selection algorithm that attempts to maximize the high-SNR sum rate upper bound. Simulations show that the algorithm outperforms other user selection algorithms of similar complexity.
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paper_title: On the Performance of Downlink Beamforming with Synchronized Beam Cycles

paper_content:

The next generation of wireless networks (e.g.,) will use multiple techniques to improve channel spectral efficiencies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each frame, the scheduler chooses a beam and then schedules one or more UEs that lie within that beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors. If a neighboring sector schedules a UE that lies within the coverage of this beam then the rate for that UE will be low. The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. The first approach (interference avoidance) requires coordination among the sectors with the associated communication overheads and delays. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period. Although all NBs use the same beam cycle period, they may occasionally change the specific beam schedule based on local factors such as the geographical distribution of UEs within its beams. Such changes should be made infrequently since the approach is based on the assumption that the interference experienced by a UE repeats with the beam cycle period.
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paper_title: Parametrization Based Limited Feedback Design for Correlated MIMO Channels Using New Statistical Models

paper_content:

Parametrization of unitary matrices using Givens rotations has been used for limited feedback in multiple-input multiple-output (MIMO) systems. Feedback based on these rotations has been adopted in IEEE 802.11n and other upcoming standards. However, the probability distributions of Givens rotations is not known for correlated channels, forcing the use of uniform quantization. In this paper, novel probability density function (PDF) models, based on beta and wrapped Cauchy distributions, are proposed for Givens rotations in correlated MIMO channels. Empirical distributions and goodness-of-fit tests show that the proposed distributions characterize the spatial correlation behavior with good accuracy. Moreover, it is shown that the distributions known in the literature for uncorrelated MIMO channels are only special cases. Distributions of Givens rotations are useful to understand the behavior of singular vectors of correlated channels. In this paper, the PDF models are utilized for bit allocation and optimized codebook design. Simulations show that precoding using the proposed codebooks achieves significant performance improvement, in terms of mean square error and sum rate, as compared to using uniform codebooks. It is also shown that the bit allocations proposed in this paper reduce to that of IEEE 802.11n standard when the MIMO channel is not spatially correlated.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.
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paper_title: A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System

paper_content:

Massive MIMO has been recognized as a promising technology to meet the demand for higher data capacity for mobile networks in 2020 and beyond. Although promising, each base station needs accurate estimation of the channel state information (CSI), either through feedback or channel reciprocity schemes in order to achieve the benefits of massive MIMO in practice. Time division duplex (TDD) has been suggested as a better mode to acquire timely CSI in massive MIMO systems. The use of non-orthogonal pilot schemes, proposed for channel estimation in multi-cell TDD networks, is considered as a major source of pilot contamination in the literature due to the limitations of coherence time. Given the importance of pilot contamination in massive MIMO systems, we provide an extensive survey on pilot contamination, and identify other possible sources of pilot contamination, which include hardware impairment and non-reciprocal transceivers. We review established theories that have analyzed the effect of pilot contamination on the performance of massive MIMO systems, particularly on achievable rates. Next, we categorize the different proposed mitigation techniques for pilot contamination using the following taxonomy: pilot-based approach and subspace-based approach. Finally, we highlight the open issues, such as training overhead, deployment scenario, computational complexity, use of channel reciprocity, and conclude with broader perspective and a look at future trends in pilot contamination in massive MIMO systems.
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paper_title: Two-Phase Multiuser Scheduling for Multiantenna Downlinks Exploiting Reduced Finite-Rate Feedback

paper_content:

This paper considers a multiantenna system with an M -antenna base station and K single antenna users, employing zero-forcing beamforming (ZFBF) and a finite-rate feedback strategy. We study scheduling to select KS users for transmit beamforming. To reduce the feedback requirement, we propose a two-phase scheduling scheme that exploits quantized channel direction information (CDI) from only a small subset of the overall users, as well as a 1-bit signal-to-interference-plus-noise ratio (SINR) indicator feedback per user. In the proposed scheme, we introduce a newly defined expression for evaluating SINR that extends the existing SINR approximation for KS = M to a more general case with arbitrary KS ? M. Asymptotic analysis reveals that the proposed two-phase scheduling is asymptotically optimal for large user numbers. Through numerical simulations, we also show that the proposed scheme requires less feedback than conventional schemes, whereas the resulting sum rate loss due to the reduced feedback is negligible. Moreover, we find that the choice of KS < M, instead of a full-multiplexing case with KS = M, for scheduling may achieve a better tradeoff between performance and feedback requirement in systems where fewer bits are utilized for feeding back CDI.
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paper_title: Memory-based opportunistic multi-user beamforming

paper_content:

A scheme exploiting memory in opportunistic multiuser beamforming is proposed. The scheme builds on recent advances realized in M. Sharif and B. Hassibi, 2005, in the area of multi-user downlink preceding and scheduling based on partial transmitter channel state information (CSIT). Although the preceding and scheduling done in M. Sharif and B. Hassibi, 2005 is optimal within the set of unitary precoders, it is only so asymptotically for large number of users. Secondly, this scheme is unable to exploit potential time correlation of the channel. In this paper, we show (1) that exploiting memory in the transmitter allows to fill the gap to optimality for fixed (even low) number of users for time correlated channels, (2) how such schemes can be extended to take fairness into account in the proportional fair sense
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paper_title: Multiuser Diversity - Multiplexing Tradeoff in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider joint scheduling and beamforming in a broadcast channel with multiple antennas at the transmitter and a single antenna at the mobile receiver. Perfect channel knowledge is assumed to be available at the receiver while the transmitter is provided with partial channel state information (CSIT) through a limited rate feedback channel. Each user feeds back quantized information regarding the channel vector direction (from a codebook) and a quantized (scalar) channel quality indicator. We identify the tradeoff between multiuser diversity and spatial multiplexing gain given a limited amount of feedback bits. Scaling laws of the above parameters are derived in order to achieve a target rate performance. Our results reveal useful design guidelines for the split of feedback bits for channel quantization and channel quality.
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paper_title: Weighted max-min fair beamforming, power control, and scheduling for a MISO downlink

paper_content:

In this paper, we consider the joint beamforming, power control and scheduling problem in a multiple-input single- output (MISO) downlink for maximizing the minimum weighted rate among all users. We solve this problem by formulating it as a convex optimization problem whose function evaluations require maximization of a difference of convex functions (D.C. Programming). We also propose a simpler heuristic that finds the best policy under restricted set of power vectors. We then compare the performance of these policies against the dirty paper coding (DPC) policy to quantify the performance gap between an optimal point-to-point coding approach and an optimal joint encoding/decoding approach.
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paper_title: Maximum volume criterion for user selection of multiuser MIMO downlink with multiantenna users and block diagonalization beamforming

paper_content:

Compared with capacity-achieving dirty paper coding [1], block diagonalization (BD) algorithm [2] is known as a suboptimal but more practical beamforming scheme for multiuser MIMO downlink systems with multiantenna users. However BD suffers from two major drawbacks: the dimensionality constraint on antennas arrangement and the difficulty in handling spatially correlated users. User selection capable of selecting some most sum-rate-contributive users is a promising measure to alleviating this situation.
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paper_title: Fundamental Limits in MIMO Broadcast Channels

paper_content:

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system parameters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.
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paper_title: Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider a downlink channel where a base station equipped with M transmit antennas communicates with K ≥ M single-antenna receivers and has partial channel knowledge obtained via a limited rate feedback channel. We propose scalar feedback metrics that provide an estimate of the received signal-to-noise plus interference ratio (SINR), which are combined with efficient user selection algorithms and zero-forcing beamforming. The asymptotic system sum rate for large K is analyzed and numerical results are provided, showing the performance of each metric in different scenarios.
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paper_title: Stability and Delay of Zero-Forcing SDMA With Limited Feedback

paper_content:

This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor M >; 1. For given M → 1, the number of feedback bits per mobile is proved to be O(-log2(1-1/M)) .
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paper_title: Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization

paper_content:

Block diagonalization (BD) is a preceding technique that eliminates inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. With the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission, the number of simultaneously supportable users with BD is limited by the ratio of the number of basestation transmit antennas to the number of user receive antennas. In a downlink MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput The brute-force search for the optimal user set, however, is computationally prohibitive. We propose two low-complexity suboptimal user selection algorithms for multiuser MIMO systems with BD. Both algorithms aim to select a subset of users such that the total throughput is nearly maximized. The first user selection algorithm greedily maximizes the total throughput, whereas the criterion of the second algorithm is based on the channel energy. We show that both algorithms have linear complexity in the total number of users and achieve around 95% of the total throughput of the complete search method in simulations
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paper_title: Multiuser MIMO User Selection Based on Chordal Distance

paper_content:

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.
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paper_title: Efficient Margin Adaptive Scheduling for MIMO-OFDMA Systems

paper_content:

In this paper we address the problem of margin adaptive scheduling in the downlink of an orthogonal frequency division multiple access (OFDMA) multiple-input multiple-output (MIMO) system. Optimal resource allocation in MIMO systems requires the joint optimization of: a) linear transmit and receive spatial filters, b) channel assignment and c) power allocation. This problem is not convex and its complexity becomes thus intractable already for small sets of users and subcarriers. To reduce the complexity of the problem at hand, we propose a novel heuristic strategy that partitions the users in different groups according to their average channel quality and addresses the original problem by solving a succession of lower-complexity allocation problems. The spatial dimension is employed to prevent multiple access interference from hindering the performance of the sequential allocation. To further reduce the complexity burden we introduce a linear programming formulation in combination with a waterfilling-based strategy to allocate channels and power to the groups of users. Numerical results and evaluation of the computational complexity show that, though suboptimal, in most cases the proposed algorithm manages to exploit in an original way the inherent multi-user diversity of multi-carrier systems to ease the task of resource allocation with a very limited performance loss from the theoretic optimum.
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paper_title: Limited Feedback Multiuser Scheduling of Spatially Correlated Broadcast Channels

paper_content:

This paper investigates the transmission scheduling of users under spatially correlated multiple-input-multiple-output (MIMO) channels. By maximizing an upper bound of the sum capacity, we propose a scheduling scheme that requires only scalar feedback from each receiving user. To simplify user information feedback and better exploit the spatial channel correlation, we further develop a more efficient scheduling method that only requires a 1-bit indicator from each user and selects users based on the MIMO channel correlation information. Additionally, we then extend the proposed scheduling schemes for the system with imperfect (finite-rate) channel information feedback. Numerical results finally show that the proposed scheduling schemes can effectively improve the system sum capacity performance by exploiting the statistic channel-correlation information.
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paper_title: On the Capacity of MIMO Broadcast Channels With Partial Side Information

paper_content:

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.
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paper_title: A comparison of scheduling strategies for MIMO broadcast channel with limited feedback on OFDM systems

paper_content:

We consider a multiuser downlink transmission from a base station with multiple antennas (MIMO) to mobile terminals (users) with a single antenna, using orthogonal frequency division multiplexing (OFDM). Channel conditions are reported by a feedback from users with limited rate, and the base station schedules transmissions and beamforms signals to users. We show that an important set of schedulers using a general utility function can be reduced to a scheduler maximizing the weighted sum rate of the system. For this case we then focus on scheduling methods with many users and OFDM subcarriers. Various scheduling strategies are compared in terms of achieved throughput and computational complexity and a good tradeoff is identified in greedy and semiorthogonal user selection algorithms. In the greedy selection algorithm, users are selected one by one as long as the throughput increases, while in the semiorthogonal approach users are selected based on the channel correlation. An extension of these approaches from a flat-fading channel to OFDM is considered and simplifications that may be useful for a large number of subcarriers are presented. Results are reported for a typical cellular transmission of the long-term evolution (LTE) of 3GPP.
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paper_title: Multi-mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

paper_content:

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.
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paper_title: Joint Antenna Beamforming, Multiuser Scheduling, and Power Allocation for Hierarchical Cellular Systems

paper_content:

Cognitive radio (CR) is concretely embodied in hierarchical cellular systems by deploying an underlying microcellular system to reuse the underutilized spectrum of a macrocellular system. One of the key challenges to the success of hierarchical cellular systems is to manage the intercell interference between the macrocell and the microcell and to maximize the spectrum efficiency. In this paper, antenna beamforming, power allocation, and multiuser scheduling are jointly designed to opportunistically utilize the macrocell's uplink spectrum in serving multiple secondary microcellular users concurrently. The joint design of antenna beamforming, power allocation, and scheduling with the objective of maximizing the sum rate is indeed a mixed-integer nonlinear programming NP-hard problem. The proposed simpler iterative subgradient projection and semidefinite programming approach can obtain better performance than the conventional zero-forcing beamforming. Furthermore, unlike the optimal singular value decomposition (SVD) beamforming that requires all users to have channel knowledge at the receiver for cooperation, the proposed joint design methodology requires no channel knowledge at the receiver and can outperform the SVD beamforming without user scheduling. When considering both implementation complexity and performance enhancement issues, the proposed joint power allocation, multiuser scheduling, and antenna beamforming technique can help provide important insights into the design of interference management techniques for hierarchical CR systems.
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paper_title: An Effective Inter-Cell Interference Coordination Scheme for Downlink CoMP in LTE-A Systems

paper_content:

Coordinated multi-point (CoMP) has been adopted in 3GPP LTE-Advanced to improve the coverage of high data rates. Downlink CoMP is mainly categorized into joint transmission (JT) and coordinated beamforming (CB). Previous research shows that JT does not benefit cell average throughput. Moreover, traditional CB algorithms are based on iterative evaluation, resulting in very high computational complexity. To address these issues, in this paper, we propose an effective inter-cell interference coordination scheme for downlink CoMP, which includes two phases. Firstly, in order to improve the performance of all user equipments (UEs), cell edge UEs employ JT, while CB is adopted by both cell edge and cell center UEs. Secondly, we design linear CB precoders by maximizing a signal to leakage and noise ratio (SLNR) metric, so as to reduce processing complexity. System-level simulations validate that, in contrast to non-CoMP, the proposed scheme brings a cell average spectral efficiency (SE) gain up to 21.50% and a cell edge SE gain up to 119.2%.
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paper_title: Optimal downlink space-time scheduling design with convex utility functions-multiple-antenna systems with orthogonal spatial multiplexing

paper_content:

It is well known that link level throughput could be significantly increased by using multiple antennae at the transmitter and receiver without increasing the bandwidth and power budget. However, optimizing the link level performance of multiple-antenna systems does not always imply achieving system level optimization. Therefore, cross-layer optimization across the link layer and the scheduling layer is very important to fully exploit the temporal and spatial dimensions of the communication channel. In this paper, we consider the optimal downlink space-time scheduling design for a general class of convex utility functions. The access point or base station is equipped with n/sub T/ transmit antennas. There are K mobiles in the system with a single receive antenna. For practical reasons, we assume zero-forcing processing at the physical layer of the base station and mobile. We will apply the design framework to two common utility functions, namely the maximum throughput and the proportional fair. The cross-layer scheduling design is a mixed convex and combinatorial optimization problem and the search space of the optimal solution is enormous. Greedy algorithm, which has been widely used in today's wireless data systems (3G1X, high data rate system (HDR), Universal Mobile Terrestrial Service), is optimal when n/sub T/=1. However, we found that there is a large performance penalty of greedy algorithms (relative to optimal performance) when n/sub T/>1 and this motivates the search for more efficient heuristics. In this paper, we will address genetic-based heuristics and discuss their complexity-performance tradeoff.
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paper_title: On the balance of multiuser diversity and spatial multiplexing gain in random beamforming

paper_content:

This paper is concerned with the problem of exploiting spatial multiplexing gain through opportunistic beamforming with multiple random beams. The base station transmits multiple pilot sequences using orthogonal beams, and each user feeds the channel gain of each beam back. Then, the base station selects the subset of users and beams for which the sum-rate is maximized. We aim to exploit spatial multiplexing gain in a controlled fashion, i.e., the number of beams used for data transmission is chosen depending on the available multiuser diversity in the system. Two schemes are proposed: dynamic Orthonormal Random Beamforming with Systematic Beam Selection (ORBF/SBS), for which the number of beams used for data transmission is dynamically changed from one fading block to another so that the sum-rate is maximized; and static ORBF/SBS, which selects a fixed number of beams for a given signal-to-noise ratio and user number. The static scheme achieves the sum-rate of the dynamic one up to a small gap with much reduced computational and feedback complexity. We derive an approximate expression for the sum-rate achieved by the dynamic scheme, and provide insight into the optimal data stream number in the static scheme by means of asymptotical results. Computer simulations are provided to evaluate the performance of the proposed schemes.
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paper_title: Joint Feedback and Scheduling Scheme for Service-Differentiated Multiuser MIMO Systems

paper_content:

In this correspondence, we consider the problem of scheduling, in closed-loop multiuser MIMO systems, a large set of users with different Quality of Service (QoS) requirements, supplied by a single base station (BS) by means of Zero-Forcing Beamforming (ZFBF). We provide a power-and-bandwidth ef- ficient feedback scheme in which only ZFBF-optimal users feedback their CSI, thereby reducing the number of required feedbacks and the computational burden of exhaustive search for best users at the BS. Afterwards, we show that conventional sum- capacity maximizing scheduling policies fall short to meet the req- uisites of delay-sensitive applications, and we provide appropriate scheduling scheme for such-constrained users. Simulation results demonstrate that the proposed scheduling approach successfully meets both average and instantaneous delay constraints of delay- sensitive applications.
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paper_title: Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

paper_content:

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC.
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paper_title: Two-Stage Channel Quantization for Scheduling and Beamforming in Network MIMO Systems: Feedback Design and Scaling Laws

paper_content:

This paper proposes an efficient two-stage channel quantization and feedback scheme for the downlink limited-feedback network multiple-input multiple-output (MIMO) system. In the first stage, the users report their best set of base-station antenna and physical resource block combinations, and the base-stations schedule the best user for each antenna in each resource block. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. This paper proposes an analytical framework to show that, under a total feedback budget of B bits, the number of bits assigned to the second feedback stage should scale as log B, and in quantizing channel vectors from different base-stations, each user should allocate feedback bits in proportion to the channel magnitudes in dB scale. Under these optimized bit allocations, the overall sum rate of the system is shown to scale double-logarithmically with B, linearly with the total number of antennas, and logarithmically with transmit power, thus achieving both multiuser diversity and spatial multiplexing gains under limited feedback. Finally, realistic wireless propagation model of an urban small-cell deployment is used to show that the proposed scheme can approach the performance of a network MIMO system with full channel state information with only modest amount of channel feedback.
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paper_title: Large deviation delay analysis of queue-aware multi-user MIMO systems with two timescale mobile-driven feedback

paper_content:

Multi-user multi-input-multi-output (MU-MIMO) systems usually require users to feedback the channel state information (CSI) for scheduling. Most of the existing literature on the reduced feedback user scheduling focused on the throughput performance and the queueing delay was usually ignored. As the delay is important for real-time applications, it is desirable to have a low feedback queue-aware user scheduling algorithm for MU-MIMO systems. This paper proposes a two timescale queue-aware user scheduling algorithm, which consists of a queue-aware mobile-driven feedback filtering stage and a SINR-based user scheduling stage. The feedback policy is obtained by solving a queue-weighted optimization problem. In addition, we evaluate the associated queueing delay performance by using the large deviation analysis. The large deviation decay rate for the proposed algorithm is shown to be much larger than the CSI-only scheduling algorithm. Numerical results demonstrate the large performance gain of the proposed algorithm over the CSI-only algorithm, while the proposed one requires only a small amount of feedback.
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paper_title: Downlink Scheduling via Genetic Algorithms for Multiuser Single-Carrier and Multicarrier MIMO Systems With Dirty Paper Coding

paper_content:

Multiple-input-multiple-output (MIMO) systems are of interest for meeting the expected demand for higher data rates and lower delays in future wireless packet data systems. In such systems, it is optimal to simultaneously transmit to multiple users compared with a single user in a single-input-single-output system. In addition, multicarrier systems are of interest to combat frequency-selective fading that is experienced over the larger bandwidth that these future broadband systems will use. The use of dirty paper coding further complicates the matter, because the order in which the users are encoded will affect the rates that they can achieve. A well-designed cross-layer scheduling algorithm must take into account the multiple dimensions of this resource-allocation problem and other quality-of-service (QoS) parameters to fully exploit the communications channel. The scheduling problem is often expressed in terms of optimizing some utility function. Unfortunately, the search space for this optimization problem is extremely large, which prohibits an optimal exhaustive search. To this end, we investigate the use of genetic algorithms to reduce the complexity of the scheduling. This paper builds upon prior work that implements scheduling via genetic algorithms in the context of single-carrier systems using zero-forcing beamforming (ZFB). In this paper, we investigate how the genetic algorithm can be adapted to account for the effect of encoding order on the scheduling and how the scheduling can be extended to a multicarrier system. In particular, we investigate the maximum throughput and proportionally fair scheduling criteria. We demonstrate that the performance of the genetic algorithm is near optimal compared with an exhaustive search at a greatly reduced computational complexity. Furthermore, in the case of a multicarrier orthogonal frequency-division multiplexing (OFDM) system, an increase in capacity is shown relative to the single-carrier case.
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paper_title: System evaluation of optimal downlink beamforming with congestion control in wireless communication

paper_content:

We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.
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paper_title: Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

paper_content:

A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Limited Feedback Design for Interference Alignment on MIMO Interference Networks with Heterogeneous Path Loss and Spatial Correlations

paper_content:

Interference alignment is degree of freedom optimal in K -user MIMO interference channels and many previous works have studied the transceiver designs. However, these works predominantly focus on networks with perfect channel state information at the transmitters and symmetrical interference topology. In this paper, we consider a limited feedback system with heterogeneous path loss and spatial correlations, and investigate how the dynamics of the interference topology can be exploited to improve the feedback efficiency. We propose a novel spatial codebook design, and perform dynamic quantization via bit allocations to adapt to the asymmetry of the interference topology. We bound the system throughput under the proposed dynamic scheme in terms of the transmit SNR, feedback bits and the interference topology parameters. It is shown that when the number of feedback bits scales with SNR as C_{s}\cdot\log\textrm{SNR}, the sum degrees of freedom of the network are preserved. Moreover, the value of scaling coefficient C_{s} can be significantly reduced in networks with asymmetric interference topology.
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paper_title: Constructive Interference in Linear Precoding Systems: Power Allocation and User Selection

paper_content:

The exploitation of interference in a constructive manner has recently been proposed for the downlink of multiuser, multi-antenna transmitters. This novel linear precoding technique, herein referred to as constructive interference zero forcing (CIZF) precoding, has exhibited substantial gains over conventional approaches; the concept is to cancel, on a symbol-by-symbol basis, only the interfering users that do not add to the intended signal power. In this paper, the power allocation problem towards maximizing the performance of a CIZF system with respect to some metric (throughput or fairness) is investigated. What is more, it is shown that the performance of the novel precoding scheme can be further boosted by choosing some of the constructive multiuser interference terms in the precoder design. Finally, motivated by the significant effect of user selection on conventional, zero forcing (ZF) precoding, the problem of user selection for the novel precoding method is tackled. A new iterative, low complexity algorithm for user selection in CIZF is developed. Simulation results are provided to display the gains of the algorithm compared to known user selection approaches.
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paper_title: Recent Advances in Radio Resource Management for Heterogeneous LTE/LTE-A Networks

paper_content:

As heterogeneous networks (HetNets) emerge as one of the most promising developments toward realizing the target specifications of Long Term Evolution (LTE) and LTE-Advanced (LTE-A) networks, radio resource management (RRM) research for such networks has, in recent times, been intensively pursued. Clearly, recent research mainly concentrates on the aspect of interference mitigation. Other RRM aspects, such as radio resource utilization, fairness, complexity, and QoS, have not been given much attention. In this paper, we aim to provide an overview of the key challenges arising from HetNets and highlight their importance. Subsequently, we present a comprehensive survey of the RRM schemes that have been studied in recent years for LTE/LTE-A HetNets, with a particular focus on those for femtocells and relay nodes. Furthermore, we classify these RRM schemes according to their underlying approaches. In addition, these RRM schemes are qualitatively analyzed and compared to each other. We also identify a number of potential research directions for future RRM development. Finally, we discuss the lack of current RRM research and the importance of multi-objective RRM studies.
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paper_title: A User Selection Algorithm Using Angle between Subspaces for Downlink MU-MIMO Systems

paper_content:

One of major issues in the efficient use of radio resource for multiuser multiple-input/multiple-output (MU-MIMO) systems is the selection of users to achieve the maximum system throughput. The optimal user selection algorithm, which requires exhaustive search, is prohibitive due to its high computational complexity where Block diagonalization (BD) method is applied and known as a suboptimal precoding technique for downlink MU-MIMO systems, which intents to perfectly eliminate inter-user interference. In this paper, we propose efficient, iterative user selection algorithms with low complexity, where the product of eigenvalues of effective channels is utilized as a selection metric by applying the concept of principal angles between subspaces. And, we further examined the applicability of the proposed algorithms to limited feedback systems and proportional fair (PF) scheduling. Through computational complexity analysis, we show that the proposed algorithm has low complexity with a little loss in throughput. Simulation results validate that the proposed algorithm achieves almost the same system throughput by a capacity-based algorithm under high SNR regime with considerable reduction in complexity.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Space Division Multiple Access with a Sum Feedback Rate Constraint

paper_content:

On a multi-antenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

paper_content:

In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

paper_content:

In this paper, we tackle the problem of semidistributed user selection with distributed linear precoding for sum-rate maximization in multiuser multicell systems. A set of adjacent base stations (BSs) forms a cluster to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling, and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to nonintended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, namely, distributed zero forcing and distributed virtual signal-to-interference-plus-noise ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First, we investigate how the signal-to-noise ratio regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the BSs.
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paper_title: Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search

paper_content:

We consider a multi-user MIMO downlink system employing zero-forcing beamforming (ZFBF) as a spatial multiplexing strategy, and propose low-complexity user subset selection methods based on a clique (fully connected subgraph) search. The proposed algorithms, maximum weighted clique (MWC)-ZFBF and greedy weighted clique (GWC)-ZFBF, are shown to achieve the asymptotic sum-capacity of MIMO downlink channels as the number of users goes to infinity. Thus, clique search based ZFBF is an appealing strategy in MIMO downlink systems with a large number of users.
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paper_title: Convex approximation techniques for joint multiuser downlink beamforming and admission control

paper_content:

Multiuser downlink beamforming under quality of service (QoS) constraints has attracted considerable interest in years, because it is particularly appealing from a network operator's perspective (e.g., UMTS, 802.16e). When there are many co-channel users and/or the service constraints are stringent, the problem becomes infeasible and some form of admission control is necessary. We advocate a cross-layer approach to joint multiuser transmit beamforming and admission control, aiming to maximize the number of users that can be served at their desired QoS. It is shown that the core problem is NP-hard, yet amenable to convex approximation tools. Two computationally efficient convex approximation algorithms are proposed: one is based on semidefinite relaxation of an equivalent problem reformulation; the other takes a penalized second-order cone approach. Their performance is assessed in a range of experiments, using both simulated and measured channel data. In all experiments considered, the proposed algorithms work remarkably well in terms of the attained performance-complexity trade-off, consistently exhibiting close to optimal performance at an affordable computational complexity.
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paper_title: Coordinated beamforming with limited feedback in the MIMO broadcast channel

paper_content:

In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.
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paper_title: Multi-Antenna Downlink Channels with Limited Feedback and User Selection

paper_content:

We analyze the sum-rate performance of a multi- antenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load.
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paper_title: Traffic-Aware Training and Scheduling for MISO Wireless Downlink Systems

paper_content:

In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback/training decision. This should be leveraged in future communication systems.
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paper_title: Network MIMO with Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation and Reduced-Complexity Scheduling

paper_content:

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.
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paper_title: Multicell Coordination via Joint Scheduling, Beamforming, and Power Spectrum Adaptation

paper_content:

The mitigation of intercell interference is an importance issue for current and next-generation wireless cellular networks where frequencies are aggressively reused and hierarchical cellular structures may heavily overlap. The paper examines the benefit of coordinating transmission strategies and resource allocation schemes across multiple base-stations for interference mitigation. Two different wireless cellular architectures are studied: a multicell network where base-stations coordinate in their transmission strategies, and a mixed macrocell and femtocell/picocell deployment with coordination among macro and femto/pico base-stations. For both scenarios, this paper proposes a heuristic joint proportionally fair scheduling, spatial multiplexing, and power spectrum adaptation algorithm that coordinates multiple base-stations with an objective of optimizing the overall network utility. The proposed scheme optimizes the user schedule, transmit and receive beamforming vectors, and transmit power spectra jointly, while taking into consideration both the intercell and intracell interference and the fairness among the users. System-level simulation results show that coordination at the transmission strategy and resource allocation level can already significantly improve the overall network throughput as compared to a conventional network design with fixed transmit power and per-cell zero-forcing beamforming.
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paper_title: Iterative Precoder Design and User Scheduling for Block-Diagonalized Systems

paper_content:

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices.
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paper_title: Coordinated user scheduling in the multi-cell MIMO downlink

paper_content:

We propose a novel, coordinated user scheduling (CUS) algorithm for inter-cell interference (ICI) mitigation in the downlink of a multi-cell multi-user MIMO system. In the proposed algorithm, ICI mitigation is performed through the exchange of necessary channel state information (CSI) among the base stations, and the revision of the scheduling decisions and beamformer designs at each base station. Furthermore, ICI mitigation is performed only for the cell-edge users so that the amount of inter-base station signaling overhead is minimized. Our simulation results demonstrate that the proposed coordination scheduling algorithm significantly improves the cell-edge users' throughput compared to conventional systems with only a negligible amount of CSI sharing among the base stations and a relatively small throughput loss for the cell-interior users.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming and User Grouping

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a two stage downlink beamforming: a pre-beamformer that depends on the channel covariances and minimizes interference across groups and a multiuser MIMO precoder for the effective channel after pre-beamforming, to counteract interference within a group. We first focus on the regime of a fixed number of antennas and large number of users, and show that opportunistic beamforming with user selection yields significant gain, and thus, channel correlation may yield a capacity improvement over the uncorrelated "isotropic" channel result of Sharif and Hassibi. We prove that in the presence of different correlations among groups, a block diagonalization approach for the design of pre-beamformers achieves the optimal sum-rate scaling. Next, we consider the regime of large number of antennas and users, where user selection does not provide significant gain. Here, we propose a simplified user grouping algorithm to cluster users into groups when the number of antennas becomes very large, in a realistic setting where users are randomly distributed and have different angles of arrival and angular spreads depending on the propagation environment. Our subsequent analysis leads to a probabilistic scheduling algorithm, where users within each group are preselected at random based on probabilities derived from the large system analysis, depending on the fairness criterion. This is advantageous since only the selected users are required to feedback their channel state information (CSIT).
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paper_title: An improved partial CSIT random beamforming for multibeam satellite systems

paper_content:

A novel multiple input multiple output (MIMO) transmitting scheme is presented for multibeam satellite systems, where the objective is to increase the system sum rate, availability and variance performance.
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paper_title: Adaptive Modulation in PU2RC Systems with Finite Rate Feedback

paper_content:

This paper addresses a per user unitary precoding and rate control (PU 2 RC) system with adaptive multi-level quadrature amplitude modulation (QAM) modulation, where both the PU 2 RC operation and adaptive modulation are based on finite rate feedback. The system supports two transmission modes (single user transmit beamforming and multiuser transmission with orthogonal beamforming), and switches between the two modes to maximize the average throughput. We first study single user transmit beamforming, and derive closed-form expressions for the average throughput and bit-error rate (BER) with outdated channel information. Then, multiuser transmission with orthogonal beamforming is investigated. We analyze the throughput and BER performance without feedback delay in the normal signal noise ratio (SNR) regime, and the performance with feedback delay in the interference-limited regime. Simulation results demonstrate the effect of time delay, and the preferred regions of the single user transmission mode and multiuser transmission mode.
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paper_title: Joint Beamforming and Scheduling for a Multi-Antenna Downlink with Imperfect Transmitter Channel Knowledge

paper_content:

We consider the downlink of a wireless system where the base-station has M ges 1 antennas and K user terminals have one antenna each. We study the weighted rate sum maximization in the case of non-perfect Channel State Information at the Transmitter (CSIT). Some relevant downlink optimization problems, such as the stabilization of the transmission queues under random packet arrivals and the proportional fair scheduling for infinite backlogged systems, can be solved as special cases of the proposed problem. We restrict the transmitter strategy to be based on Gaussian coding and beamforming. Even under this simplifying condition, the problem at hand is non-convex and it does not appear to lend itself to a simple algorithmic solution. Therefore, we introduce some approximations that yield a definition of signal-to-interference plus noise ratio (SINR) commonly used in the classical array- processing/beamforming literature. For the simpler (but still non-convex) approximated problem, we propose a powerful heuristic solution based on greedy user selection and a gradient iteration that converges to a local maximum of the objective function. This method yields very competitive results with relatively low computational complexity. Extensive simulations show that, in the case of perfect CSIT, the proposed heuristic scheme performs very closely to the optimal (dirty-paper coding) strategy while, in the case of non-perfect CSIT, it significantly outperforms previously proposed suboptimal approaches, such as random beamforming and approximated zero-forcing with greedy user selection.
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paper_title: Interference Coordination through Network-Synchronized Cyclic Beamforming

paper_content:

The next generation of wireless networks (e.g., (10)) will use multiple techniques to improve channel spectral efficien- cies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each subband in each frame, the scheduler chooses a beam and then schedules one or more UEs within the corresponding beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors (flashlight effect). The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period but this can be changed occasionally.
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paper_title: Dynamic Multi-User MIMO scheduling with limited feedback in LTE-Advanced

paper_content:

Multi-User MIMO (MU-MIMO) systems have gained numerous attention from researchers in the past decade due to its substantial gains in the system throughput. Most of the initial research assumes the knowledge of perfect channel state information at the transmitter (CSIT). However, this is considered impractical and research over the past few years has been focused on receivers feeding back limited information to the transmitter. In this work, we consider a transparent MU-MIMO system model with limited feedback. We propose a general framework for dynamic MU-MIMO scheduling with the capability to switch between Single-User MIMO mode and (Multi-Rank) Multi-User MIMO mode without users feeding back additional multi-user information. Specifically, this is done by each user carefully estimating its CQI under the hypothesis of Multi-Rank MultiUser MIMO transmission and taking advantage of the codebook structure. We consider the sum rate of the system assuming each user uses ML and LMMSE receiver and show that our proposed scheduler, with significantly reduced feedback load, outperforms the best-companion user pairing.
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paper_title: Low Complexity Scheduling and Beamforming for Multiuser MIMO Systems

paper_content:

The problem of joint scheduling and beam-forming for a multiple antenna broadcast channel with partial channel state information at the transmitter (CSIT) is considered. We show how long-term statistical channel knowledge can be efficiently combined with instantaneous low-rate feedback for user selection and linear beamforming. A low complexity algorithm based on an estimate (bound) of the multiuser interference is proposed. Our scheme is shown to exhibit significant throughput gain over opportunistic techniques, approaching the sum rate of full CSIT for small angle spreads.
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paper_title: MU-MISO Transmission with Limited Feedback

paper_content:

Downlink multi-user transmission techniques that allow several users to be served simultaneously in frequency and time have been recognized as a promising means to increase system capacity. However they require accurate channel state information (CSI) at the base station (BS) such that appropriate signal processing can be performed to separate multiple users in the space domain. In practice however, CSI cannot be perfectly known to the BS due to the capacity-limited feedback channel in FDD systems for instance. In this letter we investigate multiuser multiple-input single-output (MU-MISO) transmission with limited feedback. In particular we identify the useful information that the BS needs to deal with inter-user interference and a codebook design is derived accordingly. In addition, an adaptive threshold-based feedback approach is proposed, where only users with good feedback quality are allowed to do feedback. It is shown that the adaptive scheme can effectively improve the system performance given a fixed number of feedback bits.
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paper_title: Joint User Scheduling and Adaptive Intercell Interference Cancelation for MISO Downlink Cellular Systems

paper_content:

Recently, an adaptive intercell interference (ICI) mitigation technique has been proposed for downlink cellular systems as a means to increase throughput with low system complexity. However, in the prior work, the issue of intercell user scheduling has not been considered. In this paper, we study multiple-input-single-output (MISO) downlink cellular systems that jointly design adaptive ICI cancelation (ICIC) and intercell user scheduling assuming that partial channel state information (CSI) is shared among base stations (BSs). Since the optimal solution would require high complexity, we investigate a new low-complexity algorithm that selects the best users and their beamforming strategies in terms of maximizing the weighted sum rate (WSR). To this end, we first develop a simple threshold criterion for each user to decide the preferred beamforming strategy based on the derivation of the expected signal-to-interference-plus-noise ratio (SINR). Then, according to users' feedback about their decisions, a successive user and beamforming selection algorithm is performed at the BSs. From simulation results, we show that, combined with proportional fair scheduling, the proposed scheme provides excellent throughput performance with very low computational complexity and the amount of inter-BS CSI exchange. Furthermore, we discuss an extension of the proposed scheme to limited feedback systems and observe that our algorithm also provides similar advantages over conventional schemes with quantized feedback.
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paper_title: Efficient Sum Rate Maximization and Resource Allocation in Block-Diagonalized Space-Division Multiplexing

paper_content:

For space-division multiplexing (SDM) via block diagonalization on multiuser multiple-input multiple-output (MIMO) wireless downlink, it is shown that receive antenna selection (RAS) is necessary for maximizing the achievable sum rate. This is true even when all receive antennas are equipped with radio frequency (RF) chains and RAS reduces the upper bound on the broadcast sum capacity, and when the orthogonalized channels use optimal processing. Similarly, spatial-mode selection (SMS) is necessary for sum rate maximization when receive-weight matrices are used for spatial-mode allocation. RAS/SMS may release transmission resources that can fully be utilized via additional user scheduling to yield further sum rate gains. Optimal user selection for sum rate maximization is subsumed within an exhaustive RAS/SMS process for multiantenna terminals, and both selection processes become identical for single-antenna terminals. RAS/SMS thus helps reduce the performance gap from the optimal sum capacity even for small user pool sizes. A block antenna/mode selection approach is introduced to help overcome the drawbacks of existing algorithms. Since RAS/SMS involves antenna/mode ranking, a systematic method for resource allocation with sum rate loss minimization is inherently provided. This way, a streamlined process that combines user selection, RAS/SMS, and resource allocation is developed for sum rate maximization of block-diagonalized SDM.
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paper_title: MIMO wireless linear precoding

paper_content:

This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues. The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation. It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding. A precoded system structure is then described, involving an encoder and a linear precoder. Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios.
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paper_title: Multimode Transmission for Multiuser MIMO Systems With Block Diagonalization

paper_content:

A low-complexity multimode transmission technique for downlink multiuser multiple-input-multiple-output (MIMO) systems with block diagonalization (BD) is proposed. The proposed technique adaptively configures the number of data streams for each user by adjusting its number of active receive antenna and switching between single-stream beamforming and multistream spatial multiplexing, as a means to exploit the multimode switching diversity. We consider a highly loaded system where there are a large number of users, hence a subset of users need to be selected. Joint user and antenna selection has been proposed as a multiuser multimode switching technique, where the optimal subset of receive antennas and users are chosen to maximize the sum throughput. The brute-force search, however, is prohibitively complicated. In this paper, two low-complexity near-optimal user/antenna selection algorithms are developed. The first algorithm aims at maximizing a capacity lower bound, derived in terms of the sum Frobenius norm of the channel, while the second algorithm greedily maximizes the sum capacity. We analytically evaluate the complexity of the proposed algorithms and show that it is orders of magnitude lower than that of the exhaustive search. Simulation results demonstrate that the proposed algorithms achieve up to 98% of the sum throughput of the exhaustive search, for most system configurations, while the complexity is substantially reduced.
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paper_title: Utilizing the Spatial Information Provided by Channel Norm Feedback in SDMA Systems

paper_content:

To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.
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paper_title: Precoding Schemes for the MIMO-GBC

paper_content:

The use of M antennas at the base station and of transmitter channel state information can boost the downlink throughput by a factor M (multiplexing gain), even though the receivers have a single antenna and do not cooperate. In this semi-tutorial work, we discuss some low-complexity alternatives to achieve a downlink throughput very close to the optimal sum capacity. We review and compare these alternatives and we show that, in the simple setting of independently fading channels, relatively traditional forms of linear beamforming achieve the best tradeoff between performance and complexity. These results somehow call for a reconsideration of the emphasis that certain recently proposed precoding techniques have enjoyed both in scientific literature and in technology development
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: An efficient greedy scheduler for zero-forcing dirty-paper coding

paper_content:

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.
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paper_title: MIMO Broadcast Channels with Spatial Heterogeneity

paper_content:

We develop a realistic model for multiple-input multiple-output (MIMO) broadcast channels, where each randomly located user's average SNR depends on its distance from the transmitter. With perfect channel state information at the transmitter (CSIT), the average sum capacity is proven to scale for many users like αM/2 log K instead of M log log K, where α, M, and K denote the path loss exponent, the number of transmit antennas, and the number of users in a cell. With only partial CSIT, the sum capacity at high SNR eventually saturates due to interference, and the saturation value scales for large B like MB/M-1, where B denotes the quantization resolution for channel feedback.
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paper_title: On the user selection for MIMO broadcast channels

paper_content:

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.
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paper_title: Downlink Multiuser MIMO Systems With Adaptive Feedback Rate

paper_content:

In this paper, an efficient channel feedback scheme for downlink multiuser multiple-input-multiple-output (MU-MIMO) systems is proposed. The objective of the new feedback design is to adaptively control the feedback rate of each user, depending on the individual channel status, while the overall sum feedback rate is kept the same. The proposed channel feedback scheme is composed of two stages: 1) the common channel feedback stage of all users and 2) the user-specific channel feedback stage of the selected users. We present a low-complexity algorithm to determine the individual feedback rates of users, which utilizes convex optimization, followed by iterative steepest descent direction searching. Numerical results show that zero-forcing beamforming (ZFBF), combined with the proposed channel feedback scheme, considerably outperforms ZFBF with conventional channel feedback schemes.
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paper_title: Low-Complexity Downlink User Selection for Massive MIMO Systems

paper_content:

In this paper, we propose a pair of low-complexity user selection schemes with zero-forcing precoding for multiuser massive multiple-input–multiple-output downlink systems, in which the base station is equipped with a large-scale antenna array. First, we derive approximations of the ergodic sum rates of the systems invoking the conventional random user selection (RUS) and the location-dependent user selection (LUS). Then, the optimal number of simultaneously served user equipments (UEs),i.e., $K^\ast$ , is investigated to maximize the sum rate approximations. Upon exploiting $K^\ast$ , we develop two user selection schemes, namely, $K^\ast$ -RUS and $K^\ast$ -LUS, where $K^\ast$ UEs are selected either randomly or based on their locations. Both the proposed schemes are independent of the instantaneous channel state information of small-scale fading, therefore enjoying the same extremely low computational complexity as that of the conventional RUS scheme. Moreover, both of our proposed schemes achieve significant sum rate improvement over the conventional RUS. In addition, it is worth noting that, like the conventional RUS, the $K^\ast$ -RUS achieves good fairness among UEs.
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paper_title: User Scheduling for Heterogeneous Multiuser MIMO Systems: A Subspace Viewpoint

paper_content:

In downlink multiuser multiple-input-multiple-output (MU-MIMO) systems, users are practically heterogeneous. However, many existing user-scheduling algorithms are designed with an implicit assumption that users are homogeneous. In this paper, we revisit the problem by exploring the characteristics of heterogeneous users from a subspace viewpoint. With an objective of minimizing interference nonorthogonality among users, three new angular-based user-scheduling criteria are proposed. While the first criterion is heuristically determined by identifying the incapability of the largest principal angle to characterize subspace correlation and, hence, interference nonorthogonality between users, the second and third criteria are derived by using the sum rate capacity bounds with block diagonalization and the change in capacity by adding a new user into an existing user subset, respectively. Aiming to capture fairness among heterogeneous users while maintaining multiuser diversity gain, two new hybrid user-scheduling algorithms, whose computational complexities are only linearly proportional to the number of users, are proposed. We show by simulations the effectiveness of our proposed user-scheduling criteria and algorithms with respect to those commonly used in a homogeneous environment.
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paper_title: Adaptive scheduling for MIMO wireless networks: cross-layer approach and application to HSDPA

paper_content:

In this paper, we consider the scheduling problem in multiple-input multiple-output (MIMO) wireless networks. The main important characteristic of an optimal scheduler is to maximize throughput while servicing users in a fair manner. Herein, we formulate MIMO scheduling as a generalized assignment problem (GAP) and propose a general solution for the GAP, namely, a cross-layer MIMO scheduler (CMS), which uses a novel adaptive proportional fairness (APF) mapping approach in conjunction with a new fast transmit antenna selection (FTAS) technique, to determine the set of users to transmit to and the antenna over which the data associated to each user should be transmitted. The proposed scheduler is applied for packet transmission in high-speed downlink packet access (HSDPA), taking advantage of the use of adaptive modulation and coding while coping with the constraints on the maximum number of simultaneous codes a user equipment can support, the limited uplink signalling, and the absence of fast power control. Numerical results show that the proposed CMS provides up to 70% increase in total throughput compared to other scheduling schemes
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paper_title: Joint Spatial Division and Multiplexing—The Large-Scale Array Regime

paper_content:

We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink/downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users.
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paper_title: Interference mitigation techniques for broadband satellite system

paper_content:

This paper presents an overview of possible interference mitigation techniques aiming at increasing the system capacity of broadband multimedia satellite systems. A multi-star network topology using a bent-pipe transparent satellite is assumed. After a general overview, the paper concentrates on the assessment of Linear Precoding techniques for increasing the potential system capacity on the Forward Link. Potential performance improvements achievable in real systems are investigated as well as resulting system constraints.
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paper_title: An overview of limited feedback in wireless communication systems

paper_content:

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
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paper_title: Maximum product of effective channel gains: an innovative user selection algorithm for downlink multi-user multiple input and multiple output

paper_content:

Recently, zero-forcing beamforming has been widely used for multiple-input and multiple-output broadcast channels, because it could provide suboptimal capacity with low complexity. To increase the sum data rate, a good user selection algorithm is attractive. In this paper, a new user selection algorithm named maximum product of effective channel gains is presented. The proposed algorithm is described mathematically, and the lower bound of the sum capacity is demonstrated to be proportional to the product of effective channel gains. Our simulation results show that maximum product of effective channel gains can achieve higher sum rate compared with the classical algorithm, semi-orthogonal user selection, with the same complexity order, especially when the signal-to-noise ratio is high; in addition, the complexity of the proposed algorithm is superior to minimum of the Frobenius norm of the pseudo-inverse algorithm. Meanwhile, the number of users that can be served simultaneously is equal to the number of transmission antennas, which is the maximum performance that can be achieved.Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: MIMO Broadcast Scheduling with Limited Feedback

paper_content:

We consider multiuser scheduling with limited feedback of partial channel state information in MIMO broadcast channels. By using spatial multiplexing at the base station (BS) and antenna selection for each user, we propose a multiuser scheduling method that allocates independent information streams from all M transmit antennas to the M most favorable users with the highest signal-to-interference-plus-noise ratio (SINR). A close approximation of the achievable sum-rate throughput for the proposed method is obtained and shown to match the simulation results very well. Moreover, two reduced feedback scheduling approaches are proposed. In the first approach, which we shall refer to as selected feedback scheduling, the users are selected based on their SINR compared to a predesigned threshold. Only those selected users are allowed to feed back limited information to the BS. The resultant feedback load and achievable throughput are derived. It will then be demonstrated that with a proper choice of the threshold, the feedback load can be greatly reduced with a negligible performance loss. The second reduced feedback scheduling approach employs quantization for each user, in which only few bits of quantized SINR are fed back to the BS. Performance analysis will show that even with only 1-bit quantization, the proposed quantized feedback scheduling approach can exploit the multiuser diversity at the expense of slight decrease of throughput.
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paper_title: Transmit Diversity Versus Opportunistic Beamforming in Data Packet Mobile Downlink Transmission

paper_content:

We compare space-time coding (transmit diversity) and random "opportunistic" beamforming in a space-division multiple access/time-division multiple access single-cell downlink system with random packet arrivals, correlated block-fading channels, and non-perfect channel state information at the transmitter due to a feedback delay. Our comparison is based on system stability. The ability of accurately predicting the channel signal-to-noise ratio dominates the performance of opportunistic beamforming, even under the optimistic assumption that the sequence of beamforming matrices is perfectly known a priori by the receivers. Our results show that the relative merit of opportunistic beamforming versus space-time coding strongly depends on the channel Doppler bandwidth. Therefore, previous naive conclusions on the fact that transmit diversity always hurts the system performance under multiuser-diversity scheduling should be taken with great care
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paper_title: Adaptive downlink multi-user MIMO wireless systems for correlated channels with imperfect CSI

paper_content:

Multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. However the capacity increase is limited when the number of antennas at the receiver is fixed or restricted (due to mobile size constraints for example). To overcome this limitation multi-user MIMO can be used, which allows several users to be served simultaneously in frequency and time. A disadvantage of these multi-user MIMO systems, when used in the downlink however, is that they need accurate channel state information (CSI) at the transmitter and also uncorrelated channels among users. In this paper we investigate methods to address the problems of multi-user MIMO systems in spatially correlated channels. We adopt the concept of angle between subspaces to characterize the inter-user spatial correlation and adapt the algorithm to those conditions. We also investigate the impact of the accuracy of CSI at the transmitter (CSIT) and whether more limited CSI such as channel correlation information alone can be used to provide good multi-user MIMO performance. Results are presented as various simulated capacity measures and we use them to make comparisons between the various multi-user MIMO configurations
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paper_title: MIMO broadcast channels with finite rate feedback

paper_content:

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where the receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. Simple expressions for the capacity degradation due to finite rate feedback as well as the required increases in feedback load per mobile as a function of the number of access point antennas and the system SNR are provided.
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paper_title: How Many Users should be Turned On in a Multi-Antenna Broadcast Channel

paper_content:

This paper considers broadcast channels with L antennas at the base station and m single-antenna users, where each user has perfect channel knowledge and the base station obtains channel information through a finite rate feedback. The key observation of this paper is that the optimal number of on-users (users turned on), say s, is a function of signal-to-noise ratio (SNR) and other system parameters. Towards this observation, we use asymptotic analysis to guide the design of feedback and transmission strategies. As L, m and the feedback rates approach infinity linearly, we derive the asymptotic optimal feedback strategy and a realistic criterion to decide which users should be turned on. Define the corresponding asymptotic throughput per antenna as the spatial efficiency. It is a function of the number of on-users s, and therefore, s should be appropriately chosen. Based on the above asymptotic results, we also develop a scheme for a system with finite many antennas and users. Compared with other works where s is presumed constant, our scheme achieves a significant gain by choosing the appropriate s. Furthermore, our analysis and scheme is valid for heterogeneous systems where different users may have different path loss coefficients and feedback rates.
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paper_title: Impact of Spatial Correlation and Precoding Design in OSTBC MIMO Systems

paper_content:

The impact of transmission design and spatial correlation on the symbol error rate (SER) is analyzed for multi-antenna communication links. The receiver has perfect channel state information (CSI), while the transmitter has either statistical or no CSI. The transmission is based on orthogonal space-time block codes (OSTBCs) and linear precoding. The precoding strategy that minimizes the worst-case SER is derived for the case when the transmitter has no CSI. Based on this strategy, the intuitive result that spatial correlation degrades the SER performance is proved mathematically. In the case when the transmitter knows the channel statistics, the correlation matrix is assumed to be jointly-correlated (a generalization of the Kronecker model). The eigenvectors of the SER-optimal precoding matrix are shown to originate from the correlation matrix and the remaining power allocation is a convex problem. Equal power allocation is SER-optimal at high SNR. Beamforming is SER-optimal at low SNR, or for increasing constellation sizes, and its optimality range is characterized. A heuristic low-complexity power allocation is proposed and evaluated numerically. Finally, it is proved analytically that receive-side correlation always degrades the SER. Transmit-side correlation will however improve the SER at low to medium SNR, while its impact is negligible at high SNR.
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paper_title: User selection schemes in multiple antenna broadcast channels with guaranteed performance

paper_content:

Recently, user selection algorithms in combination with linear pre- coding have been proposed that achieve the same scaling as the sum capacity of the MIMO BC. In this work, we study the properties of four user selection algorithms in conjunction with beamforming that guarantee certain SINR requirements under transmit power minimization. It is shown that for a large number of transmit antennas, the norm-based user selection performs close to the optimum. The results are illustrated by various numerical simulations.
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paper_title: Opportunistic Space-Division Multiple Access With Beam Selection

paper_content:

In this paper, a novel transmission technique for the multiple-input multiple-output (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple sets of randomly chosen orthogonal beamforming vectors. Each user sends the index of the best beamforming vector and the corresponding signal-to-interference-plus-noise ratio for that set of orthogonal vectors back to the base station. The base station opportunistically determines the users and corresponding orthogonal vectors that maximize the sum capacity. Based on the capacity expressions, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20% gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100% gain (for a large number of users) over conventional opportunistic beamforming when the number of transmit antennas is four.
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paper_title: Transmit Selection Diversity for Unitary Precoded Multiuser Spatial Multiplexing Systems With Linear Receivers

paper_content:

Multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference. In such a system, the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain. This paper proposes two precoding methods that use extra transmit antennas, beyond the minimum required, to provide additional degrees of diversity. The approach taken is to solve for a unitary transmit precoder, under a zero interuser interference constraint, that minimizes an upper bound on the symbol error rate (SER) for each user. Solutions where all transmit antennas are employed, as well as subsets of antennas (to reduce analog components), are described. Numerical results confirm a dramatic improvement in terms of SER and mutual information over single-user multiple-input multiple-output (MIMO) methods and static allocation methods. For example, the proposed techniques achieve a signal-to-noise ratio (SNR) improvement of 6-10 dB at an uncoded SER of 10-3, with only one extra transmit antenna
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paper_title: Scheduling of multi-antenna broadcast systems with heterogeneous users

paper_content:

We study the problem of efficiently scheduling users in a Gaussian broadcast channel with M transmit antennas and K independent receivers, each with a single antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the next L - 1 strongest ones to form the best pair, taking channel orientations into account as well. We prove that the expected rate gap converges to 1/(L- 1) nats/symbol when the total number of users K tends to infinity. Allowing L to increase with K, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while considerably reducing the feedback overhead and scheduling complexity. Next, we tackle the problem of maximizing a weighted sum rate in a scenario with heterogeneous user characteristics. We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at most MC users, where C denotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users.
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paper_title: Performance of Orthogonal Beamforming for SDMA With Limited Feedback

paper_content:

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.
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paper_title: Joint Scheduling and ARQ for MU-MIMO Downlink in the Presence of Inter-Cell Interference

paper_content:

User scheduling and multiuser multi-antenna (MU-MIMO) transmission are at the core of high-rate data-oriented downlink schemes of the next-generation of cellular systems (e.g., LTE-Advanced). Scheduling selects groups of users according to their channels vector directions and SINR levels. However, when scheduling is applied independently in each cell, the inter-cell interference (ICI) power at each user receiver is not known in advance since it changes at each new scheduling slot depending on the scheduling decisions of all interfering base stations. In order to cope with this uncertainty, we consider the joint operation of scheduling, MU-MIMO beamforming and Automatic Repeat reQuest (ARQ). We develop a game-theoretic framework for this problem and build on stochastic optimization techniques in order to find optimal scheduling and ARQ schemes. Particularizing our framework to the case of "outage service rates", we obtain a scheme based on adaptive variable-rate coding at the physical layer, combined with ARQ at the Logical Link Control (ARQ-LLC). Then, we present a novel scheme based on incremental redundancy Hybrid ARQ (HARQ) that is able to achieve a throughput performance arbitrarily close to the "genie-aided service rates", with no need for a genie that provides non-causally the ICI power levels. The novel HARQ scheme is both easier to implement and superior in performance with respect to the conventional combination of adaptive variable-rate coding and ARQ-LLC.
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paper_title: Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels

paper_content:

The full diversity gain provided by a multi-antenna channel can be achieved by transmit beamforming and receive combining. This requires the knowledge of channel state information (CSI) at the transmitter which is difficult to obtain in practice. Quantized beamforming where fixed codebooks known at both the transmitter and the receiver are used to quantize the CSI has been proposed to solve this problem. Most recent works focus attention on limited feedback codebook design for the uncorrelated Rayleigh fading channel. Such designs are sub-optimal when used in correlated channels. In this paper, we propose systematic codebook design for correlated channels when channel statistical information is known at the transmitter. This design is motivated by studying the performance of pure statistical beamforming in correlated channels and is implemented by maps that can rotate and scale spherical caps on the Grassmannian manifold. Based on this study, we show that even statistical beamforming is near-optimal if the transmitter covariance matrix is ill-conditioned and receiver covariance matrix is well-conditioned. This leads to a partitioning of the transmit and receive covariance spaces based on their conditioning with variable feedback requirements to achieve an operational performance level in the different partitions. When channel statistics are difficult to obtain at the transmitter, we propose a universal codebook design (also implemented by the rotation-scaling maps) that is robust to channel statistics. Numerical studies show that even few bits of feedback, when applied with our designs, lead to near perfect CSI performance in a variety of correlated channel conditions.
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paper_title: Scheduling for Multiuser MIMO Downlink Channels with Ranking-Based Feedback

paper_content:

We consider a multi-antenna broadcast channel with more single-antenna receivers than transmit antennas and partial channel state information at the transmitter (CSIT). We propose a novel type of CSIT representation for the purpose of user selection, coined as ranking-based feedback. Each user calculates and feeds back the rank, an integer between 1 and W + 1, of its instantaneous channel quality information (CQI) among a set of W past CQI measurements. Apart from reducing significantly the required feedback load, ranking-based feedback enables the transmitter to select users that are on the highest peak (quantile) with respect to their own channel distribution, independently of the distribution of other users. It can also be shown that this feedback metric can restore temporal fairness in heterogeneous networks, in which users' channels are not identically distributed and mobile terminals experience different average signal-to-noise ratio (SNR). The performance of a system that performs user selection using ranking-based CSIT in the context of random opportunistic beamforming is analyzed, and we provide design guidelines on the number of required past CSIT samples and the impact of finite W on average throughput. Simulation results show that feedback reduction of order of 40-50% can be achieved with negligible decrease in system throughput.
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paper_title: An efficient resource-allocation scheme for spatial multiuser access in MIMO/OFDM systems

paper_content:

Fast adaptive transmission has been recently identified as a key technology for exploiting potential system diversity and improving power-spectral efficiency in wireless communication systems. An adaptive resource-allocation approach, which jointly adapts subcarrier allocation, power distribution, and bit distribution according to instantaneous channel conditions, is proposed for multiuser multiple-input multiple-output (MIMO)/orthogonal frequency-division multiplexing systems. The resultant scheme is able to: 1) optimize the power efficiency; 2) guarantee each user's quality of service requirements, including bit-error rate and data rate; 3) ensure fairness to all the active users; and 4) be applied to systems with various types of multiuser-detection schemes at the receiver. For practical implementation, a reduced-complexity allocation algorithm is developed. This algorithm decouples the complex multiuser joint resource-allocation problem into simple single-user optimization problems by controlling the subcarrier sharing according to the users' spatial separability. Numerical results show that significant power and diversity gains are achievable, compared with nonadaptive systems. It is also demonstrated that the MIMO system is able to multiplex several users without sacrificing antenna diversity by using the proposed algorithm.
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paper_title: The impact of space division multiplexing on resource allocation: a unified treatment of TDMA, OFDMA and CDMA

paper_content:

Space division multiple access (SDMA) with an antenna array at the transmitter is a promising means for increasing system capacity and supporting rate-demanding services. However, the presence of an antenna array at the physical layer raises significant issues at higher layers. In this paper, we attempt to capture the impact of SDMA on access layer channel allocation, reflected on channel reuse. This impact obtains different twists in TDMA, CDMA and OFDMA due to the different nature of co-channel and cross-channel interference and the different interaction of user spatial channel characteristics with system channels, namely time slots, codes and subcarriers. We consider these access schemes in a generalized unified framework and propose heuristic algorithms for channel allocation, downlink beamforming and transmit power control so as to increase total provisioned system rate and provide QoS to users in the form of minimum rate guarantees. We study the class of greedy algorithms that rely on criteria such as induced or received interference and signal-to-interference ratio (SIR), and a class of SIR balancing algorithms. Results show superior performance for SIR balancing resource allocation and expose the performance benefits of cross-layer design.
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paper_title: Exploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems

paper_content:

In the design of narrowband multi-antenna systems, a limiting factor is the amount of channel state information (CSI) available at the transmitter. This is especially evident in multi-user systems, where the spatial user separability determines the multiplexing gain, but it is also important for transmission-rate adaptation in single-user systems. To limit the feedback load, the unknown and multi-dimensional channel needs to be represented by a limited number of bits. When combined with long-term channel statistics, the norm of the channel matrix has been shown to provide substantial CSI that permits efficient user selection, linear precoder design, and rate adaptation. Herein, we consider quantized feedback of the squared Frobenius norm in a Rayleigh fading environment with arbitrary spatial correlation. The conditional channel statistics are characterized and their moments are derived for both identical, distinct, and sets of repeated eigenvalues. These results are applied for minimum mean square error (MMSE) estimation of signal and interference powers in single- and multi-user systems, for the purpose of reliable rate adaptation and resource allocation. The problem of efficient feedback quantization is discussed and an entropy-maximizing framework is developed where the post-user-selection distribution can be taken into account in the design of the quantization levels. The analytic results of this paper are directly applicable in many widely used communication techniques, such as space-time block codes, linear precoding, space division multiple access (SDMA), and scheduling.
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paper_title: On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

paper_content:

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.
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paper_title: Leakage-based user scheduling in MU-MIMO broadcast channel

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This paper investigates user scheduling in multi-user MIMO broadcast channel. We propose a leakagebased user scheduling scheme, in which a user’s leakage power to other users is an important factor to determine whether the user should be selected. The accuracy of closed-form solution of SLNR (signal to leakage plus noise ratio) makes the proposed scheme outperform the traditional scheduling method based on SINR (signal to interference plus noise ratio). The proposed algorithms can work in case of perfect or limited feedback of CSI (channel state information) at transmitter, and the advantage is verified with numerical results. A tradeoff relation among feedback bits number, active user number and transmit/receive antennas number is analyzed, which serves as a system design guideline.
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paper_title: Fundamental Limits of Cooperation

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Cooperation is viewed as a key ingredient for interference management in wireless networks. This paper shows that cooperation has fundamental limitations. First, it is established that in systems that rely on pilot-assisted channel estimation, the spectral efficiency is upper-bounded by a quantity that does not depend on the transmit powers; in this framework, cooperation is possible only within clusters of limited size, which are subject to out-of-cluster interference whose power scales with that of the in-cluster signals. Second, an upper bound is also shown to exist if the cooperation extends to an entire (large) system operating as a single cluster; here, pilot-assisted transmission is necessarily transcended. Altogether, it is concluded that cooperation cannot in general change an interference-limited network to a noise-limited one. Consequently, the existing literature that routinely assumes that the high-power spectral efficiency scales with the log-scale transmit power provides only a partial characterization. The complete characterization proposed in this paper subdivides the high-power regime into a degree-of-freedom regime, where the scaling with the log-scale transmit power holds approximately, and a saturation regime, where the spectral efficiency hits a ceiling that is independent of the power. Using a cellular system as an example, it is demonstrated that the spectral efficiency saturates at power levels of operational relevance.
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paper_title: Multi-mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

paper_content:

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.
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paper_title: Recent Advances in Radio Resource Management for Heterogeneous LTE/LTE-A Networks

paper_content:

As heterogeneous networks (HetNets) emerge as one of the most promising developments toward realizing the target specifications of Long Term Evolution (LTE) and LTE-Advanced (LTE-A) networks, radio resource management (RRM) research for such networks has, in recent times, been intensively pursued. Clearly, recent research mainly concentrates on the aspect of interference mitigation. Other RRM aspects, such as radio resource utilization, fairness, complexity, and QoS, have not been given much attention. In this paper, we aim to provide an overview of the key challenges arising from HetNets and highlight their importance. Subsequently, we present a comprehensive survey of the RRM schemes that have been studied in recent years for LTE/LTE-A HetNets, with a particular focus on those for femtocells and relay nodes. Furthermore, we classify these RRM schemes according to their underlying approaches. In addition, these RRM schemes are qualitatively analyzed and compared to each other. We also identify a number of potential research directions for future RRM development. Finally, we discuss the lack of current RRM research and the importance of multi-objective RRM studies.
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paper_title: Multiple-antenna techniques for wireless communications - a comprehensive literature survey

paper_content:

The use of multiple antennas for wireless communication systems has gained overwhelming interest during the last decade - both in academia and industry. Multiple antennas can be utilized in order to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. With an enormous amount of yearly publications, the field of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly. To date, there are numerous papers on the performance limits of MIMO systems, and an abundance of transmitter and receiver concepts has been proposed. The objective of this literature survey is to provide non-specialists working in the general area of digital communications with a comprehensive overview of this exciting research field. To this end, the last ten years of research efforts are recapitulated, with focus on spatial multiplexing and spatial diversity techniques. In particular, topics such as transmitter and receiver structures, channel coding, MIMO techniques for frequency-selective fading channels, diversity reception and space-time coding techniques, differential and non-coherent schemes, beamforming techniques and closed-loop MIMO techniques, cooperative diversity schemes, as well as practical aspects influencing the performance of multiple-antenna systems are addressed. Although the list of references is certainly not intended to be exhaustive, the publications cited will serve as a good starting point for further reading.
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paper_title: Traffic-Aware Training and Scheduling for MISO Wireless Downlink Systems

paper_content:

In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback/training decision. This should be leveraged in future communication systems.
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paper_title: MIMO wireless linear precoding

paper_content:

This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues. The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation. It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding. A precoded system structure is then described, involving an encoder and a linear precoder. Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios.
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paper_title: Transmit Diversity Versus Opportunistic Beamforming in Data Packet Mobile Downlink Transmission

paper_content:

We compare space-time coding (transmit diversity) and random "opportunistic" beamforming in a space-division multiple access/time-division multiple access single-cell downlink system with random packet arrivals, correlated block-fading channels, and non-perfect channel state information at the transmitter due to a feedback delay. Our comparison is based on system stability. The ability of accurately predicting the channel signal-to-noise ratio dominates the performance of opportunistic beamforming, even under the optimistic assumption that the sequence of beamforming matrices is perfectly known a priori by the receivers. Our results show that the relative merit of opportunistic beamforming versus space-time coding strongly depends on the channel Doppler bandwidth. Therefore, previous naive conclusions on the fact that transmit diversity always hurts the system performance under multiuser-diversity scheduling should be taken with great care
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paper_title: MIMO broadcast channels with finite rate feedback

paper_content:

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where the receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. Simple expressions for the capacity degradation due to finite rate feedback as well as the required increases in feedback load per mobile as a function of the number of access point antennas and the system SNR are provided.
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paper_title: Fading correlation and its effect on the capacity of multielement antenna systems

paper_content:

We investigate the effects of fading correlations in multielement antenna (MEA) communication systems. Pioneering studies showed that if the fades connecting pairs of transmit and receive antenna elements are independently, identically distributed, MEAs offer a large increase in capacity compared to single-antenna systems. An MEA system can be described in terms of spatial eigenmodes, which are single-input single-output subchannels. The channel capacity of an MEA is the sum of capacities of these subchannels. We show that the fading correlation affects the MEA capacity by modifying the distributions of the gains of these subchannels. The fading correlation depends on the physical parameters of MEA and the scatterer characteristics. In this paper, to characterize the fading correlation, we employ an abstract model, which is appropriate for modeling narrow-band Rayleigh fading in fixed wireless systems.
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paper_title: On MIMO channel capacity, correlations, and keyholes: Analysis of degenerate channels

paper_content:

It has been demonstrated that zero correlation of a random multiple-input multiple-output channel is not a guarantee of its high capacity. Degenerate channels exist, which have zero correlation and still low capacity. We provide a statistical analysis of this phenomenon, formulate the general condition for a channel to be degenerate, and propose a method to estimate its capacity.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: On limits of wireless communications in a fading environment when using multiple antennas

paper_content:

This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. ::: ::: We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.
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paper_title: Massive MIMO and mmWave for 5G Wireless HetNet: Potential Benefits and Challenges

paper_content:

There has been active research worldwide to develop the next-generation, i.e., fifth-generation (5G), wireless network. The 5G network is expected to support a significantly large amount of mobile data traffic and a huge number of wireless connections and achieve better costand energy-efficiency as well as quality of service (QoS) in terms of communication delay, reliability, and security. To this end, the 5G wireless network should exploit the potential of new developments, including superdense and heterogeneous deployment of cells and massive antenna arrays [i.e., massive multiple-input, multiple-output (MIMO) technologies] and utilization of higher frequencies, particularly millimeter-wave (mmWave) frequencies. This article discusses the potential benefits and challenges of the 5G wireless heterogeneous network (HetNet) that incorporates massive MIMO and mmWave technologies.
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paper_title: Adaptive radio resource allocation for downlink OFDMA/SDMA systems with multimedia traffic

paper_content:

This paper proposes an adaptive radio resource allocation (ARRA) algorithm for downlink OFDMA/SDMA systems with multimedia traffic. Considering multiple service classes and diverse QoS requirements of multimedia traffic, the ARRA algorithm is designed with the goal to maximize spectrum efficiency and to fulfill quality of service (QoS) requirements. It is composed of two parts, a dynamic priority adjustment (DPA) scheme and a priority-based greedy (PBG) scheme. The DPA adopts a type of time-to-expiration to indicate the degree of user's urgency, and dynamically gives high priorities to urgent users. The PBG allocates the radio resource iteratively, based on a cost value, to maximize the system throughput while allocating enough resource to high-priority users. Simulation results show that the ARRA algorithm outperforms conventional algorithms in terms of system throughput and satisfaction extent of QoS requirements; it can sustain users' QoS requirements up till a traffic load of 0.8, while the conventional algorithms cannot guarantee QoS requirements after a traffic load of 0.3.
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paper_title: Capacity Analysis of Correlated MIMO Channels

paper_content:

This paper gives expressions for the capacity of ergodic multiple-input multiple-output channels with finite dimensions, in which the channel gains have a correlated complex normal distribution and receivers experience independent Gaussian noise. The particular correlated normal distribution considered corresponds to flat Rayleigh fading with arbitrary transmit and receive correlation. Knowledge of the correlation matrices is assumed at both the transmitter and receiver, while the receiver, but not the transmitter, has complete knowledge of the channel realization. The optimal input density is characterized via a necessary and sufficient condition for optimality, along with an iterative algorithm for its numerical computation. The resulting capacity is expressed in terms of hypergeometric functions of matrix argument, which depend on the channel correlation matrices only through their eigenvalues. Some closed-form expressions are also given in the case of single-sided correlation. Some consideration is given to high- and low-power asymptotics. Easily computable asymptotic expressions are also given for receive-side only correlation in the case that the number of transmitters is large. In that case, the capacity can be divided into two components: one arising from the dominant eigenvalues of the receiver-end correlation matrix, and the other from the remaining spherically distributed eigenvalues. Some numerical results are also presented.
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paper_title: Acquiring Partial CSI for Spatially Selective Transmission by Instantaneous Channel Norm Feedback

paper_content:

In the design of next-generation multiuser communication systems, multiple-antenna transmission is an essential part providing additional spatial degrees of freedom and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. Herein, we show that the Euclidean norm of the instantaneous channel, when combined with long-term channel statistics provides sufficient information for the transmitter to efficiently utilize multiuser diversity in time, frequency, and space. We consider the downlink of a communication system where the base station has multiple transmit antennas whereas each user terminal has a single receive antenna. The CSI provided by channel statistics and feedback of the norm of the instantaneous channel vector is studied in depth for correlated Rayleigh and Ricean fading channels, within a minimum mean-square error (MMSE) estimation framework. An asymptotic analysis (high instantaneous SNR) is presented which shows that channel realizations with large channel norm provide additional spatial CSI at the transmitter. This makes the proposed scheme ideal for multiuser diversity transmission schemes, where resources are only allocated to users experiencing favorable channel conditions.
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paper_title: Call admission control in wireless networks: a comprehensive survey

paper_content:

Radio resource management (RRM) plays a major role in Quality of Service (QoS) provisioning for wireless communication systems. The performance of RRM techniques has a direct impact on each user's individual performance and on the overall network performance. Arriving (new and handoff) calls are granted/denied access to the network by the call admission scheme (CAC) based on predefined criteria, taking the network loading conditions into consideration. CAC in wireless networks has been receiving a great deal of attention during the last two decades due to the growing popularity of wireless communications and the central role that CAC plays in QoS provisioning in terms of the signal quality, call blocking and dropping probabilities, packet delay and loss rate, and transmission rate. In the first and second generation of wireless systems, CAC has been developed for a single service environment. In the third generation and beyond wireless systems, multimedia services such as voice, video, data, and audio are to be offered with various QoS profiles. Hence, more sophisticated CAC schemes are developed to cope with these changes. This article provides a comprehensive survey of CAC schemes in modern wireless networks.
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paper_title: User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming

paper_content:

In this paper, we propose a greedy user selection with swap (GUSS) algorithm based on zero-forcing beamforming for multiuser multiple-input-multiple-output (MIMO) downlink channels. Existing user selection algorithms such as zero forcing with selection (ZFS) have the flaws of “redundant users” and “local optimum,” which compromise the achieved sum rate. GUSS improves the performance by adding the “delete” and “swap” operations to the user selection procedure of ZFS to eliminate “redundant users” and escape from “local optimum,” respectively. In addition, an effective-channel-vector-based effective-channel-gain-updating scheme is proposed to reduce the complexity of GUSS. With the help of this updating scheme, GUSS has the same order of complexity as ZFS with only a linear increment. Simulation results indicate that over the range of transmit signal-to-noise ratios (SNRs) considered, on average, the sum rate of GUSS reaches 99.3% of the upper bound that is achieved by exhaustive search, with only 1.51 to 2.29 times the complexity of ZFS.
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paper_title: Multiuser MIMO Scheduling for LTE-A Downlink Cellular Networks

paper_content:

In this paper, we investigate multiuser MIMO scheduling in LTE downlink cellular networks. We formulate the downlink LTE-A MIMO scheduling as a weighted sum rate maximization problem by allocating the RBs to users or user pairs subject to some constraints in LTE-A. We develop a low-complexity MU-MIMO scheduling and resource allocation algorithm and propose an adaptive switching approach between SU-MIMO and MU-MIMO to improve network performance. System-level simulation results demonstrate significantly performance improvement of the proposed MU-MIMO scheduling algorithm and the adaptive switching algorithm.
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paper_title: Coverage and Rate Analysis for Millimeter-Wave Cellular Networks

paper_content:

Millimeter wave (mmWave) holds promise as a carrier frequency for fifth generation cellular networks. Because mmWave signals are sensitive to blockage, prior models for cellular networks operated in the ultra high frequency (UHF) band do not apply to analyze mmWave cellular networks directly. Leveraging concepts from stochastic geometry, this paper proposes a general framework to evaluate the coverage and rate performance in mmWave cellular networks. Using a distance-dependent line-of-site (LOS) probability function, the locations of the LOS and non-LOS base stations are modeled as two independent non-homogeneous Poisson point processes, to which different path loss laws are applied. Based on the proposed framework, expressions for the signal-to-noise-and-interference ratio (SINR) and rate coverage probability are derived. The mmWave coverage and rate performance are examined as a function of the antenna geometry and base station density. The case of dense networks is further analyzed by applying a simplified system model, in which the LOS region of a user is approximated as a fixed LOS ball. The results show that dense mmWave networks can achieve comparable coverage and much higher data rates than conventional UHF cellular systems, despite the presence of blockages. The results suggest that the cell size to achieve the optimal SINR scales with the average size of the area that is LOS to a user.
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paper_title: Millimeter Wave Cellular Networks: A MAC Layer Perspective

paper_content:

The millimeter-wave (mmWave) frequency band is seen as a key enabler of multigigabit wireless access in future cellular networks. In order to overcome the propagation challenges, mmWave systems use a large number of antenna elements both at the base station and at the user equipment, which leads to high directivity gains, fully directional communications, and possible noise-limited operations. The fundamental differences between mmWave networks and traditional ones challenge the classical design constraints, objectives, and available degrees of freedom. This paper addresses the implications that highly directional communication has on the design of an efficient medium access control (MAC) layer. The paper discusses key MAC layer issues, such as synchronization, random access, handover, channelization, interference management, scheduling, and association. This paper provides an integrated view on MAC layer issues for cellular networks, identifies new challenges and tradeoffs, and provides novel insights and solution approaches.
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paper_title: Design Guidelines for Limited Feedback in the Spatially Correlated Broadcast Channel

paper_content:

A linear beamformer design for the broadcast channel where the base station is equipped with $N_t$ antennas and signals to $M = 2$ users (each with a single antenna)and where the vector channels are spatially correlated is considered. This problem is of relevance in wireless standardization efforts where two users are simultaneously scheduled (instead of the theoretically feasible $N_t$ user scheduling)to minimize signaling overhead. The users are assumed to have perfect channel state information (CSI), whereas the base station has statistical information of the channels. In the first part of this work, the role of the relevance of feedback is studied via the quantification of the gap in ergodic sum-rate between the perfect CSI and statistics-only extremes. In this direction, the importance of orthogonality of the dominant eigenmodes of the two users in maximizing the gap is established. In the second part of this work, in scenarios with a large gap, limited feedback beamforming codebooks and a codeword selection metric are designed for the low-rate feedback setting. The main contribution here is the proposal of a generalized eigenvector codebook and feedback of the codeword index that maximizes an estimate of the signal-to-interference-and-noise ratio $(\textsf{SINR})$ of each user. Extensions of this scheme are also proposed for the general $N_t$ antenna case with $M$ users, where $M \le N_t$ . It is shown via numerical studies that this scheme leads to significant performance improvement across a large family of channels over schemes such as Grassmannian/Random Vector Quantization/single-user codebooks with the channel projection metric for codeword selection.
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paper_title: Optimal Resource Allocation for Multiuser MIMO-OFDM Systems With User Rate Constraints

paper_content:

With the proliferation of wireless services, personal connectivity is quickly becoming ubiquitous. As the user population demands greater multimedia interactivity, data rate requirements are set to soar. Future wireless systems, e.g., multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), need to cater to not only a burgeoning subscriber pool but also to a higher throughput per user. Furthermore, resource allocation for multiuser MIMO-OFDM systems is vital for the optimization of the subcarrier and power allocations to improve overall system performance. Using convex optimization techniques, this paper proposes an efficient solution to minimize the total transmit power subject to each user's data rate requirement. Using a Lagrangian dual decomposition, the complexity is reduced from one that is exponential in the number of subcarriers M to one that is only linear in M. To keep the complexity low, linear beamforming is incorporated at both the transmitter and the receiver. Although frequency-flat fading has been known to plague OFDM resource allocation systems, a modification, i.e., dual proportional fairness, seamlessly handles flat or partially frequency-selective fading. Due to the nonconvexity of the optimization problem, the proposed solution is not guaranteed to be optimal. However, for a realistic number of subcarriers, the duality gap is practically zero, and optimal resource allocation can be evaluated efficiently. Simulation results show large performance gains over a fixed subcarrier allocation.
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paper_title: Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels

paper_content:

We investigate multiple-input multiple-output (MIMO) eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.
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paper_title: Stability and Delay of Zero-Forcing SDMA With Limited Feedback

paper_content:

This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor M >; 1. For given M → 1, the number of feedback bits per mobile is proved to be O(-log2(1-1/M)) .
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paper_title: MIMO over Satellite: A Review

paper_content:

The present article carries out a review of MIMO-based techniques that have been recently proposed for satellite communications. Due to the plethora of MIMO interpretations in terrestrial systems and the particularities of satellite communications, this review is built on two pillars, namely fixed satellite and mobile satellite. Special attention is given to the characteristics of the satellite channel, which will ultimately determine the viability of MIMO over satellite. Finally, some future research directions are identified.
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paper_title: A comparison of scheduling strategies for MIMO broadcast channel with limited feedback on OFDM systems

paper_content:

We consider a multiuser downlink transmission from a base station with multiple antennas (MIMO) to mobile terminals (users) with a single antenna, using orthogonal frequency division multiplexing (OFDM). Channel conditions are reported by a feedback from users with limited rate, and the base station schedules transmissions and beamforms signals to users. We show that an important set of schedulers using a general utility function can be reduced to a scheduler maximizing the weighted sum rate of the system. For this case we then focus on scheduling methods with many users and OFDM subcarriers. Various scheduling strategies are compared in terms of achieved throughput and computational complexity and a good tradeoff is identified in greedy and semiorthogonal user selection algorithms. In the greedy selection algorithm, users are selected one by one as long as the throughput increases, while in the semiorthogonal approach users are selected based on the channel correlation. An extension of these approaches from a flat-fading channel to OFDM is considered and simplifications that may be useful for a large number of subcarriers are presented. Results are reported for a typical cellular transmission of the long-term evolution (LTE) of 3GPP.
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paper_title: Fading Channels: InformationTheoretic and Communications Aspects

paper_content:

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Multiple-antenna techniques for wireless communications - a comprehensive literature survey

paper_content:

The use of multiple antennas for wireless communication systems has gained overwhelming interest during the last decade - both in academia and industry. Multiple antennas can be utilized in order to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. With an enormous amount of yearly publications, the field of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly. To date, there are numerous papers on the performance limits of MIMO systems, and an abundance of transmitter and receiver concepts has been proposed. The objective of this literature survey is to provide non-specialists working in the general area of digital communications with a comprehensive overview of this exciting research field. To this end, the last ten years of research efforts are recapitulated, with focus on spatial multiplexing and spatial diversity techniques. In particular, topics such as transmitter and receiver structures, channel coding, MIMO techniques for frequency-selective fading channels, diversity reception and space-time coding techniques, differential and non-coherent schemes, beamforming techniques and closed-loop MIMO techniques, cooperative diversity schemes, as well as practical aspects influencing the performance of multiple-antenna systems are addressed. Although the list of references is certainly not intended to be exhaustive, the publications cited will serve as a good starting point for further reading.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

paper_content:

In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Keyhole Effect in MIMO Wireless Channels: Measurements and Theory

paper_content:

It has been predicted theoretically that for some environments, the capacity of wireless multiple-input multiple-output systems can become very low even for uncorrelated signals; this effect has been termed "keyhole" or "pinhole". In this paper the first unique measurements of this effect are presented. The measurements were performed in a controlled indoor environment that was designed to obtain a keyhole channel. We analyze limitations due to measurement imperfections for measurement-based capacity calculations and keyhole investigations. We further present a bound for the higher eigenmodes as a function of the finite measurement signal-to-noise ratio and multipath component leakage. The bound is compared to the measurement results and shows excellent agreement. Finally, we analyze the envelope distribution and, as expected from theory, it follows a double-Rayleigh distribution
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paper_title: Traffic-Aware Training and Scheduling for MISO Wireless Downlink Systems

paper_content:

In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback/training decision. This should be leveraged in future communication systems.
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paper_title: An improved partial CSIT random beamforming for multibeam satellite systems

paper_content:

A novel multiple input multiple output (MIMO) transmitting scheme is presented for multibeam satellite systems, where the objective is to increase the system sum rate, availability and variance performance.
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paper_title: On the Number of RF Chains and Phase Shifters, and Scheduling Design With Hybrid Analog–Digital Beamforming

paper_content:

This paper considers hybrid beamforming (HB) for downlink multiuser massive multiple-input multiple-output (MIMO) systems with frequency selective channels. The proposed HB design employs sets of digitally controlled phase (fixed phase) paired phase shifters (PSs) and switches. For this system, first we determine the required number of radio frequency (RF) chains and PSs such that the proposed HB achieves the same performance as that of the digital beamforming (DB) which utilizes $N$ (number of transmitter antennas) RF chains. We show that the performance of the DB can be achieved with our HB just by utilizing $r_t$ RF chains and $2r_t(N-r_t + \text{1})$ PSs, where $r_t \leq N$ is the rank of the combined digital precoder matrices of all subcarriers. Second, we provide a simple and novel approach to reduce the number of PSs with only a negligible performance degradation. Numerical results reveal that only ${20}{-}{40}$ PSs per RF chain are sufficient for practically relevant parameter settings. Finally, for the scenario where the deployed number of RF chains $(N_a) $ is less than $r_t$ , we propose a simple user scheduling algorithm to select the best set of users in each subcarrier. Simulation results validate theoretical expressions, and demonstrate the superiority of the proposed HB design over the existing HB designs in both flat fading and frequency selective channels.
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paper_title: Interference mitigation techniques for broadband satellite system

paper_content:

This paper presents an overview of possible interference mitigation techniques aiming at increasing the system capacity of broadband multimedia satellite systems. A multi-star network topology using a bent-pipe transparent satellite is assumed. After a general overview, the paper concentrates on the assessment of Linear Precoding techniques for increasing the potential system capacity on the Forward Link. Potential performance improvements achievable in real systems are investigated as well as resulting system constraints.
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paper_title: An overview of limited feedback in wireless communication systems

paper_content:

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
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paper_title: Majorization and Matrix-Monotone Functions in Wireless Communications

paper_content:

This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions, reviews their basic definitions and describes their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions. ::: ::: The techniques are applied to solve communication and information theoretic problems in wireless communications. The impact of spatial correlation in multiple antenna systems is characterized for many important performance measures, e.g., average mutual information, outage probability, error performance, minimum Eb/N0 and wide-band slope, zero-outage capacity, and capacity region. The impact of user distribution in cellular systems is characterized for different scenarios including perfectly informed transmitters and receivers, regarding, e.g., the average sum rate, the outage sum rate, maximum throughput. Finally, a unified framework for the performance analysis of multiple antenna systems is developed based on matrix-monotone functions. The optimization of transmit strategies for multiple antennas is carried out by optimization of matrix-monotone functions. The results within this framework resemble and complement the various results on optimal transmit strategies in single-user and multiple-user multiple-antenna systems.
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paper_title: A Unified Approach to QoS-Guaranteed Scheduling for Channel-Adaptive Wireless Networks

paper_content:

Scheduling amounts to allocating optimally channel, rate and power resources to multiple connections with diverse quality-of-service (QoS) requirements. It consti- tutes a throughput-critical task at the medium access control layer of today's wireless networks that has been tackled by seemingly unrelated information-theoretic and protocol design approaches. Capitalizing on convex optimization and stochastic approximation tools, the present paper develops a unified framework for channel-aware QoS-guaranteed scheduling protocols for use in adaptive wireless networks whereby multiple terminals are linked through orthogonal fading channels to an access point, and transmissions are (opportu- nistically) adjusted to the intended channel. The unification encompasses downlink and uplink with time-division or frequency-division duplex operation; full and quantized chan- nel state information comprising a few bits communicated over a limited-rate feedback channel; different types of traffic (best effort, non-real-time, real-time); uniform and optimal power loading; off-line optimal scheduling schemes benchmarking fundamentally achievable rate limits; as well as on-line scheduling algorithms capable of dynamically learning the intended channel statistics and converging to the optimal benchmarks from any initial value. The take-home message offers an important cross-layer design guideline: judiciously developed, yet surprisingly simple, channel-adaptive, on-line schedulers can approach information-theoretic rate limits with QoS guarantees.
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paper_title: Beamforming for Millimeter Wave Communications: An Inclusive Survey

paper_content:

The remarkable growth of wireless data traffic in recent times has driven the need to explore suitable regions in the radio spectrum to meet the projected requirements. In pursuance of this, millimeter wave communications have received considerable attention in the research fraternity. Due to the high path and penetration losses at millimeter wavelengths, antenna beamforming assumes a pivotal role in establishing and maintaining a robust communication link. Beamforming for millimeter wave communications poses a multitude of diverse challenges due to the large channel bandwidth, unique channel characteristics, and hardware constraints. In this paper, we track the evolution and advancements in antenna beamforming for millimeter wave communications in the context of the distinct requirements for indoor and outdoor communication scenarios. We expand the scope of discussion by including the developments in radio frequency system design and implementation for millimeter wave beamforming. We explore the suitability of millimeter wave beamforming methods, both, existing and proposed till midyear 2015, and identify the exciting new prospects unfolding in this domain.
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paper_title: Impact of Spatial Correlation and Precoding Design in OSTBC MIMO Systems

paper_content:

The impact of transmission design and spatial correlation on the symbol error rate (SER) is analyzed for multi-antenna communication links. The receiver has perfect channel state information (CSI), while the transmitter has either statistical or no CSI. The transmission is based on orthogonal space-time block codes (OSTBCs) and linear precoding. The precoding strategy that minimizes the worst-case SER is derived for the case when the transmitter has no CSI. Based on this strategy, the intuitive result that spatial correlation degrades the SER performance is proved mathematically. In the case when the transmitter knows the channel statistics, the correlation matrix is assumed to be jointly-correlated (a generalization of the Kronecker model). The eigenvectors of the SER-optimal precoding matrix are shown to originate from the correlation matrix and the remaining power allocation is a convex problem. Equal power allocation is SER-optimal at high SNR. Beamforming is SER-optimal at low SNR, or for increasing constellation sizes, and its optimality range is characterized. A heuristic low-complexity power allocation is proposed and evaluated numerically. Finally, it is proved analytically that receive-side correlation always degrades the SER. Transmit-side correlation will however improve the SER at low to medium SNR, while its impact is negligible at high SNR.
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paper_title: Random Matrix Methods for Wireless Communications

paper_content:

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.
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paper_title: The impact of space division multiplexing on resource allocation: a unified treatment of TDMA, OFDMA and CDMA

paper_content:

Space division multiple access (SDMA) with an antenna array at the transmitter is a promising means for increasing system capacity and supporting rate-demanding services. However, the presence of an antenna array at the physical layer raises significant issues at higher layers. In this paper, we attempt to capture the impact of SDMA on access layer channel allocation, reflected on channel reuse. This impact obtains different twists in TDMA, CDMA and OFDMA due to the different nature of co-channel and cross-channel interference and the different interaction of user spatial channel characteristics with system channels, namely time slots, codes and subcarriers. We consider these access schemes in a generalized unified framework and propose heuristic algorithms for channel allocation, downlink beamforming and transmit power control so as to increase total provisioned system rate and provide QoS to users in the form of minimum rate guarantees. We study the class of greedy algorithms that rely on criteria such as induced or received interference and signal-to-interference ratio (SIR), and a class of SIR balancing algorithms. Results show superior performance for SIR balancing resource allocation and expose the performance benefits of cross-layer design.
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paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

paper_content:

This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
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paper_title: Networked MIMO with clustered linear precoding

paper_content:

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination to enhance the sum rate and limited inter-cluster coordination to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.
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paper_title: Multi-Cell MIMO Cooperative Networks: A New Look at Interference

paper_content:

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.
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paper_title: A Survey on Opportunistic Scheduling in Wireless Communications

paper_content:

Wireless technology advancements made opportunistic scheduling a popular topic in recent times. However, opportunistic schedulers for wireless systems have been studied since nearly twenty years, but not implemented in real systems due to their high complexity and hardly achievable requirements. In contrast, today's popularity of opportunistic schedulers extends to implementation proposals for next generation cellular technologies. Motivated by such a novel interest towards opportunistic scheduling, we provide a taxonomy for opportunistic schedulers, which is based on scheduling design's objectives; accordingly, we provide an extensive review of opportunistic scheduling proposals which have appeared in the literature during nearly two decades. The huge number of papers available in the literature propose different techniques to perform opportunistic scheduling, ranging from simple heuristic algorithms to complex mathematical models. Some proposals are only designed to increase the total network capacity, while others enhance QoS objectives such as throughput and fairness. Interestingly, our survey helps to unveil two major issues: (i) the research in opportunistic is mature enough to jump from pure theory to implementation, and (ii) there are still under-explored and interesting research areas in opportunistic scheduling, e.g., opportunistic offloading of cellular traffic to 802.11-like networks, or cooperative/distributed opportunistic scheduling.
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paper_title: Coordinated Beamforming for MISO Interference Channel: Complexity Analysis and Efficient Algorithms

paper_content:

In a cellular wireless system, users located at cell edges often suffer significant out-of-cell interference. Assuming each base station is equipped with multiple antennas, we can model this scenario as a multiple-input single-output (MISO) interference channel. In this paper we consider a coordinated beamforming approach whereby multiple base stations jointly optimize their downlink beamforming vectors in order to simultaneously improve the data rates of a given group of cell edge users. Assuming perfect channel knowledge, we formulate this problem as the maximization of a system utility (which balances user fairness and average user rates), subject to individual power constraints at each base station. We show that, for the single-carrier case and when the number of antennas at each base station is at least two, the optimal coordinated beamforming problem is NP-hard for both the harmonic mean utility and the proportional fairness utility. For general utilities, we propose a cyclic coordinate descent algorithm, which enables each transmitter to update its beamformer locally with limited information exchange and establish its global convergence to a stationary point. We illustrate its effectiveness in computer simulations by using the space matched beamformer as the benchmark.
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paper_title: Two-Stage Channel Quantization for Scheduling and Beamforming in Network MIMO Systems: Feedback Design and Scaling Laws

paper_content:

This paper proposes an efficient two-stage channel quantization and feedback scheme for the downlink limited-feedback network multiple-input multiple-output (MIMO) system. In the first stage, the users report their best set of base-station antenna and physical resource block combinations, and the base-stations schedule the best user for each antenna in each resource block. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. This paper proposes an analytical framework to show that, under a total feedback budget of B bits, the number of bits assigned to the second feedback stage should scale as log B, and in quantizing channel vectors from different base-stations, each user should allocate feedback bits in proportion to the channel magnitudes in dB scale. Under these optimized bit allocations, the overall sum rate of the system is shown to scale double-logarithmically with B, linearly with the total number of antennas, and logarithmically with transmit power, thus achieving both multiuser diversity and spatial multiplexing gains under limited feedback. Finally, realistic wireless propagation model of an urban small-cell deployment is used to show that the proposed scheme can approach the performance of a network MIMO system with full channel state information with only modest amount of channel feedback.
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paper_title: Coordinated multipoint transmission and reception in LTE-advanced: deployment scenarios and operational challenges

paper_content:

3GPP has completed a study on coordinated multipoint transmission and reception techniques to facilitate cooperative communications across multiple transmission and reception points (e.g., cells) for the LTE-Advanced system. In CoMP operation, multiple points coordinate with each other in such a way that the transmission signals from/to other points do not incur serious interference or even can be exploited as a meaningful signal. The goal of the study is to evaluate the potential performance benefits of CoMP techniques and the implementation aspects including the complexity of the standards support for CoMP. This article discusses some of the deployment scenarios in which CoMP techniques will likely be most beneficial and provides an overview of CoMP schemes that might be supported in LTE-Advanced given the modern silicon/DSP technologies and backhaul designs available today. In addition, practical implementation and operational challenges are discussed. We also assess the performance benefits of CoMP in these deployment scenarios with traffic varying from low to high load.
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paper_title: 4G: LTE/LTE-Advanced for Mobile Broadband

paper_content:

Based on the bestseller "3G Evolution - HSPA and LTE for mobile broadband" and reflecting the ongoing success of LTE throughout the world, this book focuses on LTE with full updates including LTE-Advanced to provide a complete picture of the LTE system. Overview and detailed explanations are given for the latest LTE standards for radio interface architecture, the physical layer, access procedures, broadcast, relaying, spectrum and RF characteristics, and system performance. Key technologies presented include multi-carrier transmission, advanced single-carrier transmission, advanced receivers, OFDM, MIMO and adaptive antenna solutions, advanced radio resource management and protocols, and different radio network architectures. Their role and use in the context of mobile broadband access in general is explained. Both a high-level overview and more detailed step-by-step explanations of the LTE/LTE-Advanced implementation are given. An overview of other related systems such as GSM/EDGE, HSPA, CDMA2000, and WIMAX is also provided. This book is a 'must-have' resource for engineers and other professionals in the telecommunications industry, working with cellular or wireless broadband technologies, giving an understanding of how to utilize the new technology in order to stay ahead of the competition. The authors of the book all work at Ericsson Research and have been deeply involved in 3G and 4G development and standardisation since the early days of 3G research. They are leading experts in the field and are today still actively contributing to the standardisation of LTE within 3GPP. Includes full details of the latest additions to the LTE Radio Access standards and technologies up to and including 3GPP Release 10Clear explanations of the role of the underlying technologies for LTE, including OFDM and MIMO Full coverage of LTE-Advanced, including LTE carrier aggregation, extended multi-antenna transmission, relaying functionality and heterogeneous deploymentsLTE radio interface architecture, physical layer, access procedures, MBMS, RF characteristics and system performance covered in detail
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paper_title: Mobile and Wireless Communications for IMT-Advanced and Beyond

paper_content:

A timely addition to the understanding of IMT-Advanced, this book places particular emphasis on the new areas which IMT-Advanced technologies rely on compared with their predecessors. These latest areas include Radio Resource Management, Carrier Aggregation, improved MIMO support and Relaying.Each technique is thoroughly described and illustrated before being surveyed in context of the LTE-Advanced standards. The book also presents state-of-the-art information on the different aspects of the work of standardization bodies (such as 3GPP and IEEE), making global links between them.Explores the latest research innovations to assess the future of the LTE standardCovers the latest research techniques for beyond IMT-Advanced such as Coordinated multi-point systems (CoMP), Network Coding, Device-to-Device and Spectrum SharingContains key information for researchers from academia and industry, engineers, regulators and decision makers working on LTE-Advanced and beyond
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paper_title: Multiuser MIMO Scheduling for LTE-A Downlink Cellular Networks

paper_content:

In this paper, we investigate multiuser MIMO scheduling in LTE downlink cellular networks. We formulate the downlink LTE-A MIMO scheduling as a weighted sum rate maximization problem by allocating the RBs to users or user pairs subject to some constraints in LTE-A. We develop a low-complexity MU-MIMO scheduling and resource allocation algorithm and propose an adaptive switching approach between SU-MIMO and MU-MIMO to improve network performance. System-level simulation results demonstrate significantly performance improvement of the proposed MU-MIMO scheduling algorithm and the adaptive switching algorithm.
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paper_title: 802.11 WLAN: history and new enabling MIMO techniques for next generation standards

paper_content:

IEEE 802.11, which designs wireless local area networks (WLAN), is one of the most successful standards in wireless communication systems. In this article, we review the history of WLAN standards, and provide technical overviews of the recent development of WLAN systems. Especially, as the original inventor and the proposer, we focus on beamforming and compressed feedback schemes, which have been adopted in 802.11 WLAN standards, to improve the throughput for a multiple-input multiple-output (MIMO) system. These techniques are essential to maximize the downlink system throughput for multiple user transmission as well as for single user transmission. Also, we present discussions on new technologies to further enhance user throughput, which are currently considered for future WLAN systems.
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paper_title: MU-MIMO MAC Protocols for Wireless Local Area Networks: A Survey

paper_content:

As wireless devices boom and bandwidth-hungry applications (e.g., video and cloud uploading) get popular, today's wireless local area networks (WLANs) become not only crowded but also stressed at throughput. Multiuser multiple-input–multiple-output (MU-MIMO), an advanced form of MIMO, has gained attention due to its huge potential in improving the performance of WLANs. This paper surveys random access-based medium access control (MAC) protocols for MU-MIMO-enabled WLANs. It first provides background information about the evolution and the fundamental MAC schemes of IEEE 802.11 Standards and Amendments, and then identifies the key requirements of designing MU-MIMO MAC protocols for WLANs. After this, the most representative MU-MIMO MAC proposals in the literature are overviewed by benchmarking their MAC procedures and examining the key components, such as the channel state information acquisition, decoding/precoding, and scheduling schemes. Classifications and discussions on important findings of the surveyed MAC protocols are provided, based on which, the research challenges for designing effective MU-MIMO MAC protocols, as well as the envisaged MAC's role in the future heterogeneous networks, are highlighted.
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paper_title: 4G: LTE/LTE-Advanced for Mobile Broadband

paper_content:

Based on the bestseller "3G Evolution - HSPA and LTE for mobile broadband" and reflecting the ongoing success of LTE throughout the world, this book focuses on LTE with full updates including LTE-Advanced to provide a complete picture of the LTE system. Overview and detailed explanations are given for the latest LTE standards for radio interface architecture, the physical layer, access procedures, broadcast, relaying, spectrum and RF characteristics, and system performance. Key technologies presented include multi-carrier transmission, advanced single-carrier transmission, advanced receivers, OFDM, MIMO and adaptive antenna solutions, advanced radio resource management and protocols, and different radio network architectures. Their role and use in the context of mobile broadband access in general is explained. Both a high-level overview and more detailed step-by-step explanations of the LTE/LTE-Advanced implementation are given. An overview of other related systems such as GSM/EDGE, HSPA, CDMA2000, and WIMAX is also provided. This book is a 'must-have' resource for engineers and other professionals in the telecommunications industry, working with cellular or wireless broadband technologies, giving an understanding of how to utilize the new technology in order to stay ahead of the competition. The authors of the book all work at Ericsson Research and have been deeply involved in 3G and 4G development and standardisation since the early days of 3G research. They are leading experts in the field and are today still actively contributing to the standardisation of LTE within 3GPP. Includes full details of the latest additions to the LTE Radio Access standards and technologies up to and including 3GPP Release 10Clear explanations of the role of the underlying technologies for LTE, including OFDM and MIMO Full coverage of LTE-Advanced, including LTE carrier aggregation, extended multi-antenna transmission, relaying functionality and heterogeneous deploymentsLTE radio interface architecture, physical layer, access procedures, MBMS, RF characteristics and system performance covered in detail
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paper_title: Recent trend of multiuser MIMO in LTE-advanced

paper_content:

Recently, the mobile communication industry is moving rapidly toward Long Term Evolution, or LTE, systems. The leading carriers and vendors are committed to launching LTE service in the near future; in fact, a number of major operators such as Verizon have initiated LTE service already. LTE aims to provide improved service quality over 3G systems in terms of throughput, spectral efficiency, latency, and peak data rate, and the MIMO technique is one of the key enablers of the LTE system for achieving these diverse goals. Among several operational modes of MIMO, multiuser MIMO (MU-MIMO), in which the base station transmits multiple streams to multiple users, has received much attention as a way of achieving improvement in performance. From the initial release (Rel. 8) to the recent release (Rel. 10), so called LTE-Advanced, MUMIMO techniques have evolved from their premature form to a more elaborate version. In this article, we provide an overview of design challenges and the specific solutions for MU-MIMO systems developed in the LTE-Advanced standard.
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paper_title: 5G Network Capacity: Key Elements and Technologies

paper_content:

It has been projected that, in the next decade, a mobile traffic increase on the order of 1,000 times is expected compared to what we experience today. To meet that dramatic traffic growth, next-generation mobile networks are also expected to achieve a 1,000-fold capacity increase compared to the current generation of wireless network deployments. In this article, we discuss how such capacity growth could be achieved in a ten-year time frame. We discuss the techniques that we expect to have the highest opportunity for increasing the system capacity and estimate their gains based on analysis and simulation. We observe that the main driver of capacity growth is expected to come from network architecture advancements, with heterogeneous networks and convergence of information and communication technology being two of the key techniques. We also estimate that the air-interface evolution would focus not only on improving the link and system spectrum efficiency but also on facilitating the required network efficiency improvements. This article provides insights into the communication technology evolution and can be used as a guideline for technology development toward the fifth generation (5G).
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paper_title: Multiple-antenna techniques for wireless communications - a comprehensive literature survey

paper_content:

The use of multiple antennas for wireless communication systems has gained overwhelming interest during the last decade - both in academia and industry. Multiple antennas can be utilized in order to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. With an enormous amount of yearly publications, the field of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly. To date, there are numerous papers on the performance limits of MIMO systems, and an abundance of transmitter and receiver concepts has been proposed. The objective of this literature survey is to provide non-specialists working in the general area of digital communications with a comprehensive overview of this exciting research field. To this end, the last ten years of research efforts are recapitulated, with focus on spatial multiplexing and spatial diversity techniques. In particular, topics such as transmitter and receiver structures, channel coding, MIMO techniques for frequency-selective fading channels, diversity reception and space-time coding techniques, differential and non-coherent schemes, beamforming techniques and closed-loop MIMO techniques, cooperative diversity schemes, as well as practical aspects influencing the performance of multiple-antenna systems are addressed. Although the list of references is certainly not intended to be exhaustive, the publications cited will serve as a good starting point for further reading.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: Asymptotically optimal simple user scheduling for massive MIMO downlink with two-stage beamforming

paper_content:

In this paper, a simple user-scheduling-and-beamforming method is proposed for massive multi-user multiple-input multiple-output (MU-MIMO) downlink adopting two-stage beamforming. The key ideas of the proposed scheduling-and-beamforming method are to divide users into several candidate subsets according to the level of alignment of user channels to the dominant directions of the channel covariance matrix and select the user in each candidate subset based on a certain channel quality indicator (CQI) and to apply post-selection zero-forcing beamforming (ZFBF) to the selected users based on their channel state information (CSI). It is proved that the proposed scheduling-and-beamformingmethod is asymptotically optimal as the number of users increases. Furthermore, the proposed method significantly reduces the feedback overhead and shows superior sum rate performance compared to existing scheduling methods for MU-MIMO downlink.
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paper_title: Subchannel allocation in multiuser multiple input multiple output systems

paper_content:

Assuming perfect channel state information at the transmitter of a Gaussian broadcast channel, strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel. For the general sum capacity maximizing solution, which has recently been found, a method is proposed that transforms each of the resulting vector channels into a set of scalar channels. This makes possible to achieve capacity by simply using scalar coding and detection techniques. The high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero-forcing allocation strategy that directly results in a set of virtually decoupled scalar channels. Simulation results show that this technique tightly approaches the performance of the optimum solution, i.e., complexity reduction comes at almost no cost in terms of sum capacity. As the optimum solution, the zero-forcing allocation strategy applies to any number of transmit antennas, receive antennas and users
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paper_title: Eigen-Based Transceivers for the MIMO Broadcast Channel with Semi-Orthogonal User Selection

paper_content:

This paper studies the sum rate performance of two low complexity eigenmode-based transmission techniques for the MIMO broadcast channel, employing greedy semi-orthogonal user selection (SUS). The first approach, termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first employ new analytical methods to prove that as the number of users K grows large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that the average sum rates of both techniques converge to the average sum capacity of the MIMO broadcast channel for large K. In addition to the asymptotic analysis, we investigate the sum rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS has significant performance advantages. Our results also provide key insights into the benefit of multiple receive antennas, and the effect of the SUS algorithm. In particular, we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second-order behavior of the multi-user diversity gain; for finite K, the benefit can be very significant. We also show the interesting result that the semi-orthogonality constraint imposed by SUS, whilst facilitating a very low complexity user selection procedure, asymptotically does not reduce the multi-user diversity gain in either first (log K) or second-order (loglog K) terms.
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paper_title: Efficient MAC protocol for JT CoMP in small cells

paper_content:

In this paper, we investigate an efficient MAC protocol for interference coordination in small cells embedded in a macro-cell mobile network. We perform joint transmission (JT)-coordinated multi-point (CoMP), where cells in the cluster include adjacent macro-cells as suggested by the small-cell terminal. Most gains compared to uncoordinated transmission come from selecting the right users in these macro-cells. For minimizing the feedback overhead, we propose successive channel state information (CSI) requests. Thereby we replace users in the set until all of them experience consistently enhanced performance when using JT-CoMP. Gains can be further increased by MIMO mode switching in each cell and frequency-selective scheduling. We tested our algorithms over coherently measured multi-cell channels in the LTE-Advanced testbed in Berlin where small cells were embedded at several places. Using these algorithms, performance becomes comparable to a popular bound assuming no more intra-cluster interference while feedback overhead and complexity are substantially reduced.
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paper_title: MIMO Downlink Scheduling with Non-Perfect Channel State Knowledge

paper_content:

Downlink scheduling schemes are well-known and widely investigated under the assumption that the channel state is perfectly known to the scheduler. In the multiuser MIMO (broadcast) case, downlink scheduling in the presence of non-perfect channel state information (CSI) is only scantly treated. In this paper we provide a general framework that addresses the problem systematically. Also, we illuminate the key role played by the channel state prediction error: our scheme treats in a fundamentally different way users with small channel prediction error ("predictable" users) and users with large channel prediction error ("non-predictable" users), and can be interpreted as a near-optimal opportunistic time-sharing strategy between MIMO downlink beamforming to predictable users and space-time coding to non-predictable users. Our results, based on a realistic MIMO channel model used in 3GPP standardization, show that the proposed algorithms can significantly outperform a conventional "mismatched" scheduling scheme that treats the available CSI as if it was perfect.
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paper_title: Learning-Based Adaptive Transmission for Limited Feedback Multiuser MIMO-OFDM

paper_content:

Performing link adaptation in a multiantenna and multiuser system is challenging because of the coupling between precoding, user selection, spatial mode selection and use of limited feedback about the channel. The problem is exacerbated by the difficulty of selecting the proper modulation and coding scheme when using orthogonal frequency division multiplexing (OFDM). This paper presents a data-driven approach to link adaptation for multiuser multiple input mulitple output (MIMO) OFDM systems. A machine learning classifier is used to select the modulation and coding scheme, taking as input the SNR values in the different subcarriers and spatial streams. A new approximation is developed to estimate the unknown interuser interference due to the use of limited feedback. This approximation allows to obtain SNR information at the transmitter with a minimum communication overhead. A greedy algorithm is used to perform spatial mode and user selection with affordable complexity, without resorting to an exhaustive search. The proposed adaptation is studied in the context of the IEEE 802.11ac standard, and is shown to schedule users and adjust the transmission parameters to the channel conditions as well as to the rate of the feedback channel.
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paper_title: User scheduling for massive MIMO OFDMA systems with hybrid analog-digital beamforming

paper_content:

This paper proposes a new user scheduling and sub-carrier allocation algorithm for multiuser downlink massive multiple input multiple output (MIMO) orthogonal frequency division multiple access (OFDMA) systems with hybrid analogdigital beamforming (HB). We assume that the transmitter having N antennas is serving K i decentralized single antenna receivers by sub-carrier i. The scheduling algorithm leverages the solutions of the digital beamforming (DB) result and is designed to maximize the total sum rate of all sub-carriers under per carrier power constraint. For this system and problem setup, the proposed algorithm is explained as follows: First, we express the HB matrix of sub-carrier i as a product of AB i , where the high dimensional matrix A ∈ CN×Na is common to all subcarriers whereas, B i ∈ CNa×Ki is a low dimensional matrix which is designed for sub-carrier i, and Na is the number of RF chains satisfying N ≥ Na ≥ K i . Second, we compute A as the first Na eigenvectors of the left singular value decomposition of the combined DB precoder matrices of sub-carriers having the highest sum rate. Finally, for fixed A, we compute Bi and its corresponding users such that the total sum rate of all sub-carriers is maximized. The performance of the proposed scheduling is studied analytically. Furthermore, the superiority of the proposed algorithm over that of the existing one is quantified analytically and demonstrated by computer simulations.
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paper_title: Enhanced multiuser random beamforming: dealing with the not so large number of users case

paper_content:

We consider the downlink of a wireless system with an M-antenna base station and K single-antenna users. A limited feedback-based scheduling and precoding scenario is considered that builds on the multiuser random beamforming (RBF). Such a scheme was shown to yield the same capacity scaling, in terms of multiplexing and multiuser diversity gain, as the optimal full CSIT-based (channel state information at transmitter) precoding scheme, in the large number of users K regime. Unfortunately, for more practically relevant (low to moderate) K values, RBF yields degraded performance. In this work, we investigate solutions to this problem. We introduce a two-stage framework that decouples the scheduling and beamforming problems. In our scenario, RBF is exploited to identify good, spatially separable, users in a first stage. In the second stage, the initial random beams are refined based on the available feedback to offer improved performance toward the selected users. Specifically, we propose beam power control techniques that do not change the direction of the second-stage beams, offering feedback reduction and performance tradeoffs. The common feature of these schemes is to restore robustness of RBF with respect to sparse network settings (low K), at the cost of moderate complexity increase.
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paper_title: User Selection With Zero-Forcing Beamforming Achieves the Asymptotically Optimal Sum Rate

paper_content:

In this paper, we propose a generalized greedy (G-greedy) algorithm based on zero-forcing beamforming (ZFBF) for the multiple-input multiple-output (MIMO) broadcast channel. This algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations. As previous results only give the scaling law of the sum rate of dirty paper coding (DPC), with the help of the G-greedy structure, we are able to obtain the exact limit of the DPC sum rate for a large number of users. We also prove that the difference between the sum rates obtained by G-greedy user selection and by DPC goes to zero as the number of users increases. In addition to this, we investigate one particular greedy user selection scheme called sequential water-filling (SWF). For this algorithm, a complexity reduction is achieved by an iterative procedure based on an LQ decomposition, which converts the calculation of the Moore-Penrose matrix inverse to one vector-matrix multiplication. A sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction. With the help of the G-greedy algorithm, we prove that SWF achieves the full DPC sum rate for a large number of users. For a moderate number of users, simulation demonstrates that, compared with other user selection algorithms, SWF achieves a higher sum rate that is close to the maximal sum rate achievable by ZFBF with the same order of complexity.
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paper_title: A New Approach to User Scheduling in Massive Multi-User MIMO Broadcast Channels

paper_content:

In this paper, a new user-scheduling-and-beamforming method is proposed for multi-user massive multiple-input multiple-output (massive MIMO) broadcast channels in the context of two-stage beamforming. The key ideas of the proposed scheduling method are 1) to use a set of orthogonal reference beams and construct a double cone around each reference beam to select `nearly-optimal' semi-orthogonal users based only on channel quality indicator (CQI) feedback and 2) to apply post-user-selection beam refinement with zero-forcing beamforming (ZFBF) based on channel state information (CSI) feedback only from the selected users. It is proved that the proposed scheduling-and-beamforming method is asymptotically optimal as the number of users increases. Furthermore, the proposed scheduling-and-beamforming method almost achieves the performance of the existing semi-orthogonal user selection with ZFBF (SUS-ZFBF) that requires full CSI feedback from all users, with significantly reduced feedback overhead which is even less than that required by random beamforming.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: On the achievable throughput of a multiantenna Gaussian broadcast channel

paper_content:

A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j<i is taken into account by coding for noncausally known interference. Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR). We conclude by providing some numerical results for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.
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paper_title: Networked MIMO with clustered linear precoding

paper_content:

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination to enhance the sum rate and limited inter-cluster coordination to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.
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paper_title: Adaptive radio resource allocation for downlink OFDMA/SDMA systems with multimedia traffic

paper_content:

This paper proposes an adaptive radio resource allocation (ARRA) algorithm for downlink OFDMA/SDMA systems with multimedia traffic. Considering multiple service classes and diverse QoS requirements of multimedia traffic, the ARRA algorithm is designed with the goal to maximize spectrum efficiency and to fulfill quality of service (QoS) requirements. It is composed of two parts, a dynamic priority adjustment (DPA) scheme and a priority-based greedy (PBG) scheme. The DPA adopts a type of time-to-expiration to indicate the degree of user's urgency, and dynamically gives high priorities to urgent users. The PBG allocates the radio resource iteratively, based on a cost value, to maximize the system throughput while allocating enough resource to high-priority users. Simulation results show that the ARRA algorithm outperforms conventional algorithms in terms of system throughput and satisfaction extent of QoS requirements; it can sustain users' QoS requirements up till a traffic load of 0.8, while the conventional algorithms cannot guarantee QoS requirements after a traffic load of 0.3.
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paper_title: Greedy scheduling performance for a zero-forcing dirty-paper coded system

paper_content:

This letter presents two results for multiuser wireless systems employing dirty-paper coding strategies along with greedy scheduling over the broadcast multiple-input multiple-output channel. Specifically, an efficient and suboptimal downlink scheduler is proposed to approximate the maximum sum rate using equal power allocation, and it is shown to approach the maximum sum rate of optimal power allocation for a large number of users under optimal scheduling. The second result demonstrates that the average maximum sum rate can be tightly upper bounded when spatial multiplexing is maximized.
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paper_title: On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm

paper_content:

This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple "beams" directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of the same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum's scheme and, thus, offers an attractive alternative to DP-based schemes.
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paper_title: Opportunistic Two-Stage Feedback and Scheduling for MIMO Downlink Systems

paper_content:

We propose an opportunistic two-stage feedback and scheduling algorithm that is based upon zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) to reduce its feedback load. In an SUS algorithm, a base station schedules semi-orthogonal users using the feedback of all users' channel information. However, such feedback overhead significantly increases with the number of users. To reduce the feedback load of ZFBF-SUS systems, the proposed two-stage feedback scheme opportunistically and separately exploits the signal-to-interference-plus-noise ratio and orthogonality in each stage such that only a fraction of users feed back their channel information. Based on this opportunistic feedback scheme, we decouple the entire process of the SUS into two sub-processes. The proposed two-stage feedback and scheduling scheme effectively exclude the inappropriate users for ZFBF transmission in both feedback and scheduling periods, and thus save the scarce resources consumed for the feedback process. We derive an analytical expression for the average number of feedback bits of the proposed system and optimize it in an averaged sense. Further, the sum-rate of the proposed system is theoretically investigated. Both analytical and simulation results show that the proposed algorithm achieves the performance of conventional ZFBF-SUS systems with a significantly reduced number of feedback bits.
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paper_title: User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming

paper_content:

In this paper, we propose a greedy user selection with swap (GUSS) algorithm based on zero-forcing beamforming for multiuser multiple-input-multiple-output (MIMO) downlink channels. Existing user selection algorithms such as zero forcing with selection (ZFS) have the flaws of “redundant users” and “local optimum,” which compromise the achieved sum rate. GUSS improves the performance by adding the “delete” and “swap” operations to the user selection procedure of ZFS to eliminate “redundant users” and escape from “local optimum,” respectively. In addition, an effective-channel-vector-based effective-channel-gain-updating scheme is proposed to reduce the complexity of GUSS. With the help of this updating scheme, GUSS has the same order of complexity as ZFS with only a linear increment. Simulation results indicate that over the range of transmit signal-to-noise ratios (SNRs) considered, on average, the sum rate of GUSS reaches 99.3% of the upper bound that is achieved by exhaustive search, with only 1.51 to 2.29 times the complexity of ZFS.
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paper_title: Multiuser MIMO Scheduling for LTE-A Downlink Cellular Networks

paper_content:

In this paper, we investigate multiuser MIMO scheduling in LTE downlink cellular networks. We formulate the downlink LTE-A MIMO scheduling as a weighted sum rate maximization problem by allocating the RBs to users or user pairs subject to some constraints in LTE-A. We develop a low-complexity MU-MIMO scheduling and resource allocation algorithm and propose an adaptive switching approach between SU-MIMO and MU-MIMO to improve network performance. System-level simulation results demonstrate significantly performance improvement of the proposed MU-MIMO scheduling algorithm and the adaptive switching algorithm.
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paper_title: Hierarchical Interference Mitigation for Massive MIMO Cellular Networks

paper_content:

We propose a hierarchical interference mitigation scheme for massive MIMO cellular networks. The MIMO precoder at each base station (BS) is partitioned into an inner precoder and an outer precoder. The inner precoder controls the intra-cell interference and is adaptive to local channel state information (CSI) at each BS (CSIT). The outer precoder controls the inter-cell interference and is adaptive to channel statistics. Such hierarchical precoding structure reduces the number of pilot symbols required for CSI estimation in massive MIMO downlink and is robust to the backhaul latency. We study joint optimization of the outer precoders, the user selection, and the power allocation to maximize a general concave utility which has no closed-form expression. We first apply random matrix theory to obtain an approximated problem with closed-form objective. We show that the solution of the approximated problem is asymptotically optimal with respect to the original problem as the number of antennas per BS grows large. Then using the hidden convexity of the problem, we propose an iterative algorithm to find the optimal solution for the approximated problem. We also obtain a low complexity algorithm with provable convergence. Simulations show that the proposed design has significant gain over various state-of-the-art baselines.
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paper_title: Optimizing User Selection Schemes in Vector Broadcast Channels

paper_content:

In this paper, we focus on the ergodic downlink sum-rate performance of a system consisting of a set of heterogeneous users. We study three user selection schemes to group near-orthogonal users for simultaneous transmission. The first scheme is a random selection policy that achieves fairness, but does not exploit multi-user diversity. The second scheme is a greedy selection policy that fully exploits multi-user diversity, but does not achieve fairness, and the third scheme achieves fairness while partially exploiting multi-user diversity. We also consider two beamforming methods for data transmission, namely, maximum-ratio transmission and zero-forcing beamforming. In all scheduling schemes studied in the paper, there is a key parameter that controls the degrees of orthogonality of channel directions between co-scheduled users. We focus on optimally setting this parameter for each scheduling scheme such that the ergodic downlink sum-rate is maximized. To this end, we derive analytical expressions for the ergodic downlink sum-rate considering each scheduling scheme. Numerical results are also presented to provide further insights.
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paper_title: Scheduling Methods with MIMO Interference Alignment for Mutually Interfering Broadcast Channels

paper_content:

In this paper, we investigate an interference alignment (IA) technique introduced by Cadambe and Jafar in mutually interfering broadcast channels (IFBCs). First, we study the spatial multiplexing gain (SMG) for the 3-cell IFBC where all base stations and mobile users are equipped with multiple antennas. To achieve the derived optimal SMG, we extend the IA algorithm designed for K-user multi-input multi-output (MIMO) interference channels (IFCs) to the IFBC. In this paper, we present the IA scheme in conjunction with user selection which outperforms the time division multiple access (TDMA) technique in the IFBC environment. The optimal scheduling method capitalizes on multiuser diversity to achieve a significant fraction of sum capacity by using an exhaustive search algorithm. Since the computational complexity of the optimal scheduling method is prohibitive, a reduced complexity suboptimal scheduling method is proposed based on a coordinate ascent approach. Simulation results confirm that the reduced complexity scheduling algorithm achieves the sum rate close to the optimal algorithm with much reduced complexity.
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paper_title: Scheduling for Multiuser MIMO Broadcast Systems: Transmit or Receive Beamforming?

paper_content:

In this paper, we present an approximation formula and the close-form expression for the sum rate of the transmit and the receive zero-forcing (ZF) multiple-input multiple-output (MIMO) broadcast systems with user selection, respectively. Instead of assuming a large number of users to obtain a scaling law as most current work, we derive the sum rate formulas of the ZF MIMO broadcast systems with a small number of scheduled users. By analysis and simulations, we find that when taking the variations of feedback channel into account, the receive ZF MIMO broadcast system is more robust to feedback errors and can deliver equal or even higher sum rate than the transmit ZF MIMO broadcast system. We discuss whether a feedback channel is suitable to send channel state information (CSI) for calculating transmit antenna beamforming weights, or suitable to send CSI for selecting users in the receive ZF MIMO broadcast system. Our results show that as the variation of feedback channel errors increases from 0.5 to 1.5, the receive ZF 3 × 3 MIMO broadcast system can provide 36% to 116% higher sum rate than the transmit ZF 3 × 3 MIMO broadcast system in the case of 20 users at signal to noise ratio (SNR) equal to 20 dB. Providing that more feedback bandwidth and an error-free feedback channel are available, the transmit ZF MIMO broadcast system can achieve higher sum rate than the receive ZF MIMO broadcast system.
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paper_title: Decremental User Selection for Large-Scale Multi-User MIMO Downlink with Zero-Forcing Beamforming

paper_content:

This paper proposes a decremental user selection algorithm based on zero-forcing beamforming when the number of users K in the network is smaller than the number of antennas M at a base station. The algorithm is specifically designed for large-scale multi-user multiple-input multiple-output (MIMO) downlink channels. While previous user selection algorithms are based on incremental search that starts from an empty user set, our proposed delete the minimum lambda (DML) algorithm starts by selecting all users and then deleting one user per iteration. DML substantially reduces the computational complexity as the cardinality of the final user set is close to K. Simulation results indicate that on average DML achieves an equal or higher sum rate performance than previous algorithms with greatly reduced complexity of O(MK2).
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paper_title: Beamforming and User Selection in SDMA Systems Utilizing Channel Statistics and Instantaneous SNR Feedback

paper_content:

Spatial division multiple access (SDMA) systems efficiently take advantage of the spatial dimensions of the channel to increase the performance of the system. A major difficulty, common to all SDMA systems, is the requirement of channel knowledge at the transmitter to enable transmission of multiple streams without catastrophic interference. Herein we show that, in wide area scenarios, statistical channel information combined with the Euclidean norm of the channel realization, fed back from the users, provide sufficient information for SDMA systems to efficiently allocate users in time and space. A joint beamforming and scheduling algorithm is proposed for the downlink, which extends the proportional fair scheduling criterion to an SDMA setting, resulting in a weighted sum rate maximization.
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paper_title: Transmit correlation-aided opportunistic beamforming and scheduling

paper_content:

The problem of multiuser scheduling and beamforming with partial channel state information at the transmitter (CSIT) is considered here in the particular context of opportunistic beamforming. We consider a random multiuser beamforming scheme and show how long-term statistical information of users' channels can be efficiently combined with short-term SINR feedback to increase system performance substantially over a conventional opportunistic beamforming scheme. We propose a channel estimation method to be used by the transmitter which exploits the second-order channel statistics, the fading statistics and the information contained in the instantaneous SINR feedback of random opportunistic beamforming. This coarse (low feedback-based) channel estimate is shown to be particularly valuable for the purpose of user selection, as well as for the precoding matrix design.
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paper_title: Round-Robin Scheduling for Orthogonal Beamforming with Limited Feedback

paper_content:

We propose a round-robin scheduling algorithm for orthogonal beamforming with a strict signal to interference-plus-noise ratio (SINR) constraint and limited feedback. The presented algorithm aims at scheduling the users at identical slots over different blocks, in order to reduce the necessary scheduling overhead, and to minimize the maximum delay between serving the same user. Thus, the presented algorithm is especially suited for real-time multimedia traffic. The algorithm allocates the users using orthogonal beamforming based on the quantized feedback provided by the users. The quantized feedback consists of the estimated power that is necessary to fulfill a predefined SINR constraint. Further, we propose an algorithm to design codebooks to quantize the estimated power. Using the feedback, the base station redistributes power from users with spare power to users that lack power so that they fulfill their SINR constraints. The performance of the algorithm is demonstrated through simulations.
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paper_title: Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

paper_content:

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.
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paper_title: Packet Scheduling and Fairness for Multiuser MIMO Systems

paper_content:

This paper investigates the network resource allocation in multiuser downlink wireless systems where the base station and the mobile stations are equipped with multiple antennas to provide fair and efficient transmission services to the mobile users. We focus on packet scheduling, given that it has a significant impact on the overall performance of a multiple-input-multiple-output (MIMO) system. Most previous schedulers designed at the packet level do not take into account the traffic characteristics (different packet lengths and the arrival process parameters); consequently, they fall short of simultaneously providing fairness and a low average packet transmission delay. We are making use of a flexible packet transmission algorithm at the medium access control (MAC) layer to develop and propose a novel scheduler, which is referred to as MIMO packet-based proportional fairness (MP-PF). The new scheduler is designed with the goal of providing high performance in terms of a low average packet transmission delay and time and service fairness among the users based on the concept of proportional fairness. The scheduler also conserves work and takes into consideration the packet length, the user queue length, the user transmission rate (related to its channel quality), and the service guarantees for heterogeneous users. The well-known ideal service fair scheduler called max-min can also significantly be improved using our framework by taking into consideration the traffic characteristics. We also provide an analysis for the fairness of the new scheduler in terms of time and service allocation, which is the key contribution of this paper. Simulations that consider the traffic characteristics and the mobility of users show the relatively low average packet transmission delay and demonstrate the time and service fairness capabilities of MP-PF, compared with other well-known MIMO schedulers.
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paper_title: Simplified Semi-Orthogonal User Selection for MU-MIMO Systems with ZFBF

paper_content:

In this letter, we simplify the well-known semi-orthogonal user selection (SUS) algorithm for the multi-user multiple-input multiple-output (MU-MIMO) system with zero-forcing beamforming (ZFBF). Compared with the original SUS algorithm, the proposed user selection algorithm achieves the same performance, but with significantly less complexity. Simulation results show that the proposed algorithm can make a good tradeoff between performance and complexity for the MU-MIMO system with ZFBF.
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paper_title: The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel

paper_content:

The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the nondegraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints
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paper_title: Robust multi-user opportunistic beamforming for sparse networks

paper_content:

A scheme exploiting reduced feedback for the purpose of opportunistic multi-user beamforming is proposed. The scheme builds on recent promising advances realized in the area of multi-user downlink precoding and scheduling based on partial transmitter channel state information (CSIT) using random beamforming-based SDMA. Although random precoding followed by SDMA scheduling is optimal within the set of unitary precoders, it is only so in the asymptotic number of users K. For-practically relevant-sparse networks (i.e., with low to moderate number of users) random beam-forming SDMA yields severely degraded performance. In this work we present a scheme allowing to restore robustness with respect to cell sparsity. The core idea here is to preserve the low complexity low feedback advantage of random opportunistic beamforming in selecting a target group of users, while much more efficient beamforming schemes can be used to serve the group of users once it has been identified. We propose different designs, optimal and suboptimal, based upon variable levels of feedback requirement. We show substantial gain over opportunistic beamforming for a range of K.
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paper_title: Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels

paper_content:

In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total system-wide feedback load, is it preferable to get low-rate/coarse channel feedback from a large number of receivers or high-rate/high-quality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multi-user diversity to be exploited, while high-rate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining high-quality feedback, and that obtaining near-perfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users.
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paper_title: CoMP-CSB for ICI Nulling with User Selection

paper_content:

The capacity of downlink multiple-input multiple-output (MIMO) cellular networks is significantly limited by inter-cell interference (ICI), particularly at cell boundaries. Recently, two types of coordinated multiple point transmission (CoMP) technologies, joint processing and transmission (JPT) and coordinated scheduling and beamforming (CSB), were proposed. These technologies are intended for the latest cellular communication standard in order to improve the performance of cell-edge users who suffer from significant ICI. In this paper, we propose an ICI cancellation technique based on a user selection algorithm for CoMP-CSB. Under partial channel state information (CSI) and no data sharing condition, each base station (BS) concentrates more on the direction of interference to the adjacent cell's users, during the user selection process. Unlike prior concepts for a single-cell environment, in which each BS generates a precoding matrix for selected users to be served, the proposed technique considers the effects of interference to users located in adjacent cells. Although there are obvious trade-offs between ICI mitigation and the number of simultaneous scheduled users in terms of system capacity, the simulation results demonstrate that our proposed algorithm achieves higher sector throughput and is more robust against ICI if the system is limited by interference. Furthermore, through simulation we are able to obtain the preferred option for the coordination distance (R) and the number of degrees of freedom for ICI nulling (ξ).
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: Spatial Transmission Mode Switching in Multiuser MIMO-OFDM Systems With User Fairness

paper_content:

Multiantenna radio systems allow accessing the channel in diversity or spatial multiplexing (SMUX) mode. Adequate switching between these modes according to current channel conditions was shown to yield significant performance improvements while requiring little feedback from the receiving side. We present a transmission concept for the downlink of a multiuser multiple-input-multiple-output orthogonal frequency-division-multiplexing (MU-MIMO-OFDM) system aiming at high user rates with limited feedback demands. An extended score-based scheduling (SB) approach ensures fair-resource allocation to the users, whereas transmission mode switching is used to guarantee high user rates. The degree of fairness of the scheduler can be adapted by adequately configuring a weighting function for the scores. Comparison with single-mode schemes reveals substantial throughput gains of the adaptive switching concept. Furthermore, targeting maximum throughput, we show that a considerable proportion of the capacity of the MIMO broadcast channel (BC) can be achieved with a comparatively low amount of required feedback.
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paper_title: On the Performance of Downlink Beamforming with Synchronized Beam Cycles

paper_content:

The next generation of wireless networks (e.g.,) will use multiple techniques to improve channel spectral efficiencies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each frame, the scheduler chooses a beam and then schedules one or more UEs that lie within that beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors. If a neighboring sector schedules a UE that lies within the coverage of this beam then the rate for that UE will be low. The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. The first approach (interference avoidance) requires coordination among the sectors with the associated communication overheads and delays. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period. Although all NBs use the same beam cycle period, they may occasionally change the specific beam schedule based on local factors such as the geographical distribution of UEs within its beams. Such changes should be made infrequently since the approach is based on the assumption that the interference experienced by a UE repeats with the beam cycle period.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.
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paper_title: Two-Phase Multiuser Scheduling for Multiantenna Downlinks Exploiting Reduced Finite-Rate Feedback

paper_content:

This paper considers a multiantenna system with an M -antenna base station and K single antenna users, employing zero-forcing beamforming (ZFBF) and a finite-rate feedback strategy. We study scheduling to select KS users for transmit beamforming. To reduce the feedback requirement, we propose a two-phase scheduling scheme that exploits quantized channel direction information (CDI) from only a small subset of the overall users, as well as a 1-bit signal-to-interference-plus-noise ratio (SINR) indicator feedback per user. In the proposed scheme, we introduce a newly defined expression for evaluating SINR that extends the existing SINR approximation for KS = M to a more general case with arbitrary KS ? M. Asymptotic analysis reveals that the proposed two-phase scheduling is asymptotically optimal for large user numbers. Through numerical simulations, we also show that the proposed scheme requires less feedback than conventional schemes, whereas the resulting sum rate loss due to the reduced feedback is negligible. Moreover, we find that the choice of KS < M, instead of a full-multiplexing case with KS = M, for scheduling may achieve a better tradeoff between performance and feedback requirement in systems where fewer bits are utilized for feeding back CDI.
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paper_title: Memory-based opportunistic multi-user beamforming

paper_content:

A scheme exploiting memory in opportunistic multiuser beamforming is proposed. The scheme builds on recent advances realized in M. Sharif and B. Hassibi, 2005, in the area of multi-user downlink preceding and scheduling based on partial transmitter channel state information (CSIT). Although the preceding and scheduling done in M. Sharif and B. Hassibi, 2005 is optimal within the set of unitary precoders, it is only so asymptotically for large number of users. Secondly, this scheme is unable to exploit potential time correlation of the channel. In this paper, we show (1) that exploiting memory in the transmitter allows to fill the gap to optimality for fixed (even low) number of users for time correlated channels, (2) how such schemes can be extended to take fairness into account in the proportional fair sense
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paper_title: Multiuser Diversity - Multiplexing Tradeoff in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider joint scheduling and beamforming in a broadcast channel with multiple antennas at the transmitter and a single antenna at the mobile receiver. Perfect channel knowledge is assumed to be available at the receiver while the transmitter is provided with partial channel state information (CSIT) through a limited rate feedback channel. Each user feeds back quantized information regarding the channel vector direction (from a codebook) and a quantized (scalar) channel quality indicator. We identify the tradeoff between multiuser diversity and spatial multiplexing gain given a limited amount of feedback bits. Scaling laws of the above parameters are derived in order to achieve a target rate performance. Our results reveal useful design guidelines for the split of feedback bits for channel quantization and channel quality.
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paper_title: Weighted max-min fair beamforming, power control, and scheduling for a MISO downlink

paper_content:

In this paper, we consider the joint beamforming, power control and scheduling problem in a multiple-input single- output (MISO) downlink for maximizing the minimum weighted rate among all users. We solve this problem by formulating it as a convex optimization problem whose function evaluations require maximization of a difference of convex functions (D.C. Programming). We also propose a simpler heuristic that finds the best policy under restricted set of power vectors. We then compare the performance of these policies against the dirty paper coding (DPC) policy to quantify the performance gap between an optimal point-to-point coding approach and an optimal joint encoding/decoding approach.
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paper_title: Maximum volume criterion for user selection of multiuser MIMO downlink with multiantenna users and block diagonalization beamforming

paper_content:

Compared with capacity-achieving dirty paper coding [1], block diagonalization (BD) algorithm [2] is known as a suboptimal but more practical beamforming scheme for multiuser MIMO downlink systems with multiantenna users. However BD suffers from two major drawbacks: the dimensionality constraint on antennas arrangement and the difficulty in handling spatially correlated users. User selection capable of selecting some most sum-rate-contributive users is a promising measure to alleviating this situation.
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paper_title: Fundamental Limits in MIMO Broadcast Channels

paper_content:

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system parameters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.
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paper_title: Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider a downlink channel where a base station equipped with M transmit antennas communicates with K ≥ M single-antenna receivers and has partial channel knowledge obtained via a limited rate feedback channel. We propose scalar feedback metrics that provide an estimate of the received signal-to-noise plus interference ratio (SINR), which are combined with efficient user selection algorithms and zero-forcing beamforming. The asymptotic system sum rate for large K is analyzed and numerical results are provided, showing the performance of each metric in different scenarios.
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paper_title: Stability and Delay of Zero-Forcing SDMA With Limited Feedback

paper_content:

This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor M >; 1. For given M → 1, the number of feedback bits per mobile is proved to be O(-log2(1-1/M)) .
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paper_title: A vector-perturbation technique for near-capacity multiantenna multiuser communication-part II: perturbation

paper_content:

Recent theoretical results describing the sum-capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves near-capacity at sum-rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a "sphere encoder" to perturb the data to reduce the energy of the transmitted signal. The paper is comprised of two parts. In this second part, we show that, after the regularization of the channel inverse introduced in the first part, a certain perturbation of the data using a "sphere encoder" can be chosen to further reduce the energy of the transmitted signal. The performance difference with and without this perturbation is shown to be dramatic. With the perturbation, we achieve excellent performance at all signal-to-noise ratios. The results of both uncoded and turbo-coded simulations are presented.
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paper_title: Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization

paper_content:

Block diagonalization (BD) is a preceding technique that eliminates inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. With the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission, the number of simultaneously supportable users with BD is limited by the ratio of the number of basestation transmit antennas to the number of user receive antennas. In a downlink MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput The brute-force search for the optimal user set, however, is computationally prohibitive. We propose two low-complexity suboptimal user selection algorithms for multiuser MIMO systems with BD. Both algorithms aim to select a subset of users such that the total throughput is nearly maximized. The first user selection algorithm greedily maximizes the total throughput, whereas the criterion of the second algorithm is based on the channel energy. We show that both algorithms have linear complexity in the total number of users and achieve around 95% of the total throughput of the complete search method in simulations
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paper_title: Multiuser MIMO User Selection Based on Chordal Distance

paper_content:

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.
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paper_title: Efficient Margin Adaptive Scheduling for MIMO-OFDMA Systems

paper_content:

In this paper we address the problem of margin adaptive scheduling in the downlink of an orthogonal frequency division multiple access (OFDMA) multiple-input multiple-output (MIMO) system. Optimal resource allocation in MIMO systems requires the joint optimization of: a) linear transmit and receive spatial filters, b) channel assignment and c) power allocation. This problem is not convex and its complexity becomes thus intractable already for small sets of users and subcarriers. To reduce the complexity of the problem at hand, we propose a novel heuristic strategy that partitions the users in different groups according to their average channel quality and addresses the original problem by solving a succession of lower-complexity allocation problems. The spatial dimension is employed to prevent multiple access interference from hindering the performance of the sequential allocation. To further reduce the complexity burden we introduce a linear programming formulation in combination with a waterfilling-based strategy to allocate channels and power to the groups of users. Numerical results and evaluation of the computational complexity show that, though suboptimal, in most cases the proposed algorithm manages to exploit in an original way the inherent multi-user diversity of multi-carrier systems to ease the task of resource allocation with a very limited performance loss from the theoretic optimum.
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paper_title: Limited Feedback Multiuser Scheduling of Spatially Correlated Broadcast Channels

paper_content:

This paper investigates the transmission scheduling of users under spatially correlated multiple-input-multiple-output (MIMO) channels. By maximizing an upper bound of the sum capacity, we propose a scheduling scheme that requires only scalar feedback from each receiving user. To simplify user information feedback and better exploit the spatial channel correlation, we further develop a more efficient scheduling method that only requires a 1-bit indicator from each user and selects users based on the MIMO channel correlation information. Additionally, we then extend the proposed scheduling schemes for the system with imperfect (finite-rate) channel information feedback. Numerical results finally show that the proposed scheduling schemes can effectively improve the system sum capacity performance by exploiting the statistic channel-correlation information.
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paper_title: A comparison of scheduling strategies for MIMO broadcast channel with limited feedback on OFDM systems

paper_content:

We consider a multiuser downlink transmission from a base station with multiple antennas (MIMO) to mobile terminals (users) with a single antenna, using orthogonal frequency division multiplexing (OFDM). Channel conditions are reported by a feedback from users with limited rate, and the base station schedules transmissions and beamforms signals to users. We show that an important set of schedulers using a general utility function can be reduced to a scheduler maximizing the weighted sum rate of the system. For this case we then focus on scheduling methods with many users and OFDM subcarriers. Various scheduling strategies are compared in terms of achieved throughput and computational complexity and a good tradeoff is identified in greedy and semiorthogonal user selection algorithms. In the greedy selection algorithm, users are selected one by one as long as the throughput increases, while in the semiorthogonal approach users are selected based on the channel correlation. An extension of these approaches from a flat-fading channel to OFDM is considered and simplifications that may be useful for a large number of subcarriers are presented. Results are reported for a typical cellular transmission of the long-term evolution (LTE) of 3GPP.
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paper_title: Multi-mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

paper_content:

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.
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paper_title: Joint Antenna Beamforming, Multiuser Scheduling, and Power Allocation for Hierarchical Cellular Systems

paper_content:

Cognitive radio (CR) is concretely embodied in hierarchical cellular systems by deploying an underlying microcellular system to reuse the underutilized spectrum of a macrocellular system. One of the key challenges to the success of hierarchical cellular systems is to manage the intercell interference between the macrocell and the microcell and to maximize the spectrum efficiency. In this paper, antenna beamforming, power allocation, and multiuser scheduling are jointly designed to opportunistically utilize the macrocell's uplink spectrum in serving multiple secondary microcellular users concurrently. The joint design of antenna beamforming, power allocation, and scheduling with the objective of maximizing the sum rate is indeed a mixed-integer nonlinear programming NP-hard problem. The proposed simpler iterative subgradient projection and semidefinite programming approach can obtain better performance than the conventional zero-forcing beamforming. Furthermore, unlike the optimal singular value decomposition (SVD) beamforming that requires all users to have channel knowledge at the receiver for cooperation, the proposed joint design methodology requires no channel knowledge at the receiver and can outperform the SVD beamforming without user scheduling. When considering both implementation complexity and performance enhancement issues, the proposed joint power allocation, multiuser scheduling, and antenna beamforming technique can help provide important insights into the design of interference management techniques for hierarchical CR systems.
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paper_title: An Effective Inter-Cell Interference Coordination Scheme for Downlink CoMP in LTE-A Systems

paper_content:

Coordinated multi-point (CoMP) has been adopted in 3GPP LTE-Advanced to improve the coverage of high data rates. Downlink CoMP is mainly categorized into joint transmission (JT) and coordinated beamforming (CB). Previous research shows that JT does not benefit cell average throughput. Moreover, traditional CB algorithms are based on iterative evaluation, resulting in very high computational complexity. To address these issues, in this paper, we propose an effective inter-cell interference coordination scheme for downlink CoMP, which includes two phases. Firstly, in order to improve the performance of all user equipments (UEs), cell edge UEs employ JT, while CB is adopted by both cell edge and cell center UEs. Secondly, we design linear CB precoders by maximizing a signal to leakage and noise ratio (SLNR) metric, so as to reduce processing complexity. System-level simulations validate that, in contrast to non-CoMP, the proposed scheme brings a cell average spectral efficiency (SE) gain up to 21.50% and a cell edge SE gain up to 119.2%.
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paper_title: Optimal downlink space-time scheduling design with convex utility functions-multiple-antenna systems with orthogonal spatial multiplexing

paper_content:

It is well known that link level throughput could be significantly increased by using multiple antennae at the transmitter and receiver without increasing the bandwidth and power budget. However, optimizing the link level performance of multiple-antenna systems does not always imply achieving system level optimization. Therefore, cross-layer optimization across the link layer and the scheduling layer is very important to fully exploit the temporal and spatial dimensions of the communication channel. In this paper, we consider the optimal downlink space-time scheduling design for a general class of convex utility functions. The access point or base station is equipped with n/sub T/ transmit antennas. There are K mobiles in the system with a single receive antenna. For practical reasons, we assume zero-forcing processing at the physical layer of the base station and mobile. We will apply the design framework to two common utility functions, namely the maximum throughput and the proportional fair. The cross-layer scheduling design is a mixed convex and combinatorial optimization problem and the search space of the optimal solution is enormous. Greedy algorithm, which has been widely used in today's wireless data systems (3G1X, high data rate system (HDR), Universal Mobile Terrestrial Service), is optimal when n/sub T/=1. However, we found that there is a large performance penalty of greedy algorithms (relative to optimal performance) when n/sub T/>1 and this motivates the search for more efficient heuristics. In this paper, we will address genetic-based heuristics and discuss their complexity-performance tradeoff.
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paper_title: Joint Feedback and Scheduling Scheme for Service-Differentiated Multiuser MIMO Systems

paper_content:

In this correspondence, we consider the problem of scheduling, in closed-loop multiuser MIMO systems, a large set of users with different Quality of Service (QoS) requirements, supplied by a single base station (BS) by means of Zero-Forcing Beamforming (ZFBF). We provide a power-and-bandwidth ef- ficient feedback scheme in which only ZFBF-optimal users feedback their CSI, thereby reducing the number of required feedbacks and the computational burden of exhaustive search for best users at the BS. Afterwards, we show that conventional sum- capacity maximizing scheduling policies fall short to meet the req- uisites of delay-sensitive applications, and we provide appropriate scheduling scheme for such-constrained users. Simulation results demonstrate that the proposed scheduling approach successfully meets both average and instantaneous delay constraints of delay- sensitive applications.
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paper_title: Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

paper_content:

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC.
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paper_title: Two-Stage Channel Quantization for Scheduling and Beamforming in Network MIMO Systems: Feedback Design and Scaling Laws

paper_content:

This paper proposes an efficient two-stage channel quantization and feedback scheme for the downlink limited-feedback network multiple-input multiple-output (MIMO) system. In the first stage, the users report their best set of base-station antenna and physical resource block combinations, and the base-stations schedule the best user for each antenna in each resource block. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. This paper proposes an analytical framework to show that, under a total feedback budget of B bits, the number of bits assigned to the second feedback stage should scale as log B, and in quantizing channel vectors from different base-stations, each user should allocate feedback bits in proportion to the channel magnitudes in dB scale. Under these optimized bit allocations, the overall sum rate of the system is shown to scale double-logarithmically with B, linearly with the total number of antennas, and logarithmically with transmit power, thus achieving both multiuser diversity and spatial multiplexing gains under limited feedback. Finally, realistic wireless propagation model of an urban small-cell deployment is used to show that the proposed scheme can approach the performance of a network MIMO system with full channel state information with only modest amount of channel feedback.
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paper_title: Large deviation delay analysis of queue-aware multi-user MIMO systems with two timescale mobile-driven feedback

paper_content:

Multi-user multi-input-multi-output (MU-MIMO) systems usually require users to feedback the channel state information (CSI) for scheduling. Most of the existing literature on the reduced feedback user scheduling focused on the throughput performance and the queueing delay was usually ignored. As the delay is important for real-time applications, it is desirable to have a low feedback queue-aware user scheduling algorithm for MU-MIMO systems. This paper proposes a two timescale queue-aware user scheduling algorithm, which consists of a queue-aware mobile-driven feedback filtering stage and a SINR-based user scheduling stage. The feedback policy is obtained by solving a queue-weighted optimization problem. In addition, we evaluate the associated queueing delay performance by using the large deviation analysis. The large deviation decay rate for the proposed algorithm is shown to be much larger than the CSI-only scheduling algorithm. Numerical results demonstrate the large performance gain of the proposed algorithm over the CSI-only algorithm, while the proposed one requires only a small amount of feedback.
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paper_title: System evaluation of optimal downlink beamforming with congestion control in wireless communication

paper_content:

We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Multi-user MIMO systems: the future in the making

paper_content:

The consummation of all the research work in MU-MIMO systems will be in the form of a standard. It will require collating all the research findings into a deployable standard with well defined transmit and receive processing, scheduling options, receiver training fields, CSI feedback rates, and other specifications essential for compatibility. MU-MIMO technology offers aspiring researchers an exciting challenge and an opportunity to work on a solution that vies for a spot that will make it key technology in future cellular systems. This article aims at giving an insight into MU-MIMO systems - its concept, fundamentals, and trends including an overview/of important research results. It is intended at giving a good start to amateurs interested in being part of the community that shapes the future of wireless systems.
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paper_title: A User Selection Algorithm Using Angle between Subspaces for Downlink MU-MIMO Systems

paper_content:

One of major issues in the efficient use of radio resource for multiuser multiple-input/multiple-output (MU-MIMO) systems is the selection of users to achieve the maximum system throughput. The optimal user selection algorithm, which requires exhaustive search, is prohibitive due to its high computational complexity where Block diagonalization (BD) method is applied and known as a suboptimal precoding technique for downlink MU-MIMO systems, which intents to perfectly eliminate inter-user interference. In this paper, we propose efficient, iterative user selection algorithms with low complexity, where the product of eigenvalues of effective channels is utilized as a selection metric by applying the concept of principal angles between subspaces. And, we further examined the applicability of the proposed algorithms to limited feedback systems and proportional fair (PF) scheduling. Through computational complexity analysis, we show that the proposed algorithm has low complexity with a little loss in throughput. Simulation results validate that the proposed algorithm achieves almost the same system throughput by a capacity-based algorithm under high SNR regime with considerable reduction in complexity.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Space Division Multiple Access with a Sum Feedback Rate Constraint

paper_content:

On a multi-antenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

paper_content:

In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

paper_content:

In this paper, we tackle the problem of semidistributed user selection with distributed linear precoding for sum-rate maximization in multiuser multicell systems. A set of adjacent base stations (BSs) forms a cluster to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling, and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to nonintended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, namely, distributed zero forcing and distributed virtual signal-to-interference-plus-noise ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First, we investigate how the signal-to-noise ratio regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the BSs.
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paper_title: Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search

paper_content:

We consider a multi-user MIMO downlink system employing zero-forcing beamforming (ZFBF) as a spatial multiplexing strategy, and propose low-complexity user subset selection methods based on a clique (fully connected subgraph) search. The proposed algorithms, maximum weighted clique (MWC)-ZFBF and greedy weighted clique (GWC)-ZFBF, are shown to achieve the asymptotic sum-capacity of MIMO downlink channels as the number of users goes to infinity. Thus, clique search based ZFBF is an appealing strategy in MIMO downlink systems with a large number of users.
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paper_title: Convex approximation techniques for joint multiuser downlink beamforming and admission control

paper_content:

Multiuser downlink beamforming under quality of service (QoS) constraints has attracted considerable interest in years, because it is particularly appealing from a network operator's perspective (e.g., UMTS, 802.16e). When there are many co-channel users and/or the service constraints are stringent, the problem becomes infeasible and some form of admission control is necessary. We advocate a cross-layer approach to joint multiuser transmit beamforming and admission control, aiming to maximize the number of users that can be served at their desired QoS. It is shown that the core problem is NP-hard, yet amenable to convex approximation tools. Two computationally efficient convex approximation algorithms are proposed: one is based on semidefinite relaxation of an equivalent problem reformulation; the other takes a penalized second-order cone approach. Their performance is assessed in a range of experiments, using both simulated and measured channel data. In all experiments considered, the proposed algorithms work remarkably well in terms of the attained performance-complexity trade-off, consistently exhibiting close to optimal performance at an affordable computational complexity.
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paper_title: Coordinated beamforming with limited feedback in the MIMO broadcast channel

paper_content:

In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.
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paper_title: Multi-Antenna Downlink Channels with Limited Feedback and User Selection

paper_content:

We analyze the sum-rate performance of a multi- antenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load.
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paper_title: Traffic-Aware Training and Scheduling for MISO Wireless Downlink Systems

paper_content:

In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback/training decision. This should be leveraged in future communication systems.
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paper_title: Network MIMO with Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation and Reduced-Complexity Scheduling

paper_content:

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.
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paper_title: Multicell Coordination via Joint Scheduling, Beamforming, and Power Spectrum Adaptation

paper_content:

The mitigation of intercell interference is an importance issue for current and next-generation wireless cellular networks where frequencies are aggressively reused and hierarchical cellular structures may heavily overlap. The paper examines the benefit of coordinating transmission strategies and resource allocation schemes across multiple base-stations for interference mitigation. Two different wireless cellular architectures are studied: a multicell network where base-stations coordinate in their transmission strategies, and a mixed macrocell and femtocell/picocell deployment with coordination among macro and femto/pico base-stations. For both scenarios, this paper proposes a heuristic joint proportionally fair scheduling, spatial multiplexing, and power spectrum adaptation algorithm that coordinates multiple base-stations with an objective of optimizing the overall network utility. The proposed scheme optimizes the user schedule, transmit and receive beamforming vectors, and transmit power spectra jointly, while taking into consideration both the intercell and intracell interference and the fairness among the users. System-level simulation results show that coordination at the transmission strategy and resource allocation level can already significantly improve the overall network throughput as compared to a conventional network design with fixed transmit power and per-cell zero-forcing beamforming.
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paper_title: Iterative Precoder Design and User Scheduling for Block-Diagonalized Systems

paper_content:

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices.
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paper_title: Coordinated user scheduling in the multi-cell MIMO downlink

paper_content:

We propose a novel, coordinated user scheduling (CUS) algorithm for inter-cell interference (ICI) mitigation in the downlink of a multi-cell multi-user MIMO system. In the proposed algorithm, ICI mitigation is performed through the exchange of necessary channel state information (CSI) among the base stations, and the revision of the scheduling decisions and beamformer designs at each base station. Furthermore, ICI mitigation is performed only for the cell-edge users so that the amount of inter-base station signaling overhead is minimized. Our simulation results demonstrate that the proposed coordination scheduling algorithm significantly improves the cell-edge users' throughput compared to conventional systems with only a negligible amount of CSI sharing among the base stations and a relatively small throughput loss for the cell-interior users.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming and User Grouping

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a two stage downlink beamforming: a pre-beamformer that depends on the channel covariances and minimizes interference across groups and a multiuser MIMO precoder for the effective channel after pre-beamforming, to counteract interference within a group. We first focus on the regime of a fixed number of antennas and large number of users, and show that opportunistic beamforming with user selection yields significant gain, and thus, channel correlation may yield a capacity improvement over the uncorrelated "isotropic" channel result of Sharif and Hassibi. We prove that in the presence of different correlations among groups, a block diagonalization approach for the design of pre-beamformers achieves the optimal sum-rate scaling. Next, we consider the regime of large number of antennas and users, where user selection does not provide significant gain. Here, we propose a simplified user grouping algorithm to cluster users into groups when the number of antennas becomes very large, in a realistic setting where users are randomly distributed and have different angles of arrival and angular spreads depending on the propagation environment. Our subsequent analysis leads to a probabilistic scheduling algorithm, where users within each group are preselected at random based on probabilities derived from the large system analysis, depending on the fairness criterion. This is advantageous since only the selected users are required to feedback their channel state information (CSIT).
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paper_title: An improved partial CSIT random beamforming for multibeam satellite systems

paper_content:

A novel multiple input multiple output (MIMO) transmitting scheme is presented for multibeam satellite systems, where the objective is to increase the system sum rate, availability and variance performance.
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paper_title: Adaptive Modulation in PU2RC Systems with Finite Rate Feedback

paper_content:

This paper addresses a per user unitary precoding and rate control (PU 2 RC) system with adaptive multi-level quadrature amplitude modulation (QAM) modulation, where both the PU 2 RC operation and adaptive modulation are based on finite rate feedback. The system supports two transmission modes (single user transmit beamforming and multiuser transmission with orthogonal beamforming), and switches between the two modes to maximize the average throughput. We first study single user transmit beamforming, and derive closed-form expressions for the average throughput and bit-error rate (BER) with outdated channel information. Then, multiuser transmission with orthogonal beamforming is investigated. We analyze the throughput and BER performance without feedback delay in the normal signal noise ratio (SNR) regime, and the performance with feedback delay in the interference-limited regime. Simulation results demonstrate the effect of time delay, and the preferred regions of the single user transmission mode and multiuser transmission mode.
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paper_title: Joint Beamforming and Scheduling for a Multi-Antenna Downlink with Imperfect Transmitter Channel Knowledge

paper_content:

We consider the downlink of a wireless system where the base-station has M ges 1 antennas and K user terminals have one antenna each. We study the weighted rate sum maximization in the case of non-perfect Channel State Information at the Transmitter (CSIT). Some relevant downlink optimization problems, such as the stabilization of the transmission queues under random packet arrivals and the proportional fair scheduling for infinite backlogged systems, can be solved as special cases of the proposed problem. We restrict the transmitter strategy to be based on Gaussian coding and beamforming. Even under this simplifying condition, the problem at hand is non-convex and it does not appear to lend itself to a simple algorithmic solution. Therefore, we introduce some approximations that yield a definition of signal-to-interference plus noise ratio (SINR) commonly used in the classical array- processing/beamforming literature. For the simpler (but still non-convex) approximated problem, we propose a powerful heuristic solution based on greedy user selection and a gradient iteration that converges to a local maximum of the objective function. This method yields very competitive results with relatively low computational complexity. Extensive simulations show that, in the case of perfect CSIT, the proposed heuristic scheme performs very closely to the optimal (dirty-paper coding) strategy while, in the case of non-perfect CSIT, it significantly outperforms previously proposed suboptimal approaches, such as random beamforming and approximated zero-forcing with greedy user selection.
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paper_title: Interference Coordination through Network-Synchronized Cyclic Beamforming

paper_content:

The next generation of wireless networks (e.g., (10)) will use multiple techniques to improve channel spectral efficien- cies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each subband in each frame, the scheduler chooses a beam and then schedules one or more UEs within the corresponding beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors (flashlight effect). The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period but this can be changed occasionally.
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paper_title: Dynamic Multi-User MIMO scheduling with limited feedback in LTE-Advanced

paper_content:

Multi-User MIMO (MU-MIMO) systems have gained numerous attention from researchers in the past decade due to its substantial gains in the system throughput. Most of the initial research assumes the knowledge of perfect channel state information at the transmitter (CSIT). However, this is considered impractical and research over the past few years has been focused on receivers feeding back limited information to the transmitter. In this work, we consider a transparent MU-MIMO system model with limited feedback. We propose a general framework for dynamic MU-MIMO scheduling with the capability to switch between Single-User MIMO mode and (Multi-Rank) Multi-User MIMO mode without users feeding back additional multi-user information. Specifically, this is done by each user carefully estimating its CQI under the hypothesis of Multi-Rank MultiUser MIMO transmission and taking advantage of the codebook structure. We consider the sum rate of the system assuming each user uses ML and LMMSE receiver and show that our proposed scheduler, with significantly reduced feedback load, outperforms the best-companion user pairing.
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paper_title: Low Complexity Scheduling and Beamforming for Multiuser MIMO Systems

paper_content:

The problem of joint scheduling and beam-forming for a multiple antenna broadcast channel with partial channel state information at the transmitter (CSIT) is considered. We show how long-term statistical channel knowledge can be efficiently combined with instantaneous low-rate feedback for user selection and linear beamforming. A low complexity algorithm based on an estimate (bound) of the multiuser interference is proposed. Our scheme is shown to exhibit significant throughput gain over opportunistic techniques, approaching the sum rate of full CSIT for small angle spreads.
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paper_title: MU-MISO Transmission with Limited Feedback

paper_content:

Downlink multi-user transmission techniques that allow several users to be served simultaneously in frequency and time have been recognized as a promising means to increase system capacity. However they require accurate channel state information (CSI) at the base station (BS) such that appropriate signal processing can be performed to separate multiple users in the space domain. In practice however, CSI cannot be perfectly known to the BS due to the capacity-limited feedback channel in FDD systems for instance. In this letter we investigate multiuser multiple-input single-output (MU-MISO) transmission with limited feedback. In particular we identify the useful information that the BS needs to deal with inter-user interference and a codebook design is derived accordingly. In addition, an adaptive threshold-based feedback approach is proposed, where only users with good feedback quality are allowed to do feedback. It is shown that the adaptive scheme can effectively improve the system performance given a fixed number of feedback bits.
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paper_title: Joint User Scheduling and Adaptive Intercell Interference Cancelation for MISO Downlink Cellular Systems

paper_content:

Recently, an adaptive intercell interference (ICI) mitigation technique has been proposed for downlink cellular systems as a means to increase throughput with low system complexity. However, in the prior work, the issue of intercell user scheduling has not been considered. In this paper, we study multiple-input-single-output (MISO) downlink cellular systems that jointly design adaptive ICI cancelation (ICIC) and intercell user scheduling assuming that partial channel state information (CSI) is shared among base stations (BSs). Since the optimal solution would require high complexity, we investigate a new low-complexity algorithm that selects the best users and their beamforming strategies in terms of maximizing the weighted sum rate (WSR). To this end, we first develop a simple threshold criterion for each user to decide the preferred beamforming strategy based on the derivation of the expected signal-to-interference-plus-noise ratio (SINR). Then, according to users' feedback about their decisions, a successive user and beamforming selection algorithm is performed at the BSs. From simulation results, we show that, combined with proportional fair scheduling, the proposed scheme provides excellent throughput performance with very low computational complexity and the amount of inter-BS CSI exchange. Furthermore, we discuss an extension of the proposed scheme to limited feedback systems and observe that our algorithm also provides similar advantages over conventional schemes with quantized feedback.
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paper_title: Efficient Sum Rate Maximization and Resource Allocation in Block-Diagonalized Space-Division Multiplexing

paper_content:

For space-division multiplexing (SDM) via block diagonalization on multiuser multiple-input multiple-output (MIMO) wireless downlink, it is shown that receive antenna selection (RAS) is necessary for maximizing the achievable sum rate. This is true even when all receive antennas are equipped with radio frequency (RF) chains and RAS reduces the upper bound on the broadcast sum capacity, and when the orthogonalized channels use optimal processing. Similarly, spatial-mode selection (SMS) is necessary for sum rate maximization when receive-weight matrices are used for spatial-mode allocation. RAS/SMS may release transmission resources that can fully be utilized via additional user scheduling to yield further sum rate gains. Optimal user selection for sum rate maximization is subsumed within an exhaustive RAS/SMS process for multiantenna terminals, and both selection processes become identical for single-antenna terminals. RAS/SMS thus helps reduce the performance gap from the optimal sum capacity even for small user pool sizes. A block antenna/mode selection approach is introduced to help overcome the drawbacks of existing algorithms. Since RAS/SMS involves antenna/mode ranking, a systematic method for resource allocation with sum rate loss minimization is inherently provided. This way, a streamlined process that combines user selection, RAS/SMS, and resource allocation is developed for sum rate maximization of block-diagonalized SDM.
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paper_title: Multimode Transmission for Multiuser MIMO Systems With Block Diagonalization

paper_content:

A low-complexity multimode transmission technique for downlink multiuser multiple-input-multiple-output (MIMO) systems with block diagonalization (BD) is proposed. The proposed technique adaptively configures the number of data streams for each user by adjusting its number of active receive antenna and switching between single-stream beamforming and multistream spatial multiplexing, as a means to exploit the multimode switching diversity. We consider a highly loaded system where there are a large number of users, hence a subset of users need to be selected. Joint user and antenna selection has been proposed as a multiuser multimode switching technique, where the optimal subset of receive antennas and users are chosen to maximize the sum throughput. The brute-force search, however, is prohibitively complicated. In this paper, two low-complexity near-optimal user/antenna selection algorithms are developed. The first algorithm aims at maximizing a capacity lower bound, derived in terms of the sum Frobenius norm of the channel, while the second algorithm greedily maximizes the sum capacity. We analytically evaluate the complexity of the proposed algorithms and show that it is orders of magnitude lower than that of the exhaustive search. Simulation results demonstrate that the proposed algorithms achieve up to 98% of the sum throughput of the exhaustive search, for most system configurations, while the complexity is substantially reduced.
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paper_title: Utilizing the Spatial Information Provided by Channel Norm Feedback in SDMA Systems

paper_content:

To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.
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paper_title: Precoding Schemes for the MIMO-GBC

paper_content:

The use of M antennas at the base station and of transmitter channel state information can boost the downlink throughput by a factor M (multiplexing gain), even though the receivers have a single antenna and do not cooperate. In this semi-tutorial work, we discuss some low-complexity alternatives to achieve a downlink throughput very close to the optimal sum capacity. We review and compare these alternatives and we show that, in the simple setting of independently fading channels, relatively traditional forms of linear beamforming achieve the best tradeoff between performance and complexity. These results somehow call for a reconsideration of the emphasis that certain recently proposed precoding techniques have enjoyed both in scientific literature and in technology development
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: An efficient greedy scheduler for zero-forcing dirty-paper coding

paper_content:

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.
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paper_title: MIMO Broadcast Channels with Spatial Heterogeneity

paper_content:

We develop a realistic model for multiple-input multiple-output (MIMO) broadcast channels, where each randomly located user's average SNR depends on its distance from the transmitter. With perfect channel state information at the transmitter (CSIT), the average sum capacity is proven to scale for many users like αM/2 log K instead of M log log K, where α, M, and K denote the path loss exponent, the number of transmit antennas, and the number of users in a cell. With only partial CSIT, the sum capacity at high SNR eventually saturates due to interference, and the saturation value scales for large B like MB/M-1, where B denotes the quantization resolution for channel feedback.
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paper_title: On the user selection for MIMO broadcast channels

paper_content:

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.
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paper_title: Downlink Multiuser MIMO Systems With Adaptive Feedback Rate

paper_content:

In this paper, an efficient channel feedback scheme for downlink multiuser multiple-input-multiple-output (MU-MIMO) systems is proposed. The objective of the new feedback design is to adaptively control the feedback rate of each user, depending on the individual channel status, while the overall sum feedback rate is kept the same. The proposed channel feedback scheme is composed of two stages: 1) the common channel feedback stage of all users and 2) the user-specific channel feedback stage of the selected users. We present a low-complexity algorithm to determine the individual feedback rates of users, which utilizes convex optimization, followed by iterative steepest descent direction searching. Numerical results show that zero-forcing beamforming (ZFBF), combined with the proposed channel feedback scheme, considerably outperforms ZFBF with conventional channel feedback schemes.
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paper_title: Low-Complexity Downlink User Selection for Massive MIMO Systems

paper_content:

In this paper, we propose a pair of low-complexity user selection schemes with zero-forcing precoding for multiuser massive multiple-input–multiple-output downlink systems, in which the base station is equipped with a large-scale antenna array. First, we derive approximations of the ergodic sum rates of the systems invoking the conventional random user selection (RUS) and the location-dependent user selection (LUS). Then, the optimal number of simultaneously served user equipments (UEs),i.e., $K^\ast$ , is investigated to maximize the sum rate approximations. Upon exploiting $K^\ast$ , we develop two user selection schemes, namely, $K^\ast$ -RUS and $K^\ast$ -LUS, where $K^\ast$ UEs are selected either randomly or based on their locations. Both the proposed schemes are independent of the instantaneous channel state information of small-scale fading, therefore enjoying the same extremely low computational complexity as that of the conventional RUS scheme. Moreover, both of our proposed schemes achieve significant sum rate improvement over the conventional RUS. In addition, it is worth noting that, like the conventional RUS, the $K^\ast$ -RUS achieves good fairness among UEs.
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paper_title: User Scheduling for Heterogeneous Multiuser MIMO Systems: A Subspace Viewpoint

paper_content:

In downlink multiuser multiple-input-multiple-output (MU-MIMO) systems, users are practically heterogeneous. However, many existing user-scheduling algorithms are designed with an implicit assumption that users are homogeneous. In this paper, we revisit the problem by exploring the characteristics of heterogeneous users from a subspace viewpoint. With an objective of minimizing interference nonorthogonality among users, three new angular-based user-scheduling criteria are proposed. While the first criterion is heuristically determined by identifying the incapability of the largest principal angle to characterize subspace correlation and, hence, interference nonorthogonality between users, the second and third criteria are derived by using the sum rate capacity bounds with block diagonalization and the change in capacity by adding a new user into an existing user subset, respectively. Aiming to capture fairness among heterogeneous users while maintaining multiuser diversity gain, two new hybrid user-scheduling algorithms, whose computational complexities are only linearly proportional to the number of users, are proposed. We show by simulations the effectiveness of our proposed user-scheduling criteria and algorithms with respect to those commonly used in a homogeneous environment.
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paper_title: Joint Spatial Division and Multiplexing—The Large-Scale Array Regime

paper_content:

We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink/downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users.
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paper_title: Interference mitigation techniques for broadband satellite system

paper_content:

This paper presents an overview of possible interference mitigation techniques aiming at increasing the system capacity of broadband multimedia satellite systems. A multi-star network topology using a bent-pipe transparent satellite is assumed. After a general overview, the paper concentrates on the assessment of Linear Precoding techniques for increasing the potential system capacity on the Forward Link. Potential performance improvements achievable in real systems are investigated as well as resulting system constraints.
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paper_title: Maximum product of effective channel gains: an innovative user selection algorithm for downlink multi-user multiple input and multiple output

paper_content:

Recently, zero-forcing beamforming has been widely used for multiple-input and multiple-output broadcast channels, because it could provide suboptimal capacity with low complexity. To increase the sum data rate, a good user selection algorithm is attractive. In this paper, a new user selection algorithm named maximum product of effective channel gains is presented. The proposed algorithm is described mathematically, and the lower bound of the sum capacity is demonstrated to be proportional to the product of effective channel gains. Our simulation results show that maximum product of effective channel gains can achieve higher sum rate compared with the classical algorithm, semi-orthogonal user selection, with the same complexity order, especially when the signal-to-noise ratio is high; in addition, the complexity of the proposed algorithm is superior to minimum of the Frobenius norm of the pseudo-inverse algorithm. Meanwhile, the number of users that can be served simultaneously is equal to the number of transmission antennas, which is the maximum performance that can be achieved.Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: MIMO Broadcast Scheduling with Limited Feedback

paper_content:

We consider multiuser scheduling with limited feedback of partial channel state information in MIMO broadcast channels. By using spatial multiplexing at the base station (BS) and antenna selection for each user, we propose a multiuser scheduling method that allocates independent information streams from all M transmit antennas to the M most favorable users with the highest signal-to-interference-plus-noise ratio (SINR). A close approximation of the achievable sum-rate throughput for the proposed method is obtained and shown to match the simulation results very well. Moreover, two reduced feedback scheduling approaches are proposed. In the first approach, which we shall refer to as selected feedback scheduling, the users are selected based on their SINR compared to a predesigned threshold. Only those selected users are allowed to feed back limited information to the BS. The resultant feedback load and achievable throughput are derived. It will then be demonstrated that with a proper choice of the threshold, the feedback load can be greatly reduced with a negligible performance loss. The second reduced feedback scheduling approach employs quantization for each user, in which only few bits of quantized SINR are fed back to the BS. Performance analysis will show that even with only 1-bit quantization, the proposed quantized feedback scheduling approach can exploit the multiuser diversity at the expense of slight decrease of throughput.
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paper_title: Writing on dirty paper

paper_content:

A channel with output Y = X + S + Z is examined, The state S \sim N(0, QI) and the noise Z \sim N(0, NI) are multivariate Gaussian random variables ( I is the identity matrix.). The input X \in R^{n} satisfies the power constraint (l/n) \sum_{i=1}^{n}X_{i}^{2} \leq P . If S is unknown to both transmitter and receiver then the capacity is \frac{1}{2} \ln (1 + P/( N + Q)) nats per channel use. However, if the state S is known to the encoder, the capacity is shown to be C^{\ast} =\frac{1}{2} \ln (1 + P/N) , independent of Q . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N . Therefore, the state S does not affect the capacity of the channel, even though S is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it.
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paper_title: Adaptive downlink multi-user MIMO wireless systems for correlated channels with imperfect CSI

paper_content:

Multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. However the capacity increase is limited when the number of antennas at the receiver is fixed or restricted (due to mobile size constraints for example). To overcome this limitation multi-user MIMO can be used, which allows several users to be served simultaneously in frequency and time. A disadvantage of these multi-user MIMO systems, when used in the downlink however, is that they need accurate channel state information (CSI) at the transmitter and also uncorrelated channels among users. In this paper we investigate methods to address the problems of multi-user MIMO systems in spatially correlated channels. We adopt the concept of angle between subspaces to characterize the inter-user spatial correlation and adapt the algorithm to those conditions. We also investigate the impact of the accuracy of CSI at the transmitter (CSIT) and whether more limited CSI such as channel correlation information alone can be used to provide good multi-user MIMO performance. Results are presented as various simulated capacity measures and we use them to make comparisons between the various multi-user MIMO configurations
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paper_title: How Many Users should be Turned On in a Multi-Antenna Broadcast Channel

paper_content:

This paper considers broadcast channels with L antennas at the base station and m single-antenna users, where each user has perfect channel knowledge and the base station obtains channel information through a finite rate feedback. The key observation of this paper is that the optimal number of on-users (users turned on), say s, is a function of signal-to-noise ratio (SNR) and other system parameters. Towards this observation, we use asymptotic analysis to guide the design of feedback and transmission strategies. As L, m and the feedback rates approach infinity linearly, we derive the asymptotic optimal feedback strategy and a realistic criterion to decide which users should be turned on. Define the corresponding asymptotic throughput per antenna as the spatial efficiency. It is a function of the number of on-users s, and therefore, s should be appropriately chosen. Based on the above asymptotic results, we also develop a scheme for a system with finite many antennas and users. Compared with other works where s is presumed constant, our scheme achieves a significant gain by choosing the appropriate s. Furthermore, our analysis and scheme is valid for heterogeneous systems where different users may have different path loss coefficients and feedback rates.
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paper_title: Opportunistic Space-Division Multiple Access With Beam Selection

paper_content:

In this paper, a novel transmission technique for the multiple-input multiple-output (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple sets of randomly chosen orthogonal beamforming vectors. Each user sends the index of the best beamforming vector and the corresponding signal-to-interference-plus-noise ratio for that set of orthogonal vectors back to the base station. The base station opportunistically determines the users and corresponding orthogonal vectors that maximize the sum capacity. Based on the capacity expressions, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20% gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100% gain (for a large number of users) over conventional opportunistic beamforming when the number of transmit antennas is four.
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paper_title: Capacity Maximization for Zero-Forcing MIMO-OFDMA Downlink Systems with Multiuser Diversity

paper_content:

This paper considers the optimal resource allocation for a multiuser MIMO-OFDMA downlink system using zero-forcing SDMA, with the objective of maximizing the system capacity. We provide the general mathematical formulation of the capacity maximization problem whose resource allocation includes user selection, power allocation and receive signal subspace selection. While the optimal solution of this problem is difficult to obtain, we consider two special cases: user selection based only and antenna selection based only optimization, and develop the optimal solution by reformulating the combinatorial optimization problem into a convex problem. Our proposed algorithms for these special cases can be extended to develop a suboptimal algorithm for the original general optimization problem which allows subspace selection. Moreover, we develop reduced-complexity algorithms for these problems which incur negligible capacity loss. Numerical results and analysis are provided to evaluate the system capacity and to study the effect of the number of users and the receive antennas per user on the performance. Comparisons on the capacity achieved by user selection only, antenna selection only and suboptimal subspace selection are discussed
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paper_title: Transmit Selection Diversity for Unitary Precoded Multiuser Spatial Multiplexing Systems With Linear Receivers

paper_content:

Multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference. In such a system, the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain. This paper proposes two precoding methods that use extra transmit antennas, beyond the minimum required, to provide additional degrees of diversity. The approach taken is to solve for a unitary transmit precoder, under a zero interuser interference constraint, that minimizes an upper bound on the symbol error rate (SER) for each user. Solutions where all transmit antennas are employed, as well as subsets of antennas (to reduce analog components), are described. Numerical results confirm a dramatic improvement in terms of SER and mutual information over single-user multiple-input multiple-output (MIMO) methods and static allocation methods. For example, the proposed techniques achieve a signal-to-noise ratio (SNR) improvement of 6-10 dB at an uncoded SER of 10-3, with only one extra transmit antenna
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paper_title: Performance of Orthogonal Beamforming for SDMA With Limited Feedback

paper_content:

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.
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paper_title: Joint Scheduling and ARQ for MU-MIMO Downlink in the Presence of Inter-Cell Interference

paper_content:

User scheduling and multiuser multi-antenna (MU-MIMO) transmission are at the core of high-rate data-oriented downlink schemes of the next-generation of cellular systems (e.g., LTE-Advanced). Scheduling selects groups of users according to their channels vector directions and SINR levels. However, when scheduling is applied independently in each cell, the inter-cell interference (ICI) power at each user receiver is not known in advance since it changes at each new scheduling slot depending on the scheduling decisions of all interfering base stations. In order to cope with this uncertainty, we consider the joint operation of scheduling, MU-MIMO beamforming and Automatic Repeat reQuest (ARQ). We develop a game-theoretic framework for this problem and build on stochastic optimization techniques in order to find optimal scheduling and ARQ schemes. Particularizing our framework to the case of "outage service rates", we obtain a scheme based on adaptive variable-rate coding at the physical layer, combined with ARQ at the Logical Link Control (ARQ-LLC). Then, we present a novel scheme based on incremental redundancy Hybrid ARQ (HARQ) that is able to achieve a throughput performance arbitrarily close to the "genie-aided service rates", with no need for a genie that provides non-causally the ICI power levels. The novel HARQ scheme is both easier to implement and superior in performance with respect to the conventional combination of adaptive variable-rate coding and ARQ-LLC.
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paper_title: Scheduling for Multiuser MIMO Downlink Channels with Ranking-Based Feedback

paper_content:

We consider a multi-antenna broadcast channel with more single-antenna receivers than transmit antennas and partial channel state information at the transmitter (CSIT). We propose a novel type of CSIT representation for the purpose of user selection, coined as ranking-based feedback. Each user calculates and feeds back the rank, an integer between 1 and W + 1, of its instantaneous channel quality information (CQI) among a set of W past CQI measurements. Apart from reducing significantly the required feedback load, ranking-based feedback enables the transmitter to select users that are on the highest peak (quantile) with respect to their own channel distribution, independently of the distribution of other users. It can also be shown that this feedback metric can restore temporal fairness in heterogeneous networks, in which users' channels are not identically distributed and mobile terminals experience different average signal-to-noise ratio (SNR). The performance of a system that performs user selection using ranking-based CSIT in the context of random opportunistic beamforming is analyzed, and we provide design guidelines on the number of required past CSIT samples and the impact of finite W on average throughput. Simulation results show that feedback reduction of order of 40-50% can be achieved with negligible decrease in system throughput.
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paper_title: An efficient resource-allocation scheme for spatial multiuser access in MIMO/OFDM systems

paper_content:

Fast adaptive transmission has been recently identified as a key technology for exploiting potential system diversity and improving power-spectral efficiency in wireless communication systems. An adaptive resource-allocation approach, which jointly adapts subcarrier allocation, power distribution, and bit distribution according to instantaneous channel conditions, is proposed for multiuser multiple-input multiple-output (MIMO)/orthogonal frequency-division multiplexing systems. The resultant scheme is able to: 1) optimize the power efficiency; 2) guarantee each user's quality of service requirements, including bit-error rate and data rate; 3) ensure fairness to all the active users; and 4) be applied to systems with various types of multiuser-detection schemes at the receiver. For practical implementation, a reduced-complexity allocation algorithm is developed. This algorithm decouples the complex multiuser joint resource-allocation problem into simple single-user optimization problems by controlling the subcarrier sharing according to the users' spatial separability. Numerical results show that significant power and diversity gains are achievable, compared with nonadaptive systems. It is also demonstrated that the MIMO system is able to multiplex several users without sacrificing antenna diversity by using the proposed algorithm.
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paper_title: The impact of space division multiplexing on resource allocation: a unified treatment of TDMA, OFDMA and CDMA

paper_content:

Space division multiple access (SDMA) with an antenna array at the transmitter is a promising means for increasing system capacity and supporting rate-demanding services. However, the presence of an antenna array at the physical layer raises significant issues at higher layers. In this paper, we attempt to capture the impact of SDMA on access layer channel allocation, reflected on channel reuse. This impact obtains different twists in TDMA, CDMA and OFDMA due to the different nature of co-channel and cross-channel interference and the different interaction of user spatial channel characteristics with system channels, namely time slots, codes and subcarriers. We consider these access schemes in a generalized unified framework and propose heuristic algorithms for channel allocation, downlink beamforming and transmit power control so as to increase total provisioned system rate and provide QoS to users in the form of minimum rate guarantees. We study the class of greedy algorithms that rely on criteria such as induced or received interference and signal-to-interference ratio (SIR), and a class of SIR balancing algorithms. Results show superior performance for SIR balancing resource allocation and expose the performance benefits of cross-layer design.
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paper_title: On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

paper_content:

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.
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paper_title: Leakage-based user scheduling in MU-MIMO broadcast channel

paper_content:

This paper investigates user scheduling in multi-user MIMO broadcast channel. We propose a leakagebased user scheduling scheme, in which a user’s leakage power to other users is an important factor to determine whether the user should be selected. The accuracy of closed-form solution of SLNR (signal to leakage plus noise ratio) makes the proposed scheme outperform the traditional scheduling method based on SINR (signal to interference plus noise ratio). The proposed algorithms can work in case of perfect or limited feedback of CSI (channel state information) at transmitter, and the advantage is verified with numerical results. A tradeoff relation among feedback bits number, active user number and transmit/receive antennas number is analyzed, which serves as a system design guideline.
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paper_title: Eigen-Based Transceivers for the MIMO Broadcast Channel with Semi-Orthogonal User Selection

paper_content:

This paper studies the sum rate performance of two low complexity eigenmode-based transmission techniques for the MIMO broadcast channel, employing greedy semi-orthogonal user selection (SUS). The first approach, termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first employ new analytical methods to prove that as the number of users K grows large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that the average sum rates of both techniques converge to the average sum capacity of the MIMO broadcast channel for large K. In addition to the asymptotic analysis, we investigate the sum rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS has significant performance advantages. Our results also provide key insights into the benefit of multiple receive antennas, and the effect of the SUS algorithm. In particular, we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second-order behavior of the multi-user diversity gain; for finite K, the benefit can be very significant. We also show the interesting result that the semi-orthogonality constraint imposed by SUS, whilst facilitating a very low complexity user selection procedure, asymptotically does not reduce the multi-user diversity gain in either first (log K) or second-order (loglog K) terms.
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paper_title: On the achievable throughput of a multiantenna Gaussian broadcast channel

paper_content:

A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j<i is taken into account by coding for noncausally known interference. Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR). We conclude by providing some numerical results for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.
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paper_title: Precoding for Multiple Antenna Gaussian Broadcast Channels With Successive Zero-Forcing

paper_content:

In this paper, we consider the multiuser Gaussian broadcast channel with multiple transmit antennas at the base station and multiple receive antennas at each user. Assuming full knowledge of the channel state information at the transmitter and the different receivers, a new transmission scheme that employs partial interference cancellation at the transmitter with dirty-paper encoding and decoding is proposed. The maximal achievable throughput of this system is characterized, and it is shown that given any ordered set of users the proposed scheme is asymptotically optimal in the high signal-to-noise ratio (SNR) regime. In addition, with optimal user ordering, the proposed scheme is shown to be optimal in the low-SNR regime. We also consider a linear transmission scheme which employs only partial interuser interference cancellation at the base station without dirty-paper coding. Given a transmit power constraint at the base station, the sum-rate capacity of this scheme is characterized and a suboptimal precoding algorithm is proposed. In several cases, it is shown that, for all values of the SNR, the achievable throughput of this scheme is strictly larger than a system which employs full interference cancellation at the base station (Spencer et al., 2004). In addition, it is shown that, in some cases, the linear transmission scheme can support simultaneously an increased number of users while achieving a larger system throughput.
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paper_title: Solution of the multiuser downlink beamforming problem with individual SINR constraints

paper_content:

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.
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paper_title: Matrix Algebra: Theory, Computations, and Applications in Statistics

paper_content:

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
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paper_title: A vector-perturbation technique for near-capacity multiantenna multiuser communication-part I: channel inversion and regularization

paper_content:

Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves near-capacity at sum rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a "sphere encoder" to perturb the data to reduce the power of the transmitted signal. This work is comprised of two parts. In this first part, we show that while the sum capacity grows linearly with the minimum of the number of antennas and users, the sum rate of channel inversion does not. This poor performance is due to the large spread in the singular values of the channel matrix. We introduce regularization to improve the condition of the inverse and maximize the signal-to-interference-plus-noise ratio at the receivers. Regularization enables linear growth and works especially well at low signal-to-noise ratios (SNRs), but as we show in the second part, an additional step is needed to achieve near-capacity performance at all SNRs.
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Dynamic linear precoding for the exploitation of known interference in MIMO broadcast systems

paper_content:

This paper introduces a novel channel inversion (CI) precoding scheme for the downlink of phase shift keying (PSK)-based multiple input multiple output (MIMO) systems. In contrast to common practice where knowledge of the interference is used to eliminate it, the main idea proposed here is to use this knowledge to glean benefit from the interference. It will be shown that the system performance can be enhanced by exploiting some of the existent inter-channel interference (ICI). This is achieved by applying partial channel inversion such that the constructive part of ICI is preserved and exploited while the destructive part is eliminated by means of CI precoding. By doing so, the effective signal to interference-plus-noise ratio (SINR) delivered to the mobile unit (MU) receivers is enhanced without the need to invest additional transmitted signal power at the MIMO base station (BS). It is shown that the trade-off to this benefit is a minor increase in the complexity of the BS processing. The presented theoretical analysis and simulations demonstrate that due to the SINR enhancement, significant performance and throughput gains are offered by the proposed MIMO precoding technique compared to its conventional counterparts.
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paper_title: Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels

paper_content:

The use of space-division multiple access (SDMA) in the downlink of a multiuser multiple-input, multiple-output (MIMO) wireless communications network can provide a substantial gain in system throughput. The challenge in such multiuser systems is designing transmit vectors while considering the co-channel interference of other users. Typical optimization problems of interest include the capacity problem - maximizing the sum information rate subject to a power constraint-or the power control problem-minimizing transmitted power such that a certain quality-of-service metric for each user is met. Neither of these problems possess closed-form solutions for the general multiuser MIMO channel, but the imposition of certain constraints can lead to closed-form solutions. This paper presents two such constrained solutions. The first, referred to as "block-diagonalization," is a generalization of channel inversion when there are multiple antennas at each receiver. It is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high SNR. The second, known as "successive optimization," is an alternative method for solving the power minimization problem one user at a time, and it yields superior results in some (e.g., low SNR) situations. Both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined. In order to accommodate more general scenarios, we also propose a framework for coordinated transmitter-receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas. While the proposed algorithms are suboptimal, they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity.
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paper_title: Coordinated Beamforming for MISO Interference Channel: Complexity Analysis and Efficient Algorithms

paper_content:

In a cellular wireless system, users located at cell edges often suffer significant out-of-cell interference. Assuming each base station is equipped with multiple antennas, we can model this scenario as a multiple-input single-output (MISO) interference channel. In this paper we consider a coordinated beamforming approach whereby multiple base stations jointly optimize their downlink beamforming vectors in order to simultaneously improve the data rates of a given group of cell edge users. Assuming perfect channel knowledge, we formulate this problem as the maximization of a system utility (which balances user fairness and average user rates), subject to individual power constraints at each base station. We show that, for the single-carrier case and when the number of antennas at each base station is at least two, the optimal coordinated beamforming problem is NP-hard for both the harmonic mean utility and the proportional fairness utility. For general utilities, we propose a cyclic coordinate descent algorithm, which enables each transmitter to update its beamformer locally with limited information exchange and establish its global convergence to a stationary point. We illustrate its effectiveness in computer simulations by using the space matched beamformer as the benchmark.
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paper_title: Constructive Multiuser Interference in Symbol Level Precoding for the MISO Downlink Channel

paper_content:

This paper investigates the problem of interference among the simultaneous multiuser transmissions in the downlink of multiple-antenna systems. Using symbol-level precoding, a new approach to exploit the multiuser interference is discussed. The concept of exploiting the interference between spatial multiuser transmissions by jointly utilizing data information (DI) and channel state information (CSI), in order to design symbol-level precoders, is proposed. To this end, the interference between data streams is transformed under certain conditions into useful signal that can improve the signal to interference noise ratio (SINR) of the downlink transmissions. We propose a maximum ratio transmission (MRT) based algorithm that jointly exploits DI and CSI to glean the benefits from constructive multiuser interference. Subsequently, a relation between the constructive interference downlink transmission and physical layer multicasting is established. In this context, novel constructive interference precoding techniques that tackle the transmit power minimization (min-power) with individual SINR constraints at each user's receivers is proposed. Furthermore, fairness through maximizing the weighted minimum SINR (max-min SINR) of the users is addressed by finding the link between the min power and max min SINR problems. Moreover, heuristic precoding techniques are proposed to tackle the weighted sum rate problem. Finally, extensive numerical results show that the proposed schemes outperform other state of the art techniques.
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paper_title: Generalized Design of Multi-User MIMO Precoding Matrices

paper_content:

In this paper we introduce a novel linear precoding technique. The approach used for the design of the precoding matrix is general and the resulting algorithm can address several optimization criteria with an arbitrary number of antennas at the user terminals. We have achieved this by designing the precoding matrices in two steps. In the first step we minimize the overlap of the row spaces spanned by the effective channel matrices of different users using a new cost function. In the next step, we optimize the system performance with respect to specific optimization criteria assuming a set of parallel single- user MIMO channels. By combining the closed form solution with Tomlinson-Harashima precoding we reach the maximum sum-rate capacity when the total number of antennas at the user terminals is less or equal to the number of antennas at the base station. By iterating the closed form solution with appropriate power loading we are able to extract the full diversity in the system and reach the maximum sum-rate capacity in case of high multi-user interference. Joint processing over a group of multi-user MIMO channels in different frequency and time slots yields maximum diversity regardless of the level of multi-user interference.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: MIMO wireless linear precoding

paper_content:

This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues. The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation. It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding. A precoded system structure is then described, involving an encoder and a linear precoder. Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios.
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paper_title: A Leakage-Based Precoding Scheme for Downlink Multi-User MIMO Channels

paper_content:

In multiuser MIMO downlink communications, it is necessary to design precoding schemes that are able to suppress co-channel interference. This paper proposes designing precoders by maximizing the so-called signal-to-leakage-and-noise ratio (SLNR) for all users simultaneously. The presentation considers communications with both single- and multi-stream cases, as well as MIMO systems that employ Alamouti coding. The effect of channel estimation errors on system performance is also studied. Compared with zero-forcing solutions, the proposed method does not impose a condition on the relation between the number of transmit and receive antennas, and it also avoids noise enhancement. Simulations illustrate the performance of the scheme
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paper_title: Complete Characterization of the Pareto Boundary for the MISO Interference Channel

paper_content:

In this correspondence, we study the achievable rate region of the multiple-input single-output (MISO) interference channel, under the assumption that all receivers treat the interference as additive Gaussian noise. Our main result is an explicit parametrization of the Pareto boundary for an arbitrary number of users and antennas. The parametrization describes the boundary in terms of a low-dimensional manifold. For the two-user case we show that a single real-valued parameter per user is sufficient to achieve all points on the Pareto boundary and that any point on the Pareto boundary corresponds to beamforming vectors that are linear combinations of the zero-forcing (ZF) and maximum-ratio transmission (MRT) beamformers. We further specialize the results to the MISO broadcast channel (BC). A numerical example illustrates the result.
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paper_title: Competition Versus Cooperation on the MISO Interference Channel

paper_content:

We consider the problem of coordinating two competing multiple-antenna wireless systems (operators) that operate in the same spectral band. We formulate a rate region which is achievable by scalar coding followed by power allocation and beamforming. We show that all interesting points on the Pareto boundary correspond to transmit strategies where both systems use the maximum available power. We then argue that there is a fundamental need for base station cooperation when performing spectrum sharing with multiple transmit antennas. More precisely, we show that if the systems do not cooperate, there is a unique Nash equilibrium which is inefficient in the sense that the achievable rate is bounded by a constant, regardless of the available transmit power. An extension of this result to the case where the receivers use successive interference cancellation (SIC) is also provided. Next we model the problem of agreeing on beamforming vectors as a non-transferable utility (NTU) cooperative gametheoretic problem, with the two operators as players. Specifically we compute numerically the Nash bargaining solution, which is a likely resolution of the resource conflict assuming that the players are rational. Numerical experiments indicate that selfish but cooperating operators may achieve a performance which is close to the maximum-sum-rate bound.
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paper_title: Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design

paper_content:

This paper studies linear transmit filter design for Weighted Sum-Rate (WSR) maximization in the Multiple Input Multiple Output Broadcast Channel (MIMO-BC). The problem of finding the optimal transmit filter is non-convex and intractable to solve using low complexity methods. Motivated by recent results highlighting the relationship between mutual information and Minimum Mean Square Error (MMSE), this paper establishes a relationship between weighted sum-rate and weighted MMSE in the MIMO-BC. The relationship is used to propose a low complexity algorithm for finding a local weighted sum-rate optimum based on alternating optimization. Numerical results studying sum-rate show that the proposed algorithm achieves high performance with few iterations.
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paper_title: Design Guidelines for Limited Feedback in the Spatially Correlated Broadcast Channel

paper_content:

A linear beamformer design for the broadcast channel where the base station is equipped with $N_t$ antennas and signals to $M = 2$ users (each with a single antenna)and where the vector channels are spatially correlated is considered. This problem is of relevance in wireless standardization efforts where two users are simultaneously scheduled (instead of the theoretically feasible $N_t$ user scheduling)to minimize signaling overhead. The users are assumed to have perfect channel state information (CSI), whereas the base station has statistical information of the channels. In the first part of this work, the role of the relevance of feedback is studied via the quantification of the gap in ergodic sum-rate between the perfect CSI and statistics-only extremes. In this direction, the importance of orthogonality of the dominant eigenmodes of the two users in maximizing the gap is established. In the second part of this work, in scenarios with a large gap, limited feedback beamforming codebooks and a codeword selection metric are designed for the low-rate feedback setting. The main contribution here is the proposal of a generalized eigenvector codebook and feedback of the codeword index that maximizes an estimate of the signal-to-interference-and-noise ratio $(\textsf{SINR})$ of each user. Extensions of this scheme are also proposed for the general $N_t$ antenna case with $M$ users, where $M \le N_t$ . It is shown via numerical studies that this scheme leads to significant performance improvement across a large family of channels over schemes such as Grassmannian/Random Vector Quantization/single-user codebooks with the channel projection metric for codeword selection.
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paper_title: 802.11 WLAN: history and new enabling MIMO techniques for next generation standards

paper_content:

IEEE 802.11, which designs wireless local area networks (WLAN), is one of the most successful standards in wireless communication systems. In this article, we review the history of WLAN standards, and provide technical overviews of the recent development of WLAN systems. Especially, as the original inventor and the proposer, we focus on beamforming and compressed feedback schemes, which have been adopted in 802.11 WLAN standards, to improve the throughput for a multiple-input multiple-output (MIMO) system. These techniques are essential to maximize the downlink system throughput for multiple user transmission as well as for single user transmission. Also, we present discussions on new technologies to further enhance user throughput, which are currently considered for future WLAN systems.
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paper_title: Parametrization Based Limited Feedback Design for Correlated MIMO Channels Using New Statistical Models

paper_content:

Parametrization of unitary matrices using Givens rotations has been used for limited feedback in multiple-input multiple-output (MIMO) systems. Feedback based on these rotations has been adopted in IEEE 802.11n and other upcoming standards. However, the probability distributions of Givens rotations is not known for correlated channels, forcing the use of uniform quantization. In this paper, novel probability density function (PDF) models, based on beta and wrapped Cauchy distributions, are proposed for Givens rotations in correlated MIMO channels. Empirical distributions and goodness-of-fit tests show that the proposed distributions characterize the spatial correlation behavior with good accuracy. Moreover, it is shown that the distributions known in the literature for uncorrelated MIMO channels are only special cases. Distributions of Givens rotations are useful to understand the behavior of singular vectors of correlated channels. In this paper, the PDF models are utilized for bit allocation and optimized codebook design. Simulations show that precoding using the proposed codebooks achieves significant performance improvement, in terms of mean square error and sum rate, as compared to using uniform codebooks. It is also shown that the bit allocations proposed in this paper reduce to that of IEEE 802.11n standard when the MIMO channel is not spatially correlated.
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paper_title: On beamforming with finite rate feedback in multiple-antenna systems

paper_content:

We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t-1)2/sup -B/t-1/, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.
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paper_title: On the Capacity of MIMO Broadcast Channels With Partial Side Information

paper_content:

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.
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paper_title: Limited Feedback Design for Interference Alignment on MIMO Interference Networks with Heterogeneous Path Loss and Spatial Correlations

paper_content:

Interference alignment is degree of freedom optimal in K -user MIMO interference channels and many previous works have studied the transceiver designs. However, these works predominantly focus on networks with perfect channel state information at the transmitters and symmetrical interference topology. In this paper, we consider a limited feedback system with heterogeneous path loss and spatial correlations, and investigate how the dynamics of the interference topology can be exploited to improve the feedback efficiency. We propose a novel spatial codebook design, and perform dynamic quantization via bit allocations to adapt to the asymmetry of the interference topology. We bound the system throughput under the proposed dynamic scheme in terms of the transmit SNR, feedback bits and the interference topology parameters. It is shown that when the number of feedback bits scales with SNR as C_{s}\cdot\log\textrm{SNR}, the sum degrees of freedom of the network are preserved. Moreover, the value of scaling coefficient C_{s} can be significantly reduced in networks with asymmetric interference topology.
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paper_title: Opportunistic beamforming using dumb antennas

paper_content:

An important means to cope with fading in wireless channels is the use of diversity. Diversity can be obtained over time (interleaving of coded bits), frequency (combining of multipaths in CDMA systems) and space (multiple antennas). The basic idea is to improve performance by creating several independent signal paths between the transmitter and the receiver. In this paper, we propose a scheme that induces random fading when the environment has little scattering and/or the fading is slow. We focus on the downlink of a cellular system. We use multiple antennas at the base-station to transmit the same signal from each antenna modulated by a gain whose phase and magnitude is changing in time in a controlled but pseudo random fashion.
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paper_title: An overview of limited feedback in wireless communication systems

paper_content:

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
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paper_title: Grassmannian beamforming for multiple-input multiple-output wireless systems

paper_content:

Multiple-input multiple-output (MIMO) wireless systems provides capacity much larger than that provided by traditional single-input single-output (SISO) wireless systems. Beamforming is a low complexity technique that increases the receive signal-to-noise ratio (SNR), however, it requires channel knowledge. Since in practice channel knowledge at the transmitter is difficult to realize, we propose a technique where the receiver designs the beamforming vector and sends it to the transmitter by transmitting a label in a finite set, or codebook, of beamforming vectors. A codebook design method for quantized versions of maximum ratio transmission, equal gain transmission, and generalized selection diversity with maximum ratio combining at the receiver is presented. The codebook design criterion exploits the quantization problem's relationship with Grassmannian line packing. Systems using the beamforming codebooks are shown to have a diversity order of the product of the number of transmit and the number of receive antennas. Monte Carlo simulations compare the performance of systems using this new codebook method with the performance of systems using previously proposed quantized and unquantized systems.
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paper_title: A Unified Approach to QoS-Guaranteed Scheduling for Channel-Adaptive Wireless Networks

paper_content:

Scheduling amounts to allocating optimally channel, rate and power resources to multiple connections with diverse quality-of-service (QoS) requirements. It consti- tutes a throughput-critical task at the medium access control layer of today's wireless networks that has been tackled by seemingly unrelated information-theoretic and protocol design approaches. Capitalizing on convex optimization and stochastic approximation tools, the present paper develops a unified framework for channel-aware QoS-guaranteed scheduling protocols for use in adaptive wireless networks whereby multiple terminals are linked through orthogonal fading channels to an access point, and transmissions are (opportu- nistically) adjusted to the intended channel. The unification encompasses downlink and uplink with time-division or frequency-division duplex operation; full and quantized chan- nel state information comprising a few bits communicated over a limited-rate feedback channel; different types of traffic (best effort, non-real-time, real-time); uniform and optimal power loading; off-line optimal scheduling schemes benchmarking fundamentally achievable rate limits; as well as on-line scheduling algorithms capable of dynamically learning the intended channel statistics and converging to the optimal benchmarks from any initial value. The take-home message offers an important cross-layer design guideline: judiciously developed, yet surprisingly simple, channel-adaptive, on-line schedulers can approach information-theoretic rate limits with QoS guarantees.
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paper_title: MIMO broadcast channels with finite rate feedback

paper_content:

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where the receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. Simple expressions for the capacity degradation due to finite rate feedback as well as the required increases in feedback load per mobile as a function of the number of access point antennas and the system SNR are provided.
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paper_title: Opportunistic Space-Division Multiple Access With Beam Selection

paper_content:

In this paper, a novel transmission technique for the multiple-input multiple-output (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple sets of randomly chosen orthogonal beamforming vectors. Each user sends the index of the best beamforming vector and the corresponding signal-to-interference-plus-noise ratio for that set of orthogonal vectors back to the base station. The base station opportunistically determines the users and corresponding orthogonal vectors that maximize the sum capacity. Based on the capacity expressions, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20% gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100% gain (for a large number of users) over conventional opportunistic beamforming when the number of transmit antennas is four.
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paper_title: Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels

paper_content:

The full diversity gain provided by a multi-antenna channel can be achieved by transmit beamforming and receive combining. This requires the knowledge of channel state information (CSI) at the transmitter which is difficult to obtain in practice. Quantized beamforming where fixed codebooks known at both the transmitter and the receiver are used to quantize the CSI has been proposed to solve this problem. Most recent works focus attention on limited feedback codebook design for the uncorrelated Rayleigh fading channel. Such designs are sub-optimal when used in correlated channels. In this paper, we propose systematic codebook design for correlated channels when channel statistical information is known at the transmitter. This design is motivated by studying the performance of pure statistical beamforming in correlated channels and is implemented by maps that can rotate and scale spherical caps on the Grassmannian manifold. Based on this study, we show that even statistical beamforming is near-optimal if the transmitter covariance matrix is ill-conditioned and receiver covariance matrix is well-conditioned. This leads to a partitioning of the transmit and receive covariance spaces based on their conditioning with variable feedback requirements to achieve an operational performance level in the different partitions. When channel statistics are difficult to obtain at the transmitter, we propose a universal codebook design (also implemented by the rotation-scaling maps) that is robust to channel statistics. Numerical studies show that even few bits of feedback, when applied with our designs, lead to near perfect CSI performance in a variety of correlated channel conditions.
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paper_title: On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

paper_content:

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.
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paper_title: MU-MISO Transmission with Limited Feedback

paper_content:

Downlink multi-user transmission techniques that allow several users to be served simultaneously in frequency and time have been recognized as a promising means to increase system capacity. However they require accurate channel state information (CSI) at the base station (BS) such that appropriate signal processing can be performed to separate multiple users in the space domain. In practice however, CSI cannot be perfectly known to the BS due to the capacity-limited feedback channel in FDD systems for instance. In this letter we investigate multiuser multiple-input single-output (MU-MISO) transmission with limited feedback. In particular we identify the useful information that the BS needs to deal with inter-user interference and a codebook design is derived accordingly. In addition, an adaptive threshold-based feedback approach is proposed, where only users with good feedback quality are allowed to do feedback. It is shown that the adaptive scheme can effectively improve the system performance given a fixed number of feedback bits.
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paper_title: Minimum Codebook Size to Achieve Maximal Diversity Order for RVQ-Based MIMO Systems

paper_content:

Multiple-antenna systems provide both capacity and diversity gains relatively to single-antenna-based networks. These gains rely heavily on the availability of channel state information. In this paper, we assume that the receiver has accurate channel information, which is quantized and fed back to the transmitter. Sufficient conditions for the feedback rate are provided, which guarantee no loss of diversity due to channel quantization. Considering a K × M MIMO system, we show that to achieve a diversity of D = M - K + 1, which is the maximum allowable, a feedback channel with a rate of log2(1 + D) bits per channel use is enough.
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paper_title: Opportunistic Space-Division Multiple Access With Beam Selection

paper_content:

In this paper, a novel transmission technique for the multiple-input multiple-output (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple sets of randomly chosen orthogonal beamforming vectors. Each user sends the index of the best beamforming vector and the corresponding signal-to-interference-plus-noise ratio for that set of orthogonal vectors back to the base station. The base station opportunistically determines the users and corresponding orthogonal vectors that maximize the sum capacity. Based on the capacity expressions, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20% gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100% gain (for a large number of users) over conventional opportunistic beamforming when the number of transmit antennas is four.
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paper_title: An overview of scheduling algorithms in MIMO-based fourth-generation wireless systems

paper_content:

In this article an overview of the scheduling algorithms proposed for fourth-generation multiuser wireless networks based on multiple-input multiple-output technology is presented. In MIMO systems a multi-user diversity gain can be extracted by tracking the channel fluctuations between each user and the base station, and scheduling transmission for the "best" user. Based on this idea, several opportunistic scheduling schemes that attempt to improve global capacity or satisfy users with different QoS requirements have been proposed. Transmit beamforming procedures aimed at increasing the channel fluctuations have been proposed. The simultaneous exploitation of both spatial and multi-user diversity is not straightforward; however, it may be achieved by a refined selection of the "best" user. In addition, a multiple access gain can be obtained from a simple SDMA/TOMA system. Finally, several resource allocation schemes are discussed for this hybrid multiple access system.
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paper_title: Downlink Interference Alignment

paper_content:

We develop an interference alignment (IA) technique for a downlink cellular system. In the uplink, IA schemes need channel-state-information exchange across base-stations of different cells, but our downlink IA technique requires feedback only within a cell. As a result, the proposed scheme can be implemented with a few changes to an existing cellular system where the feedback mechanism (within a cell) is already being considered for supporting multi-user MIMO. Not only is our proposed scheme implementable with little effort, it can in fact provide substantial gain especially when interference from a dominant interferer is significantly stronger than the remaining interference: it is shown that in the two-isolated cell layout, our scheme provides four-fold gain in throughput performance over a standard multi-user MIMO technique. We also show through simulations that our technique provides respectable gain under a more realistic scenario: it gives approximately 28% gain for a 19 hexagonal wrap-around-cell layout. Furthermore, we show that our scheme has the potential to provide substantial gain for macro-pico cellular networks where pico-users can be significantly interfered with by the nearby macro-BS.
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paper_title: Networked MIMO with clustered linear precoding

paper_content:

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination to enhance the sum rate and limited inter-cluster coordination to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.
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paper_title: Multi-Cell MIMO Cooperative Networks: A New Look at Interference

paper_content:

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.
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paper_title: Hierarchical Interference Mitigation for Massive MIMO Cellular Networks

paper_content:

We propose a hierarchical interference mitigation scheme for massive MIMO cellular networks. The MIMO precoder at each base station (BS) is partitioned into an inner precoder and an outer precoder. The inner precoder controls the intra-cell interference and is adaptive to local channel state information (CSI) at each BS (CSIT). The outer precoder controls the inter-cell interference and is adaptive to channel statistics. Such hierarchical precoding structure reduces the number of pilot symbols required for CSI estimation in massive MIMO downlink and is robust to the backhaul latency. We study joint optimization of the outer precoders, the user selection, and the power allocation to maximize a general concave utility which has no closed-form expression. We first apply random matrix theory to obtain an approximated problem with closed-form objective. We show that the solution of the approximated problem is asymptotically optimal with respect to the original problem as the number of antennas per BS grows large. Then using the hidden convexity of the problem, we propose an iterative algorithm to find the optimal solution for the approximated problem. We also obtain a low complexity algorithm with provable convergence. Simulations show that the proposed design has significant gain over various state-of-the-art baselines.
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paper_title: Fast Algorithms and Performance Bounds for Sum Rate Maximization in Wireless Networks

paper_content:

Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying the solutions to two related problems, sum rate maximization using an SIR approximation and max-min weighted SIR optimization. We also show that these two problems can be solved very efficiently, using much faster algorithms than the existing ones in the literature. Furthermore, using a new parameterization of the sum rate maximization problem, we obtain a characterization of the power controlled rate region and its convexity property in various asymptotic regimes. Engineering implications are discussed for IEEE 802.11 networks.
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paper_title: Min-Max Power Allocation in Cellular Networks With Coordinated Beamforming

paper_content:

This paper considers base station (BS) cooperation in the form of coordinated beamforming, focusing on min-max fairness in the power usage subject to target SINR constraints at each single-antenna user. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. In the asymptotic regime where the number of antennas at each BS and that of users in each cell both grow large with their ratio tending to a finite constant, the dimensionality of the optimization problem that needs to be solved is greatly reduced, and only knowledge of statistics is required to solve it. The optimal solution is characterized in general, and an algorithm is proposed that converges to the optimal transmit parameters, for feasible SINR targets. For the two cell case, a simple single parameter characterization is obtained. These asymptotic results provide insights into the average performance, as well as simple but efficient beamforming strategies for the finite system case. In particular, the asymptotically optimal beamformers only require the BSs to have local instantaneous channel state information; the remaining parameters of the beamformers can be calculated using channel statistics, thereby reducing the channel state information estimation and signaling overhead.
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Survey of Large-Scale MIMO Systems

paper_content:

The escalating teletraffic growth imposed by the proliferation of smartphones and tablet computers outstrips the capacity increase of wireless communications networks. Furthermore, it results in substantially increased carbon dioxide emissions. As a powerful countermeasure, in the case of full-rank channel matrices, MIMO techniques are potentially capable of linearly increasing the capacity or decreasing the transmit power upon commensurately increasing the number of antennas. Hence, the recent concept of large-scale MIMO (LS-MIMO) systems has attracted substantial research attention and been regarded as a promising technique for next-generation wireless communications networks. Therefore, this paper surveys the state of the art of LS-MIMO systems. First, we discuss the measurement and modeling of LS-MIMO channels. Then, some typical application scenarios are classified and analyzed. Key techniques of both the physical and network layers are also detailed. Finally, we conclude with a range of challenges and future research topics.
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paper_title: ⋄ Convex Optimization,

paper_content:

Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.
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paper_title: Downlink Cellular Interference Alignment

paper_content:

Cellular networks have been notoriously interference-limited systems in dense urban areas, where base stations are deployed in close proximity to one-another. Recently, a signal processing method called Interference Alignment has emerged, making use of the increasing signal dimensions available in the system through multiple-input multiple output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) technologies. In this report, we review the state of the art of interference alignment since its foundation, and we detail algorithms and baseline comparisons to make when applying interference alignment schemes to downlink cellular networks. We also propose a number of research directions of interest which are not yet answered in the current literature.
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paper_title: Linear Precoding and Equalization for Network MIMO with Partial Cooperation

paper_content:

A cellular multiple-input-multiple-output (MIMO) downlink system is studied, in which each base station (BS) transmits to some of the users so that each user receives its intended signal from a subset of the BSs. This scenario is referred to as network MIMO with partial cooperation since only a subset of the BSs is able to coordinate their transmission toward any user. The focus of this paper is on the optimization of linear beamforming strategies at the BSs and at the users for network MIMO with partial cooperation. Individual power constraints at the BSs are enforced, along with constraints on the number of streams per user. It is first shown that the system is equivalent to a MIMO interference channel with generalized linear constraints (MIMO-IFC-GC). The problems of maximizing the sum rate (SR) and minimizing the weighted sum mean square error (WSMSE) of the data estimates are nonconvex, and suboptimal solutions with reasonable complexity need to be devised. Based on this, suboptimal techniques that aim at maximizing the SR for the MIMO-IFC-GC are reviewed from recent literature and extended to the MIMO-IFC-GC where necessary. Novel designs that aim at minimizing the WSMSE are then proposed. Extensive numerical simulations are provided to compare the performance of the considered schemes for realistic cellular systems.
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paper_title: Egoistic vs. altruistic beamforming in multi-cell systems with feedback and back-haul delays

paper_content:

Base station cooperation is an attractive technique to increase the spectral efficiency of multi-cell systems. One of the challenges in multi-cell systems is obtaining accurate channel state information (CSI) at the base station. One source of CSI inaccuracy is the delay incurred in obtaining CSI and exchanging it among base stations. The presence of delay is inevitable when CSI is exchanged over the back-haul. In addition, CSI is commonly obtained using limited feedback techniques which further contribute to its inaccuracy. In this paper, we re-visit the comparison between competitive (egoistic) and cooperative (altruistic) beamforming strategies in the presence of imperfect CSI. The impact of CSI inaccuracy due to delay and finite codebook size on the achieved sum rate is analyzed. Closed-form expressions for a lower bound and a first-order approximation of the average sum rates achieved by these beamforming strategies are derived. Using the closed-form expressions, a mode switching criterion is proposed to switch between competitive and cooperative beamforming based on the signal-to-noise ratio (SNR), delay, Doppler frequency and codebook size. It is shown that competitive beamforming is preferred in the limit of low SNR irrespective of the quality of CSI, while cooperative beamforming is preferred only at high SNR and low Doppler frequencies, confirming that base station cooperation is not always advantageous.
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paper_title: Cooperative Multicell Precoding: Rate Region Characterization and Distributed Strategies With Instantaneous and Statistical CSI

paper_content:

Base station cooperation is an attractive way of increasing the spectral efficiency in multiantenna communication. By serving each terminal through several base stations in a given area, intercell interference can be coordinated and higher performance achieved, especially for terminals at cell edges. Most previous work in the area has assumed that base stations have common knowledge of both data dedicated to all terminals and full or partial channel state information (CSI) of all links. Herein, we analyze the case of distributed cooperation where each base station has only local CSI, either instantaneous or statistical. In the case of instantaneous CSI, the beamforming vectors that can attain the outer boundary of the achievable rate region are characterized for an arbitrary number of multiantenna transmitters and single-antenna receivers. This characterization only requires local CSI and justifies distributed precoding design based on a novel virtual signal-to-interference noise ratio (SINR) framework, which can handle an arbitrary SNR and achieves the optimal multiplexing gain. The local power allocation between terminals is solved heuristically. Conceptually, analogous results for the achievable rate region characterization and precoding design are derived in the case of local statistical CSI. The benefits of distributed cooperative transmission are illustrated numerically, and it is shown that most of the performance with centralized cooperation can be obtained using only local CSI.
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paper_title: A novel distributed power allocation scheme for coordinated multicell systems

paper_content:

Coordination between base stations (BSs) is a promising solution for cellular wireless systems to mitigate intercell interference, improving system fairness, and increasing capacity in the years to come. The aim of this manuscript is to propose a new distributed power allocation scheme for the downlink of distributed precoded multicell MISO-OFDM systems. By treating the multicell system as a superposition of single cell systems we define the average virtual bit error rate (BER) of one single-cell system, allowing us to compute the power allocation in a distributed manner at each BS. The precoders are designed in two phases: first the precoder vectors are computed in a distributed manner at each BS considering two criteria, distributed zero-forcing and virtual signal-to-interference noise ratio; then the system is optimized through distributed power allocation with per-BS power constraint. The proposed power allocation scheme minimizes the average virtual BER over all user terminals and the available subcarriers. Both the precoder vectors and the power allocation are computed by assuming that the BSs have only knowledge of local channel state information. The performance of the proposed scheme is compared against other power allocation schemes that have recently been proposed for precoded multicell systems based on LTE specifications. The results also show that although our power allocation scheme is based on the minimization of the virtual uncoded BER, it also has significant gains in coded systems.
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paper_title: Joint Beamforming and Power Control in Coordinated Multicell: Max-Min Duality, Effective Network and Large System Transition

paper_content:

This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signal-to-interference-plus-noise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear Perron-Frobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear Perron-Frobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: Joint Spatial Division and Multiplexing—The Large-Scale Array Regime

paper_content:

We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink/downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users.
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

paper_content:

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: Optimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure

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Transmit beamforming is a versatile technique for signal transmission from an array of antennas to one or multiple users [1]. In wireless communications, the goal is to increase the signal power at the intended user and reduce interference to nonintended users. A high signal power is achieved by transmitting the same data signal from all antennas but with different amplitudes and phases, such that the signal components add coherently at the user. Low interference is accomplished by making the signal components add destructively at nonintended users. This corresponds mathematically to designing beamforming vectors (that describe the amplitudes and phases) to have large inner products with the vectors describing the intended channels and small inner products with nonintended user channels.
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paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

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This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
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paper_title: On the Capacity of MIMO Broadcast Channels With Partial Side Information

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In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.
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paper_title: Coordinated multipoint transmission and reception in LTE-advanced: deployment scenarios and operational challenges

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3GPP has completed a study on coordinated multipoint transmission and reception techniques to facilitate cooperative communications across multiple transmission and reception points (e.g., cells) for the LTE-Advanced system. In CoMP operation, multiple points coordinate with each other in such a way that the transmission signals from/to other points do not incur serious interference or even can be exploited as a meaningful signal. The goal of the study is to evaluate the potential performance benefits of CoMP techniques and the implementation aspects including the complexity of the standards support for CoMP. This article discusses some of the deployment scenarios in which CoMP techniques will likely be most beneficial and provides an overview of CoMP schemes that might be supported in LTE-Advanced given the modern silicon/DSP technologies and backhaul designs available today. In addition, practical implementation and operational challenges are discussed. We also assess the performance benefits of CoMP in these deployment scenarios with traffic varying from low to high load.
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paper_title: 4G: LTE/LTE-Advanced for Mobile Broadband

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Based on the bestseller "3G Evolution - HSPA and LTE for mobile broadband" and reflecting the ongoing success of LTE throughout the world, this book focuses on LTE with full updates including LTE-Advanced to provide a complete picture of the LTE system. Overview and detailed explanations are given for the latest LTE standards for radio interface architecture, the physical layer, access procedures, broadcast, relaying, spectrum and RF characteristics, and system performance. Key technologies presented include multi-carrier transmission, advanced single-carrier transmission, advanced receivers, OFDM, MIMO and adaptive antenna solutions, advanced radio resource management and protocols, and different radio network architectures. Their role and use in the context of mobile broadband access in general is explained. Both a high-level overview and more detailed step-by-step explanations of the LTE/LTE-Advanced implementation are given. An overview of other related systems such as GSM/EDGE, HSPA, CDMA2000, and WIMAX is also provided. This book is a 'must-have' resource for engineers and other professionals in the telecommunications industry, working with cellular or wireless broadband technologies, giving an understanding of how to utilize the new technology in order to stay ahead of the competition. The authors of the book all work at Ericsson Research and have been deeply involved in 3G and 4G development and standardisation since the early days of 3G research. They are leading experts in the field and are today still actively contributing to the standardisation of LTE within 3GPP. Includes full details of the latest additions to the LTE Radio Access standards and technologies up to and including 3GPP Release 10Clear explanations of the role of the underlying technologies for LTE, including OFDM and MIMO Full coverage of LTE-Advanced, including LTE carrier aggregation, extended multi-antenna transmission, relaying functionality and heterogeneous deploymentsLTE radio interface architecture, physical layer, access procedures, MBMS, RF characteristics and system performance covered in detail
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paper_title: Adaptive Modulation in PU2RC Systems with Finite Rate Feedback

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This paper addresses a per user unitary precoding and rate control (PU 2 RC) system with adaptive multi-level quadrature amplitude modulation (QAM) modulation, where both the PU 2 RC operation and adaptive modulation are based on finite rate feedback. The system supports two transmission modes (single user transmit beamforming and multiuser transmission with orthogonal beamforming), and switches between the two modes to maximize the average throughput. We first study single user transmit beamforming, and derive closed-form expressions for the average throughput and bit-error rate (BER) with outdated channel information. Then, multiuser transmission with orthogonal beamforming is investigated. We analyze the throughput and BER performance without feedback delay in the normal signal noise ratio (SNR) regime, and the performance with feedback delay in the interference-limited regime. Simulation results demonstrate the effect of time delay, and the preferred regions of the single user transmission mode and multiuser transmission mode.
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paper_title: Recent trend of multiuser MIMO in LTE-advanced

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Recently, the mobile communication industry is moving rapidly toward Long Term Evolution, or LTE, systems. The leading carriers and vendors are committed to launching LTE service in the near future; in fact, a number of major operators such as Verizon have initiated LTE service already. LTE aims to provide improved service quality over 3G systems in terms of throughput, spectral efficiency, latency, and peak data rate, and the MIMO technique is one of the key enablers of the LTE system for achieving these diverse goals. Among several operational modes of MIMO, multiuser MIMO (MU-MIMO), in which the base station transmits multiple streams to multiple users, has received much attention as a way of achieving improvement in performance. From the initial release (Rel. 8) to the recent release (Rel. 10), so called LTE-Advanced, MUMIMO techniques have evolved from their premature form to a more elaborate version. In this article, we provide an overview of design challenges and the specific solutions for MU-MIMO systems developed in the LTE-Advanced standard.
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paper_title: MIMO broadcast channels with finite rate feedback

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Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where the receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. Simple expressions for the capacity degradation due to finite rate feedback as well as the required increases in feedback load per mobile as a function of the number of access point antennas and the system SNR are provided.
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paper_title: Performance of Orthogonal Beamforming for SDMA With Limited Feedback

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On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.
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paper_title: Learning-Based Adaptive Transmission for Limited Feedback Multiuser MIMO-OFDM

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Performing link adaptation in a multiantenna and multiuser system is challenging because of the coupling between precoding, user selection, spatial mode selection and use of limited feedback about the channel. The problem is exacerbated by the difficulty of selecting the proper modulation and coding scheme when using orthogonal frequency division multiplexing (OFDM). This paper presents a data-driven approach to link adaptation for multiuser multiple input mulitple output (MIMO) OFDM systems. A machine learning classifier is used to select the modulation and coding scheme, taking as input the SNR values in the different subcarriers and spatial streams. A new approximation is developed to estimate the unknown interuser interference due to the use of limited feedback. This approximation allows to obtain SNR information at the transmitter with a minimum communication overhead. A greedy algorithm is used to perform spatial mode and user selection with affordable complexity, without resorting to an exhaustive search. The proposed adaptation is studied in the context of the IEEE 802.11ac standard, and is shown to schedule users and adjust the transmission parameters to the channel conditions as well as to the rate of the feedback channel.
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paper_title: Matrix Algebra: Theory, Computations, and Applications in Statistics

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Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
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paper_title: 802.11 WLAN: history and new enabling MIMO techniques for next generation standards

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IEEE 802.11, which designs wireless local area networks (WLAN), is one of the most successful standards in wireless communication systems. In this article, we review the history of WLAN standards, and provide technical overviews of the recent development of WLAN systems. Especially, as the original inventor and the proposer, we focus on beamforming and compressed feedback schemes, which have been adopted in 802.11 WLAN standards, to improve the throughput for a multiple-input multiple-output (MIMO) system. These techniques are essential to maximize the downlink system throughput for multiple user transmission as well as for single user transmission. Also, we present discussions on new technologies to further enhance user throughput, which are currently considered for future WLAN systems.
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paper_title: MU-MIMO MAC Protocols for Wireless Local Area Networks: A Survey

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As wireless devices boom and bandwidth-hungry applications (e.g., video and cloud uploading) get popular, today's wireless local area networks (WLANs) become not only crowded but also stressed at throughput. Multiuser multiple-input–multiple-output (MU-MIMO), an advanced form of MIMO, has gained attention due to its huge potential in improving the performance of WLANs. This paper surveys random access-based medium access control (MAC) protocols for MU-MIMO-enabled WLANs. It first provides background information about the evolution and the fundamental MAC schemes of IEEE 802.11 Standards and Amendments, and then identifies the key requirements of designing MU-MIMO MAC protocols for WLANs. After this, the most representative MU-MIMO MAC proposals in the literature are overviewed by benchmarking their MAC procedures and examining the key components, such as the channel state information acquisition, decoding/precoding, and scheduling schemes. Classifications and discussions on important findings of the surveyed MAC protocols are provided, based on which, the research challenges for designing effective MU-MIMO MAC protocols, as well as the envisaged MAC's role in the future heterogeneous networks, are highlighted.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

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A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: IEEE 802.11ac: from channelization to multi-user MIMO

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The IEEE 802.11ac amendment has been proposed to enhance the throughput of IEEE 802.11n beyond gigabit-per-second rates. In this article we present an overview of the most important features proposed in the 802.11ac amendment, including channel bonding mechanisms and multi-user MIMO.
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paper_title: User scheduling for massive MIMO OFDMA systems with hybrid analog-digital beamforming

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This paper proposes a new user scheduling and sub-carrier allocation algorithm for multiuser downlink massive multiple input multiple output (MIMO) orthogonal frequency division multiple access (OFDMA) systems with hybrid analogdigital beamforming (HB). We assume that the transmitter having N antennas is serving K i decentralized single antenna receivers by sub-carrier i. The scheduling algorithm leverages the solutions of the digital beamforming (DB) result and is designed to maximize the total sum rate of all sub-carriers under per carrier power constraint. For this system and problem setup, the proposed algorithm is explained as follows: First, we express the HB matrix of sub-carrier i as a product of AB i , where the high dimensional matrix A ∈ CN×Na is common to all subcarriers whereas, B i ∈ CNa×Ki is a low dimensional matrix which is designed for sub-carrier i, and Na is the number of RF chains satisfying N ≥ Na ≥ K i . Second, we compute A as the first Na eigenvectors of the left singular value decomposition of the combined DB precoder matrices of sub-carriers having the highest sum rate. Finally, for fixed A, we compute Bi and its corresponding users such that the total sum rate of all sub-carriers is maximized. The performance of the proposed scheduling is studied analytically. Furthermore, the superiority of the proposed algorithm over that of the existing one is quantified analytically and demonstrated by computer simulations.
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paper_title: Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems

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Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks, as it offers orders of magnitude greater spectrum than current cellular bands. In contrast to conventional multiple-input–multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.
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paper_title: An Overview of Massive MIMO: Benefits and Challenges

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Massive multiple-input multiple-output (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of state-of-the-art research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of non-orthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient single-carrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.
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paper_title: Spatially Sparse Precoding in Millimeter Wave MIMO Systems

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Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications. MmWave systems must therefore leverage large antenna arrays, made possible by the decrease in wavelength, to combat pathloss with beamforming gain. Beamforming with multiple data streams, known as precoding, can be used to further improve mmWave spectral efficiency. Both beamforming and precoding are done digitally at baseband in traditional multi-antenna systems. The high cost and power consumption of mixed-signal devices in mmWave systems, however, make analog processing in the RF domain more attractive. This hardware limitation restricts the feasible set of precoders and combiners that can be applied by practical mmWave transceivers. In this paper, we consider transmit precoding and receiver combining in mmWave systems with large antenna arrays. We exploit the spatial structure of mmWave channels to formulate the precoding/combining problem as a sparse reconstruction problem. Using the principle of basis pursuit, we develop algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware. We present numerical results on the performance of the proposed algorithms and show that they allow mmWave systems to approach their unconstrained performance limits, even when transceiver hardware constraints are considered.
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paper_title: Low RF-Complexity Technologies for 5G Millimeter-Wave MIMO Systems with Large Antenna Arrays

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Millimeter-wave (mmWave) MIMO with large antenna array has attracted considerable interests from academic and industry, as it can simultaneously provide wider bandwidth and higher spectrum efficiency. However, with hundreds of antennas employed at mmWave frequencies, the number of radio frequency (RF) chains required by mmWave MIMO is also huge, leading to unaffordable hardware cost and energy consumption in practice. In this paper, we review low RFcomplexity technologies to solve this bottleneck in mmWave MIMO systems.We first describe the evolution of low RF-complexity technologies from cellular frequencies to mmWave frequencies. Then, we discuss two attractive low RF-complexity technologies for mmWave MIMO systems in detail, i.e., hybrid precoding and beamspace MIMO, including their fundamental principles, application advantages, and design challenges. We compare the performance of these two low RF-complexity technologies to draw some insights about how they should be employed in practical mmWave MIMO systems. Finally, we conclude this paper by highlighting the potential opportunities in this emerging research direction.
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paper_title: Massive MIMO Systems with Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits

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The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.
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paper_title: On the Number of RF Chains and Phase Shifters, and Scheduling Design With Hybrid Analog–Digital Beamforming

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This paper considers hybrid beamforming (HB) for downlink multiuser massive multiple-input multiple-output (MIMO) systems with frequency selective channels. The proposed HB design employs sets of digitally controlled phase (fixed phase) paired phase shifters (PSs) and switches. For this system, first we determine the required number of radio frequency (RF) chains and PSs such that the proposed HB achieves the same performance as that of the digital beamforming (DB) which utilizes $N$ (number of transmitter antennas) RF chains. We show that the performance of the DB can be achieved with our HB just by utilizing $r_t$ RF chains and $2r_t(N-r_t + \text{1})$ PSs, where $r_t \leq N$ is the rank of the combined digital precoder matrices of all subcarriers. Second, we provide a simple and novel approach to reduce the number of PSs with only a negligible performance degradation. Numerical results reveal that only ${20}{-}{40}$ PSs per RF chain are sufficient for practically relevant parameter settings. Finally, for the scenario where the deployed number of RF chains $(N_a) $ is less than $r_t$ , we propose a simple user scheduling algorithm to select the best set of users in each subcarrier. Simulation results validate theoretical expressions, and demonstrate the superiority of the proposed HB design over the existing HB designs in both flat fading and frequency selective channels.
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paper_title: Hybrid Digital and Analog Beamforming Design for Large-Scale Antenna Arrays

paper_content:

The potential of using of millimeter wave (mmWave) frequency for future wireless cellular communication systems has motivated the study of large-scale antenna arrays for achieving highly directional beamforming. However, the conventional fully digital beamforming methods which require one radio frequency (RF) chain per antenna element is not viable for large-scale antenna arrays due to the high cost and high power consumption of RF chain components in high frequencies. To address the challenge of this hardware limitation, this paper considers a hybrid beamforming architecture in which the overall beamformer consists of a low-dimensional digital beamformer followed by an RF beamformer implemented using analog phase shifters. Our aim is to show that such an architecture can approach the performance of a fully digital scheme with much fewer number of RF chains. Specifically, this paper establishes that if the number of RF chains is twice the total number of data streams, the hybrid beamforming structure can realize any fully digital beamformer exactly, regardless of the number of antenna elements. For cases with fewer number of RF chains, this paper further considers the hybrid beamforming design problem for both the transmission scenario of a point-to-point multiple-input multiple-output (MIMO) system and a downlink multi-user multiple-input single-output (MU-MISO) system. For each scenario, we propose a heuristic hybrid beamforming design that achieves a performance close to the performance of the fully digital beamforming baseline. Finally, the proposed algorithms are modified for the more practical setting in which only finite resolution phase shifters are available. Numerical simulations show that the proposed schemes are effective even when phase shifters with very low resolution are used.
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paper_title: Beamforming for Millimeter Wave Communications: An Inclusive Survey

paper_content:

The remarkable growth of wireless data traffic in recent times has driven the need to explore suitable regions in the radio spectrum to meet the projected requirements. In pursuance of this, millimeter wave communications have received considerable attention in the research fraternity. Due to the high path and penetration losses at millimeter wavelengths, antenna beamforming assumes a pivotal role in establishing and maintaining a robust communication link. Beamforming for millimeter wave communications poses a multitude of diverse challenges due to the large channel bandwidth, unique channel characteristics, and hardware constraints. In this paper, we track the evolution and advancements in antenna beamforming for millimeter wave communications in the context of the distinct requirements for indoor and outdoor communication scenarios. We expand the scope of discussion by including the developments in radio frequency system design and implementation for millimeter wave beamforming. We explore the suitability of millimeter wave beamforming methods, both, existing and proposed till midyear 2015, and identify the exciting new prospects unfolding in this domain.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: CoMP-CSB for ICI Nulling with User Selection

paper_content:

The capacity of downlink multiple-input multiple-output (MIMO) cellular networks is significantly limited by inter-cell interference (ICI), particularly at cell boundaries. Recently, two types of coordinated multiple point transmission (CoMP) technologies, joint processing and transmission (JPT) and coordinated scheduling and beamforming (CSB), were proposed. These technologies are intended for the latest cellular communication standard in order to improve the performance of cell-edge users who suffer from significant ICI. In this paper, we propose an ICI cancellation technique based on a user selection algorithm for CoMP-CSB. Under partial channel state information (CSI) and no data sharing condition, each base station (BS) concentrates more on the direction of interference to the adjacent cell's users, during the user selection process. Unlike prior concepts for a single-cell environment, in which each BS generates a precoding matrix for selected users to be served, the proposed technique considers the effects of interference to users located in adjacent cells. Although there are obvious trade-offs between ICI mitigation and the number of simultaneous scheduled users in terms of system capacity, the simulation results demonstrate that our proposed algorithm achieves higher sector throughput and is more robust against ICI if the system is limited by interference. Furthermore, through simulation we are able to obtain the preferred option for the coordination distance (R) and the number of degrees of freedom for ICI nulling (ξ).
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paper_title: Constructive Interference in Linear Precoding Systems: Power Allocation and User Selection

paper_content:

The exploitation of interference in a constructive manner has recently been proposed for the downlink of multiuser, multi-antenna transmitters. This novel linear precoding technique, herein referred to as constructive interference zero forcing (CIZF) precoding, has exhibited substantial gains over conventional approaches; the concept is to cancel, on a symbol-by-symbol basis, only the interfering users that do not add to the intended signal power. In this paper, the power allocation problem towards maximizing the performance of a CIZF system with respect to some metric (throughput or fairness) is investigated. What is more, it is shown that the performance of the novel precoding scheme can be further boosted by choosing some of the constructive multiuser interference terms in the precoder design. Finally, motivated by the significant effect of user selection on conventional, zero forcing (ZF) precoding, the problem of user selection for the novel precoding method is tackled. A new iterative, low complexity algorithm for user selection in CIZF is developed. Simulation results are provided to display the gains of the algorithm compared to known user selection approaches.
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paper_title: User selection and power schedule for downlink non-orthogonal multiple access (NOMA) system

paper_content:

As a promising multiple access techniques for 5th generation (5G) wireless systems, non-orthogonal multiple access (NOMA) has received many attentions recently. In this paper, we study the NOMA based downlink multi-user beamforming system, where the base station (BS) tries to transmit information to multiple user clusters and each beam serves one user cluster compromising of two users simultaneously. User selection algorithm is proposed to reduce the interference and improve the system information rate. Moreover, we also provide the user power schedule scheme to guarantee the advantage of the proposed NOMA downlink multi-user beamforming system. Simulation results show that the proposed user selection algorithm and the power schedule scheme can improve the sum-rate of NOMA based downlink multi-user system.
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paper_title: On the achievable throughput of a multiantenna Gaussian broadcast channel

paper_content:

A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j<i is taken into account by coding for noncausally known interference. Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR). We conclude by providing some numerical results for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.
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paper_title: Matrix Algebra: Theory, Computations, and Applications in Statistics

paper_content:

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
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paper_title: Scheduling for Multiuser MIMO Broadcast Systems: Transmit or Receive Beamforming?

paper_content:

In this paper, we present an approximation formula and the close-form expression for the sum rate of the transmit and the receive zero-forcing (ZF) multiple-input multiple-output (MIMO) broadcast systems with user selection, respectively. Instead of assuming a large number of users to obtain a scaling law as most current work, we derive the sum rate formulas of the ZF MIMO broadcast systems with a small number of scheduled users. By analysis and simulations, we find that when taking the variations of feedback channel into account, the receive ZF MIMO broadcast system is more robust to feedback errors and can deliver equal or even higher sum rate than the transmit ZF MIMO broadcast system. We discuss whether a feedback channel is suitable to send channel state information (CSI) for calculating transmit antenna beamforming weights, or suitable to send CSI for selecting users in the receive ZF MIMO broadcast system. Our results show that as the variation of feedback channel errors increases from 0.5 to 1.5, the receive ZF 3 × 3 MIMO broadcast system can provide 36% to 116% higher sum rate than the transmit ZF 3 × 3 MIMO broadcast system in the case of 20 users at signal to noise ratio (SNR) equal to 20 dB. Providing that more feedback bandwidth and an error-free feedback channel are available, the transmit ZF MIMO broadcast system can achieve higher sum rate than the receive ZF MIMO broadcast system.
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paper_title: An Overview of Massive MIMO: Benefits and Challenges

paper_content:

Massive multiple-input multiple-output (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of state-of-the-art research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of non-orthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient single-carrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.
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paper_title: Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

paper_content:

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.
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paper_title: Sum Rates, Rate Allocation, and User Scheduling for Multi-User MIMO Vector Perturbation Precoding

paper_content:

This paper considers the multiuser multiple-input multiple-output (MIMO) broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via vector perturbation. We derive expressions for the sum rate in terms of the average energy of the precoded vector, and use this to derive a high signal-to-noise ratio (SNR) closed-form upper bound, which we show to be tight via simulation. We also propose a modification to vector perturbation where different rates can be allocated to different users. We conclude that for vector perturbation precoding most of the sum rate gains can be achieved by reducing the rate allocation problem to the user selection problem. We then propose a low-complexity user selection algorithm that attempts to maximize the high-SNR sum rate upper bound. Simulations show that the algorithm outperforms other user selection algorithms of similar complexity.
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paper_title: Two-Phase Multiuser Scheduling for Multiantenna Downlinks Exploiting Reduced Finite-Rate Feedback

paper_content:

This paper considers a multiantenna system with an M -antenna base station and K single antenna users, employing zero-forcing beamforming (ZFBF) and a finite-rate feedback strategy. We study scheduling to select KS users for transmit beamforming. To reduce the feedback requirement, we propose a two-phase scheduling scheme that exploits quantized channel direction information (CDI) from only a small subset of the overall users, as well as a 1-bit signal-to-interference-plus-noise ratio (SINR) indicator feedback per user. In the proposed scheme, we introduce a newly defined expression for evaluating SINR that extends the existing SINR approximation for KS = M to a more general case with arbitrary KS ? M. Asymptotic analysis reveals that the proposed two-phase scheduling is asymptotically optimal for large user numbers. Through numerical simulations, we also show that the proposed scheme requires less feedback than conventional schemes, whereas the resulting sum rate loss due to the reduced feedback is negligible. Moreover, we find that the choice of KS < M, instead of a full-multiplexing case with KS = M, for scheduling may achieve a better tradeoff between performance and feedback requirement in systems where fewer bits are utilized for feeding back CDI.
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paper_title: Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization

paper_content:

Block diagonalization (BD) is a preceding technique that eliminates inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. With the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission, the number of simultaneously supportable users with BD is limited by the ratio of the number of basestation transmit antennas to the number of user receive antennas. In a downlink MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput The brute-force search for the optimal user set, however, is computationally prohibitive. We propose two low-complexity suboptimal user selection algorithms for multiuser MIMO systems with BD. Both algorithms aim to select a subset of users such that the total throughput is nearly maximized. The first user selection algorithm greedily maximizes the total throughput, whereas the criterion of the second algorithm is based on the channel energy. We show that both algorithms have linear complexity in the total number of users and achieve around 95% of the total throughput of the complete search method in simulations
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paper_title: Null space learning in cooperative MIMO cellular networks using interference feedback

paper_content:

Cooperative Multi-Point is a technology for improved spectrum utilization where a group of neighboring base stations coordinate their transmissions. However, the performance gain is severely degraded due to out-of-group interference. We propose simple schemes for null space learning and tracking of the interference channel between a terminal and an interfering base station group, whose only required network information is the interference levels at the terminal. In the proposed schemes, the interfering base station group transmits a sequence of learning signals which inflict low interference on a terminal of a neighboring group. The schemes utilize the fact that each terminal normally measures its interference levels and feeds them back to its serving base stations. Then, the serving group distributes this information to the interfering group, from which it learns the null space of the interfering channel. The proposed algorithms do not affect the transmission protocol between the terminal and the serving base stations, and do not add any signaling to the control channel between them. Each terminal communicates only with its serving group and treats the learning signals of the interfering group as noise.
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paper_title: Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

paper_content:

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

paper_content:

In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

paper_content:

In this paper, we tackle the problem of semidistributed user selection with distributed linear precoding for sum-rate maximization in multiuser multicell systems. A set of adjacent base stations (BSs) forms a cluster to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling, and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to nonintended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, namely, distributed zero forcing and distributed virtual signal-to-interference-plus-noise ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First, we investigate how the signal-to-noise ratio regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the BSs.
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paper_title: Iterative Precoder Design and User Scheduling for Block-Diagonalized Systems

paper_content:

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices.
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paper_title: Utilizing the Spatial Information Provided by Channel Norm Feedback in SDMA Systems

paper_content:

To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.
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paper_title: On the user selection for MIMO broadcast channels

paper_content:

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.
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paper_title: Maximum product of effective channel gains: an innovative user selection algorithm for downlink multi-user multiple input and multiple output

paper_content:

Recently, zero-forcing beamforming has been widely used for multiple-input and multiple-output broadcast channels, because it could provide suboptimal capacity with low complexity. To increase the sum data rate, a good user selection algorithm is attractive. In this paper, a new user selection algorithm named maximum product of effective channel gains is presented. The proposed algorithm is described mathematically, and the lower bound of the sum capacity is demonstrated to be proportional to the product of effective channel gains. Our simulation results show that maximum product of effective channel gains can achieve higher sum rate compared with the classical algorithm, semi-orthogonal user selection, with the same complexity order, especially when the signal-to-noise ratio is high; in addition, the complexity of the proposed algorithm is superior to minimum of the Frobenius norm of the pseudo-inverse algorithm. Meanwhile, the number of users that can be served simultaneously is equal to the number of transmission antennas, which is the maximum performance that can be achieved.Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: Adaptive downlink multi-user MIMO wireless systems for correlated channels with imperfect CSI

paper_content:

Multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. However the capacity increase is limited when the number of antennas at the receiver is fixed or restricted (due to mobile size constraints for example). To overcome this limitation multi-user MIMO can be used, which allows several users to be served simultaneously in frequency and time. A disadvantage of these multi-user MIMO systems, when used in the downlink however, is that they need accurate channel state information (CSI) at the transmitter and also uncorrelated channels among users. In this paper we investigate methods to address the problems of multi-user MIMO systems in spatially correlated channels. We adopt the concept of angle between subspaces to characterize the inter-user spatial correlation and adapt the algorithm to those conditions. We also investigate the impact of the accuracy of CSI at the transmitter (CSIT) and whether more limited CSI such as channel correlation information alone can be used to provide good multi-user MIMO performance. Results are presented as various simulated capacity measures and we use them to make comparisons between the various multi-user MIMO configurations
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paper_title: Capacity Maximization for Zero-Forcing MIMO-OFDMA Downlink Systems with Multiuser Diversity

paper_content:

This paper considers the optimal resource allocation for a multiuser MIMO-OFDMA downlink system using zero-forcing SDMA, with the objective of maximizing the system capacity. We provide the general mathematical formulation of the capacity maximization problem whose resource allocation includes user selection, power allocation and receive signal subspace selection. While the optimal solution of this problem is difficult to obtain, we consider two special cases: user selection based only and antenna selection based only optimization, and develop the optimal solution by reformulating the combinatorial optimization problem into a convex problem. Our proposed algorithms for these special cases can be extended to develop a suboptimal algorithm for the original general optimization problem which allows subspace selection. Moreover, we develop reduced-complexity algorithms for these problems which incur negligible capacity loss. Numerical results and analysis are provided to evaluate the system capacity and to study the effect of the number of users and the receive antennas per user on the performance. Comparisons on the capacity achieved by user selection only, antenna selection only and suboptimal subspace selection are discussed
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paper_title: Eigen-Based Transceivers for the MIMO Broadcast Channel with Semi-Orthogonal User Selection

paper_content:

This paper studies the sum rate performance of two low complexity eigenmode-based transmission techniques for the MIMO broadcast channel, employing greedy semi-orthogonal user selection (SUS). The first approach, termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first employ new analytical methods to prove that as the number of users K grows large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that the average sum rates of both techniques converge to the average sum capacity of the MIMO broadcast channel for large K. In addition to the asymptotic analysis, we investigate the sum rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS has significant performance advantages. Our results also provide key insights into the benefit of multiple receive antennas, and the effect of the SUS algorithm. In particular, we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second-order behavior of the multi-user diversity gain; for finite K, the benefit can be very significant. We also show the interesting result that the semi-orthogonality constraint imposed by SUS, whilst facilitating a very low complexity user selection procedure, asymptotically does not reduce the multi-user diversity gain in either first (log K) or second-order (loglog K) terms.
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paper_title: Order Statistics in Wireless Communications: Diversity, Adaptation, and Scheduling in MIMO and OFDM Systems

paper_content:

Covering fundamental principles through to practical applications, this self-contained guide describes indispensable mathematical tools for the analysis and design of advanced wireless transmission and reception techniques in MIMO and OFDM systems. The analysis-oriented approach develops a thorough understanding of core concepts and discussion of various example schemes shows how to apply these concepts in practice. The book focuses on techniques for advanced diversity combining, channel adaptive transmission and multiuser scheduling, the foundations of future wireless systems for the delivery of highly spectrum-efficient wireless multimedia services. Bringing together conventional and novel results from a wide variety of sources, it will teach you to accurately quantify trade-offs between performance and complexity for different design options so that you can determine the most suitable design choice based on your specific practical implementation constraints.
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paper_title: Enhanced multiuser random beamforming: dealing with the not so large number of users case

paper_content:

We consider the downlink of a wireless system with an M-antenna base station and K single-antenna users. A limited feedback-based scheduling and precoding scenario is considered that builds on the multiuser random beamforming (RBF). Such a scheme was shown to yield the same capacity scaling, in terms of multiplexing and multiuser diversity gain, as the optimal full CSIT-based (channel state information at transmitter) precoding scheme, in the large number of users K regime. Unfortunately, for more practically relevant (low to moderate) K values, RBF yields degraded performance. In this work, we investigate solutions to this problem. We introduce a two-stage framework that decouples the scheduling and beamforming problems. In our scenario, RBF is exploited to identify good, spatially separable, users in a first stage. In the second stage, the initial random beams are refined based on the available feedback to offer improved performance toward the selected users. Specifically, we propose beam power control techniques that do not change the direction of the second-stage beams, offering feedback reduction and performance tradeoffs. The common feature of these schemes is to restore robustness of RBF with respect to sparse network settings (low K), at the cost of moderate complexity increase.
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paper_title: User Selection With Zero-Forcing Beamforming Achieves the Asymptotically Optimal Sum Rate

paper_content:

In this paper, we propose a generalized greedy (G-greedy) algorithm based on zero-forcing beamforming (ZFBF) for the multiple-input multiple-output (MIMO) broadcast channel. This algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations. As previous results only give the scaling law of the sum rate of dirty paper coding (DPC), with the help of the G-greedy structure, we are able to obtain the exact limit of the DPC sum rate for a large number of users. We also prove that the difference between the sum rates obtained by G-greedy user selection and by DPC goes to zero as the number of users increases. In addition to this, we investigate one particular greedy user selection scheme called sequential water-filling (SWF). For this algorithm, a complexity reduction is achieved by an iterative procedure based on an LQ decomposition, which converts the calculation of the Moore-Penrose matrix inverse to one vector-matrix multiplication. A sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction. With the help of the G-greedy algorithm, we prove that SWF achieves the full DPC sum rate for a large number of users. For a moderate number of users, simulation demonstrates that, compared with other user selection algorithms, SWF achieves a higher sum rate that is close to the maximal sum rate achievable by ZFBF with the same order of complexity.
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paper_title: A New Approach to User Scheduling in Massive Multi-User MIMO Broadcast Channels

paper_content:

In this paper, a new user-scheduling-and-beamforming method is proposed for multi-user massive multiple-input multiple-output (massive MIMO) broadcast channels in the context of two-stage beamforming. The key ideas of the proposed scheduling method are 1) to use a set of orthogonal reference beams and construct a double cone around each reference beam to select `nearly-optimal' semi-orthogonal users based only on channel quality indicator (CQI) feedback and 2) to apply post-user-selection beam refinement with zero-forcing beamforming (ZFBF) based on channel state information (CSI) feedback only from the selected users. It is proved that the proposed scheduling-and-beamforming method is asymptotically optimal as the number of users increases. Furthermore, the proposed scheduling-and-beamforming method almost achieves the performance of the existing semi-orthogonal user selection with ZFBF (SUS-ZFBF) that requires full CSI feedback from all users, with significantly reduced feedback overhead which is even less than that required by random beamforming.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: Opportunistic Two-Stage Feedback and Scheduling for MIMO Downlink Systems

paper_content:

We propose an opportunistic two-stage feedback and scheduling algorithm that is based upon zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) to reduce its feedback load. In an SUS algorithm, a base station schedules semi-orthogonal users using the feedback of all users' channel information. However, such feedback overhead significantly increases with the number of users. To reduce the feedback load of ZFBF-SUS systems, the proposed two-stage feedback scheme opportunistically and separately exploits the signal-to-interference-plus-noise ratio and orthogonality in each stage such that only a fraction of users feed back their channel information. Based on this opportunistic feedback scheme, we decouple the entire process of the SUS into two sub-processes. The proposed two-stage feedback and scheduling scheme effectively exclude the inappropriate users for ZFBF transmission in both feedback and scheduling periods, and thus save the scarce resources consumed for the feedback process. We derive an analytical expression for the average number of feedback bits of the proposed system and optimize it in an averaged sense. Further, the sum-rate of the proposed system is theoretically investigated. Both analytical and simulation results show that the proposed algorithm achieves the performance of conventional ZFBF-SUS systems with a significantly reduced number of feedback bits.
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paper_title: 5G Network Capacity: Key Elements and Technologies

paper_content:

It has been projected that, in the next decade, a mobile traffic increase on the order of 1,000 times is expected compared to what we experience today. To meet that dramatic traffic growth, next-generation mobile networks are also expected to achieve a 1,000-fold capacity increase compared to the current generation of wireless network deployments. In this article, we discuss how such capacity growth could be achieved in a ten-year time frame. We discuss the techniques that we expect to have the highest opportunity for increasing the system capacity and estimate their gains based on analysis and simulation. We observe that the main driver of capacity growth is expected to come from network architecture advancements, with heterogeneous networks and convergence of information and communication technology being two of the key techniques. We also estimate that the air-interface evolution would focus not only on improving the link and system spectrum efficiency but also on facilitating the required network efficiency improvements. This article provides insights into the communication technology evolution and can be used as a guideline for technology development toward the fifth generation (5G).
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paper_title: Matrix Algebra: Theory, Computations, and Applications in Statistics

paper_content:

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
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paper_title: Optimizing User Selection Schemes in Vector Broadcast Channels

paper_content:

In this paper, we focus on the ergodic downlink sum-rate performance of a system consisting of a set of heterogeneous users. We study three user selection schemes to group near-orthogonal users for simultaneous transmission. The first scheme is a random selection policy that achieves fairness, but does not exploit multi-user diversity. The second scheme is a greedy selection policy that fully exploits multi-user diversity, but does not achieve fairness, and the third scheme achieves fairness while partially exploiting multi-user diversity. We also consider two beamforming methods for data transmission, namely, maximum-ratio transmission and zero-forcing beamforming. In all scheduling schemes studied in the paper, there is a key parameter that controls the degrees of orthogonality of channel directions between co-scheduled users. We focus on optimally setting this parameter for each scheduling scheme such that the ergodic downlink sum-rate is maximized. To this end, we derive analytical expressions for the ergodic downlink sum-rate considering each scheduling scheme. Numerical results are also presented to provide further insights.
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paper_title: Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

paper_content:

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.
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paper_title: Simplified Semi-Orthogonal User Selection for MU-MIMO Systems with ZFBF

paper_content:

In this letter, we simplify the well-known semi-orthogonal user selection (SUS) algorithm for the multi-user multiple-input multiple-output (MU-MIMO) system with zero-forcing beamforming (ZFBF). Compared with the original SUS algorithm, the proposed user selection algorithm achieves the same performance, but with significantly less complexity. Simulation results show that the proposed algorithm can make a good tradeoff between performance and complexity for the MU-MIMO system with ZFBF.
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paper_title: Survey of Large-Scale MIMO Systems

paper_content:

The escalating teletraffic growth imposed by the proliferation of smartphones and tablet computers outstrips the capacity increase of wireless communications networks. Furthermore, it results in substantially increased carbon dioxide emissions. As a powerful countermeasure, in the case of full-rank channel matrices, MIMO techniques are potentially capable of linearly increasing the capacity or decreasing the transmit power upon commensurately increasing the number of antennas. Hence, the recent concept of large-scale MIMO (LS-MIMO) systems has attracted substantial research attention and been regarded as a promising technique for next-generation wireless communications networks. Therefore, this paper surveys the state of the art of LS-MIMO systems. First, we discuss the measurement and modeling of LS-MIMO channels. Then, some typical application scenarios are classified and analyzed. Key techniques of both the physical and network layers are also detailed. Finally, we conclude with a range of challenges and future research topics.
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paper_title: Sum Rates, Rate Allocation, and User Scheduling for Multi-User MIMO Vector Perturbation Precoding

paper_content:

This paper considers the multiuser multiple-input multiple-output (MIMO) broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via vector perturbation. We derive expressions for the sum rate in terms of the average energy of the precoded vector, and use this to derive a high signal-to-noise ratio (SNR) closed-form upper bound, which we show to be tight via simulation. We also propose a modification to vector perturbation where different rates can be allocated to different users. We conclude that for vector perturbation precoding most of the sum rate gains can be achieved by reducing the rate allocation problem to the user selection problem. We then propose a low-complexity user selection algorithm that attempts to maximize the high-SNR sum rate upper bound. Simulations show that the algorithm outperforms other user selection algorithms of similar complexity.
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paper_title: On beamforming with finite rate feedback in multiple-antenna systems

paper_content:

We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t-1)2/sup -B/t-1/, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.
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paper_title: Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider a downlink channel where a base station equipped with M transmit antennas communicates with K ≥ M single-antenna receivers and has partial channel knowledge obtained via a limited rate feedback channel. We propose scalar feedback metrics that provide an estimate of the received signal-to-noise plus interference ratio (SINR), which are combined with efficient user selection algorithms and zero-forcing beamforming. The asymptotic system sum rate for large K is analyzed and numerical results are provided, showing the performance of each metric in different scenarios.
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paper_title: Sum-rate analysis of multiuser MIMO system with zero-forcing transmit beamforming

paper_content:

In this letter, we present the exact sum-rate analysis of the multiuser multiple-input multiple-output (MIMO) systems with zero-forcing transmit beamforming (ZFBF). We develop the analytical expressions of the ergodic sum-rate for two low-complexity user selection strategies for the dual-transmit-antenna scenario. Based on the analytical results, we examine the parameter optimization problem to properly trade off between channel power gain and directional gain in term of maximizing the ergodic sum rate.
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paper_title: Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search

paper_content:

We consider a multi-user MIMO downlink system employing zero-forcing beamforming (ZFBF) as a spatial multiplexing strategy, and propose low-complexity user subset selection methods based on a clique (fully connected subgraph) search. The proposed algorithms, maximum weighted clique (MWC)-ZFBF and greedy weighted clique (GWC)-ZFBF, are shown to achieve the asymptotic sum-capacity of MIMO downlink channels as the number of users goes to infinity. Thus, clique search based ZFBF is an appealing strategy in MIMO downlink systems with a large number of users.
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paper_title: Iterative Precoder Design and User Scheduling for Block-Diagonalized Systems

paper_content:

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices.
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paper_title: Dynamic Multi-User MIMO scheduling with limited feedback in LTE-Advanced

paper_content:

Multi-User MIMO (MU-MIMO) systems have gained numerous attention from researchers in the past decade due to its substantial gains in the system throughput. Most of the initial research assumes the knowledge of perfect channel state information at the transmitter (CSIT). However, this is considered impractical and research over the past few years has been focused on receivers feeding back limited information to the transmitter. In this work, we consider a transparent MU-MIMO system model with limited feedback. We propose a general framework for dynamic MU-MIMO scheduling with the capability to switch between Single-User MIMO mode and (Multi-Rank) Multi-User MIMO mode without users feeding back additional multi-user information. Specifically, this is done by each user carefully estimating its CQI under the hypothesis of Multi-Rank MultiUser MIMO transmission and taking advantage of the codebook structure. We consider the sum rate of the system assuming each user uses ML and LMMSE receiver and show that our proposed scheduler, with significantly reduced feedback load, outperforms the best-companion user pairing.
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paper_title: Recent trend of multiuser MIMO in LTE-advanced

paper_content:

Recently, the mobile communication industry is moving rapidly toward Long Term Evolution, or LTE, systems. The leading carriers and vendors are committed to launching LTE service in the near future; in fact, a number of major operators such as Verizon have initiated LTE service already. LTE aims to provide improved service quality over 3G systems in terms of throughput, spectral efficiency, latency, and peak data rate, and the MIMO technique is one of the key enablers of the LTE system for achieving these diverse goals. Among several operational modes of MIMO, multiuser MIMO (MU-MIMO), in which the base station transmits multiple streams to multiple users, has received much attention as a way of achieving improvement in performance. From the initial release (Rel. 8) to the recent release (Rel. 10), so called LTE-Advanced, MUMIMO techniques have evolved from their premature form to a more elaborate version. In this article, we provide an overview of design challenges and the specific solutions for MU-MIMO systems developed in the LTE-Advanced standard.
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paper_title: On the performance of random vector quantization limited feedback beamforming in a MISO system

paper_content:

In multiple antenna wireless systems, beamforming is a simple technique for guarding against the negative effects of fading. Unfortunately, beamforming requires the transmitter to have knowledge of the forward-link channel which is often not available a priori. One way of overcoming this problem is to design the beamforming vector using a limited number of feedback bits sent from the receiver to the transmitter. In limited feedback beamforming, the beamforming vector is restricted to lie in a codebook that is known to both the transmitter and receiver. Random vector quantization (RVQ) is a simple approach to codebook design that generates the vectors independently from a uniform distribution on the complex unit sphere. This correspondence presents performance analysis results for RVQ limited feedback beamforming
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paper_title: MIMO Broadcast Channels with Spatial Heterogeneity

paper_content:

We develop a realistic model for multiple-input multiple-output (MIMO) broadcast channels, where each randomly located user's average SNR depends on its distance from the transmitter. With perfect channel state information at the transmitter (CSIT), the average sum capacity is proven to scale for many users like αM/2 log K instead of M log log K, where α, M, and K denote the path loss exponent, the number of transmit antennas, and the number of users in a cell. With only partial CSIT, the sum capacity at high SNR eventually saturates due to interference, and the saturation value scales for large B like MB/M-1, where B denotes the quantization resolution for channel feedback.
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paper_title: On the user selection for MIMO broadcast channels

paper_content:

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.
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paper_title: Adaptive downlink multi-user MIMO wireless systems for correlated channels with imperfect CSI

paper_content:

Multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. However the capacity increase is limited when the number of antennas at the receiver is fixed or restricted (due to mobile size constraints for example). To overcome this limitation multi-user MIMO can be used, which allows several users to be served simultaneously in frequency and time. A disadvantage of these multi-user MIMO systems, when used in the downlink however, is that they need accurate channel state information (CSI) at the transmitter and also uncorrelated channels among users. In this paper we investigate methods to address the problems of multi-user MIMO systems in spatially correlated channels. We adopt the concept of angle between subspaces to characterize the inter-user spatial correlation and adapt the algorithm to those conditions. We also investigate the impact of the accuracy of CSI at the transmitter (CSIT) and whether more limited CSI such as channel correlation information alone can be used to provide good multi-user MIMO performance. Results are presented as various simulated capacity measures and we use them to make comparisons between the various multi-user MIMO configurations
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paper_title: MIMO broadcast channels with finite rate feedback

paper_content:

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where the receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. Simple expressions for the capacity degradation due to finite rate feedback as well as the required increases in feedback load per mobile as a function of the number of access point antennas and the system SNR are provided.
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paper_title: User selection schemes in multiple antenna broadcast channels with guaranteed performance

paper_content:

Recently, user selection algorithms in combination with linear pre- coding have been proposed that achieve the same scaling as the sum capacity of the MIMO BC. In this work, we study the properties of four user selection algorithms in conjunction with beamforming that guarantee certain SINR requirements under transmit power minimization. It is shown that for a large number of transmit antennas, the norm-based user selection performs close to the optimum. The results are illustrated by various numerical simulations.
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paper_title: Scheduling of multi-antenna broadcast systems with heterogeneous users

paper_content:

We study the problem of efficiently scheduling users in a Gaussian broadcast channel with M transmit antennas and K independent receivers, each with a single antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the next L - 1 strongest ones to form the best pair, taking channel orientations into account as well. We prove that the expected rate gap converges to 1/(L- 1) nats/symbol when the total number of users K tends to infinity. Allowing L to increase with K, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while considerably reducing the feedback overhead and scheduling complexity. Next, we tackle the problem of maximizing a weighted sum rate in a scenario with heterogeneous user characteristics. We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at most MC users, where C denotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users.
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paper_title: An efficient resource-allocation scheme for spatial multiuser access in MIMO/OFDM systems

paper_content:

Fast adaptive transmission has been recently identified as a key technology for exploiting potential system diversity and improving power-spectral efficiency in wireless communication systems. An adaptive resource-allocation approach, which jointly adapts subcarrier allocation, power distribution, and bit distribution according to instantaneous channel conditions, is proposed for multiuser multiple-input multiple-output (MIMO)/orthogonal frequency-division multiplexing systems. The resultant scheme is able to: 1) optimize the power efficiency; 2) guarantee each user's quality of service requirements, including bit-error rate and data rate; 3) ensure fairness to all the active users; and 4) be applied to systems with various types of multiuser-detection schemes at the receiver. For practical implementation, a reduced-complexity allocation algorithm is developed. This algorithm decouples the complex multiuser joint resource-allocation problem into simple single-user optimization problems by controlling the subcarrier sharing according to the users' spatial separability. Numerical results show that significant power and diversity gains are achievable, compared with nonadaptive systems. It is also demonstrated that the MIMO system is able to multiplex several users without sacrificing antenna diversity by using the proposed algorithm.
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paper_title: 5G Network Capacity: Key Elements and Technologies

paper_content:

It has been projected that, in the next decade, a mobile traffic increase on the order of 1,000 times is expected compared to what we experience today. To meet that dramatic traffic growth, next-generation mobile networks are also expected to achieve a 1,000-fold capacity increase compared to the current generation of wireless network deployments. In this article, we discuss how such capacity growth could be achieved in a ten-year time frame. We discuss the techniques that we expect to have the highest opportunity for increasing the system capacity and estimate their gains based on analysis and simulation. We observe that the main driver of capacity growth is expected to come from network architecture advancements, with heterogeneous networks and convergence of information and communication technology being two of the key techniques. We also estimate that the air-interface evolution would focus not only on improving the link and system spectrum efficiency but also on facilitating the required network efficiency improvements. This article provides insights into the communication technology evolution and can be used as a guideline for technology development toward the fifth generation (5G).
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paper_title: Matrix Algebra: Theory, Computations, and Applications in Statistics

paper_content:

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
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paper_title: Maximum volume criterion for user selection of multiuser MIMO downlink with multiantenna users and block diagonalization beamforming

paper_content:

Compared with capacity-achieving dirty paper coding [1], block diagonalization (BD) algorithm [2] is known as a suboptimal but more practical beamforming scheme for multiuser MIMO downlink systems with multiantenna users. However BD suffers from two major drawbacks: the dimensionality constraint on antennas arrangement and the difficulty in handling spatially correlated users. User selection capable of selecting some most sum-rate-contributive users is a promising measure to alleviating this situation.
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paper_title: Multiuser MIMO User Selection Based on Chordal Distance

paper_content:

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.
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paper_title: Limited Feedback Multiuser Scheduling of Spatially Correlated Broadcast Channels

paper_content:

This paper investigates the transmission scheduling of users under spatially correlated multiple-input-multiple-output (MIMO) channels. By maximizing an upper bound of the sum capacity, we propose a scheduling scheme that requires only scalar feedback from each receiving user. To simplify user information feedback and better exploit the spatial channel correlation, we further develop a more efficient scheduling method that only requires a 1-bit indicator from each user and selects users based on the MIMO channel correlation information. Additionally, we then extend the proposed scheduling schemes for the system with imperfect (finite-rate) channel information feedback. Numerical results finally show that the proposed scheduling schemes can effectively improve the system sum capacity performance by exploiting the statistic channel-correlation information.
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paper_title: Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

paper_content:

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC.
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paper_title: A User Selection Algorithm Using Angle between Subspaces for Downlink MU-MIMO Systems

paper_content:

One of major issues in the efficient use of radio resource for multiuser multiple-input/multiple-output (MU-MIMO) systems is the selection of users to achieve the maximum system throughput. The optimal user selection algorithm, which requires exhaustive search, is prohibitive due to its high computational complexity where Block diagonalization (BD) method is applied and known as a suboptimal precoding technique for downlink MU-MIMO systems, which intents to perfectly eliminate inter-user interference. In this paper, we propose efficient, iterative user selection algorithms with low complexity, where the product of eigenvalues of effective channels is utilized as a selection metric by applying the concept of principal angles between subspaces. And, we further examined the applicability of the proposed algorithms to limited feedback systems and proportional fair (PF) scheduling. Through computational complexity analysis, we show that the proposed algorithm has low complexity with a little loss in throughput. Simulation results validate that the proposed algorithm achieves almost the same system throughput by a capacity-based algorithm under high SNR regime with considerable reduction in complexity.
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paper_title: Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

paper_content:

In this paper, we tackle the problem of semidistributed user selection with distributed linear precoding for sum-rate maximization in multiuser multicell systems. A set of adjacent base stations (BSs) forms a cluster to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling, and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to nonintended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, namely, distributed zero forcing and distributed virtual signal-to-interference-plus-noise ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First, we investigate how the signal-to-noise ratio regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the BSs.
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paper_title: Coordinated beamforming with limited feedback in the MIMO broadcast channel

paper_content:

In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.
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paper_title: Bounds on packings of spheres in the Grassmann manifold

paper_content:

We derive the Gilbert-Varshamov and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over R and C. Asymptotic expressions are obtained for the geodesic metric and projection Frobenius (chordal) metric on the manifold.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: Elements of Information Theory

paper_content:

Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
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paper_title: On the user selection for MIMO broadcast channels

paper_content:

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.
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paper_title: User Scheduling for Heterogeneous Multiuser MIMO Systems: A Subspace Viewpoint

paper_content:

In downlink multiuser multiple-input-multiple-output (MU-MIMO) systems, users are practically heterogeneous. However, many existing user-scheduling algorithms are designed with an implicit assumption that users are homogeneous. In this paper, we revisit the problem by exploring the characteristics of heterogeneous users from a subspace viewpoint. With an objective of minimizing interference nonorthogonality among users, three new angular-based user-scheduling criteria are proposed. While the first criterion is heuristically determined by identifying the incapability of the largest principal angle to characterize subspace correlation and, hence, interference nonorthogonality between users, the second and third criteria are derived by using the sum rate capacity bounds with block diagonalization and the change in capacity by adding a new user into an existing user subset, respectively. Aiming to capture fairness among heterogeneous users while maintaining multiuser diversity gain, two new hybrid user-scheduling algorithms, whose computational complexities are only linearly proportional to the number of users, are proposed. We show by simulations the effectiveness of our proposed user-scheduling criteria and algorithms with respect to those commonly used in a homogeneous environment.
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paper_title: Spatial separation of multi-user MIMO channels

paper_content:

Since multi-antenna (MIMO) systems are becoming more popular thanks to their inherent potential for capacity improvement, interference from MIMO transceivers is an increasingly serious concern. Spatial multiplexing schemes are particularly vulnerable to multi-user interference. Fortunately, this interference can be mitigated, when the channel matrices show a sufficient spatial separation. In this paper, we quantify the separability of multi-user MIMO channels using actual measurements in a scenario where a single outdoor base station transmits to two indoor mobile receivers. To quantify the spatial distance between the two users, we compare the spatial correlation matrices using two simple measures: (i) matrix collinearity, and (ii) the condition number ratio. Both measures are directly linked to MIMO system performance. Our measurement-based evaluations demonstrate that the downlink channels of different users can have a significantly different spatial structure, even when the users are in the same room. This leads to the following conclusions: (i) new multi-user MIMO models are needed to describe the spatial characteristics of different users, and (ii) spatial interference can be well managed by appropriate scheduling and precoding algorithms.
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paper_title: Grassmannian beamforming for multiple-input multiple-output wireless systems

paper_content:

Multiple-input multiple-output (MIMO) wireless systems provides capacity much larger than that provided by traditional single-input single-output (SISO) wireless systems. Beamforming is a low complexity technique that increases the receive signal-to-noise ratio (SNR), however, it requires channel knowledge. Since in practice channel knowledge at the transmitter is difficult to realize, we propose a technique where the receiver designs the beamforming vector and sends it to the transmitter by transmitting a label in a finite set, or codebook, of beamforming vectors. A codebook design method for quantized versions of maximum ratio transmission, equal gain transmission, and generalized selection diversity with maximum ratio combining at the receiver is presented. The codebook design criterion exploits the quantization problem's relationship with Grassmannian line packing. Systems using the beamforming codebooks are shown to have a diversity order of the product of the number of transmit and the number of receive antennas. Monte Carlo simulations compare the performance of systems using this new codebook method with the performance of systems using previously proposed quantized and unquantized systems.
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paper_title: Adaptive downlink multi-user MIMO wireless systems for correlated channels with imperfect CSI

paper_content:

Multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. However the capacity increase is limited when the number of antennas at the receiver is fixed or restricted (due to mobile size constraints for example). To overcome this limitation multi-user MIMO can be used, which allows several users to be served simultaneously in frequency and time. A disadvantage of these multi-user MIMO systems, when used in the downlink however, is that they need accurate channel state information (CSI) at the transmitter and also uncorrelated channels among users. In this paper we investigate methods to address the problems of multi-user MIMO systems in spatially correlated channels. We adopt the concept of angle between subspaces to characterize the inter-user spatial correlation and adapt the algorithm to those conditions. We also investigate the impact of the accuracy of CSI at the transmitter (CSIT) and whether more limited CSI such as channel correlation information alone can be used to provide good multi-user MIMO performance. Results are presented as various simulated capacity measures and we use them to make comparisons between the various multi-user MIMO configurations
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paper_title: Transmit correlation-aided opportunistic beamforming and scheduling

paper_content:

The problem of multiuser scheduling and beamforming with partial channel state information at the transmitter (CSIT) is considered here in the particular context of opportunistic beamforming. We consider a random multiuser beamforming scheme and show how long-term statistical information of users' channels can be efficiently combined with short-term SINR feedback to increase system performance substantially over a conventional opportunistic beamforming scheme. We propose a channel estimation method to be used by the transmitter which exploits the second-order channel statistics, the fading statistics and the information contained in the instantaneous SINR feedback of random opportunistic beamforming. This coarse (low feedback-based) channel estimate is shown to be particularly valuable for the purpose of user selection, as well as for the precoding matrix design.
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paper_title: Survey of Large-Scale MIMO Systems

paper_content:

The escalating teletraffic growth imposed by the proliferation of smartphones and tablet computers outstrips the capacity increase of wireless communications networks. Furthermore, it results in substantially increased carbon dioxide emissions. As a powerful countermeasure, in the case of full-rank channel matrices, MIMO techniques are potentially capable of linearly increasing the capacity or decreasing the transmit power upon commensurately increasing the number of antennas. Hence, the recent concept of large-scale MIMO (LS-MIMO) systems has attracted substantial research attention and been regarded as a promising technique for next-generation wireless communications networks. Therefore, this paper surveys the state of the art of LS-MIMO systems. First, we discuss the measurement and modeling of LS-MIMO channels. Then, some typical application scenarios are classified and analyzed. Key techniques of both the physical and network layers are also detailed. Finally, we conclude with a range of challenges and future research topics.
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paper_title: Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels

paper_content:

We investigate multiple-input multiple-output (MIMO) eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.
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paper_title: Parametrization Based Limited Feedback Design for Correlated MIMO Channels Using New Statistical Models

paper_content:

Parametrization of unitary matrices using Givens rotations has been used for limited feedback in multiple-input multiple-output (MIMO) systems. Feedback based on these rotations has been adopted in IEEE 802.11n and other upcoming standards. However, the probability distributions of Givens rotations is not known for correlated channels, forcing the use of uniform quantization. In this paper, novel probability density function (PDF) models, based on beta and wrapped Cauchy distributions, are proposed for Givens rotations in correlated MIMO channels. Empirical distributions and goodness-of-fit tests show that the proposed distributions characterize the spatial correlation behavior with good accuracy. Moreover, it is shown that the distributions known in the literature for uncorrelated MIMO channels are only special cases. Distributions of Givens rotations are useful to understand the behavior of singular vectors of correlated channels. In this paper, the PDF models are utilized for bit allocation and optimized codebook design. Simulations show that precoding using the proposed codebooks achieves significant performance improvement, in terms of mean square error and sum rate, as compared to using uniform codebooks. It is also shown that the bit allocations proposed in this paper reduce to that of IEEE 802.11n standard when the MIMO channel is not spatially correlated.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.
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paper_title: Maximum volume criterion for user selection of multiuser MIMO downlink with multiantenna users and block diagonalization beamforming

paper_content:

Compared with capacity-achieving dirty paper coding [1], block diagonalization (BD) algorithm [2] is known as a suboptimal but more practical beamforming scheme for multiuser MIMO downlink systems with multiantenna users. However BD suffers from two major drawbacks: the dimensionality constraint on antennas arrangement and the difficulty in handling spatially correlated users. User selection capable of selecting some most sum-rate-contributive users is a promising measure to alleviating this situation.
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paper_title: Multiuser MIMO User Selection Based on Chordal Distance

paper_content:

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming and User Grouping

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a two stage downlink beamforming: a pre-beamformer that depends on the channel covariances and minimizes interference across groups and a multiuser MIMO precoder for the effective channel after pre-beamforming, to counteract interference within a group. We first focus on the regime of a fixed number of antennas and large number of users, and show that opportunistic beamforming with user selection yields significant gain, and thus, channel correlation may yield a capacity improvement over the uncorrelated "isotropic" channel result of Sharif and Hassibi. We prove that in the presence of different correlations among groups, a block diagonalization approach for the design of pre-beamformers achieves the optimal sum-rate scaling. Next, we consider the regime of large number of antennas and users, where user selection does not provide significant gain. Here, we propose a simplified user grouping algorithm to cluster users into groups when the number of antennas becomes very large, in a realistic setting where users are randomly distributed and have different angles of arrival and angular spreads depending on the propagation environment. Our subsequent analysis leads to a probabilistic scheduling algorithm, where users within each group are preselected at random based on probabilities derived from the large system analysis, depending on the fairness criterion. This is advantageous since only the selected users are required to feedback their channel state information (CSIT).
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paper_title: MIMO wireless linear precoding

paper_content:

This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues. The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation. It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding. A precoded system structure is then described, involving an encoder and a linear precoder. Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios.
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paper_title: Utilizing the Spatial Information Provided by Channel Norm Feedback in SDMA Systems

paper_content:

To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: User Scheduling for Heterogeneous Multiuser MIMO Systems: A Subspace Viewpoint

paper_content:

In downlink multiuser multiple-input-multiple-output (MU-MIMO) systems, users are practically heterogeneous. However, many existing user-scheduling algorithms are designed with an implicit assumption that users are homogeneous. In this paper, we revisit the problem by exploring the characteristics of heterogeneous users from a subspace viewpoint. With an objective of minimizing interference nonorthogonality among users, three new angular-based user-scheduling criteria are proposed. While the first criterion is heuristically determined by identifying the incapability of the largest principal angle to characterize subspace correlation and, hence, interference nonorthogonality between users, the second and third criteria are derived by using the sum rate capacity bounds with block diagonalization and the change in capacity by adding a new user into an existing user subset, respectively. Aiming to capture fairness among heterogeneous users while maintaining multiuser diversity gain, two new hybrid user-scheduling algorithms, whose computational complexities are only linearly proportional to the number of users, are proposed. We show by simulations the effectiveness of our proposed user-scheduling criteria and algorithms with respect to those commonly used in a homogeneous environment.
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paper_title: Majorization and Matrix-Monotone Functions in Wireless Communications

paper_content:

This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions, reviews their basic definitions and describes their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions. ::: ::: The techniques are applied to solve communication and information theoretic problems in wireless communications. The impact of spatial correlation in multiple antenna systems is characterized for many important performance measures, e.g., average mutual information, outage probability, error performance, minimum Eb/N0 and wide-band slope, zero-outage capacity, and capacity region. The impact of user distribution in cellular systems is characterized for different scenarios including perfectly informed transmitters and receivers, regarding, e.g., the average sum rate, the outage sum rate, maximum throughput. Finally, a unified framework for the performance analysis of multiple antenna systems is developed based on matrix-monotone functions. The optimization of transmit strategies for multiple antennas is carried out by optimization of matrix-monotone functions. The results within this framework resemble and complement the various results on optimal transmit strategies in single-user and multiple-user multiple-antenna systems.
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paper_title: Majorization and Matrix-Monotone Functions in Wireless Communications

paper_content:

This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions, reviews their basic definitions and describes their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions. ::: ::: The techniques are applied to solve communication and information theoretic problems in wireless communications. The impact of spatial correlation in multiple antenna systems is characterized for many important performance measures, e.g., average mutual information, outage probability, error performance, minimum Eb/N0 and wide-band slope, zero-outage capacity, and capacity region. The impact of user distribution in cellular systems is characterized for different scenarios including perfectly informed transmitters and receivers, regarding, e.g., the average sum rate, the outage sum rate, maximum throughput. Finally, a unified framework for the performance analysis of multiple antenna systems is developed based on matrix-monotone functions. The optimization of transmit strategies for multiple antennas is carried out by optimization of matrix-monotone functions. The results within this framework resemble and complement the various results on optimal transmit strategies in single-user and multiple-user multiple-antenna systems.
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paper_title: A Quantitative Measure Of Fairness And Discrimination For Resource Allocation In Shared Computer Systems

paper_content:

Fairness is an important performance criterion in all resource allocation schemes, including those in distributed computer systems. However, it is often specified only qualitatively. The quantitative measures proposed in the literature are either too specific to a particular application, or suffer from some undesirable characteristics. In this paper, we have introduced a quantitative measure called Indiex of FRairness. The index is applicable to any resource sharing or allocation problem. It is independent of the amount of the resource. The fairness index always lies between 0 and 1. This boundedness aids intuitive understanding of the fairness index. For example, a distribution algorithm with a fairness of 0.10 means that it is unfair to 90% of the users. Also, the discrimination index can be defined as 1 - fairness index.
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paper_title: A survey of energy-efficient wireless communications

paper_content:

Reducing energy consumption in wireless communications has attracted increasing attention recently. Advanced physical layer techniques such as multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM), cognitive radio, network coding, cooperative communication, etc.; new network architectures such as heterogeneous networks, distributed antennas, multi-hop cellulars, etc.; as well as radio and network resource management schemes such as various cross-layer optimization algorithms, dynamic power saving, multiple radio access technologies coordination, etc. have been proposed to address this issue. In this article, we overview these technologies and present the state-of-the-art on each aspect. Some challenges that need to be solved in the area are also described.
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paper_title: Fair end-to-end window-based congestion control

paper_content:

In this paper, we demonstrate the existence of fair end-to- end window-based congestion control protocols for packet- switched networks with FCFS routers. Our definition of fairness generalizes proportional fairness and includes arbitrarily close approximations of max-min fairness. The protocols use only information that is available to end hosts and are designed to converge reasonably fast. Our study is based on a multiclass fluid model of the network. The convergence of the protocols is proved using a Lyapunov function. The technical challenge is in the construction of the protocols.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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paper_title: An Axiomatic Theory of Fairness in Network Resource Allocation

paper_content:

We present five axioms for fairness measures in resource allocation. A family of fairness measures satisfying the axioms is constructed. Special cases of this family include α-fairness, Jain's index, and entropy. Properties of fairness measures satisfying the axioms are proven, including Schur-concavity. Among the engineering implications is a generalized Jain's index that tunes the resolution of fairness measure, a new understanding of α-fair utility functions, and an interpretation of ``larger α is more fair''. We also construct an alternative set of axioms to capture system efficiency and feasibility constraints.
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paper_title: Multiresource Allocation: Fairness–Efficiency Tradeoffs in a Unifying Framework

paper_content:

Quantifying the notion of fairness is under-explored when users request different ratios of multiple distinct resource types. A typical example is datacenters processing jobs with heterogeneous resource requirements on CPU, memory, etc. A generalization of max-min fairness to multiple resources was recently proposed in [1], but may suffer from significant loss of efficiency. This paper develops a unifying framework addressing this fairness-efficiency tradeoff with multiple resource types. We develop two families of fairness functions which provide different tradeoffs, characterize the effect of user requests' heterogeneity, and prove conditions under which these fairness measures satisfy the Pareto efficiency, sharing incentive, and envy-free properties. Intuitions behind the analysis are explained in two visualizations of multi-resource allocation.
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Fairness in Wireless Networks:Issues, Measures and Challenges

paper_content:

The pervasiveness of wireless technology has indeed created massive opportunity to integrate almost everything into the Internet fabric. This can be seen with the advent of Internet of Things and Cyber Physical Systems, which involves cooperation of massive number of intelligent devices to provide intelligent services. Fairness amongst these devices is an important issue that can be analysed from several dimensions, e.g., energy usage, achieving required quality of services, spectrum sharing, and so on. This article focusses on these viewpoints while looking at fairness research. To generalize, mainly wireless networks are considered. First, we present a general view of fairness studies, and pose three core questions that help us delineate the nuances in defining fairness. Then, the existing fairness models are summarized and compared. We also look into the major fairness research domains in wireless networks such as fair energy consumption control, power control, topology control, link and flow scheduling, channel assignment, rate allocation, congestion control and routing protocols. We make a distinction amongst fairness, utility and resource allocation to begin with. Later, we present their inter-relation. At the end of this article, we list the common properties of fairness and give an example of fairness management. Several open research challenges that point to further work on fairness in wireless networks are also discussed. Indeed, the research on fairness is entangled with many other aspects such as performance, utility, optimization and throughput at the network and node levels. While consolidating the contributions in the literature, this article tries to explain the niceties of all these aspects in the domain of wireless networking.
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paper_title: Downlink Packet Scheduling in LTE Cellular Networks: Key Design Issues and a Survey

paper_content:

Future generation cellular networks are expected to provide ubiquitous broadband access to a continuously growing number of mobile users. In this context, LTE systems represent an important milestone towards the so called 4G cellular networks. A key feature of LTE is the adoption of advanced Radio Resource Management procedures in order to increase the system performance up to the Shannon limit. Packet scheduling mechanisms, in particular, play a fundamental role, because they are responsible for choosing, with fine time and frequency resolutions, how to distribute radio resources among different stations, taking into account channel condition and QoS requirements. This goal should be accomplished by providing, at the same time, an optimal trade-off between spectral efficiency and fairness. In this context, this paper provides an overview on the key issues that arise in the design of a resource allocation algorithm for LTE networks. It is intended for a wide range of readers as it covers the topic from basics to advanced aspects. The downlink channel under frequency division duplex configuration is considered as object of our study, but most of the considerations are valid for other configurations as well. Moreover, a survey on the most recent techniques is reported, including a classification of the different approaches presented in literature. Performance comparisons of the most well-known schemes, with particular focus on QoS provisioning capabilities, are also provided for complementing the described concepts. Thus, this survey would be useful for readers interested in learning the basic concepts before going into the details of a particular scheduling strategy, as well as for researchers aiming at deepening more specific aspects.
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paper_title: Recent Advances in Radio Resource Management for Heterogeneous LTE/LTE-A Networks

paper_content:

As heterogeneous networks (HetNets) emerge as one of the most promising developments toward realizing the target specifications of Long Term Evolution (LTE) and LTE-Advanced (LTE-A) networks, radio resource management (RRM) research for such networks has, in recent times, been intensively pursued. Clearly, recent research mainly concentrates on the aspect of interference mitigation. Other RRM aspects, such as radio resource utilization, fairness, complexity, and QoS, have not been given much attention. In this paper, we aim to provide an overview of the key challenges arising from HetNets and highlight their importance. Subsequently, we present a comprehensive survey of the RRM schemes that have been studied in recent years for LTE/LTE-A HetNets, with a particular focus on those for femtocells and relay nodes. Furthermore, we classify these RRM schemes according to their underlying approaches. In addition, these RRM schemes are qualitatively analyzed and compared to each other. We also identify a number of potential research directions for future RRM development. Finally, we discuss the lack of current RRM research and the importance of multi-objective RRM studies.
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paper_title: Proportional fair space-time scheduling for wireless communications

paper_content:

We extend the proportional fair (PF) scheduling algorithm to systems with multiple antennas. There are K client users (each with a single antenna) and one base station (with n/sub R/ antennas). We focus on the reverse link of the system, and assume a slow-fading channel where clients are moving with pedestrian speed. Qualcomm's original PF scheduling algorithm satisfies the PF criteria only when the communication is constrained to one user at a time with no power waterfilling. However, the original PF algorithm does not generalize easily when we have n/sub R/ receive antennas at the base station. In this paper, we shall formulate the PF scheduling design as a convex optimization problem. One challenge is in the optimal power allocation over the multiantenna multiaccess capacity region, which is still an open problem. For practical consideration, we consider multiuser minimum mean-square error processing at the base station. To obtain first-order insight, we propose an asymptotically optimal PF scheduling solution. Using the proposed PF solution for a multiantenna base station, the system capacity is enhanced by exploiting the multiuser selection diversity, as well as the distributed multiple-input multiple-output configuration. It is found that the PF scheduler achieves a good balance between fairness and system capacity gain.
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paper_title: Wireless packet scheduling based on the cumulative distribution function of user transmission rates

paper_content:

In this paper, we present a new wireless scheduling algorithm based on the cumulative distribution function (cdf) and its simple modification that limits the maximum starving time. This cdf-based scheduling (CS) algorithm selects the user for transmission based on the cdf of user rates, in such a way that the user whose rate is high enough, but least probable to become higher, is selected first. We prove that the CS algorithm is equivalent to a scheduling algorithm that regards the user rates as independent and identically distributed, and the average throughput of a user is independent of the probability distribution of other users. So, we can evaluate the exact user throughput only if we know the user's own distribution, which is a distinctive feature of this proposed algorithm. In addition, we try a modification on the CS algorithm to limit the maximum starving time, and prove that the modification does not affect the average interservice time. This CS with starving-time limitation (CS-STL) algorithm turns out to limit the maximum starving time at the cost of a negligible throughput loss.
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paper_title: New Beamforming Techniques Based on Virtual SINR Maximization for Coordinated Multi-Cell Transmission

paper_content:

In this paper, we propose new beamforming techniques based on virtual signal-to-interference-plus-noise ratio (VSINR) for weighted sum-rate (WSR) maximization in coordinated multi-cell transmission. In earlier works based on the VSINR maximization, the parameters which control the interference power and the noise variance were set to fixed values regardless of channel realizations and the signal-to-noise ratio level. In order to obtain an improved WSR performance, we propose a method which adaptively adjusts the parameters after establishing a connection between the WSR and VSINR. Our proposed method can be applied to the cases of various coordination levels among base stations. To address practical implementation issues, a decentralized implementation of the beamforming techniques is also proposed based on local channel state information. Numerical results confirm that the proposed centralized schemes provide near-optimal WSR performance and the proposed decentralized methods show a negligible performance loss compared to the centralized algorithms with reduced system complexity.
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paper_title: Opportunistic beamforming using dumb antennas

paper_content:

An important means to cope with fading in wireless channels is the use of diversity. Diversity can be obtained over time (interleaving of coded bits), frequency (combining of multipaths in CDMA systems) and space (multiple antennas). The basic idea is to improve performance by creating several independent signal paths between the transmitter and the receiver. In this paper, we propose a scheme that induces random fading when the environment has little scattering and/or the fading is slow. We focus on the downlink of a cellular system. We use multiple antennas at the base-station to transmit the same signal from each antenna modulated by a gain whose phase and magnitude is changing in time in a controlled but pseudo random fashion.
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paper_title: What Will 5G Be?

paper_content:

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
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paper_title: Scheduling of multi-antenna broadcast systems with heterogeneous users

paper_content:

We study the problem of efficiently scheduling users in a Gaussian broadcast channel with M transmit antennas and K independent receivers, each with a single antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the next L - 1 strongest ones to form the best pair, taking channel orientations into account as well. We prove that the expected rate gap converges to 1/(L- 1) nats/symbol when the total number of users K tends to infinity. Allowing L to increase with K, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while considerably reducing the feedback overhead and scheduling complexity. Next, we tackle the problem of maximizing a weighted sum rate in a scenario with heterogeneous user characteristics. We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at most MC users, where C denotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users.
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paper_title: Scheduling for Multiuser MIMO Downlink Channels with Ranking-Based Feedback

paper_content:

We consider a multi-antenna broadcast channel with more single-antenna receivers than transmit antennas and partial channel state information at the transmitter (CSIT). We propose a novel type of CSIT representation for the purpose of user selection, coined as ranking-based feedback. Each user calculates and feeds back the rank, an integer between 1 and W + 1, of its instantaneous channel quality information (CQI) among a set of W past CQI measurements. Apart from reducing significantly the required feedback load, ranking-based feedback enables the transmitter to select users that are on the highest peak (quantile) with respect to their own channel distribution, independently of the distribution of other users. It can also be shown that this feedback metric can restore temporal fairness in heterogeneous networks, in which users' channels are not identically distributed and mobile terminals experience different average signal-to-noise ratio (SNR). The performance of a system that performs user selection using ranking-based CSIT in the context of random opportunistic beamforming is analyzed, and we provide design guidelines on the number of required past CSIT samples and the impact of finite W on average throughput. Simulation results show that feedback reduction of order of 40-50% can be achieved with negligible decrease in system throughput.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: MIMO Downlink Scheduling with Non-Perfect Channel State Knowledge

paper_content:

Downlink scheduling schemes are well-known and widely investigated under the assumption that the channel state is perfectly known to the scheduler. In the multiuser MIMO (broadcast) case, downlink scheduling in the presence of non-perfect channel state information (CSI) is only scantly treated. In this paper we provide a general framework that addresses the problem systematically. Also, we illuminate the key role played by the channel state prediction error: our scheme treats in a fundamentally different way users with small channel prediction error ("predictable" users) and users with large channel prediction error ("non-predictable" users), and can be interpreted as a near-optimal opportunistic time-sharing strategy between MIMO downlink beamforming to predictable users and space-time coding to non-predictable users. Our results, based on a realistic MIMO channel model used in 3GPP standardization, show that the proposed algorithms can significantly outperform a conventional "mismatched" scheduling scheme that treats the available CSI as if it was perfect.
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paper_title: Adaptive radio resource allocation for downlink OFDMA/SDMA systems with multimedia traffic

paper_content:

This paper proposes an adaptive radio resource allocation (ARRA) algorithm for downlink OFDMA/SDMA systems with multimedia traffic. Considering multiple service classes and diverse QoS requirements of multimedia traffic, the ARRA algorithm is designed with the goal to maximize spectrum efficiency and to fulfill quality of service (QoS) requirements. It is composed of two parts, a dynamic priority adjustment (DPA) scheme and a priority-based greedy (PBG) scheme. The DPA adopts a type of time-to-expiration to indicate the degree of user's urgency, and dynamically gives high priorities to urgent users. The PBG allocates the radio resource iteratively, based on a cost value, to maximize the system throughput while allocating enough resource to high-priority users. Simulation results show that the ARRA algorithm outperforms conventional algorithms in terms of system throughput and satisfaction extent of QoS requirements; it can sustain users' QoS requirements up till a traffic load of 0.8, while the conventional algorithms cannot guarantee QoS requirements after a traffic load of 0.3.
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paper_title: A Unified Analysis of Max-Min Weighted SINR for MIMO Downlink System

paper_content:

This paper studies the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem in the multiple-input-multiple-output (MIMO) downlink, where multiple users are weighted according to priority and are subject to a weighted-sum-power constraint. First, we study the multiple-input-single-output (MISO) and single-input-multiple- output (SIMO) problems using nonlinear Perron-Frobenius theory. As a by-product, we solve the open problem of convergence for a previously proposed MISO algorithm by Wiesel, Eldar, and Shamai in 2006. Furthermore, we unify our analysis with respect to the previous alternate optimization algorithm proposed by Tan, Chiang, and Srikant in 2009, by showing that our MISO result can, in fact, be derived from their algorithm. Next, we combine our MISO and SIMO results into an algorithm for the MIMO problem. We show that our proposed algorithm is optimal when the channels are rank-one, or when the network is operating in the low signal-to-noise ratio (SNR) region. Finally, we prove the parametric continuity of the MIMO problem in the power constraint, and we use this insight to propose a heuristic initialization strategy for improving the performance of our (generally) suboptimal MIMO algorithm. The proposed initialization strategy exhibits improved performance over random initialization.
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paper_title: Training and Feedback Optimization for Multiuser MIMO Downlink

paper_content:

We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over time-frequency blocks that span a coherent time x a coherence bandwidth. In closed-loop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In open-loop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use closed-form lower bounds and tight approximations of the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three time-frequency block models inspired by actual systems, we provide useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.
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paper_title: Call admission control in wireless networks: a comprehensive survey

paper_content:

Radio resource management (RRM) plays a major role in Quality of Service (QoS) provisioning for wireless communication systems. The performance of RRM techniques has a direct impact on each user's individual performance and on the overall network performance. Arriving (new and handoff) calls are granted/denied access to the network by the call admission scheme (CAC) based on predefined criteria, taking the network loading conditions into consideration. CAC in wireless networks has been receiving a great deal of attention during the last two decades due to the growing popularity of wireless communications and the central role that CAC plays in QoS provisioning in terms of the signal quality, call blocking and dropping probabilities, packet delay and loss rate, and transmission rate. In the first and second generation of wireless systems, CAC has been developed for a single service environment. In the third generation and beyond wireless systems, multimedia services such as voice, video, data, and audio are to be offered with various QoS profiles. Hence, more sophisticated CAC schemes are developed to cope with these changes. This article provides a comprehensive survey of CAC schemes in modern wireless networks.
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paper_title: Solution of the multiuser downlink beamforming problem with individual SINR constraints

paper_content:

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.
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paper_title: Fast Algorithms and Performance Bounds for Sum Rate Maximization in Wireless Networks

paper_content:

Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying the solutions to two related problems, sum rate maximization using an SIR approximation and max-min weighted SIR optimization. We also show that these two problems can be solved very efficiently, using much faster algorithms than the existing ones in the literature. Furthermore, using a new parameterization of the sum rate maximization problem, we obtain a characterization of the power controlled rate region and its convexity property in various asymptotic regimes. Engineering implications are discussed for IEEE 802.11 networks.
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paper_title: A Survey on Opportunistic Scheduling in Wireless Communications

paper_content:

Wireless technology advancements made opportunistic scheduling a popular topic in recent times. However, opportunistic schedulers for wireless systems have been studied since nearly twenty years, but not implemented in real systems due to their high complexity and hardly achievable requirements. In contrast, today's popularity of opportunistic schedulers extends to implementation proposals for next generation cellular technologies. Motivated by such a novel interest towards opportunistic scheduling, we provide a taxonomy for opportunistic schedulers, which is based on scheduling design's objectives; accordingly, we provide an extensive review of opportunistic scheduling proposals which have appeared in the literature during nearly two decades. The huge number of papers available in the literature propose different techniques to perform opportunistic scheduling, ranging from simple heuristic algorithms to complex mathematical models. Some proposals are only designed to increase the total network capacity, while others enhance QoS objectives such as throughput and fairness. Interestingly, our survey helps to unveil two major issues: (i) the research in opportunistic is mature enough to jump from pure theory to implementation, and (ii) there are still under-explored and interesting research areas in opportunistic scheduling, e.g., opportunistic offloading of cellular traffic to 802.11-like networks, or cooperative/distributed opportunistic scheduling.
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Packet Scheduling and Fairness for Multiuser MIMO Systems

paper_content:

This paper investigates the network resource allocation in multiuser downlink wireless systems where the base station and the mobile stations are equipped with multiple antennas to provide fair and efficient transmission services to the mobile users. We focus on packet scheduling, given that it has a significant impact on the overall performance of a multiple-input-multiple-output (MIMO) system. Most previous schedulers designed at the packet level do not take into account the traffic characteristics (different packet lengths and the arrival process parameters); consequently, they fall short of simultaneously providing fairness and a low average packet transmission delay. We are making use of a flexible packet transmission algorithm at the medium access control (MAC) layer to develop and propose a novel scheduler, which is referred to as MIMO packet-based proportional fairness (MP-PF). The new scheduler is designed with the goal of providing high performance in terms of a low average packet transmission delay and time and service fairness among the users based on the concept of proportional fairness. The scheduler also conserves work and takes into consideration the packet length, the user queue length, the user transmission rate (related to its channel quality), and the service guarantees for heterogeneous users. The well-known ideal service fair scheduler called max-min can also significantly be improved using our framework by taking into consideration the traffic characteristics. We also provide an analysis for the fairness of the new scheduler in terms of time and service allocation, which is the key contribution of this paper. Simulations that consider the traffic characteristics and the mobility of users show the relatively low average packet transmission delay and demonstrate the time and service fairness capabilities of MP-PF, compared with other well-known MIMO schedulers.
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: Stability and Delay of Zero-Forcing SDMA With Limited Feedback

paper_content:

This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor M >; 1. For given M → 1, the number of feedback bits per mobile is proved to be O(-log2(1-1/M)) .
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paper_title: Five Disruptive Technology Directions for 5G

paper_content:

New research directions will lead to fundamental changes in the design of future 5th generation (5G) cellular networks. This paper describes five technologies that could lead to both architectural and component disruptive design changes: device-centric architectures, millimeter Wave, Massive-MIMO, smarter devices, and native support to machine-2-machine. The key ideas for each technology are described, along with their potential impact on 5G and the research challenges that remain.
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paper_title: Multi-mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

paper_content:

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.
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paper_title: Joint Feedback and Scheduling Scheme for Service-Differentiated Multiuser MIMO Systems

paper_content:

In this correspondence, we consider the problem of scheduling, in closed-loop multiuser MIMO systems, a large set of users with different Quality of Service (QoS) requirements, supplied by a single base station (BS) by means of Zero-Forcing Beamforming (ZFBF). We provide a power-and-bandwidth ef- ficient feedback scheme in which only ZFBF-optimal users feedback their CSI, thereby reducing the number of required feedbacks and the computational burden of exhaustive search for best users at the BS. Afterwards, we show that conventional sum- capacity maximizing scheduling policies fall short to meet the req- uisites of delay-sensitive applications, and we provide appropriate scheduling scheme for such-constrained users. Simulation results demonstrate that the proposed scheduling approach successfully meets both average and instantaneous delay constraints of delay- sensitive applications.
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paper_title: Large deviation delay analysis of queue-aware multi-user MIMO systems with two timescale mobile-driven feedback

paper_content:

Multi-user multi-input-multi-output (MU-MIMO) systems usually require users to feedback the channel state information (CSI) for scheduling. Most of the existing literature on the reduced feedback user scheduling focused on the throughput performance and the queueing delay was usually ignored. As the delay is important for real-time applications, it is desirable to have a low feedback queue-aware user scheduling algorithm for MU-MIMO systems. This paper proposes a two timescale queue-aware user scheduling algorithm, which consists of a queue-aware mobile-driven feedback filtering stage and a SINR-based user scheduling stage. The feedback policy is obtained by solving a queue-weighted optimization problem. In addition, we evaluate the associated queueing delay performance by using the large deviation analysis. The large deviation decay rate for the proposed algorithm is shown to be much larger than the CSI-only scheduling algorithm. Numerical results demonstrate the large performance gain of the proposed algorithm over the CSI-only algorithm, while the proposed one requires only a small amount of feedback.
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paper_title: System evaluation of optimal downlink beamforming with congestion control in wireless communication

paper_content:

We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.
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paper_title: Downlink Packet Scheduling in LTE Cellular Networks: Key Design Issues and a Survey

paper_content:

Future generation cellular networks are expected to provide ubiquitous broadband access to a continuously growing number of mobile users. In this context, LTE systems represent an important milestone towards the so called 4G cellular networks. A key feature of LTE is the adoption of advanced Radio Resource Management procedures in order to increase the system performance up to the Shannon limit. Packet scheduling mechanisms, in particular, play a fundamental role, because they are responsible for choosing, with fine time and frequency resolutions, how to distribute radio resources among different stations, taking into account channel condition and QoS requirements. This goal should be accomplished by providing, at the same time, an optimal trade-off between spectral efficiency and fairness. In this context, this paper provides an overview on the key issues that arise in the design of a resource allocation algorithm for LTE networks. It is intended for a wide range of readers as it covers the topic from basics to advanced aspects. The downlink channel under frequency division duplex configuration is considered as object of our study, but most of the considerations are valid for other configurations as well. Moreover, a survey on the most recent techniques is reported, including a classification of the different approaches presented in literature. Performance comparisons of the most well-known schemes, with particular focus on QoS provisioning capabilities, are also provided for complementing the described concepts. Thus, this survey would be useful for readers interested in learning the basic concepts before going into the details of a particular scheduling strategy, as well as for researchers aiming at deepening more specific aspects.
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paper_title: Traffic-Aware Training and Scheduling for MISO Wireless Downlink Systems

paper_content:

In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback/training decision. This should be leveraged in future communication systems.
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paper_title: Joint Beamforming and Scheduling for a Multi-Antenna Downlink with Imperfect Transmitter Channel Knowledge

paper_content:

We consider the downlink of a wireless system where the base-station has M ges 1 antennas and K user terminals have one antenna each. We study the weighted rate sum maximization in the case of non-perfect Channel State Information at the Transmitter (CSIT). Some relevant downlink optimization problems, such as the stabilization of the transmission queues under random packet arrivals and the proportional fair scheduling for infinite backlogged systems, can be solved as special cases of the proposed problem. We restrict the transmitter strategy to be based on Gaussian coding and beamforming. Even under this simplifying condition, the problem at hand is non-convex and it does not appear to lend itself to a simple algorithmic solution. Therefore, we introduce some approximations that yield a definition of signal-to-interference plus noise ratio (SINR) commonly used in the classical array- processing/beamforming literature. For the simpler (but still non-convex) approximated problem, we propose a powerful heuristic solution based on greedy user selection and a gradient iteration that converges to a local maximum of the objective function. This method yields very competitive results with relatively low computational complexity. Extensive simulations show that, in the case of perfect CSIT, the proposed heuristic scheme performs very closely to the optimal (dirty-paper coding) strategy while, in the case of non-perfect CSIT, it significantly outperforms previously proposed suboptimal approaches, such as random beamforming and approximated zero-forcing with greedy user selection.
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paper_title: Characterization of SINR Region for Interfering Links With Constrained Power

paper_content:

In this paper, a communication system including n interfering additive white Gaussian noise (AWGN) links is considered. Each transmitter uses a Gaussian codebook and each receiver only decodes the data of the corresponding transmitter. For the case that the transmit powers are subject to arbitrary linear constraints, a mathematical expression for the boundary points of the signal-to-interference-plus-noise-ratio (SINR) region is obtained. Moreover, when the channels are time-varying and the average powers are constrained, the zero-outage SINR region of the system is derived. In addition, a scenario where the demanded SINR of the users is out of the SINR region is considered. A common approach is to remove a subset of the users such that the demanded SINR can be provided for the remaining users; the removed users are serviced in a later time slot. With the aim of maximizing the number of serviced users in each time slot, a suboptimal algorithm is developed, which outperforms the other known alternatives.
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paper_title: An overview of limited feedback in wireless communication systems

paper_content:

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
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paper_title: Spatial scheduling in multiuser wireless systems: from power allocation to admission control

paper_content:

Given a zero forcing transmit beamforming, we focus on how the multi-antenna access point distributes the scarce resource (power) among the single-antenna terminals. Since there is a clear trade-off between the satisfaction of the individual needs and the global performance of the cell, several criteria are proposed, ranging from a classical physical layer point of view of capacity (rate) maximization to bit error rate (BER)-based cost functions, which are closer to the second layer of the protocol stack. Between two traditional techniques, namely the uniform power allocation and the equal BER and rate, a new one is proposed, which ultimately provides an intermediate performance. Then, we add BER (or signal to noise ratio) constraints so that the admission control problem has to be solved. Among traditional options, we propose a new mechanism to balance the above-mentioned trade-off between the total performance and the particular user behavior. The results in terms of fairness are presented by a mean vs. variance plot and by the Gini plot
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paper_title: A Unified Approach to QoS-Guaranteed Scheduling for Channel-Adaptive Wireless Networks

paper_content:

Scheduling amounts to allocating optimally channel, rate and power resources to multiple connections with diverse quality-of-service (QoS) requirements. It consti- tutes a throughput-critical task at the medium access control layer of today's wireless networks that has been tackled by seemingly unrelated information-theoretic and protocol design approaches. Capitalizing on convex optimization and stochastic approximation tools, the present paper develops a unified framework for channel-aware QoS-guaranteed scheduling protocols for use in adaptive wireless networks whereby multiple terminals are linked through orthogonal fading channels to an access point, and transmissions are (opportu- nistically) adjusted to the intended channel. The unification encompasses downlink and uplink with time-division or frequency-division duplex operation; full and quantized chan- nel state information comprising a few bits communicated over a limited-rate feedback channel; different types of traffic (best effort, non-real-time, real-time); uniform and optimal power loading; off-line optimal scheduling schemes benchmarking fundamentally achievable rate limits; as well as on-line scheduling algorithms capable of dynamically learning the intended channel statistics and converging to the optimal benchmarks from any initial value. The take-home message offers an important cross-layer design guideline: judiciously developed, yet surprisingly simple, channel-adaptive, on-line schedulers can approach information-theoretic rate limits with QoS guarantees.
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

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The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: User selection schemes in multiple antenna broadcast channels with guaranteed performance

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Recently, user selection algorithms in combination with linear pre- coding have been proposed that achieve the same scaling as the sum capacity of the MIMO BC. In this work, we study the properties of four user selection algorithms in conjunction with beamforming that guarantee certain SINR requirements under transmit power minimization. It is shown that for a large number of transmit antennas, the norm-based user selection performs close to the optimum. The results are illustrated by various numerical simulations.
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paper_title: Joint Scheduling and ARQ for MU-MIMO Downlink in the Presence of Inter-Cell Interference

paper_content:

User scheduling and multiuser multi-antenna (MU-MIMO) transmission are at the core of high-rate data-oriented downlink schemes of the next-generation of cellular systems (e.g., LTE-Advanced). Scheduling selects groups of users according to their channels vector directions and SINR levels. However, when scheduling is applied independently in each cell, the inter-cell interference (ICI) power at each user receiver is not known in advance since it changes at each new scheduling slot depending on the scheduling decisions of all interfering base stations. In order to cope with this uncertainty, we consider the joint operation of scheduling, MU-MIMO beamforming and Automatic Repeat reQuest (ARQ). We develop a game-theoretic framework for this problem and build on stochastic optimization techniques in order to find optimal scheduling and ARQ schemes. Particularizing our framework to the case of "outage service rates", we obtain a scheme based on adaptive variable-rate coding at the physical layer, combined with ARQ at the Logical Link Control (ARQ-LLC). Then, we present a novel scheme based on incremental redundancy Hybrid ARQ (HARQ) that is able to achieve a throughput performance arbitrarily close to the "genie-aided service rates", with no need for a genie that provides non-causally the ICI power levels. The novel HARQ scheme is both easier to implement and superior in performance with respect to the conventional combination of adaptive variable-rate coding and ARQ-LLC.
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paper_title: The impact of space division multiplexing on resource allocation: a unified treatment of TDMA, OFDMA and CDMA

paper_content:

Space division multiple access (SDMA) with an antenna array at the transmitter is a promising means for increasing system capacity and supporting rate-demanding services. However, the presence of an antenna array at the physical layer raises significant issues at higher layers. In this paper, we attempt to capture the impact of SDMA on access layer channel allocation, reflected on channel reuse. This impact obtains different twists in TDMA, CDMA and OFDMA due to the different nature of co-channel and cross-channel interference and the different interaction of user spatial channel characteristics with system channels, namely time slots, codes and subcarriers. We consider these access schemes in a generalized unified framework and propose heuristic algorithms for channel allocation, downlink beamforming and transmit power control so as to increase total provisioned system rate and provide QoS to users in the form of minimum rate guarantees. We study the class of greedy algorithms that rely on criteria such as induced or received interference and signal-to-interference ratio (SIR), and a class of SIR balancing algorithms. Results show superior performance for SIR balancing resource allocation and expose the performance benefits of cross-layer design.
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paper_title: Sum rate maximization via joint scheduling and link adaptation for interference-coupled wireless systems

paper_content:

The work presented in this paper addresses the sum rate maximization problem for the downlink of a wireless network where multiple transmitter-receiver links share the same medium and thus potentially interfere with each other. The solution of this problem requires the optimization of two aspects: the first one is the set of links that can be jointly scheduled, and the second is the set modulation and coding schemes (MCSs) that maximize the sum rate. A feasible link achieves a certain MCS if its signal-to-interference-plus-noise ratio (SINR) is above a threshold or target SINR associated with the MCS and the SINR of each link is coupled with the other links’ powers that are required to achieve their respective MCSs. Since the available MCSs form a finite set, the rate maximization problem has a combinatorial nature. We present iterative algorithms that find a suboptimal solution to the combinatorial problem by operating in two phases. Phase one verifies the feasibility of the MCS assignment by performing either eigenvalue analysis or power consumption analysis, and phase two uses the feasibility information delivered by phase one to modify either the set of links (user removal) or the MCS assignment if feasibility conditions are not fulfilled. Our approach extends the concept of user removal to the case of adaptive modulation, and this generalization allows us to schedule users more efficiently, improving outage probability figures. Numerical results show that the proposed algorithms achieved a good tradeoff between sum rate performance and complexity. Moreover, our algorithms are a low complex alternative to the state-of-the-art user-removal algorithms with minimum gap in outage performance.
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paper_title: Ultra-dense networks in millimeter-wave frequencies

paper_content:

Demands for very high system capacity and end-user data rates of the order of 10 Gb/s can be met in localized environments by Ultra-Dense Networks (UDN), characterized as networks with very short inter-site distances capable of ensuring low interference levels during communications. UDNs are expected to operate in the millimeter-wave band, where wide bandwidth signals needed for such high data rates can be designed, and will rely on high-gain beamforming to mitigate path loss and ensure low interference. The dense deployment of infrastructure nodes will make traditional wire-based backhaul provisioning challenging. Wireless self-backhauling over multiple hops is proposed to enhance flexibility in deployment. A description of the architecture and a concept based on separation of mobility, radio resource coordination among multiple nodes, and data plane handling, as well as on integration with wide-area networks, is introduced. A simulation of a multi-node office environment is used to demonstrate the performance of wireless self-backhauling at various loads.
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paper_title: Resource Allocation Optimization in Multi-User Multi-Cell Massive MIMO Networks Considering Pilot Contamination

paper_content:

In this paper, we study the joint pilot assignment and resource allocation for system energy efficiency (SEE) maximization in the multi-user and multi-cell massive multi-input multi-output network. We explicitly consider the pilot contamination effect during the channel estimation in the SEE maximization problem, which aims to optimize the power allocation, the number of activated antennas, and the pilot assignment. To tackle the SEE maximization problem, we transform it into a subtractive form, which can be solved more efficiently. In particular, we develop an iterative algorithm to solve the transformed problem where optimization of power allocation and number of antennas is performed, and then pilot assignment optimization is conducted sequentially in each iteration. To tackle the first sub-problem, we employ a successive convex approximation (SCA) technique to attain a solvable convex optimization problem. Moreover, we propose a novel iterative low-complexity algorithm based on the Hungarian method to solve the pilot assignment sub-problem. We also describe how the proposed solution approach can be useful to address the sum rate (SR) maximization problem. In addition to the algorithmic developments, we characterize the optimal structure of both SEE and SR maximization problems. The numerical studies are conducted to illustrate the convergence of the proposed algorithms, impacts of different parameters on the SR and SEE, and significant performance gains of the proposed solution compared the conventional design.
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paper_title: Fairness in Wireless Networks:Issues, Measures and Challenges

paper_content:

The pervasiveness of wireless technology has indeed created massive opportunity to integrate almost everything into the Internet fabric. This can be seen with the advent of Internet of Things and Cyber Physical Systems, which involves cooperation of massive number of intelligent devices to provide intelligent services. Fairness amongst these devices is an important issue that can be analysed from several dimensions, e.g., energy usage, achieving required quality of services, spectrum sharing, and so on. This article focusses on these viewpoints while looking at fairness research. To generalize, mainly wireless networks are considered. First, we present a general view of fairness studies, and pose three core questions that help us delineate the nuances in defining fairness. Then, the existing fairness models are summarized and compared. We also look into the major fairness research domains in wireless networks such as fair energy consumption control, power control, topology control, link and flow scheduling, channel assignment, rate allocation, congestion control and routing protocols. We make a distinction amongst fairness, utility and resource allocation to begin with. Later, we present their inter-relation. At the end of this article, we list the common properties of fairness and give an example of fairness management. Several open research challenges that point to further work on fairness in wireless networks are also discussed. Indeed, the research on fairness is entangled with many other aspects such as performance, utility, optimization and throughput at the network and node levels. While consolidating the contributions in the literature, this article tries to explain the niceties of all these aspects in the domain of wireless networking.
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paper_title: Joint Realtime and Nonrealtime Flows Packet Scheduling and Resource Block Allocation in Wireless OFDMA Networks

paper_content:

In this paper, we consider joint realtime (RT) and nonrealtime (NRT) flows packet scheduling and resource block (RB) allocation in orthogonal frequency division multiple access (OFDMA) wireless networks. Radio RBs in the OFDMA plane are to be distributed among RT and NRT flows. In the conventional approach, RT and NRT flows are served sequentially. This sequential approach is inefficient because an RT flow may presumably have enough time until its delay deadline while its channel is in deep fade. In this situation, the transmission of NRT flows with higher level of efficiency can be performed. Intuitively speaking, the conventional sequential approach is too conservative, which can be reengineered. We propose a novel joint RT and NRT flows disutility-based packet scheduling and RB allocation in a common pool of RBs. The proposed joint approach enlarges the effective capacity of the associated wireless system when compared with the separated pool of RBs. The joint approach is particularly relevant for improving voice over LTE (VoLTE). We use mean bit-rate, mean queue-length, and instantaneous queuing delay information, in addition to channel information, to match the demand and supply. Furthermore, we develop a novel model for input–output bit-rate behavior of the mixture of RT and NRT flows. This model sheds light on the identification of different load regions and understanding of the system in an intuitive manner. Our approach and methodology can be extended for broader quality-of-service (QoS) requirements and for the utility of future applications. Simulation results show that the proposed framework is able to unify the serving mechanism of the RT and NRT flows and is able to achieve higher admissible bit-rate when handling mixed RT and NRT flows, compared with various baselines.
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paper_title: Optimal Tradeoff Between Sum-Rate Efficiency and Jain's Fairness Index in Resource Allocation

paper_content:

The focus of this paper is on studying the tradeoff between the sum efficiency and Jain's fairness index in general resource allocation problems. Such problems are frequently encountered in wireless communication systems with M users. Among the commonly-used methods to approach these problems is the one based on the α-fair policy. Analyzing this policy, it is shown that it does not necessarily achieve the optimal Efficiency-Jain tradeoff (EJT) except for the case of M=2 users. When the number of users M>2, it is shown that the gap between the efficiency achieved by the α-fair policy and that achieved by the optimal EJT policy for the same Jain's index can be unbounded. Finding the optimal EJT corresponds to solving a family of potentially difficult non-convex optimization problems. To alleviate this difficulty, we derive sufficient conditions which are shown to be sharp and naturally satisfied in various radio resource allocation problems. These conditions provide us with a means for identifying cases in which finding the optimal EJT and the rate vectors that achieve it can be reformulated as convex optimization problems. The new formulations are used to devise computationally-efficient resource schedulers that enable the optimal EJT to be achieved for both quasi-static and ergodic time-varying communication scenarios. Analytical findings are confirmed by numerical examples.
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paper_title: Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO

paper_content:

What would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a “massive MIMO” fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.
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paper_title: A survey of green scheduling schemes for homogeneous and heterogeneous cellular networks

paper_content:

Energy efficiency is becoming an important feature for designing the next generation of communication networks, as are the multiplication of access points and the reduction of their coverage area. In this article we survey the latest development in energy-efficient scheduling, a.k.a. green scheduling, for both classic and heterogeneous cellular networks. We first introduce the main system model and framework that are considered in most of the existing green scheduling works. We then describe the main contributions on green scheduling as well as summarize their key findings. For instance, green scheduling schemes have demonstrated that they can significantly reduce transmit power and improve the energy efficiency of cellular systems. We also provide a performance analysis of some of the existing schemes in order to highlight some of the challenges that need to be addressed to make green scheduling more effective in heterogeneous networks. Indeed, the coordination between tiers and the rate fairness between the users of different tiers are important issues that have not yet been addressed. In addition, most existing designs exhibit a computational complexity that is too high for being deployed in a real system.
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paper_title: Optimized Distributed Inter-Cell Interference Coordination (ICIC) Scheme Using Projected Subgradient and Network Flow Optimization

paper_content:

In this paper, we tackle the problem of multi-cell resource scheduling, where the objective is to maximize the weighted sum-rate through inter-cell interference coordination (ICIC). The blanking method is used to mitigate the inter-cell interference, where a resource is either used with a predetermined transmit power or not used at all, i.e., blanked. This problem is known to be strongly NP-hard, which means that it is not only hard to solve in polynomial time, but it is also hard to find an approximation algorithm with guaranteed optimality gap. In this work, we identify special scenarios where a polynomial-time algorithm can be constructed to solve this problem with theoretical guarantees. In particular, we define a dominant interference environment, in which for each user the received power from each interferer is significantly greater than the aggregate received power from all other weaker interferers. We show that the originally strongly NP-hard problem can be tightly relaxed to a linear programming problem in a dominant interference environment. Consequently, we propose a polynomial time distributed algorithm that is not only guaranteed to be tight in a dominant interference environment, but which also computes an upper bound on the optimality gap without additional computational complexity. The proposed scheme is based on the primal-decomposition method, where the problem is divided into a master-problem and multiple subproblems. We solve the master-problem iteratively using the projected-subgradient method. We also show that each subproblem has a special network flow structure. By exploiting this network structure, each subproblem is solved using the network-based optimization methods, which significantly reduces the complexity in comparison to the general-purpose convex or linear optimization methods. In comparison with baseline schemes, simulation results of the International Mobile Telecommunications-Advanced (IMT-Advanced) scenarios show that the proposed scheme achieves higher gains in aggregate throughput, cell-edge throughput, and outage probability.
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paper_title: Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics in 5G Systems

paper_content:

The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by delivering a Wi-Fi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years [1], as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate requirements specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological preparations for fifth-generation (5G) networks: higher peak rates, improved coverage with uniform user experience, higher reliability and lower latency, better energy efficiency (EE), lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the existence of multiple objectives and tradeoffs between them.
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paper_title: Fundamental trade-offs on green wireless networks

paper_content:

Traditional mobile wireless network mainly design focuses on ubiquitous access and large capacity. However, as energy saving and environmental protection become global demands and inevitable trends, wireless researchers and engineers need to shift their focus to energy-efficiency-oriented design, that is, green radio. In this article, we propose a framework for green radio research and integrate the fundamental issues that are currently scattered. The skeleton of the framework consists of four fundamental tradeoffs: deployment efficiency-energy efficiency, spectrum efficiency-energy efficiency, bandwidth-power, and delay-power. With the help of the four fundamental trade-offs, we demonstrate that key network performance/cost indicators are all strung together.
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paper_title: An optimization framework for balancing throughput and fairness in wireless networks with QoS support

paper_content:

Quality-of-service (QoS) provisioning, high system throughput, and fairness assurance are indispensable for heterogeneous traffic in future wireless broadband networks. With limited radio resources, increasing system throughput and maintaining fairness are conflicting performance metrics, leading to a natural tradeoff between these two measures. Balancing system throughput and fairness is desired. In this paper, we consider an interference-limited wireless network, and derive a generic optimization framework to obtain an optimal relationship of system throughput and fairness with QoS support and efficient resource utilization, by introducing the bargaining floor. From the relationship curve, different degrees of performance tradeoff between throughput and fairness can be obtained by choosing different bargaining floors. In addition, our framework facilitates call admission control to effectively guarantee QoS of. multimedia traffic. The solutions of resource allocation obtained from the optimization framework achieve the pareto optimality, demonstrating efficient use of network resources.
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paper_title: What Will 5G Be?

paper_content:

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
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paper_title: Joint Precoding and Load Balancing Optimization for Energy-Efficient Heterogeneous Networks

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This paper considers a downlink heterogeneous network, where different types of multiantenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS operation mode are jointly optimized for improving the network energy efficiency. We minimize the weighted total power consumption while satisfying quality-of-service constraints at the users. This problem is nonconvex, but we prove that for each BS mode combination, the considered problem has a hidden convexity structure. Thus, the optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the nonconvex objective function, a heuristic algorithm is proposed to obtain a suboptimal solution of low complexity. We show that although multicell joint transmission is allowed, in most cases, it is optimal for each user to be served by a single BS. The optimal BS association condition is parameterized, which reveals how it is impacted by different system parameters. Simulation results indicate that putting a BS into sleep mode by proper load balancing is an important solution for energy savings.
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paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

paper_content:

This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: The Design of Approximation Algorithms

paper_content:

Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
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paper_title: Subchannel allocation in multiuser multiple input multiple output systems

paper_content:

Assuming perfect channel state information at the transmitter of a Gaussian broadcast channel, strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel. For the general sum capacity maximizing solution, which has recently been found, a method is proposed that transforms each of the resulting vector channels into a set of scalar channels. This makes possible to achieve capacity by simply using scalar coding and detection techniques. The high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero-forcing allocation strategy that directly results in a set of virtually decoupled scalar channels. Simulation results show that this technique tightly approaches the performance of the optimum solution, i.e., complexity reduction comes at almost no cost in terms of sum capacity. As the optimum solution, the zero-forcing allocation strategy applies to any number of transmit antennas, receive antennas and users
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paper_title: Efficient MAC protocol for JT CoMP in small cells

paper_content:

In this paper, we investigate an efficient MAC protocol for interference coordination in small cells embedded in a macro-cell mobile network. We perform joint transmission (JT)-coordinated multi-point (CoMP), where cells in the cluster include adjacent macro-cells as suggested by the small-cell terminal. Most gains compared to uncoordinated transmission come from selecting the right users in these macro-cells. For minimizing the feedback overhead, we propose successive channel state information (CSI) requests. Thereby we replace users in the set until all of them experience consistently enhanced performance when using JT-CoMP. Gains can be further increased by MIMO mode switching in each cell and frequency-selective scheduling. We tested our algorithms over coherently measured multi-cell channels in the LTE-Advanced testbed in Berlin where small cells were embedded at several places. Using these algorithms, performance becomes comparable to a popular bound assuming no more intra-cluster interference while feedback overhead and complexity are substantially reduced.
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paper_title: Learning-Based Adaptive Transmission for Limited Feedback Multiuser MIMO-OFDM

paper_content:

Performing link adaptation in a multiantenna and multiuser system is challenging because of the coupling between precoding, user selection, spatial mode selection and use of limited feedback about the channel. The problem is exacerbated by the difficulty of selecting the proper modulation and coding scheme when using orthogonal frequency division multiplexing (OFDM). This paper presents a data-driven approach to link adaptation for multiuser multiple input mulitple output (MIMO) OFDM systems. A machine learning classifier is used to select the modulation and coding scheme, taking as input the SNR values in the different subcarriers and spatial streams. A new approximation is developed to estimate the unknown interuser interference due to the use of limited feedback. This approximation allows to obtain SNR information at the transmitter with a minimum communication overhead. A greedy algorithm is used to perform spatial mode and user selection with affordable complexity, without resorting to an exhaustive search. The proposed adaptation is studied in the context of the IEEE 802.11ac standard, and is shown to schedule users and adjust the transmission parameters to the channel conditions as well as to the rate of the feedback channel.
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paper_title: User scheduling for massive MIMO OFDMA systems with hybrid analog-digital beamforming

paper_content:

This paper proposes a new user scheduling and sub-carrier allocation algorithm for multiuser downlink massive multiple input multiple output (MIMO) orthogonal frequency division multiple access (OFDMA) systems with hybrid analogdigital beamforming (HB). We assume that the transmitter having N antennas is serving K i decentralized single antenna receivers by sub-carrier i. The scheduling algorithm leverages the solutions of the digital beamforming (DB) result and is designed to maximize the total sum rate of all sub-carriers under per carrier power constraint. For this system and problem setup, the proposed algorithm is explained as follows: First, we express the HB matrix of sub-carrier i as a product of AB i , where the high dimensional matrix A ∈ CN×Na is common to all subcarriers whereas, B i ∈ CNa×Ki is a low dimensional matrix which is designed for sub-carrier i, and Na is the number of RF chains satisfying N ≥ Na ≥ K i . Second, we compute A as the first Na eigenvectors of the left singular value decomposition of the combined DB precoder matrices of sub-carriers having the highest sum rate. Finally, for fixed A, we compute Bi and its corresponding users such that the total sum rate of all sub-carriers is maximized. The performance of the proposed scheduling is studied analytically. Furthermore, the superiority of the proposed algorithm over that of the existing one is quantified analytically and demonstrated by computer simulations.
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paper_title: User Selection With Zero-Forcing Beamforming Achieves the Asymptotically Optimal Sum Rate

paper_content:

In this paper, we propose a generalized greedy (G-greedy) algorithm based on zero-forcing beamforming (ZFBF) for the multiple-input multiple-output (MIMO) broadcast channel. This algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations. As previous results only give the scaling law of the sum rate of dirty paper coding (DPC), with the help of the G-greedy structure, we are able to obtain the exact limit of the DPC sum rate for a large number of users. We also prove that the difference between the sum rates obtained by G-greedy user selection and by DPC goes to zero as the number of users increases. In addition to this, we investigate one particular greedy user selection scheme called sequential water-filling (SWF). For this algorithm, a complexity reduction is achieved by an iterative procedure based on an LQ decomposition, which converts the calculation of the Moore-Penrose matrix inverse to one vector-matrix multiplication. A sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction. With the help of the G-greedy algorithm, we prove that SWF achieves the full DPC sum rate for a large number of users. For a moderate number of users, simulation demonstrates that, compared with other user selection algorithms, SWF achieves a higher sum rate that is close to the maximal sum rate achievable by ZFBF with the same order of complexity.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: Adaptive radio resource allocation for downlink OFDMA/SDMA systems with multimedia traffic

paper_content:

This paper proposes an adaptive radio resource allocation (ARRA) algorithm for downlink OFDMA/SDMA systems with multimedia traffic. Considering multiple service classes and diverse QoS requirements of multimedia traffic, the ARRA algorithm is designed with the goal to maximize spectrum efficiency and to fulfill quality of service (QoS) requirements. It is composed of two parts, a dynamic priority adjustment (DPA) scheme and a priority-based greedy (PBG) scheme. The DPA adopts a type of time-to-expiration to indicate the degree of user's urgency, and dynamically gives high priorities to urgent users. The PBG allocates the radio resource iteratively, based on a cost value, to maximize the system throughput while allocating enough resource to high-priority users. Simulation results show that the ARRA algorithm outperforms conventional algorithms in terms of system throughput and satisfaction extent of QoS requirements; it can sustain users' QoS requirements up till a traffic load of 0.8, while the conventional algorithms cannot guarantee QoS requirements after a traffic load of 0.3.
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paper_title: On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm

paper_content:

This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple "beams" directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of the same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum's scheme and, thus, offers an attractive alternative to DP-based schemes.
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paper_title: User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming

paper_content:

In this paper, we propose a greedy user selection with swap (GUSS) algorithm based on zero-forcing beamforming for multiuser multiple-input-multiple-output (MIMO) downlink channels. Existing user selection algorithms such as zero forcing with selection (ZFS) have the flaws of “redundant users” and “local optimum,” which compromise the achieved sum rate. GUSS improves the performance by adding the “delete” and “swap” operations to the user selection procedure of ZFS to eliminate “redundant users” and escape from “local optimum,” respectively. In addition, an effective-channel-vector-based effective-channel-gain-updating scheme is proposed to reduce the complexity of GUSS. With the help of this updating scheme, GUSS has the same order of complexity as ZFS with only a linear increment. Simulation results indicate that over the range of transmit signal-to-noise ratios (SNRs) considered, on average, the sum rate of GUSS reaches 99.3% of the upper bound that is achieved by exhaustive search, with only 1.51 to 2.29 times the complexity of ZFS.
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paper_title: Multiuser MIMO Scheduling for LTE-A Downlink Cellular Networks

paper_content:

In this paper, we investigate multiuser MIMO scheduling in LTE downlink cellular networks. We formulate the downlink LTE-A MIMO scheduling as a weighted sum rate maximization problem by allocating the RBs to users or user pairs subject to some constraints in LTE-A. We develop a low-complexity MU-MIMO scheduling and resource allocation algorithm and propose an adaptive switching approach between SU-MIMO and MU-MIMO to improve network performance. System-level simulation results demonstrate significantly performance improvement of the proposed MU-MIMO scheduling algorithm and the adaptive switching algorithm.
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paper_title: Hierarchical Interference Mitigation for Massive MIMO Cellular Networks

paper_content:

We propose a hierarchical interference mitigation scheme for massive MIMO cellular networks. The MIMO precoder at each base station (BS) is partitioned into an inner precoder and an outer precoder. The inner precoder controls the intra-cell interference and is adaptive to local channel state information (CSI) at each BS (CSIT). The outer precoder controls the inter-cell interference and is adaptive to channel statistics. Such hierarchical precoding structure reduces the number of pilot symbols required for CSI estimation in massive MIMO downlink and is robust to the backhaul latency. We study joint optimization of the outer precoders, the user selection, and the power allocation to maximize a general concave utility which has no closed-form expression. We first apply random matrix theory to obtain an approximated problem with closed-form objective. We show that the solution of the approximated problem is asymptotically optimal with respect to the original problem as the number of antennas per BS grows large. Then using the hidden convexity of the problem, we propose an iterative algorithm to find the optimal solution for the approximated problem. We also obtain a low complexity algorithm with provable convergence. Simulations show that the proposed design has significant gain over various state-of-the-art baselines.
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paper_title: A Survey on Opportunistic Scheduling in Wireless Communications

paper_content:

Wireless technology advancements made opportunistic scheduling a popular topic in recent times. However, opportunistic schedulers for wireless systems have been studied since nearly twenty years, but not implemented in real systems due to their high complexity and hardly achievable requirements. In contrast, today's popularity of opportunistic schedulers extends to implementation proposals for next generation cellular technologies. Motivated by such a novel interest towards opportunistic scheduling, we provide a taxonomy for opportunistic schedulers, which is based on scheduling design's objectives; accordingly, we provide an extensive review of opportunistic scheduling proposals which have appeared in the literature during nearly two decades. The huge number of papers available in the literature propose different techniques to perform opportunistic scheduling, ranging from simple heuristic algorithms to complex mathematical models. Some proposals are only designed to increase the total network capacity, while others enhance QoS objectives such as throughput and fairness. Interestingly, our survey helps to unveil two major issues: (i) the research in opportunistic is mature enough to jump from pure theory to implementation, and (ii) there are still under-explored and interesting research areas in opportunistic scheduling, e.g., opportunistic offloading of cellular traffic to 802.11-like networks, or cooperative/distributed opportunistic scheduling.
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paper_title: Multicell Cooperative Scheduling for Two-Tier Cellular Networks

paper_content:

Cellular wireless network architectures employing a tiered structure, consisting of traditional macro-cells and small-cells, have attracted much attention recently because of their potential to dramatically increase network capacity. These architectures can reduce the distances of transmit-receiver pairs, thus enhancing radio link qualities. However, a tiered cell deployment could incur severe cochannel interference. Prior work for single-tier networks has proposed coordinated multi-point (CoMP) transmission, which includes joint transmission, as a possible solution for overcoming the rate limitations induced by cochannel interference. Because users in each cell experience various interference conditions, each cell needs to support single transmission (in which only one cell transmits to a single user) and joint transmission. In a conventional implementation, a particular combination of transmissions over the entire network is fixed in advance for each time slot and opportunistic scheduling chooses one of the users supported by each transmission. However, when the number of users to be scheduled is small, the throughput improvement from opportunistic scheduling becomes limited. To overcome this problem, we propose a cumulative distribution function-based scheduling scheme which jointly chooses the transmitter set and the corresponding scheduled users in a two-tier network. It is shown that the throughput performance can be improved compared to those of the fixed slot resource allocation scheme because more users "compete" for slot resources.
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paper_title: Decremental User Selection for Large-Scale Multi-User MIMO Downlink with Zero-Forcing Beamforming

paper_content:

This paper proposes a decremental user selection algorithm based on zero-forcing beamforming when the number of users K in the network is smaller than the number of antennas M at a base station. The algorithm is specifically designed for large-scale multi-user multiple-input multiple-output (MIMO) downlink channels. While previous user selection algorithms are based on incremental search that starts from an empty user set, our proposed delete the minimum lambda (DML) algorithm starts by selecting all users and then deleting one user per iteration. DML substantially reduces the computational complexity as the cardinality of the final user set is close to K. Simulation results indicate that on average DML achieves an equal or higher sum rate performance than previous algorithms with greatly reduced complexity of O(MK2).
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paper_title: Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

paper_content:

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.
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paper_title: Optimal Resource Allocation for Multiuser MIMO-OFDM Systems With User Rate Constraints

paper_content:

With the proliferation of wireless services, personal connectivity is quickly becoming ubiquitous. As the user population demands greater multimedia interactivity, data rate requirements are set to soar. Future wireless systems, e.g., multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), need to cater to not only a burgeoning subscriber pool but also to a higher throughput per user. Furthermore, resource allocation for multiuser MIMO-OFDM systems is vital for the optimization of the subcarrier and power allocations to improve overall system performance. Using convex optimization techniques, this paper proposes an efficient solution to minimize the total transmit power subject to each user's data rate requirement. Using a Lagrangian dual decomposition, the complexity is reduced from one that is exponential in the number of subcarriers M to one that is only linear in M. To keep the complexity low, linear beamforming is incorporated at both the transmitter and the receiver. Although frequency-flat fading has been known to plague OFDM resource allocation systems, a modification, i.e., dual proportional fairness, seamlessly handles flat or partially frequency-selective fading. Due to the nonconvexity of the optimization problem, the proposed solution is not guaranteed to be optimal. However, for a realistic number of subcarriers, the duality gap is practically zero, and optimal resource allocation can be evaluated efficiently. Simulation results show large performance gains over a fixed subcarrier allocation.
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: Spatial Transmission Mode Switching in Multiuser MIMO-OFDM Systems With User Fairness

paper_content:

Multiantenna radio systems allow accessing the channel in diversity or spatial multiplexing (SMUX) mode. Adequate switching between these modes according to current channel conditions was shown to yield significant performance improvements while requiring little feedback from the receiving side. We present a transmission concept for the downlink of a multiuser multiple-input-multiple-output orthogonal frequency-division-multiplexing (MU-MIMO-OFDM) system aiming at high user rates with limited feedback demands. An extended score-based scheduling (SB) approach ensures fair-resource allocation to the users, whereas transmission mode switching is used to guarantee high user rates. The degree of fairness of the scheduler can be adapted by adequately configuring a weighting function for the scores. Comparison with single-mode schemes reveals substantial throughput gains of the adaptive switching concept. Furthermore, targeting maximum throughput, we show that a considerable proportion of the capacity of the MIMO broadcast channel (BC) can be achieved with a comparatively low amount of required feedback.
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paper_title: On the Performance of Downlink Beamforming with Synchronized Beam Cycles

paper_content:

The next generation of wireless networks (e.g.,) will use multiple techniques to improve channel spectral efficiencies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each frame, the scheduler chooses a beam and then schedules one or more UEs that lie within that beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors. If a neighboring sector schedules a UE that lies within the coverage of this beam then the rate for that UE will be low. The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. The first approach (interference avoidance) requires coordination among the sectors with the associated communication overheads and delays. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period. Although all NBs use the same beam cycle period, they may occasionally change the specific beam schedule based on local factors such as the geographical distribution of UEs within its beams. Such changes should be made infrequently since the approach is based on the assumption that the interference experienced by a UE repeats with the beam cycle period.
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paper_title: A comparison of scheduling strategies for MIMO broadcast channel with limited feedback on OFDM systems

paper_content:

We consider a multiuser downlink transmission from a base station with multiple antennas (MIMO) to mobile terminals (users) with a single antenna, using orthogonal frequency division multiplexing (OFDM). Channel conditions are reported by a feedback from users with limited rate, and the base station schedules transmissions and beamforms signals to users. We show that an important set of schedulers using a general utility function can be reduced to a scheduler maximizing the weighted sum rate of the system. For this case we then focus on scheduling methods with many users and OFDM subcarriers. Various scheduling strategies are compared in terms of achieved throughput and computational complexity and a good tradeoff is identified in greedy and semiorthogonal user selection algorithms. In the greedy selection algorithm, users are selected one by one as long as the throughput increases, while in the semiorthogonal approach users are selected based on the channel correlation. An extension of these approaches from a flat-fading channel to OFDM is considered and simplifications that may be useful for a large number of subcarriers are presented. Results are reported for a typical cellular transmission of the long-term evolution (LTE) of 3GPP.
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paper_title: Optimal downlink space-time scheduling design with convex utility functions-multiple-antenna systems with orthogonal spatial multiplexing

paper_content:

It is well known that link level throughput could be significantly increased by using multiple antennae at the transmitter and receiver without increasing the bandwidth and power budget. However, optimizing the link level performance of multiple-antenna systems does not always imply achieving system level optimization. Therefore, cross-layer optimization across the link layer and the scheduling layer is very important to fully exploit the temporal and spatial dimensions of the communication channel. In this paper, we consider the optimal downlink space-time scheduling design for a general class of convex utility functions. The access point or base station is equipped with n/sub T/ transmit antennas. There are K mobiles in the system with a single receive antenna. For practical reasons, we assume zero-forcing processing at the physical layer of the base station and mobile. We will apply the design framework to two common utility functions, namely the maximum throughput and the proportional fair. The cross-layer scheduling design is a mixed convex and combinatorial optimization problem and the search space of the optimal solution is enormous. Greedy algorithm, which has been widely used in today's wireless data systems (3G1X, high data rate system (HDR), Universal Mobile Terrestrial Service), is optimal when n/sub T/=1. However, we found that there is a large performance penalty of greedy algorithms (relative to optimal performance) when n/sub T/>1 and this motivates the search for more efficient heuristics. In this paper, we will address genetic-based heuristics and discuss their complexity-performance tradeoff.
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paper_title: Two-Stage Channel Quantization for Scheduling and Beamforming in Network MIMO Systems: Feedback Design and Scaling Laws

paper_content:

This paper proposes an efficient two-stage channel quantization and feedback scheme for the downlink limited-feedback network multiple-input multiple-output (MIMO) system. In the first stage, the users report their best set of base-station antenna and physical resource block combinations, and the base-stations schedule the best user for each antenna in each resource block. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. This paper proposes an analytical framework to show that, under a total feedback budget of B bits, the number of bits assigned to the second feedback stage should scale as log B, and in quantizing channel vectors from different base-stations, each user should allocate feedback bits in proportion to the channel magnitudes in dB scale. Under these optimized bit allocations, the overall sum rate of the system is shown to scale double-logarithmically with B, linearly with the total number of antennas, and logarithmically with transmit power, thus achieving both multiuser diversity and spatial multiplexing gains under limited feedback. Finally, realistic wireless propagation model of an urban small-cell deployment is used to show that the proposed scheme can approach the performance of a network MIMO system with full channel state information with only modest amount of channel feedback.
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paper_title: Large deviation delay analysis of queue-aware multi-user MIMO systems with two timescale mobile-driven feedback

paper_content:

Multi-user multi-input-multi-output (MU-MIMO) systems usually require users to feedback the channel state information (CSI) for scheduling. Most of the existing literature on the reduced feedback user scheduling focused on the throughput performance and the queueing delay was usually ignored. As the delay is important for real-time applications, it is desirable to have a low feedback queue-aware user scheduling algorithm for MU-MIMO systems. This paper proposes a two timescale queue-aware user scheduling algorithm, which consists of a queue-aware mobile-driven feedback filtering stage and a SINR-based user scheduling stage. The feedback policy is obtained by solving a queue-weighted optimization problem. In addition, we evaluate the associated queueing delay performance by using the large deviation analysis. The large deviation decay rate for the proposed algorithm is shown to be much larger than the CSI-only scheduling algorithm. Numerical results demonstrate the large performance gain of the proposed algorithm over the CSI-only algorithm, while the proposed one requires only a small amount of feedback.
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paper_title: Downlink Scheduling via Genetic Algorithms for Multiuser Single-Carrier and Multicarrier MIMO Systems With Dirty Paper Coding

paper_content:

Multiple-input-multiple-output (MIMO) systems are of interest for meeting the expected demand for higher data rates and lower delays in future wireless packet data systems. In such systems, it is optimal to simultaneously transmit to multiple users compared with a single user in a single-input-single-output system. In addition, multicarrier systems are of interest to combat frequency-selective fading that is experienced over the larger bandwidth that these future broadband systems will use. The use of dirty paper coding further complicates the matter, because the order in which the users are encoded will affect the rates that they can achieve. A well-designed cross-layer scheduling algorithm must take into account the multiple dimensions of this resource-allocation problem and other quality-of-service (QoS) parameters to fully exploit the communications channel. The scheduling problem is often expressed in terms of optimizing some utility function. Unfortunately, the search space for this optimization problem is extremely large, which prohibits an optimal exhaustive search. To this end, we investigate the use of genetic algorithms to reduce the complexity of the scheduling. This paper builds upon prior work that implements scheduling via genetic algorithms in the context of single-carrier systems using zero-forcing beamforming (ZFB). In this paper, we investigate how the genetic algorithm can be adapted to account for the effect of encoding order on the scheduling and how the scheduling can be extended to a multicarrier system. In particular, we investigate the maximum throughput and proportionally fair scheduling criteria. We demonstrate that the performance of the genetic algorithm is near optimal compared with an exhaustive search at a greatly reduced computational complexity. Furthermore, in the case of a multicarrier orthogonal frequency-division multiplexing (OFDM) system, an increase in capacity is shown relative to the single-carrier case.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Downlink Packet Scheduling in LTE Cellular Networks: Key Design Issues and a Survey

paper_content:

Future generation cellular networks are expected to provide ubiquitous broadband access to a continuously growing number of mobile users. In this context, LTE systems represent an important milestone towards the so called 4G cellular networks. A key feature of LTE is the adoption of advanced Radio Resource Management procedures in order to increase the system performance up to the Shannon limit. Packet scheduling mechanisms, in particular, play a fundamental role, because they are responsible for choosing, with fine time and frequency resolutions, how to distribute radio resources among different stations, taking into account channel condition and QoS requirements. This goal should be accomplished by providing, at the same time, an optimal trade-off between spectral efficiency and fairness. In this context, this paper provides an overview on the key issues that arise in the design of a resource allocation algorithm for LTE networks. It is intended for a wide range of readers as it covers the topic from basics to advanced aspects. The downlink channel under frequency division duplex configuration is considered as object of our study, but most of the considerations are valid for other configurations as well. Moreover, a survey on the most recent techniques is reported, including a classification of the different approaches presented in literature. Performance comparisons of the most well-known schemes, with particular focus on QoS provisioning capabilities, are also provided for complementing the described concepts. Thus, this survey would be useful for readers interested in learning the basic concepts before going into the details of a particular scheduling strategy, as well as for researchers aiming at deepening more specific aspects.
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paper_title: A User Selection Algorithm Using Angle between Subspaces for Downlink MU-MIMO Systems

paper_content:

One of major issues in the efficient use of radio resource for multiuser multiple-input/multiple-output (MU-MIMO) systems is the selection of users to achieve the maximum system throughput. The optimal user selection algorithm, which requires exhaustive search, is prohibitive due to its high computational complexity where Block diagonalization (BD) method is applied and known as a suboptimal precoding technique for downlink MU-MIMO systems, which intents to perfectly eliminate inter-user interference. In this paper, we propose efficient, iterative user selection algorithms with low complexity, where the product of eigenvalues of effective channels is utilized as a selection metric by applying the concept of principal angles between subspaces. And, we further examined the applicability of the proposed algorithms to limited feedback systems and proportional fair (PF) scheduling. Through computational complexity analysis, we show that the proposed algorithm has low complexity with a little loss in throughput. Simulation results validate that the proposed algorithm achieves almost the same system throughput by a capacity-based algorithm under high SNR regime with considerable reduction in complexity.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

paper_content:

In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Coordinated beamforming with limited feedback in the MIMO broadcast channel

paper_content:

In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.
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paper_title: Multicell Coordination via Joint Scheduling, Beamforming, and Power Spectrum Adaptation

paper_content:

The mitigation of intercell interference is an importance issue for current and next-generation wireless cellular networks where frequencies are aggressively reused and hierarchical cellular structures may heavily overlap. The paper examines the benefit of coordinating transmission strategies and resource allocation schemes across multiple base-stations for interference mitigation. Two different wireless cellular architectures are studied: a multicell network where base-stations coordinate in their transmission strategies, and a mixed macrocell and femtocell/picocell deployment with coordination among macro and femto/pico base-stations. For both scenarios, this paper proposes a heuristic joint proportionally fair scheduling, spatial multiplexing, and power spectrum adaptation algorithm that coordinates multiple base-stations with an objective of optimizing the overall network utility. The proposed scheme optimizes the user schedule, transmit and receive beamforming vectors, and transmit power spectra jointly, while taking into consideration both the intercell and intracell interference and the fairness among the users. System-level simulation results show that coordination at the transmission strategy and resource allocation level can already significantly improve the overall network throughput as compared to a conventional network design with fixed transmit power and per-cell zero-forcing beamforming.
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paper_title: Joint Beamforming and Scheduling for a Multi-Antenna Downlink with Imperfect Transmitter Channel Knowledge

paper_content:

We consider the downlink of a wireless system where the base-station has M ges 1 antennas and K user terminals have one antenna each. We study the weighted rate sum maximization in the case of non-perfect Channel State Information at the Transmitter (CSIT). Some relevant downlink optimization problems, such as the stabilization of the transmission queues under random packet arrivals and the proportional fair scheduling for infinite backlogged systems, can be solved as special cases of the proposed problem. We restrict the transmitter strategy to be based on Gaussian coding and beamforming. Even under this simplifying condition, the problem at hand is non-convex and it does not appear to lend itself to a simple algorithmic solution. Therefore, we introduce some approximations that yield a definition of signal-to-interference plus noise ratio (SINR) commonly used in the classical array- processing/beamforming literature. For the simpler (but still non-convex) approximated problem, we propose a powerful heuristic solution based on greedy user selection and a gradient iteration that converges to a local maximum of the objective function. This method yields very competitive results with relatively low computational complexity. Extensive simulations show that, in the case of perfect CSIT, the proposed heuristic scheme performs very closely to the optimal (dirty-paper coding) strategy while, in the case of non-perfect CSIT, it significantly outperforms previously proposed suboptimal approaches, such as random beamforming and approximated zero-forcing with greedy user selection.
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paper_title: Interference Coordination through Network-Synchronized Cyclic Beamforming

paper_content:

The next generation of wireless networks (e.g., (10)) will use multiple techniques to improve channel spectral efficien- cies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each subband in each frame, the scheduler chooses a beam and then schedules one or more UEs within the corresponding beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors (flashlight effect). The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period but this can be changed occasionally.
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paper_title: Dynamic Multi-User MIMO scheduling with limited feedback in LTE-Advanced

paper_content:

Multi-User MIMO (MU-MIMO) systems have gained numerous attention from researchers in the past decade due to its substantial gains in the system throughput. Most of the initial research assumes the knowledge of perfect channel state information at the transmitter (CSIT). However, this is considered impractical and research over the past few years has been focused on receivers feeding back limited information to the transmitter. In this work, we consider a transparent MU-MIMO system model with limited feedback. We propose a general framework for dynamic MU-MIMO scheduling with the capability to switch between Single-User MIMO mode and (Multi-Rank) Multi-User MIMO mode without users feeding back additional multi-user information. Specifically, this is done by each user carefully estimating its CQI under the hypothesis of Multi-Rank MultiUser MIMO transmission and taking advantage of the codebook structure. We consider the sum rate of the system assuming each user uses ML and LMMSE receiver and show that our proposed scheduler, with significantly reduced feedback load, outperforms the best-companion user pairing.
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paper_title: Joint User Scheduling and Adaptive Intercell Interference Cancelation for MISO Downlink Cellular Systems

paper_content:

Recently, an adaptive intercell interference (ICI) mitigation technique has been proposed for downlink cellular systems as a means to increase throughput with low system complexity. However, in the prior work, the issue of intercell user scheduling has not been considered. In this paper, we study multiple-input-single-output (MISO) downlink cellular systems that jointly design adaptive ICI cancelation (ICIC) and intercell user scheduling assuming that partial channel state information (CSI) is shared among base stations (BSs). Since the optimal solution would require high complexity, we investigate a new low-complexity algorithm that selects the best users and their beamforming strategies in terms of maximizing the weighted sum rate (WSR). To this end, we first develop a simple threshold criterion for each user to decide the preferred beamforming strategy based on the derivation of the expected signal-to-interference-plus-noise ratio (SINR). Then, according to users' feedback about their decisions, a successive user and beamforming selection algorithm is performed at the BSs. From simulation results, we show that, combined with proportional fair scheduling, the proposed scheme provides excellent throughput performance with very low computational complexity and the amount of inter-BS CSI exchange. Furthermore, we discuss an extension of the proposed scheme to limited feedback systems and observe that our algorithm also provides similar advantages over conventional schemes with quantized feedback.
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paper_title: Multimode Transmission for Multiuser MIMO Systems With Block Diagonalization

paper_content:

A low-complexity multimode transmission technique for downlink multiuser multiple-input-multiple-output (MIMO) systems with block diagonalization (BD) is proposed. The proposed technique adaptively configures the number of data streams for each user by adjusting its number of active receive antenna and switching between single-stream beamforming and multistream spatial multiplexing, as a means to exploit the multimode switching diversity. We consider a highly loaded system where there are a large number of users, hence a subset of users need to be selected. Joint user and antenna selection has been proposed as a multiuser multimode switching technique, where the optimal subset of receive antennas and users are chosen to maximize the sum throughput. The brute-force search, however, is prohibitively complicated. In this paper, two low-complexity near-optimal user/antenna selection algorithms are developed. The first algorithm aims at maximizing a capacity lower bound, derived in terms of the sum Frobenius norm of the channel, while the second algorithm greedily maximizes the sum capacity. We analytically evaluate the complexity of the proposed algorithms and show that it is orders of magnitude lower than that of the exhaustive search. Simulation results demonstrate that the proposed algorithms achieve up to 98% of the sum throughput of the exhaustive search, for most system configurations, while the complexity is substantially reduced.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: MIMO Broadcast Scheduling with Limited Feedback

paper_content:

We consider multiuser scheduling with limited feedback of partial channel state information in MIMO broadcast channels. By using spatial multiplexing at the base station (BS) and antenna selection for each user, we propose a multiuser scheduling method that allocates independent information streams from all M transmit antennas to the M most favorable users with the highest signal-to-interference-plus-noise ratio (SINR). A close approximation of the achievable sum-rate throughput for the proposed method is obtained and shown to match the simulation results very well. Moreover, two reduced feedback scheduling approaches are proposed. In the first approach, which we shall refer to as selected feedback scheduling, the users are selected based on their SINR compared to a predesigned threshold. Only those selected users are allowed to feed back limited information to the BS. The resultant feedback load and achievable throughput are derived. It will then be demonstrated that with a proper choice of the threshold, the feedback load can be greatly reduced with a negligible performance loss. The second reduced feedback scheduling approach employs quantization for each user, in which only few bits of quantized SINR are fed back to the BS. Performance analysis will show that even with only 1-bit quantization, the proposed quantized feedback scheduling approach can exploit the multiuser diversity at the expense of slight decrease of throughput.
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paper_title: Capacity Maximization for Zero-Forcing MIMO-OFDMA Downlink Systems with Multiuser Diversity

paper_content:

This paper considers the optimal resource allocation for a multiuser MIMO-OFDMA downlink system using zero-forcing SDMA, with the objective of maximizing the system capacity. We provide the general mathematical formulation of the capacity maximization problem whose resource allocation includes user selection, power allocation and receive signal subspace selection. While the optimal solution of this problem is difficult to obtain, we consider two special cases: user selection based only and antenna selection based only optimization, and develop the optimal solution by reformulating the combinatorial optimization problem into a convex problem. Our proposed algorithms for these special cases can be extended to develop a suboptimal algorithm for the original general optimization problem which allows subspace selection. Moreover, we develop reduced-complexity algorithms for these problems which incur negligible capacity loss. Numerical results and analysis are provided to evaluate the system capacity and to study the effect of the number of users and the receive antennas per user on the performance. Comparisons on the capacity achieved by user selection only, antenna selection only and suboptimal subspace selection are discussed
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paper_title: An efficient resource-allocation scheme for spatial multiuser access in MIMO/OFDM systems

paper_content:

Fast adaptive transmission has been recently identified as a key technology for exploiting potential system diversity and improving power-spectral efficiency in wireless communication systems. An adaptive resource-allocation approach, which jointly adapts subcarrier allocation, power distribution, and bit distribution according to instantaneous channel conditions, is proposed for multiuser multiple-input multiple-output (MIMO)/orthogonal frequency-division multiplexing systems. The resultant scheme is able to: 1) optimize the power efficiency; 2) guarantee each user's quality of service requirements, including bit-error rate and data rate; 3) ensure fairness to all the active users; and 4) be applied to systems with various types of multiuser-detection schemes at the receiver. For practical implementation, a reduced-complexity allocation algorithm is developed. This algorithm decouples the complex multiuser joint resource-allocation problem into simple single-user optimization problems by controlling the subcarrier sharing according to the users' spatial separability. Numerical results show that significant power and diversity gains are achievable, compared with nonadaptive systems. It is also demonstrated that the MIMO system is able to multiplex several users without sacrificing antenna diversity by using the proposed algorithm.
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paper_title: The impact of space division multiplexing on resource allocation: a unified treatment of TDMA, OFDMA and CDMA

paper_content:

Space division multiple access (SDMA) with an antenna array at the transmitter is a promising means for increasing system capacity and supporting rate-demanding services. However, the presence of an antenna array at the physical layer raises significant issues at higher layers. In this paper, we attempt to capture the impact of SDMA on access layer channel allocation, reflected on channel reuse. This impact obtains different twists in TDMA, CDMA and OFDMA due to the different nature of co-channel and cross-channel interference and the different interaction of user spatial channel characteristics with system channels, namely time slots, codes and subcarriers. We consider these access schemes in a generalized unified framework and propose heuristic algorithms for channel allocation, downlink beamforming and transmit power control so as to increase total provisioned system rate and provide QoS to users in the form of minimum rate guarantees. We study the class of greedy algorithms that rely on criteria such as induced or received interference and signal-to-interference ratio (SIR), and a class of SIR balancing algorithms. Results show superior performance for SIR balancing resource allocation and expose the performance benefits of cross-layer design.
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paper_title: On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

paper_content:

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.
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paper_title: The Design of Approximation Algorithms

paper_content:

Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Coordinated Beamforming for MISO Interference Channel: Complexity Analysis and Efficient Algorithms

paper_content:

In a cellular wireless system, users located at cell edges often suffer significant out-of-cell interference. Assuming each base station is equipped with multiple antennas, we can model this scenario as a multiple-input single-output (MISO) interference channel. In this paper we consider a coordinated beamforming approach whereby multiple base stations jointly optimize their downlink beamforming vectors in order to simultaneously improve the data rates of a given group of cell edge users. Assuming perfect channel knowledge, we formulate this problem as the maximization of a system utility (which balances user fairness and average user rates), subject to individual power constraints at each base station. We show that, for the single-carrier case and when the number of antennas at each base station is at least two, the optimal coordinated beamforming problem is NP-hard for both the harmonic mean utility and the proportional fairness utility. For general utilities, we propose a cyclic coordinate descent algorithm, which enables each transmitter to update its beamformer locally with limited information exchange and establish its global convergence to a stationary point. We illustrate its effectiveness in computer simulations by using the space matched beamformer as the benchmark.
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paper_title: System evaluation of optimal downlink beamforming with congestion control in wireless communication

paper_content:

We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.
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paper_title: Convex approximation techniques for joint multiuser downlink beamforming and admission control

paper_content:

Multiuser downlink beamforming under quality of service (QoS) constraints has attracted considerable interest in years, because it is particularly appealing from a network operator's perspective (e.g., UMTS, 802.16e). When there are many co-channel users and/or the service constraints are stringent, the problem becomes infeasible and some form of admission control is necessary. We advocate a cross-layer approach to joint multiuser transmit beamforming and admission control, aiming to maximize the number of users that can be served at their desired QoS. It is shown that the core problem is NP-hard, yet amenable to convex approximation tools. Two computationally efficient convex approximation algorithms are proposed: one is based on semidefinite relaxation of an equivalent problem reformulation; the other takes a penalized second-order cone approach. Their performance is assessed in a range of experiments, using both simulated and measured channel data. In all experiments considered, the proposed algorithms work remarkably well in terms of the attained performance-complexity trade-off, consistently exhibiting close to optimal performance at an affordable computational complexity.
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paper_title: The impact of space division multiplexing on resource allocation: a unified treatment of TDMA, OFDMA and CDMA

paper_content:

Space division multiple access (SDMA) with an antenna array at the transmitter is a promising means for increasing system capacity and supporting rate-demanding services. However, the presence of an antenna array at the physical layer raises significant issues at higher layers. In this paper, we attempt to capture the impact of SDMA on access layer channel allocation, reflected on channel reuse. This impact obtains different twists in TDMA, CDMA and OFDMA due to the different nature of co-channel and cross-channel interference and the different interaction of user spatial channel characteristics with system channels, namely time slots, codes and subcarriers. We consider these access schemes in a generalized unified framework and propose heuristic algorithms for channel allocation, downlink beamforming and transmit power control so as to increase total provisioned system rate and provide QoS to users in the form of minimum rate guarantees. We study the class of greedy algorithms that rely on criteria such as induced or received interference and signal-to-interference ratio (SIR), and a class of SIR balancing algorithms. Results show superior performance for SIR balancing resource allocation and expose the performance benefits of cross-layer design.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: Asymptotically optimal simple user scheduling for massive MIMO downlink with two-stage beamforming

paper_content:

In this paper, a simple user-scheduling-and-beamforming method is proposed for massive multi-user multiple-input multiple-output (MU-MIMO) downlink adopting two-stage beamforming. The key ideas of the proposed scheduling-and-beamforming method are to divide users into several candidate subsets according to the level of alignment of user channels to the dominant directions of the channel covariance matrix and select the user in each candidate subset based on a certain channel quality indicator (CQI) and to apply post-selection zero-forcing beamforming (ZFBF) to the selected users based on their channel state information (CSI). It is proved that the proposed scheduling-and-beamformingmethod is asymptotically optimal as the number of users increases. Furthermore, the proposed method significantly reduces the feedback overhead and shows superior sum rate performance compared to existing scheduling methods for MU-MIMO downlink.
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paper_title: Subchannel allocation in multiuser multiple input multiple output systems

paper_content:

Assuming perfect channel state information at the transmitter of a Gaussian broadcast channel, strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel. For the general sum capacity maximizing solution, which has recently been found, a method is proposed that transforms each of the resulting vector channels into a set of scalar channels. This makes possible to achieve capacity by simply using scalar coding and detection techniques. The high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero-forcing allocation strategy that directly results in a set of virtually decoupled scalar channels. Simulation results show that this technique tightly approaches the performance of the optimum solution, i.e., complexity reduction comes at almost no cost in terms of sum capacity. As the optimum solution, the zero-forcing allocation strategy applies to any number of transmit antennas, receive antennas and users
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paper_title: Eigen-Based Transceivers for the MIMO Broadcast Channel with Semi-Orthogonal User Selection

paper_content:

This paper studies the sum rate performance of two low complexity eigenmode-based transmission techniques for the MIMO broadcast channel, employing greedy semi-orthogonal user selection (SUS). The first approach, termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first employ new analytical methods to prove that as the number of users K grows large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that the average sum rates of both techniques converge to the average sum capacity of the MIMO broadcast channel for large K. In addition to the asymptotic analysis, we investigate the sum rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS has significant performance advantages. Our results also provide key insights into the benefit of multiple receive antennas, and the effect of the SUS algorithm. In particular, we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second-order behavior of the multi-user diversity gain; for finite K, the benefit can be very significant. We also show the interesting result that the semi-orthogonality constraint imposed by SUS, whilst facilitating a very low complexity user selection procedure, asymptotically does not reduce the multi-user diversity gain in either first (log K) or second-order (loglog K) terms.
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paper_title: User Selection With Zero-Forcing Beamforming Achieves the Asymptotically Optimal Sum Rate

paper_content:

In this paper, we propose a generalized greedy (G-greedy) algorithm based on zero-forcing beamforming (ZFBF) for the multiple-input multiple-output (MIMO) broadcast channel. This algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations. As previous results only give the scaling law of the sum rate of dirty paper coding (DPC), with the help of the G-greedy structure, we are able to obtain the exact limit of the DPC sum rate for a large number of users. We also prove that the difference between the sum rates obtained by G-greedy user selection and by DPC goes to zero as the number of users increases. In addition to this, we investigate one particular greedy user selection scheme called sequential water-filling (SWF). For this algorithm, a complexity reduction is achieved by an iterative procedure based on an LQ decomposition, which converts the calculation of the Moore-Penrose matrix inverse to one vector-matrix multiplication. A sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction. With the help of the G-greedy algorithm, we prove that SWF achieves the full DPC sum rate for a large number of users. For a moderate number of users, simulation demonstrates that, compared with other user selection algorithms, SWF achieves a higher sum rate that is close to the maximal sum rate achievable by ZFBF with the same order of complexity.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: On the achievable throughput of a multiantenna Gaussian broadcast channel

paper_content:

A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j<i is taken into account by coding for noncausally known interference. Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR). We conclude by providing some numerical results for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.
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paper_title: Multiuser diversity for a dirty paper approach

paper_content:

Multiuser diversity has attracted significant attention recently. In this letter, we propose a greedy algorithm based on QR decomposition of the channel and dirty paper precoding to exploit the multiuser diversity of the Gaussian vector broadcast channel. Simulations show the approach provides performance which is extremely close to a well-known upper bound on the sum rate. Further, exploiting multiuser diversity can provide large gain over approaches ignoring this resource.
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paper_title: Greedy scheduling performance for a zero-forcing dirty-paper coded system

paper_content:

This letter presents two results for multiuser wireless systems employing dirty-paper coding strategies along with greedy scheduling over the broadcast multiple-input multiple-output channel. Specifically, an efficient and suboptimal downlink scheduler is proposed to approximate the maximum sum rate using equal power allocation, and it is shown to approach the maximum sum rate of optimal power allocation for a large number of users under optimal scheduling. The second result demonstrates that the average maximum sum rate can be tightly upper bounded when spatial multiplexing is maximized.
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paper_title: On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm

paper_content:

This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple "beams" directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of the same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum's scheme and, thus, offers an attractive alternative to DP-based schemes.
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paper_title: Opportunistic Two-Stage Feedback and Scheduling for MIMO Downlink Systems

paper_content:

We propose an opportunistic two-stage feedback and scheduling algorithm that is based upon zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) to reduce its feedback load. In an SUS algorithm, a base station schedules semi-orthogonal users using the feedback of all users' channel information. However, such feedback overhead significantly increases with the number of users. To reduce the feedback load of ZFBF-SUS systems, the proposed two-stage feedback scheme opportunistically and separately exploits the signal-to-interference-plus-noise ratio and orthogonality in each stage such that only a fraction of users feed back their channel information. Based on this opportunistic feedback scheme, we decouple the entire process of the SUS into two sub-processes. The proposed two-stage feedback and scheduling scheme effectively exclude the inappropriate users for ZFBF transmission in both feedback and scheduling periods, and thus save the scarce resources consumed for the feedback process. We derive an analytical expression for the average number of feedback bits of the proposed system and optimize it in an averaged sense. Further, the sum-rate of the proposed system is theoretically investigated. Both analytical and simulation results show that the proposed algorithm achieves the performance of conventional ZFBF-SUS systems with a significantly reduced number of feedback bits.
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paper_title: Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems with Multi-Antenna Users

paper_content:

In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than N, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and/or to enable interference-aware receive combining. In this paper, we try to answer the question if the N data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user-the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.
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paper_title: Solution of the multiuser downlink beamforming problem with individual SINR constraints

paper_content:

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.
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paper_title: User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming

paper_content:

In this paper, we propose a greedy user selection with swap (GUSS) algorithm based on zero-forcing beamforming for multiuser multiple-input-multiple-output (MIMO) downlink channels. Existing user selection algorithms such as zero forcing with selection (ZFS) have the flaws of “redundant users” and “local optimum,” which compromise the achieved sum rate. GUSS improves the performance by adding the “delete” and “swap” operations to the user selection procedure of ZFS to eliminate “redundant users” and escape from “local optimum,” respectively. In addition, an effective-channel-vector-based effective-channel-gain-updating scheme is proposed to reduce the complexity of GUSS. With the help of this updating scheme, GUSS has the same order of complexity as ZFS with only a linear increment. Simulation results indicate that over the range of transmit signal-to-noise ratios (SNRs) considered, on average, the sum rate of GUSS reaches 99.3% of the upper bound that is achieved by exhaustive search, with only 1.51 to 2.29 times the complexity of ZFS.
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paper_title: Scheduling for Multiuser MIMO Broadcast Systems: Transmit or Receive Beamforming?

paper_content:

In this paper, we present an approximation formula and the close-form expression for the sum rate of the transmit and the receive zero-forcing (ZF) multiple-input multiple-output (MIMO) broadcast systems with user selection, respectively. Instead of assuming a large number of users to obtain a scaling law as most current work, we derive the sum rate formulas of the ZF MIMO broadcast systems with a small number of scheduled users. By analysis and simulations, we find that when taking the variations of feedback channel into account, the receive ZF MIMO broadcast system is more robust to feedback errors and can deliver equal or even higher sum rate than the transmit ZF MIMO broadcast system. We discuss whether a feedback channel is suitable to send channel state information (CSI) for calculating transmit antenna beamforming weights, or suitable to send CSI for selecting users in the receive ZF MIMO broadcast system. Our results show that as the variation of feedback channel errors increases from 0.5 to 1.5, the receive ZF 3 × 3 MIMO broadcast system can provide 36% to 116% higher sum rate than the transmit ZF 3 × 3 MIMO broadcast system in the case of 20 users at signal to noise ratio (SNR) equal to 20 dB. Providing that more feedback bandwidth and an error-free feedback channel are available, the transmit ZF MIMO broadcast system can achieve higher sum rate than the receive ZF MIMO broadcast system.
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paper_title: Decremental User Selection for Large-Scale Multi-User MIMO Downlink with Zero-Forcing Beamforming

paper_content:

This paper proposes a decremental user selection algorithm based on zero-forcing beamforming when the number of users K in the network is smaller than the number of antennas M at a base station. The algorithm is specifically designed for large-scale multi-user multiple-input multiple-output (MIMO) downlink channels. While previous user selection algorithms are based on incremental search that starts from an empty user set, our proposed delete the minimum lambda (DML) algorithm starts by selecting all users and then deleting one user per iteration. DML substantially reduces the computational complexity as the cardinality of the final user set is close to K. Simulation results indicate that on average DML achieves an equal or higher sum rate performance than previous algorithms with greatly reduced complexity of O(MK2).
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paper_title: Beamforming and User Selection in SDMA Systems Utilizing Channel Statistics and Instantaneous SNR Feedback

paper_content:

Spatial division multiple access (SDMA) systems efficiently take advantage of the spatial dimensions of the channel to increase the performance of the system. A major difficulty, common to all SDMA systems, is the requirement of channel knowledge at the transmitter to enable transmission of multiple streams without catastrophic interference. Herein we show that, in wide area scenarios, statistical channel information combined with the Euclidean norm of the channel realization, fed back from the users, provide sufficient information for SDMA systems to efficiently allocate users in time and space. A joint beamforming and scheduling algorithm is proposed for the downlink, which extends the proportional fair scheduling criterion to an SDMA setting, resulting in a weighted sum rate maximization.
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paper_title: Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

paper_content:

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.
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paper_title: Simplified Semi-Orthogonal User Selection for MU-MIMO Systems with ZFBF

paper_content:

In this letter, we simplify the well-known semi-orthogonal user selection (SUS) algorithm for the multi-user multiple-input multiple-output (MU-MIMO) system with zero-forcing beamforming (ZFBF). Compared with the original SUS algorithm, the proposed user selection algorithm achieves the same performance, but with significantly less complexity. Simulation results show that the proposed algorithm can make a good tradeoff between performance and complexity for the MU-MIMO system with ZFBF.
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: Sum Rates, Rate Allocation, and User Scheduling for Multi-User MIMO Vector Perturbation Precoding

paper_content:

This paper considers the multiuser multiple-input multiple-output (MIMO) broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via vector perturbation. We derive expressions for the sum rate in terms of the average energy of the precoded vector, and use this to derive a high signal-to-noise ratio (SNR) closed-form upper bound, which we show to be tight via simulation. We also propose a modification to vector perturbation where different rates can be allocated to different users. We conclude that for vector perturbation precoding most of the sum rate gains can be achieved by reducing the rate allocation problem to the user selection problem. We then propose a low-complexity user selection algorithm that attempts to maximize the high-SNR sum rate upper bound. Simulations show that the algorithm outperforms other user selection algorithms of similar complexity.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.
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paper_title: Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization

paper_content:

Block diagonalization (BD) is a preceding technique that eliminates inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. With the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission, the number of simultaneously supportable users with BD is limited by the ratio of the number of basestation transmit antennas to the number of user receive antennas. In a downlink MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput The brute-force search for the optimal user set, however, is computationally prohibitive. We propose two low-complexity suboptimal user selection algorithms for multiuser MIMO systems with BD. Both algorithms aim to select a subset of users such that the total throughput is nearly maximized. The first user selection algorithm greedily maximizes the total throughput, whereas the criterion of the second algorithm is based on the channel energy. We show that both algorithms have linear complexity in the total number of users and achieve around 95% of the total throughput of the complete search method in simulations
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paper_title: Multiuser MIMO User Selection Based on Chordal Distance

paper_content:

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.
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paper_title: Optimal downlink space-time scheduling design with convex utility functions-multiple-antenna systems with orthogonal spatial multiplexing

paper_content:

It is well known that link level throughput could be significantly increased by using multiple antennae at the transmitter and receiver without increasing the bandwidth and power budget. However, optimizing the link level performance of multiple-antenna systems does not always imply achieving system level optimization. Therefore, cross-layer optimization across the link layer and the scheduling layer is very important to fully exploit the temporal and spatial dimensions of the communication channel. In this paper, we consider the optimal downlink space-time scheduling design for a general class of convex utility functions. The access point or base station is equipped with n/sub T/ transmit antennas. There are K mobiles in the system with a single receive antenna. For practical reasons, we assume zero-forcing processing at the physical layer of the base station and mobile. We will apply the design framework to two common utility functions, namely the maximum throughput and the proportional fair. The cross-layer scheduling design is a mixed convex and combinatorial optimization problem and the search space of the optimal solution is enormous. Greedy algorithm, which has been widely used in today's wireless data systems (3G1X, high data rate system (HDR), Universal Mobile Terrestrial Service), is optimal when n/sub T/=1. However, we found that there is a large performance penalty of greedy algorithms (relative to optimal performance) when n/sub T/>1 and this motivates the search for more efficient heuristics. In this paper, we will address genetic-based heuristics and discuss their complexity-performance tradeoff.
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paper_title: Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

paper_content:

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

paper_content:

In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search

paper_content:

We consider a multi-user MIMO downlink system employing zero-forcing beamforming (ZFBF) as a spatial multiplexing strategy, and propose low-complexity user subset selection methods based on a clique (fully connected subgraph) search. The proposed algorithms, maximum weighted clique (MWC)-ZFBF and greedy weighted clique (GWC)-ZFBF, are shown to achieve the asymptotic sum-capacity of MIMO downlink channels as the number of users goes to infinity. Thus, clique search based ZFBF is an appealing strategy in MIMO downlink systems with a large number of users.
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paper_title: Iterative Precoder Design and User Scheduling for Block-Diagonalized Systems

paper_content:

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming and User Grouping

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a recently proposed scheme to enable massive MIMO like gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar covariances, and use a two stage downlink beamforming: a pre-beamformer that depends on the channel covariances and minimizes interference across groups and a multiuser MIMO precoder for the effective channel after pre-beamforming, to counteract interference within a group. We first focus on the regime of a fixed number of antennas and large number of users, and show that opportunistic beamforming with user selection yields significant gain, and thus, channel correlation may yield a capacity improvement over the uncorrelated "isotropic" channel result of Sharif and Hassibi. We prove that in the presence of different correlations among groups, a block diagonalization approach for the design of pre-beamformers achieves the optimal sum-rate scaling. Next, we consider the regime of large number of antennas and users, where user selection does not provide significant gain. Here, we propose a simplified user grouping algorithm to cluster users into groups when the number of antennas becomes very large, in a realistic setting where users are randomly distributed and have different angles of arrival and angular spreads depending on the propagation environment. Our subsequent analysis leads to a probabilistic scheduling algorithm, where users within each group are preselected at random based on probabilities derived from the large system analysis, depending on the fairness criterion. This is advantageous since only the selected users are required to feedback their channel state information (CSIT).
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paper_title: Efficient Sum Rate Maximization and Resource Allocation in Block-Diagonalized Space-Division Multiplexing

paper_content:

For space-division multiplexing (SDM) via block diagonalization on multiuser multiple-input multiple-output (MIMO) wireless downlink, it is shown that receive antenna selection (RAS) is necessary for maximizing the achievable sum rate. This is true even when all receive antennas are equipped with radio frequency (RF) chains and RAS reduces the upper bound on the broadcast sum capacity, and when the orthogonalized channels use optimal processing. Similarly, spatial-mode selection (SMS) is necessary for sum rate maximization when receive-weight matrices are used for spatial-mode allocation. RAS/SMS may release transmission resources that can fully be utilized via additional user scheduling to yield further sum rate gains. Optimal user selection for sum rate maximization is subsumed within an exhaustive RAS/SMS process for multiantenna terminals, and both selection processes become identical for single-antenna terminals. RAS/SMS thus helps reduce the performance gap from the optimal sum capacity even for small user pool sizes. A block antenna/mode selection approach is introduced to help overcome the drawbacks of existing algorithms. Since RAS/SMS involves antenna/mode ranking, a systematic method for resource allocation with sum rate loss minimization is inherently provided. This way, a streamlined process that combines user selection, RAS/SMS, and resource allocation is developed for sum rate maximization of block-diagonalized SDM.
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paper_title: Multimode Transmission for Multiuser MIMO Systems With Block Diagonalization

paper_content:

A low-complexity multimode transmission technique for downlink multiuser multiple-input-multiple-output (MIMO) systems with block diagonalization (BD) is proposed. The proposed technique adaptively configures the number of data streams for each user by adjusting its number of active receive antenna and switching between single-stream beamforming and multistream spatial multiplexing, as a means to exploit the multimode switching diversity. We consider a highly loaded system where there are a large number of users, hence a subset of users need to be selected. Joint user and antenna selection has been proposed as a multiuser multimode switching technique, where the optimal subset of receive antennas and users are chosen to maximize the sum throughput. The brute-force search, however, is prohibitively complicated. In this paper, two low-complexity near-optimal user/antenna selection algorithms are developed. The first algorithm aims at maximizing a capacity lower bound, derived in terms of the sum Frobenius norm of the channel, while the second algorithm greedily maximizes the sum capacity. We analytically evaluate the complexity of the proposed algorithms and show that it is orders of magnitude lower than that of the exhaustive search. Simulation results demonstrate that the proposed algorithms achieve up to 98% of the sum throughput of the exhaustive search, for most system configurations, while the complexity is substantially reduced.
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paper_title: An efficient greedy scheduler for zero-forcing dirty-paper coding

paper_content:

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.
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paper_title: MIMO Broadcast Channels with Spatial Heterogeneity

paper_content:

We develop a realistic model for multiple-input multiple-output (MIMO) broadcast channels, where each randomly located user's average SNR depends on its distance from the transmitter. With perfect channel state information at the transmitter (CSIT), the average sum capacity is proven to scale for many users like αM/2 log K instead of M log log K, where α, M, and K denote the path loss exponent, the number of transmit antennas, and the number of users in a cell. With only partial CSIT, the sum capacity at high SNR eventually saturates due to interference, and the saturation value scales for large B like MB/M-1, where B denotes the quantization resolution for channel feedback.
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paper_title: On the user selection for MIMO broadcast channels

paper_content:

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.
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paper_title: User Scheduling for Heterogeneous Multiuser MIMO Systems: A Subspace Viewpoint

paper_content:

In downlink multiuser multiple-input-multiple-output (MU-MIMO) systems, users are practically heterogeneous. However, many existing user-scheduling algorithms are designed with an implicit assumption that users are homogeneous. In this paper, we revisit the problem by exploring the characteristics of heterogeneous users from a subspace viewpoint. With an objective of minimizing interference nonorthogonality among users, three new angular-based user-scheduling criteria are proposed. While the first criterion is heuristically determined by identifying the incapability of the largest principal angle to characterize subspace correlation and, hence, interference nonorthogonality between users, the second and third criteria are derived by using the sum rate capacity bounds with block diagonalization and the change in capacity by adding a new user into an existing user subset, respectively. Aiming to capture fairness among heterogeneous users while maintaining multiuser diversity gain, two new hybrid user-scheduling algorithms, whose computational complexities are only linearly proportional to the number of users, are proposed. We show by simulations the effectiveness of our proposed user-scheduling criteria and algorithms with respect to those commonly used in a homogeneous environment.
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paper_title: Transmit Selection Diversity for Unitary Precoded Multiuser Spatial Multiplexing Systems With Linear Receivers

paper_content:

Multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference. In such a system, the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain. This paper proposes two precoding methods that use extra transmit antennas, beyond the minimum required, to provide additional degrees of diversity. The approach taken is to solve for a unitary transmit precoder, under a zero interuser interference constraint, that minimizes an upper bound on the symbol error rate (SER) for each user. Solutions where all transmit antennas are employed, as well as subsets of antennas (to reduce analog components), are described. Numerical results confirm a dramatic improvement in terms of SER and mutual information over single-user multiple-input multiple-output (MIMO) methods and static allocation methods. For example, the proposed techniques achieve a signal-to-noise ratio (SNR) improvement of 6-10 dB at an uncoded SER of 10-3, with only one extra transmit antenna
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paper_title: Artificial Intelligence in Wireless Communications

paper_content:

This cutting-edge resource offers practical overview of cognitive radio - a paradigm for wireless communications in which a network or a wireless node changes its transmission or reception parameters. The alteration of parameters is based on the active monitoring of several factors in the external and internal radio environment. This book offers a detailed description of cognitive radio and its individual parts. Practitioners learn how the basic processing elements and their capabilities are implemented as modular components. Moreover, the book explains how each component can be developed and tested independently, before integration with the rest of the engine. Practitioners discover how cognitive radio uses artificial intelligence to achieve radio optimization. The book also provides an in-depth working example of the developed cognitive engine and an experimental scenario to help engineers understand its performance and behavior.
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paper_title: Novel scheduling strategy for downlink multiuser MIMO system: Particle swarm optimization

paper_content:

In this paper the scheduling problem in downlink multiuser MIMO system is described as an optimization problem and particle swarm optimization (PSO) algorithm is introduced to address such problem. Two PSO scheduling methods with different objective functions applicable to different requirements on capacity and complexity are investigated. One is the capacity based PSO(C-PSO) scheduling method aiming at achieving the near optimal capacity; and the other is the lower bound of eigenvalue based PSO (LBE-PSO) scheduling method with the purpose of reducing computational complexity and at the same time achieving as large as possible capacity gain. Furthermore, convergence analysis of PSO from both the particle and the velocity aspects is also presented to derive the convergent condition, which is validated by several examples of different parameter values. Simulation results reveal that the C-PSO can obtain nearly the same capacity as the exhaustive search method with lower complexity, while the LBE-PSO provides a viable approach by striking a better tradeoff between capacity and computational complexity.
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paper_title: The Design of Approximation Algorithms

paper_content:

Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
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paper_title: Subchannel allocation in multiuser multiple input multiple output systems

paper_content:

Assuming perfect channel state information at the transmitter of a Gaussian broadcast channel, strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel. For the general sum capacity maximizing solution, which has recently been found, a method is proposed that transforms each of the resulting vector channels into a set of scalar channels. This makes possible to achieve capacity by simply using scalar coding and detection techniques. The high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero-forcing allocation strategy that directly results in a set of virtually decoupled scalar channels. Simulation results show that this technique tightly approaches the performance of the optimum solution, i.e., complexity reduction comes at almost no cost in terms of sum capacity. As the optimum solution, the zero-forcing allocation strategy applies to any number of transmit antennas, receive antennas and users
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paper_title: Multiuser diversity for a dirty paper approach

paper_content:

Multiuser diversity has attracted significant attention recently. In this letter, we propose a greedy algorithm based on QR decomposition of the channel and dirty paper precoding to exploit the multiuser diversity of the Gaussian vector broadcast channel. Simulations show the approach provides performance which is extremely close to a well-known upper bound on the sum rate. Further, exploiting multiuser diversity can provide large gain over approaches ignoring this resource.
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paper_title: Low complexity greedy, genetic and hybrid user scheduling algorithms for multiuser MIMO systems with successive zero‐forcing

paper_content:

In this paper, we consider low complexity user scheduling algorithms for multiuser multiple-input multiple-output systems employing successive zero-forcing precoding. Optimal scheduling involves an exhaustive search (ES), which is prohibitively complex. Greedy algorithms (GrAs) with heuristic scheduling metrics achieve performance close to that of the ES. Meanwhile, genetic algorithms (GAs) are a rapid suboptimal option of optimising utility (e.g. scheduling) metrics. Herein, we evaluate the performance and complexity of greedy and genetic scheduling algorithms for successive zero-forcing. We also propose and evaluate two hybrid algorithms combining the traits of the GrA and GA. The algorithms' performance is assessed through a series of computer simulations. We demonstrate both the GrA and GA achieve a near-optimal sum rate with low complexity, whereas the hybrid algorithms further enhance the GrA and GA performance without an increase in the order of complexity.Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: Beamforming and User Selection in SDMA Systems Utilizing Channel Statistics and Instantaneous SNR Feedback

paper_content:

Spatial division multiple access (SDMA) systems efficiently take advantage of the spatial dimensions of the channel to increase the performance of the system. A major difficulty, common to all SDMA systems, is the requirement of channel knowledge at the transmitter to enable transmission of multiple streams without catastrophic interference. Herein we show that, in wide area scenarios, statistical channel information combined with the Euclidean norm of the channel realization, fed back from the users, provide sufficient information for SDMA systems to efficiently allocate users in time and space. A joint beamforming and scheduling algorithm is proposed for the downlink, which extends the proportional fair scheduling criterion to an SDMA setting, resulting in a weighted sum rate maximization.
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paper_title: On Swarm Intelligence Inspired Self-Organized Networking: Its Bionic Mechanisms, Designing Principles and Optimization Approaches

paper_content:

Inspired by swarm intelligence observed in social species, the artificial self-organized networking (SON) systems are expected to exhibit some intelligent features (e.g., flexibility, robustness, decentralized control, and self-evolution, etc.) that may have made social species so successful in the biosphere. Self-organized networks with swarm intelligence as one possible solution have attracted a lot of attention from both academia and industry. In this paper, we survey different aspects of bio-inspired mechanisms and examine various algorithms that have been applied to artificial SON systems. The existing well-known bio-inspired algorithms such as pulse-coupled oscillators (PCO)-based synchronization, ant- and/or bee-inspired cooperation and division of labor, immune systems inspired network security and Ant Colony Optimization (ACO)-based multipath routing have been surveyed and compared. The main contributions of this survey include 1) providing principles and optimization approaches of variant bio-inspired algorithms, 2) surveying and comparing critical SON issues from the perspective of physical-layer, Media Access Control (MAC)-layer and network-layer operations, and 3) discussing advantages, drawbacks, and further design challenges of variant algorithms, and then identifying their new directions and applications. In consideration of the development trends of communications networks (e.g., large-scale, heterogeneity, spectrum scarcity, etc.), some open research issues, including SON designing tradeoffs, Self-X capabilities in the 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE)/LTE-Advanced systems, cognitive machine-to-machine (M2M) self-optimization, cross-layer design, resource scheduling, and power control, etc., are also discussed in this survey.
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paper_title: Optimal downlink space-time scheduling design with convex utility functions-multiple-antenna systems with orthogonal spatial multiplexing

paper_content:

It is well known that link level throughput could be significantly increased by using multiple antennae at the transmitter and receiver without increasing the bandwidth and power budget. However, optimizing the link level performance of multiple-antenna systems does not always imply achieving system level optimization. Therefore, cross-layer optimization across the link layer and the scheduling layer is very important to fully exploit the temporal and spatial dimensions of the communication channel. In this paper, we consider the optimal downlink space-time scheduling design for a general class of convex utility functions. The access point or base station is equipped with n/sub T/ transmit antennas. There are K mobiles in the system with a single receive antenna. For practical reasons, we assume zero-forcing processing at the physical layer of the base station and mobile. We will apply the design framework to two common utility functions, namely the maximum throughput and the proportional fair. The cross-layer scheduling design is a mixed convex and combinatorial optimization problem and the search space of the optimal solution is enormous. Greedy algorithm, which has been widely used in today's wireless data systems (3G1X, high data rate system (HDR), Universal Mobile Terrestrial Service), is optimal when n/sub T/=1. However, we found that there is a large performance penalty of greedy algorithms (relative to optimal performance) when n/sub T/>1 and this motivates the search for more efficient heuristics. In this paper, we will address genetic-based heuristics and discuss their complexity-performance tradeoff.
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paper_title: Downlink Scheduling via Genetic Algorithms for Multiuser Single-Carrier and Multicarrier MIMO Systems With Dirty Paper Coding

paper_content:

Multiple-input-multiple-output (MIMO) systems are of interest for meeting the expected demand for higher data rates and lower delays in future wireless packet data systems. In such systems, it is optimal to simultaneously transmit to multiple users compared with a single user in a single-input-single-output system. In addition, multicarrier systems are of interest to combat frequency-selective fading that is experienced over the larger bandwidth that these future broadband systems will use. The use of dirty paper coding further complicates the matter, because the order in which the users are encoded will affect the rates that they can achieve. A well-designed cross-layer scheduling algorithm must take into account the multiple dimensions of this resource-allocation problem and other quality-of-service (QoS) parameters to fully exploit the communications channel. The scheduling problem is often expressed in terms of optimizing some utility function. Unfortunately, the search space for this optimization problem is extremely large, which prohibits an optimal exhaustive search. To this end, we investigate the use of genetic algorithms to reduce the complexity of the scheduling. This paper builds upon prior work that implements scheduling via genetic algorithms in the context of single-carrier systems using zero-forcing beamforming (ZFB). In this paper, we investigate how the genetic algorithm can be adapted to account for the effect of encoding order on the scheduling and how the scheduling can be extended to a multicarrier system. In particular, we investigate the maximum throughput and proportionally fair scheduling criteria. We demonstrate that the performance of the genetic algorithm is near optimal compared with an exhaustive search at a greatly reduced computational complexity. Furthermore, in the case of a multicarrier orthogonal frequency-division multiplexing (OFDM) system, an increase in capacity is shown relative to the single-carrier case.
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paper_title: Recent Advances in Radio Resource Management for Heterogeneous LTE/LTE-A Networks

paper_content:

As heterogeneous networks (HetNets) emerge as one of the most promising developments toward realizing the target specifications of Long Term Evolution (LTE) and LTE-Advanced (LTE-A) networks, radio resource management (RRM) research for such networks has, in recent times, been intensively pursued. Clearly, recent research mainly concentrates on the aspect of interference mitigation. Other RRM aspects, such as radio resource utilization, fairness, complexity, and QoS, have not been given much attention. In this paper, we aim to provide an overview of the key challenges arising from HetNets and highlight their importance. Subsequently, we present a comprehensive survey of the RRM schemes that have been studied in recent years for LTE/LTE-A HetNets, with a particular focus on those for femtocells and relay nodes. Furthermore, we classify these RRM schemes according to their underlying approaches. In addition, these RRM schemes are qualitatively analyzed and compared to each other. We also identify a number of potential research directions for future RRM development. Finally, we discuss the lack of current RRM research and the importance of multi-objective RRM studies.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: Optimal User-Cell Association for Massive MIMO Wireless Networks

paper_content:

The use of a very large number of antennas at each base station site (referred to as"Massive MIMO") is one of the most promising approaches to cope with the predicted wireless data traffic explosion. In combination with Time Division Duplex and with simple per-cell processing, it achieves large throughput per cell, low latency, and attractive power efficiency performance. Following the current wireless technology trend of moving to higher frequency bands and denser small cell deployments, a large number of antennas can be implemented within a small form factor even in small cell base stations. In a heterogeneous network formed by large (macro) and small cell BSs, a key system optimization problem consists of"load balancing", that is, associating users to BSs in order to avoid congested hot-spots and/or under-utilized infrastructure. In this paper, we consider the user-BS association problem for a massive MIMO heterogeneous network. We formulate the problem as a network utility maximization, and provide a centralized solution in terms of the fraction of transmission resources (time-frequency slots) over which each user is served by a given BS. Furthermore, we show that such a solution is physically realizable, i.e., there exists a sequence of integer scheduling configurations realizing (by time-sharing) the optimal fractions. While this solution is optimal, it requires centralized computation. Then, we also consider decentralized user-centric schemes, formulated as non-cooperative games where each user makes individual selfish association decisions based only on its local information. We identify a class of schemes such that their Nash equilibrium is very close to the global centralized optimum. Hence, these user-centric algorithms are attractive not only for their simplicity and fully decentralized implementation, but also because they operate near the system"social"optimum.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: A Unified Analysis of Max-Min Weighted SINR for MIMO Downlink System

paper_content:

This paper studies the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem in the multiple-input-multiple-output (MIMO) downlink, where multiple users are weighted according to priority and are subject to a weighted-sum-power constraint. First, we study the multiple-input-single-output (MISO) and single-input-multiple- output (SIMO) problems using nonlinear Perron-Frobenius theory. As a by-product, we solve the open problem of convergence for a previously proposed MISO algorithm by Wiesel, Eldar, and Shamai in 2006. Furthermore, we unify our analysis with respect to the previous alternate optimization algorithm proposed by Tan, Chiang, and Srikant in 2009, by showing that our MISO result can, in fact, be derived from their algorithm. Next, we combine our MISO and SIMO results into an algorithm for the MIMO problem. We show that our proposed algorithm is optimal when the channels are rank-one, or when the network is operating in the low signal-to-noise ratio (SNR) region. Finally, we prove the parametric continuity of the MIMO problem in the power constraint, and we use this insight to propose a heuristic initialization strategy for improving the performance of our (generally) suboptimal MIMO algorithm. The proposed initialization strategy exhibits improved performance over random initialization.
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paper_title: Optimizing client association for load balancing and fairness in millimeter-wave wireless networks

paper_content:

Millimeter-wave communications in the 60-GHz band are considered one of the key technologies for enabling multigigabit wireless access. However, the special characteristics of such a band pose major obstacles to the optimal utilization of the wireless resources, where the problem of efficient client association to access points (APs) is of vital importance. In this paper, the client association in 60-GHz wireless access networks is investigated. The AP utilization and the quality of the rapidly vanishing communication links are the control parameters. Because of the tricky nonconvex and combinatorial nature of the client association optimization problem, a novel solution method is developed to guarantee balanced and fair resource allocation. A new distributed, lightweight, and easy-to-implement association algorithm, based on Lagrangian duality theory and subgradient methods, is proposed. It is shown that the algorithm is asymptotically optimal, that is, the relative duality gap diminishes to zero as the number of clients increases .
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paper_title: Solution of the multiuser downlink beamforming problem with individual SINR constraints

paper_content:

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.
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paper_title: Fast Algorithms and Performance Bounds for Sum Rate Maximization in Wireless Networks

paper_content:

Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying the solutions to two related problems, sum rate maximization using an SIR approximation and max-min weighted SIR optimization. We also show that these two problems can be solved very efficiently, using much faster algorithms than the existing ones in the literature. Furthermore, using a new parameterization of the sum rate maximization problem, we obtain a characterization of the power controlled rate region and its convexity property in various asymptotic regimes. Engineering implications are discussed for IEEE 802.11 networks.
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Low Complexity Scheduling Algorithm for the Downlink of Distributed Antenna Systems

paper_content:

In this paper we present a low-complexity user selection algorithm for the downlink of a distributed antenna system (DAS) that achieves an optimum solution for a weighted matching problem. The user selection process is modeled as a linear sum assignment problem (LSAP). The proposed solution consists of two phases. In the first phase, a set of potential users to be scheduled is found by combining two complementary approaches: greedy and minimum-throughput-loss selection. In the second phase, the set of scheduled users is refined by selecting the users that maximize sum throughput. We provide numerical results to confirm the optimality of our user selection algorithm and to compare its performance with existing solutions.
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paper_title: Optimal Resource Allocation for Multiuser MIMO-OFDM Systems With User Rate Constraints

paper_content:

With the proliferation of wireless services, personal connectivity is quickly becoming ubiquitous. As the user population demands greater multimedia interactivity, data rate requirements are set to soar. Future wireless systems, e.g., multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), need to cater to not only a burgeoning subscriber pool but also to a higher throughput per user. Furthermore, resource allocation for multiuser MIMO-OFDM systems is vital for the optimization of the subcarrier and power allocations to improve overall system performance. Using convex optimization techniques, this paper proposes an efficient solution to minimize the total transmit power subject to each user's data rate requirement. Using a Lagrangian dual decomposition, the complexity is reduced from one that is exponential in the number of subcarriers M to one that is only linear in M. To keep the complexity low, linear beamforming is incorporated at both the transmitter and the receiver. Although frequency-flat fading has been known to plague OFDM resource allocation systems, a modification, i.e., dual proportional fairness, seamlessly handles flat or partially frequency-selective fading. Due to the nonconvexity of the optimization problem, the proposed solution is not guaranteed to be optimal. However, for a realistic number of subcarriers, the duality gap is practically zero, and optimal resource allocation can be evaluated efficiently. Simulation results show large performance gains over a fixed subcarrier allocation.
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paper_title: ⋄ Convex Optimization,

paper_content:

Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.
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paper_title: Weighted max-min fair beamforming, power control, and scheduling for a MISO downlink

paper_content:

In this paper, we consider the joint beamforming, power control and scheduling problem in a multiple-input single- output (MISO) downlink for maximizing the minimum weighted rate among all users. We solve this problem by formulating it as a convex optimization problem whose function evaluations require maximization of a difference of convex functions (D.C. Programming). We also propose a simpler heuristic that finds the best policy under restricted set of power vectors. We then compare the performance of these policies against the dirty paper coding (DPC) policy to quantify the performance gap between an optimal point-to-point coding approach and an optimal joint encoding/decoding approach.
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paper_title: Efficient Margin Adaptive Scheduling for MIMO-OFDMA Systems

paper_content:

In this paper we address the problem of margin adaptive scheduling in the downlink of an orthogonal frequency division multiple access (OFDMA) multiple-input multiple-output (MIMO) system. Optimal resource allocation in MIMO systems requires the joint optimization of: a) linear transmit and receive spatial filters, b) channel assignment and c) power allocation. This problem is not convex and its complexity becomes thus intractable already for small sets of users and subcarriers. To reduce the complexity of the problem at hand, we propose a novel heuristic strategy that partitions the users in different groups according to their average channel quality and addresses the original problem by solving a succession of lower-complexity allocation problems. The spatial dimension is employed to prevent multiple access interference from hindering the performance of the sequential allocation. To further reduce the complexity burden we introduce a linear programming formulation in combination with a waterfilling-based strategy to allocate channels and power to the groups of users. Numerical results and evaluation of the computational complexity show that, though suboptimal, in most cases the proposed algorithm manages to exploit in an original way the inherent multi-user diversity of multi-carrier systems to ease the task of resource allocation with a very limited performance loss from the theoretic optimum.
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paper_title: Coordinated User Scheduling for Multi-Cell Distributed Antenna Systems

paper_content:

In this paper, we address the problem of coordinated user scheduling for the downlink of a multi-cell distributed antenna system (DAS). With the practical assumption that only large-scale channel state information (CSI) is known at the transmitter, a low-complexity greedy scheduling scheme is proposed. In order to provide fairness among users, the proposed scheme adopts round-robin scheduling within each cell and optimizes the scheduling order for each cell to maximize the minimum ergodic capacity of the users. For each user, the selection transmission scheme (just the distributed antenna element (DAE) with the largest channel gain to the user is selected for transmission) is implemented and each selected DAE transmits with equal power. Simulation results demonstrate that the proposed greedy scheme promises much better performance than that without inter-cell coordination and its performance is quite close to the optimal one. Moreover, by simulations we find that the proposed scheme achieves nearly the same system ergodic sum capacity with the one targeted to maximize the system ergodic sum capacity.
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paper_title: Joint Antenna Beamforming, Multiuser Scheduling, and Power Allocation for Hierarchical Cellular Systems

paper_content:

Cognitive radio (CR) is concretely embodied in hierarchical cellular systems by deploying an underlying microcellular system to reuse the underutilized spectrum of a macrocellular system. One of the key challenges to the success of hierarchical cellular systems is to manage the intercell interference between the macrocell and the microcell and to maximize the spectrum efficiency. In this paper, antenna beamforming, power allocation, and multiuser scheduling are jointly designed to opportunistically utilize the macrocell's uplink spectrum in serving multiple secondary microcellular users concurrently. The joint design of antenna beamforming, power allocation, and scheduling with the objective of maximizing the sum rate is indeed a mixed-integer nonlinear programming NP-hard problem. The proposed simpler iterative subgradient projection and semidefinite programming approach can obtain better performance than the conventional zero-forcing beamforming. Furthermore, unlike the optimal singular value decomposition (SVD) beamforming that requires all users to have channel knowledge at the receiver for cooperation, the proposed joint design methodology requires no channel knowledge at the receiver and can outperform the SVD beamforming without user scheduling. When considering both implementation complexity and performance enhancement issues, the proposed joint power allocation, multiuser scheduling, and antenna beamforming technique can help provide important insights into the design of interference management techniques for hierarchical CR systems.
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paper_title: Large deviation delay analysis of queue-aware multi-user MIMO systems with two timescale mobile-driven feedback

paper_content:

Multi-user multi-input-multi-output (MU-MIMO) systems usually require users to feedback the channel state information (CSI) for scheduling. Most of the existing literature on the reduced feedback user scheduling focused on the throughput performance and the queueing delay was usually ignored. As the delay is important for real-time applications, it is desirable to have a low feedback queue-aware user scheduling algorithm for MU-MIMO systems. This paper proposes a two timescale queue-aware user scheduling algorithm, which consists of a queue-aware mobile-driven feedback filtering stage and a SINR-based user scheduling stage. The feedback policy is obtained by solving a queue-weighted optimization problem. In addition, we evaluate the associated queueing delay performance by using the large deviation analysis. The large deviation decay rate for the proposed algorithm is shown to be much larger than the CSI-only scheduling algorithm. Numerical results demonstrate the large performance gain of the proposed algorithm over the CSI-only algorithm, while the proposed one requires only a small amount of feedback.
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paper_title: Low-Complexity User Selection for Rate Maximization in MIMO Broadcast Channels with Downlink Beamforming

paper_content:

We present in this work a low-complexity algorithm to solve the sum rate maximization problem in multiuser MIMO broadcast channels with downlink beamforming. Our approach decouples the user selection problem from the resource allocation problem and its main goal is to create a set of quasiorthogonal users. The proposed algorithm exploits physical metrics of the wireless channels that can be easily computed in such a way that a null space projection power can be approximated efficiently. Based on the derived metrics we present a mathematical model that describes the dynamics of the user selection process which renders the user selection problem into an integer linear program. Numerical results show that our approach is highly efficient to form groups of quasiorthogonal users when compared to previously proposed algorithms in the literature. Our user selection algorithm achieves a large portion of the optimum user selection sum rate (90%) for a moderate number of active users.
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paper_title: Monotonic Optimization Framework for Coordinated Beamforming in Multicell Networks

paper_content:

Intercell interference is the major limiting factor in wireless multicell networks. Recently, it has been shown that significant performance gains can be achieved by cooperation among base stations. Different degrees of cooperation are possible. In this paper, cooperation in the form of intercell interference management is considered. The base stations are equipped with multiple antennas, while the mobile terminals only have a single antenna. The base stations jointly coordinate beamforming and scheduling, and thus perform a weaker form of cooperation among base stations than suggested in recently proposed joint transmission techniques. The terminals treat intercell interference as noise. The corresponding resource allocation problem is cast as a utility maximization problem, which includes common performance objectives such as the arithmetic mean, the geometric mean, and the max-min operation of achievable user rates. The resulting utility maximization problem is a nonconvex optimization problem. After a suitable reformulation, the problem can be solved to global optimality using the framework of monotonic optimization. Although, the numerical complexity of the proposed method is exponential, the reformulation step leads to an optimization problem which only scales in the number of mobile terminals instead of the entire set of physical layer parameters. In essence, the proposed framework represents a powerful tool for computing benchmarks for certain scenarios and utility functions under jointly optimal beamforming and scheduling.
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paper_title: Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search

paper_content:

We consider a multi-user MIMO downlink system employing zero-forcing beamforming (ZFBF) as a spatial multiplexing strategy, and propose low-complexity user subset selection methods based on a clique (fully connected subgraph) search. The proposed algorithms, maximum weighted clique (MWC)-ZFBF and greedy weighted clique (GWC)-ZFBF, are shown to achieve the asymptotic sum-capacity of MIMO downlink channels as the number of users goes to infinity. Thus, clique search based ZFBF is an appealing strategy in MIMO downlink systems with a large number of users.
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paper_title: Convex approximation techniques for joint multiuser downlink beamforming and admission control

paper_content:

Multiuser downlink beamforming under quality of service (QoS) constraints has attracted considerable interest in years, because it is particularly appealing from a network operator's perspective (e.g., UMTS, 802.16e). When there are many co-channel users and/or the service constraints are stringent, the problem becomes infeasible and some form of admission control is necessary. We advocate a cross-layer approach to joint multiuser transmit beamforming and admission control, aiming to maximize the number of users that can be served at their desired QoS. It is shown that the core problem is NP-hard, yet amenable to convex approximation tools. Two computationally efficient convex approximation algorithms are proposed: one is based on semidefinite relaxation of an equivalent problem reformulation; the other takes a penalized second-order cone approach. Their performance is assessed in a range of experiments, using both simulated and measured channel data. In all experiments considered, the proposed algorithms work remarkably well in terms of the attained performance-complexity trade-off, consistently exhibiting close to optimal performance at an affordable computational complexity.
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paper_title: Adaptive scheduling for MIMO wireless networks: cross-layer approach and application to HSDPA

paper_content:

In this paper, we consider the scheduling problem in multiple-input multiple-output (MIMO) wireless networks. The main important characteristic of an optimal scheduler is to maximize throughput while servicing users in a fair manner. Herein, we formulate MIMO scheduling as a generalized assignment problem (GAP) and propose a general solution for the GAP, namely, a cross-layer MIMO scheduler (CMS), which uses a novel adaptive proportional fairness (APF) mapping approach in conjunction with a new fast transmit antenna selection (FTAS) technique, to determine the set of users to transmit to and the antenna over which the data associated to each user should be transmitted. The proposed scheduler is applied for packet transmission in high-speed downlink packet access (HSDPA), taking advantage of the use of adaptive modulation and coding while coping with the constraints on the maximum number of simultaneous codes a user equipment can support, the limited uplink signalling, and the absence of fast power control. Numerical results show that the proposed CMS provides up to 70% increase in total throughput compared to other scheduling schemes
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

paper_content:

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: Capacity Maximization for Zero-Forcing MIMO-OFDMA Downlink Systems with Multiuser Diversity

paper_content:

This paper considers the optimal resource allocation for a multiuser MIMO-OFDMA downlink system using zero-forcing SDMA, with the objective of maximizing the system capacity. We provide the general mathematical formulation of the capacity maximization problem whose resource allocation includes user selection, power allocation and receive signal subspace selection. While the optimal solution of this problem is difficult to obtain, we consider two special cases: user selection based only and antenna selection based only optimization, and develop the optimal solution by reformulating the combinatorial optimization problem into a convex problem. Our proposed algorithms for these special cases can be extended to develop a suboptimal algorithm for the original general optimization problem which allows subspace selection. Moreover, we develop reduced-complexity algorithms for these problems which incur negligible capacity loss. Numerical results and analysis are provided to evaluate the system capacity and to study the effect of the number of users and the receive antennas per user on the performance. Comparisons on the capacity achieved by user selection only, antenna selection only and suboptimal subspace selection are discussed
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paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

paper_content:

This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
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paper_title: On the Evolution of Multi-Cell Scheduling in 3GPP LTE / LTE-A

paper_content:

This paper provides a holistic overview of multi-cell scheduling strategies in emerging wireless systems. Towards this objective, the evolution of interference management techniques is thoroughly investigated from simple inter-cell interference coordination (ICIC) techniques towards more advanced coordinated multipoint transmissions (CoMP), while comparing and contrasting their common features and differences. Finally CoMP is explored in detail as an advanced and challenging mechanism to fully cooperate between adjacent cells in order to have an efficient resource allocation and inter-cell interference mitigation in multi-cell environments.
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paper_title: Joint Antenna Beamforming, Multiuser Scheduling, and Power Allocation for Hierarchical Cellular Systems

paper_content:

Cognitive radio (CR) is concretely embodied in hierarchical cellular systems by deploying an underlying microcellular system to reuse the underutilized spectrum of a macrocellular system. One of the key challenges to the success of hierarchical cellular systems is to manage the intercell interference between the macrocell and the microcell and to maximize the spectrum efficiency. In this paper, antenna beamforming, power allocation, and multiuser scheduling are jointly designed to opportunistically utilize the macrocell's uplink spectrum in serving multiple secondary microcellular users concurrently. The joint design of antenna beamforming, power allocation, and scheduling with the objective of maximizing the sum rate is indeed a mixed-integer nonlinear programming NP-hard problem. The proposed simpler iterative subgradient projection and semidefinite programming approach can obtain better performance than the conventional zero-forcing beamforming. Furthermore, unlike the optimal singular value decomposition (SVD) beamforming that requires all users to have channel knowledge at the receiver for cooperation, the proposed joint design methodology requires no channel knowledge at the receiver and can outperform the SVD beamforming without user scheduling. When considering both implementation complexity and performance enhancement issues, the proposed joint power allocation, multiuser scheduling, and antenna beamforming technique can help provide important insights into the design of interference management techniques for hierarchical CR systems.
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paper_title: 4G: LTE/LTE-Advanced for Mobile Broadband

paper_content:

Based on the bestseller "3G Evolution - HSPA and LTE for mobile broadband" and reflecting the ongoing success of LTE throughout the world, this book focuses on LTE with full updates including LTE-Advanced to provide a complete picture of the LTE system. Overview and detailed explanations are given for the latest LTE standards for radio interface architecture, the physical layer, access procedures, broadcast, relaying, spectrum and RF characteristics, and system performance. Key technologies presented include multi-carrier transmission, advanced single-carrier transmission, advanced receivers, OFDM, MIMO and adaptive antenna solutions, advanced radio resource management and protocols, and different radio network architectures. Their role and use in the context of mobile broadband access in general is explained. Both a high-level overview and more detailed step-by-step explanations of the LTE/LTE-Advanced implementation are given. An overview of other related systems such as GSM/EDGE, HSPA, CDMA2000, and WIMAX is also provided. This book is a 'must-have' resource for engineers and other professionals in the telecommunications industry, working with cellular or wireless broadband technologies, giving an understanding of how to utilize the new technology in order to stay ahead of the competition. The authors of the book all work at Ericsson Research and have been deeply involved in 3G and 4G development and standardisation since the early days of 3G research. They are leading experts in the field and are today still actively contributing to the standardisation of LTE within 3GPP. Includes full details of the latest additions to the LTE Radio Access standards and technologies up to and including 3GPP Release 10Clear explanations of the role of the underlying technologies for LTE, including OFDM and MIMO Full coverage of LTE-Advanced, including LTE carrier aggregation, extended multi-antenna transmission, relaying functionality and heterogeneous deploymentsLTE radio interface architecture, physical layer, access procedures, MBMS, RF characteristics and system performance covered in detail
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paper_title: Efficient MAC protocol for JT CoMP in small cells

paper_content:

In this paper, we investigate an efficient MAC protocol for interference coordination in small cells embedded in a macro-cell mobile network. We perform joint transmission (JT)-coordinated multi-point (CoMP), where cells in the cluster include adjacent macro-cells as suggested by the small-cell terminal. Most gains compared to uncoordinated transmission come from selecting the right users in these macro-cells. For minimizing the feedback overhead, we propose successive channel state information (CSI) requests. Thereby we replace users in the set until all of them experience consistently enhanced performance when using JT-CoMP. Gains can be further increased by MIMO mode switching in each cell and frequency-selective scheduling. We tested our algorithms over coherently measured multi-cell channels in the LTE-Advanced testbed in Berlin where small cells were embedded at several places. Using these algorithms, performance becomes comparable to a popular bound assuming no more intra-cluster interference while feedback overhead and complexity are substantially reduced.
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paper_title: Networked MIMO with clustered linear precoding

paper_content:

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination to enhance the sum rate and limited inter-cluster coordination to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.
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paper_title: Scheduling Methods with MIMO Interference Alignment for Mutually Interfering Broadcast Channels

paper_content:

In this paper, we investigate an interference alignment (IA) technique introduced by Cadambe and Jafar in mutually interfering broadcast channels (IFBCs). First, we study the spatial multiplexing gain (SMG) for the 3-cell IFBC where all base stations and mobile users are equipped with multiple antennas. To achieve the derived optimal SMG, we extend the IA algorithm designed for K-user multi-input multi-output (MIMO) interference channels (IFCs) to the IFBC. In this paper, we present the IA scheme in conjunction with user selection which outperforms the time division multiple access (TDMA) technique in the IFBC environment. The optimal scheduling method capitalizes on multiuser diversity to achieve a significant fraction of sum capacity by using an exhaustive search algorithm. Since the computational complexity of the optimal scheduling method is prohibitive, a reduced complexity suboptimal scheduling method is proposed based on a coordinate ascent approach. Simulation results confirm that the reduced complexity scheduling algorithm achieves the sum rate close to the optimal algorithm with much reduced complexity.
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paper_title: Multicell Cooperative Scheduling for Two-Tier Cellular Networks

paper_content:

Cellular wireless network architectures employing a tiered structure, consisting of traditional macro-cells and small-cells, have attracted much attention recently because of their potential to dramatically increase network capacity. These architectures can reduce the distances of transmit-receiver pairs, thus enhancing radio link qualities. However, a tiered cell deployment could incur severe cochannel interference. Prior work for single-tier networks has proposed coordinated multi-point (CoMP) transmission, which includes joint transmission, as a possible solution for overcoming the rate limitations induced by cochannel interference. Because users in each cell experience various interference conditions, each cell needs to support single transmission (in which only one cell transmits to a single user) and joint transmission. In a conventional implementation, a particular combination of transmissions over the entire network is fixed in advance for each time slot and opportunistic scheduling chooses one of the users supported by each transmission. However, when the number of users to be scheduled is small, the throughput improvement from opportunistic scheduling becomes limited. To overcome this problem, we propose a cumulative distribution function-based scheduling scheme which jointly chooses the transmitter set and the corresponding scheduled users in a two-tier network. It is shown that the throughput performance can be improved compared to those of the fixed slot resource allocation scheme because more users "compete" for slot resources.
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paper_title: CoMP-CSB for ICI Nulling with User Selection

paper_content:

The capacity of downlink multiple-input multiple-output (MIMO) cellular networks is significantly limited by inter-cell interference (ICI), particularly at cell boundaries. Recently, two types of coordinated multiple point transmission (CoMP) technologies, joint processing and transmission (JPT) and coordinated scheduling and beamforming (CSB), were proposed. These technologies are intended for the latest cellular communication standard in order to improve the performance of cell-edge users who suffer from significant ICI. In this paper, we propose an ICI cancellation technique based on a user selection algorithm for CoMP-CSB. Under partial channel state information (CSI) and no data sharing condition, each base station (BS) concentrates more on the direction of interference to the adjacent cell's users, during the user selection process. Unlike prior concepts for a single-cell environment, in which each BS generates a precoding matrix for selected users to be served, the proposed technique considers the effects of interference to users located in adjacent cells. Although there are obvious trade-offs between ICI mitigation and the number of simultaneous scheduled users in terms of system capacity, the simulation results demonstrate that our proposed algorithm achieves higher sector throughput and is more robust against ICI if the system is limited by interference. Furthermore, through simulation we are able to obtain the preferred option for the coordination distance (R) and the number of degrees of freedom for ICI nulling (ξ).
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paper_title: Spatial Transmission Mode Switching in Multiuser MIMO-OFDM Systems With User Fairness

paper_content:

Multiantenna radio systems allow accessing the channel in diversity or spatial multiplexing (SMUX) mode. Adequate switching between these modes according to current channel conditions was shown to yield significant performance improvements while requiring little feedback from the receiving side. We present a transmission concept for the downlink of a multiuser multiple-input-multiple-output orthogonal frequency-division-multiplexing (MU-MIMO-OFDM) system aiming at high user rates with limited feedback demands. An extended score-based scheduling (SB) approach ensures fair-resource allocation to the users, whereas transmission mode switching is used to guarantee high user rates. The degree of fairness of the scheduler can be adapted by adequately configuring a weighting function for the scores. Comparison with single-mode schemes reveals substantial throughput gains of the adaptive switching concept. Furthermore, targeting maximum throughput, we show that a considerable proportion of the capacity of the MIMO broadcast channel (BC) can be achieved with a comparatively low amount of required feedback.
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paper_title: On the Performance of Downlink Beamforming with Synchronized Beam Cycles

paper_content:

The next generation of wireless networks (e.g.,) will use multiple techniques to improve channel spectral efficiencies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each frame, the scheduler chooses a beam and then schedules one or more UEs that lie within that beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors. If a neighboring sector schedules a UE that lies within the coverage of this beam then the rate for that UE will be low. The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. The first approach (interference avoidance) requires coordination among the sectors with the associated communication overheads and delays. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period. Although all NBs use the same beam cycle period, they may occasionally change the specific beam schedule based on local factors such as the geographical distribution of UEs within its beams. Such changes should be made infrequently since the approach is based on the assumption that the interference experienced by a UE repeats with the beam cycle period.
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paper_title: Cooperative Cellular Wireless Networks

paper_content:

A self-contained guide to the state-of-the-art in cooperative communications and networking techniques for next generation cellular wireless systems, this comprehensive book provides a succinct understanding of the theory, fundamentals and techniques involved in achieving efficient cooperative wireless communications in cellular wireless networks. It consolidates the essential information, addressing both theoretical and practical aspects of cooperative communications and networking in the context of cellular design. This one-stop resource covers the basics of cooperative communications techniques for cellular systems, advanced transceiver design, relay-based cellular networks, and game-theoretic and micro-economic models for protocol design in cooperative cellular wireless networks. Details of ongoing standardization activities are also included. With contributions from experts in the field divided into five distinct sections, this easy-to-follow book delivers the background needed to develop and implement cooperative mechanisms for cellular wireless networks.
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paper_title: Coordinated User Scheduling for Multi-Cell Distributed Antenna Systems

paper_content:

In this paper, we address the problem of coordinated user scheduling for the downlink of a multi-cell distributed antenna system (DAS). With the practical assumption that only large-scale channel state information (CSI) is known at the transmitter, a low-complexity greedy scheduling scheme is proposed. In order to provide fairness among users, the proposed scheme adopts round-robin scheduling within each cell and optimizes the scheduling order for each cell to maximize the minimum ergodic capacity of the users. For each user, the selection transmission scheme (just the distributed antenna element (DAE) with the largest channel gain to the user is selected for transmission) is implemented and each selected DAE transmits with equal power. Simulation results demonstrate that the proposed greedy scheme promises much better performance than that without inter-cell coordination and its performance is quite close to the optimal one. Moreover, by simulations we find that the proposed scheme achieves nearly the same system ergodic sum capacity with the one targeted to maximize the system ergodic sum capacity.
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paper_title: Joint Antenna Beamforming, Multiuser Scheduling, and Power Allocation for Hierarchical Cellular Systems

paper_content:

Cognitive radio (CR) is concretely embodied in hierarchical cellular systems by deploying an underlying microcellular system to reuse the underutilized spectrum of a macrocellular system. One of the key challenges to the success of hierarchical cellular systems is to manage the intercell interference between the macrocell and the microcell and to maximize the spectrum efficiency. In this paper, antenna beamforming, power allocation, and multiuser scheduling are jointly designed to opportunistically utilize the macrocell's uplink spectrum in serving multiple secondary microcellular users concurrently. The joint design of antenna beamforming, power allocation, and scheduling with the objective of maximizing the sum rate is indeed a mixed-integer nonlinear programming NP-hard problem. The proposed simpler iterative subgradient projection and semidefinite programming approach can obtain better performance than the conventional zero-forcing beamforming. Furthermore, unlike the optimal singular value decomposition (SVD) beamforming that requires all users to have channel knowledge at the receiver for cooperation, the proposed joint design methodology requires no channel knowledge at the receiver and can outperform the SVD beamforming without user scheduling. When considering both implementation complexity and performance enhancement issues, the proposed joint power allocation, multiuser scheduling, and antenna beamforming technique can help provide important insights into the design of interference management techniques for hierarchical CR systems.
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paper_title: An Effective Inter-Cell Interference Coordination Scheme for Downlink CoMP in LTE-A Systems

paper_content:

Coordinated multi-point (CoMP) has been adopted in 3GPP LTE-Advanced to improve the coverage of high data rates. Downlink CoMP is mainly categorized into joint transmission (JT) and coordinated beamforming (CB). Previous research shows that JT does not benefit cell average throughput. Moreover, traditional CB algorithms are based on iterative evaluation, resulting in very high computational complexity. To address these issues, in this paper, we propose an effective inter-cell interference coordination scheme for downlink CoMP, which includes two phases. Firstly, in order to improve the performance of all user equipments (UEs), cell edge UEs employ JT, while CB is adopted by both cell edge and cell center UEs. Secondly, we design linear CB precoders by maximizing a signal to leakage and noise ratio (SLNR) metric, so as to reduce processing complexity. System-level simulations validate that, in contrast to non-CoMP, the proposed scheme brings a cell average spectral efficiency (SE) gain up to 21.50% and a cell edge SE gain up to 119.2%.
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paper_title: System evaluation of optimal downlink beamforming with congestion control in wireless communication

paper_content:

We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.
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paper_title: Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

paper_content:

In this paper, we tackle the problem of semidistributed user selection with distributed linear precoding for sum-rate maximization in multiuser multicell systems. A set of adjacent base stations (BSs) forms a cluster to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling, and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to nonintended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, namely, distributed zero forcing and distributed virtual signal-to-interference-plus-noise ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First, we investigate how the signal-to-noise ratio regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the BSs.
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paper_title: Network MIMO with Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation and Reduced-Complexity Scheduling

paper_content:

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.
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paper_title: Multicell Coordination via Joint Scheduling, Beamforming, and Power Spectrum Adaptation

paper_content:

The mitigation of intercell interference is an importance issue for current and next-generation wireless cellular networks where frequencies are aggressively reused and hierarchical cellular structures may heavily overlap. The paper examines the benefit of coordinating transmission strategies and resource allocation schemes across multiple base-stations for interference mitigation. Two different wireless cellular architectures are studied: a multicell network where base-stations coordinate in their transmission strategies, and a mixed macrocell and femtocell/picocell deployment with coordination among macro and femto/pico base-stations. For both scenarios, this paper proposes a heuristic joint proportionally fair scheduling, spatial multiplexing, and power spectrum adaptation algorithm that coordinates multiple base-stations with an objective of optimizing the overall network utility. The proposed scheme optimizes the user schedule, transmit and receive beamforming vectors, and transmit power spectra jointly, while taking into consideration both the intercell and intracell interference and the fairness among the users. System-level simulation results show that coordination at the transmission strategy and resource allocation level can already significantly improve the overall network throughput as compared to a conventional network design with fixed transmit power and per-cell zero-forcing beamforming.
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paper_title: Coordinated user scheduling in the multi-cell MIMO downlink

paper_content:

We propose a novel, coordinated user scheduling (CUS) algorithm for inter-cell interference (ICI) mitigation in the downlink of a multi-cell multi-user MIMO system. In the proposed algorithm, ICI mitigation is performed through the exchange of necessary channel state information (CSI) among the base stations, and the revision of the scheduling decisions and beamformer designs at each base station. Furthermore, ICI mitigation is performed only for the cell-edge users so that the amount of inter-base station signaling overhead is minimized. Our simulation results demonstrate that the proposed coordination scheduling algorithm significantly improves the cell-edge users' throughput compared to conventional systems with only a negligible amount of CSI sharing among the base stations and a relatively small throughput loss for the cell-interior users.
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paper_title: Interference Coordination through Network-Synchronized Cyclic Beamforming

paper_content:

The next generation of wireless networks (e.g., (10)) will use multiple techniques to improve channel spectral efficien- cies. In this paper we focus on one such technique, beamforming, in the downlink channel. In each sector, a number of fixed beams are used to serve UEs (User Equipment). For each subband in each frame, the scheduler chooses a beam and then schedules one or more UEs within the corresponding beam. Since the power is focused on a narrow beam then the served UEs can achieve higher rates and the sector coverage is also increased. However, this beam causes more interference in adjacent sectors (flashlight effect). The neighboring sectors must therefore schedule UEs outside of the beam or at least know of the interference that will be experienced. In this paper we follow the second approach and assume no coordination among sectors except for the fact that they all use the same beam cycle period but this can be changed occasionally.
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paper_title: Joint User Scheduling and Adaptive Intercell Interference Cancelation for MISO Downlink Cellular Systems

paper_content:

Recently, an adaptive intercell interference (ICI) mitigation technique has been proposed for downlink cellular systems as a means to increase throughput with low system complexity. However, in the prior work, the issue of intercell user scheduling has not been considered. In this paper, we study multiple-input-single-output (MISO) downlink cellular systems that jointly design adaptive ICI cancelation (ICIC) and intercell user scheduling assuming that partial channel state information (CSI) is shared among base stations (BSs). Since the optimal solution would require high complexity, we investigate a new low-complexity algorithm that selects the best users and their beamforming strategies in terms of maximizing the weighted sum rate (WSR). To this end, we first develop a simple threshold criterion for each user to decide the preferred beamforming strategy based on the derivation of the expected signal-to-interference-plus-noise ratio (SINR). Then, according to users' feedback about their decisions, a successive user and beamforming selection algorithm is performed at the BSs. From simulation results, we show that, combined with proportional fair scheduling, the proposed scheme provides excellent throughput performance with very low computational complexity and the amount of inter-BS CSI exchange. Furthermore, we discuss an extension of the proposed scheme to limited feedback systems and observe that our algorithm also provides similar advantages over conventional schemes with quantized feedback.
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paper_title: Elements of Information Theory

paper_content:

Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
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paper_title: Complete Characterization of the Pareto Boundary for the MISO Interference Channel

paper_content:

In this correspondence, we study the achievable rate region of the multiple-input single-output (MISO) interference channel, under the assumption that all receivers treat the interference as additive Gaussian noise. Our main result is an explicit parametrization of the Pareto boundary for an arbitrary number of users and antennas. The parametrization describes the boundary in terms of a low-dimensional manifold. For the two-user case we show that a single real-valued parameter per user is sufficient to achieve all points on the Pareto boundary and that any point on the Pareto boundary corresponds to beamforming vectors that are linear combinations of the zero-forcing (ZF) and maximum-ratio transmission (MRT) beamformers. We further specialize the results to the MISO broadcast channel (BC). A numerical example illustrates the result.
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paper_title: Competition Versus Cooperation on the MISO Interference Channel

paper_content:

We consider the problem of coordinating two competing multiple-antenna wireless systems (operators) that operate in the same spectral band. We formulate a rate region which is achievable by scalar coding followed by power allocation and beamforming. We show that all interesting points on the Pareto boundary correspond to transmit strategies where both systems use the maximum available power. We then argue that there is a fundamental need for base station cooperation when performing spectrum sharing with multiple transmit antennas. More precisely, we show that if the systems do not cooperate, there is a unique Nash equilibrium which is inefficient in the sense that the achievable rate is bounded by a constant, regardless of the available transmit power. An extension of this result to the case where the receivers use successive interference cancellation (SIC) is also provided. Next we model the problem of agreeing on beamforming vectors as a non-transferable utility (NTU) cooperative gametheoretic problem, with the two operators as players. Specifically we compute numerically the Nash bargaining solution, which is a likely resolution of the resource conflict assuming that the players are rational. Numerical experiments indicate that selfish but cooperating operators may achieve a performance which is close to the maximum-sum-rate bound.
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

paper_content:

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: Asymptotically optimal simple user scheduling for massive MIMO downlink with two-stage beamforming

paper_content:

In this paper, a simple user-scheduling-and-beamforming method is proposed for massive multi-user multiple-input multiple-output (MU-MIMO) downlink adopting two-stage beamforming. The key ideas of the proposed scheduling-and-beamforming method are to divide users into several candidate subsets according to the level of alignment of user channels to the dominant directions of the channel covariance matrix and select the user in each candidate subset based on a certain channel quality indicator (CQI) and to apply post-selection zero-forcing beamforming (ZFBF) to the selected users based on their channel state information (CSI). It is proved that the proposed scheduling-and-beamformingmethod is asymptotically optimal as the number of users increases. Furthermore, the proposed method significantly reduces the feedback overhead and shows superior sum rate performance compared to existing scheduling methods for MU-MIMO downlink.
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paper_title: User scheduling for massive MIMO OFDMA systems with hybrid analog-digital beamforming

paper_content:

This paper proposes a new user scheduling and sub-carrier allocation algorithm for multiuser downlink massive multiple input multiple output (MIMO) orthogonal frequency division multiple access (OFDMA) systems with hybrid analogdigital beamforming (HB). We assume that the transmitter having N antennas is serving K i decentralized single antenna receivers by sub-carrier i. The scheduling algorithm leverages the solutions of the digital beamforming (DB) result and is designed to maximize the total sum rate of all sub-carriers under per carrier power constraint. For this system and problem setup, the proposed algorithm is explained as follows: First, we express the HB matrix of sub-carrier i as a product of AB i , where the high dimensional matrix A ∈ CN×Na is common to all subcarriers whereas, B i ∈ CNa×Ki is a low dimensional matrix which is designed for sub-carrier i, and Na is the number of RF chains satisfying N ≥ Na ≥ K i . Second, we compute A as the first Na eigenvectors of the left singular value decomposition of the combined DB precoder matrices of sub-carriers having the highest sum rate. Finally, for fixed A, we compute Bi and its corresponding users such that the total sum rate of all sub-carriers is maximized. The performance of the proposed scheduling is studied analytically. Furthermore, the superiority of the proposed algorithm over that of the existing one is quantified analytically and demonstrated by computer simulations.
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paper_title: Robust Channel Estimation and Scheduling for Heterogeneous Multiuser Massive MIMO Systems

paper_content:

We consider a correlated multiuser (MU) massive multiple-input multiple-output (MIMO) downlink channel in which many heterogeneous users have different channel qualities (i.e., different path-losses) to a base station (BS) equipped with a large antenna array. Using the theory of extreme values of regularly varying functions, we characterize the scaling laws of the achievable sum-rate of the system, when both numbers of BS antennas and users grow large. We then prove that for a large number of users, a simple user scheduling that chooses the users with the largest instantaneous channel vector norms based on the global channel state information (CSI) can significantly improve the achievable system sum-rate. Finally, since the scheduling method needs the global CSI estimate to operate, we propose an efficient algorithm based on low-rank matrix approximation to estimate the global CSI with a moderate number of training signals. Analysis and numerical simulations show that the proposed scheme provides favourable results in terms of system sum-rate performance and computational complexity.
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paper_title: Massive MIMO and mmWave for 5G Wireless HetNet: Potential Benefits and Challenges

paper_content:

There has been active research worldwide to develop the next-generation, i.e., fifth-generation (5G), wireless network. The 5G network is expected to support a significantly large amount of mobile data traffic and a huge number of wireless connections and achieve better costand energy-efficiency as well as quality of service (QoS) in terms of communication delay, reliability, and security. To this end, the 5G wireless network should exploit the potential of new developments, including superdense and heterogeneous deployment of cells and massive antenna arrays [i.e., massive multiple-input, multiple-output (MIMO) technologies] and utilization of higher frequencies, particularly millimeter-wave (mmWave) frequencies. This article discusses the potential benefits and challenges of the 5G wireless heterogeneous network (HetNet) that incorporates massive MIMO and mmWave technologies.
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paper_title: Low-complexity user scheduling in the downlink massive MU-MIMO system with linear precoding

paper_content:

In this paper, we investigate low-complexity user scheduling schemes for the downlink (DL) massive multiuser multiple-input multiple-output (MU-MIMO) system, where an M-antenna (M is very large) base station (BS) serves K (K > 2) N-antenna (N > 1) users with linear transceivers. Establishing the theoretical foundation of our scheduling schemes, we first investigate the asymptotic sum-rates of this system with both singular value decomposition (SVD) and regularized zero-forcing (RZF) precoders. In particular, we assume that both M and N go to infinity with a bounded ratio to perform the theoretical derivations with random matrix theory (RMT). In addition, the influence of imperfect channel estimation is also considered. Interestingly, the analysis indicates the existence of an optimal number of served users K1 in terms of asymptotic sum-rate, which motivates our low complexity user scheduling schemes. Unlike the conventional schemes with complicated computations and instantaneous channel state information, our user scheduling schemes are based on semi-analytical solutions with only statistic CSI. Simulation results validate our theoretical derivations and show the advantages of our schemes in the massive MU-MIMO system.
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paper_title: Hierarchical Interference Mitigation for Massive MIMO Cellular Networks

paper_content:

We propose a hierarchical interference mitigation scheme for massive MIMO cellular networks. The MIMO precoder at each base station (BS) is partitioned into an inner precoder and an outer precoder. The inner precoder controls the intra-cell interference and is adaptive to local channel state information (CSI) at each BS (CSIT). The outer precoder controls the inter-cell interference and is adaptive to channel statistics. Such hierarchical precoding structure reduces the number of pilot symbols required for CSI estimation in massive MIMO downlink and is robust to the backhaul latency. We study joint optimization of the outer precoders, the user selection, and the power allocation to maximize a general concave utility which has no closed-form expression. We first apply random matrix theory to obtain an approximated problem with closed-form objective. We show that the solution of the approximated problem is asymptotically optimal with respect to the original problem as the number of antennas per BS grows large. Then using the hidden convexity of the problem, we propose an iterative algorithm to find the optimal solution for the approximated problem. We also obtain a low complexity algorithm with provable convergence. Simulations show that the proposed design has significant gain over various state-of-the-art baselines.
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paper_title: Millimeter Wave Cellular Networks: A MAC Layer Perspective

paper_content:

The millimeter-wave (mmWave) frequency band is seen as a key enabler of multigigabit wireless access in future cellular networks. In order to overcome the propagation challenges, mmWave systems use a large number of antenna elements both at the base station and at the user equipment, which leads to high directivity gains, fully directional communications, and possible noise-limited operations. The fundamental differences between mmWave networks and traditional ones challenge the classical design constraints, objectives, and available degrees of freedom. This paper addresses the implications that highly directional communication has on the design of an efficient medium access control (MAC) layer. The paper discusses key MAC layer issues, such as synchronization, random access, handover, channelization, interference management, scheduling, and association. This paper provides an integrated view on MAC layer issues for cellular networks, identifies new challenges and tradeoffs, and provides novel insights and solution approaches.
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paper_title: Performance of Conjugate and Zero-Forcing Beamforming in Large-Scale Antenna Systems

paper_content:

Large-Scale Antenna Systems (LSAS) is a form of multi-user MIMO technology in which unprecedented numbers of antennas serve a significantly smaller number of autonomous terminals. We compare the two most prominent linear pre-coders, conjugate beamforming and zero-forcing, with respect to net spectral-efficiency and radiated energy-efficiency in a simplified single-cell scenario where propagation is governed by independent Rayleigh fading, and where channel-state information (CSI) acquisition and data transmission are both performed during a short coherence interval. An effective-noise analysis of the pre-coded forward channel yields explicit lower bounds on net capacity which account for CSI acquisition overhead and errors as well as the sub-optimality of the pre-coders. In turn the bounds generate trade-off curves between radiated energy-efficiency and net spectral-efficiency. For high spectral-efficiency and low energy-efficiency zero-forcing outperforms conjugate beamforming, while at low spectral-efficiency and high energy-efficiency the opposite holds. Surprisingly, in an optimized system, the total LSAS-critical computational burden of conjugate beamforming may be greater than that of zero-forcing. Conjugate beamforming may still be preferable to zero-forcing because of its greater robustness, and because conjugate beamforming lends itself to a de-centralized architecture and de-centralized signal processing.
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paper_title: Survey of Large-Scale MIMO Systems

paper_content:

The escalating teletraffic growth imposed by the proliferation of smartphones and tablet computers outstrips the capacity increase of wireless communications networks. Furthermore, it results in substantially increased carbon dioxide emissions. As a powerful countermeasure, in the case of full-rank channel matrices, MIMO techniques are potentially capable of linearly increasing the capacity or decreasing the transmit power upon commensurately increasing the number of antennas. Hence, the recent concept of large-scale MIMO (LS-MIMO) systems has attracted substantial research attention and been regarded as a promising technique for next-generation wireless communications networks. Therefore, this paper surveys the state of the art of LS-MIMO systems. First, we discuss the measurement and modeling of LS-MIMO channels. Then, some typical application scenarios are classified and analyzed. Key techniques of both the physical and network layers are also detailed. Finally, we conclude with a range of challenges and future research topics.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.
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paper_title: A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System

paper_content:

Massive MIMO has been recognized as a promising technology to meet the demand for higher data capacity for mobile networks in 2020 and beyond. Although promising, each base station needs accurate estimation of the channel state information (CSI), either through feedback or channel reciprocity schemes in order to achieve the benefits of massive MIMO in practice. Time division duplex (TDD) has been suggested as a better mode to acquire timely CSI in massive MIMO systems. The use of non-orthogonal pilot schemes, proposed for channel estimation in multi-cell TDD networks, is considered as a major source of pilot contamination in the literature due to the limitations of coherence time. Given the importance of pilot contamination in massive MIMO systems, we provide an extensive survey on pilot contamination, and identify other possible sources of pilot contamination, which include hardware impairment and non-reciprocal transceivers. We review established theories that have analyzed the effect of pilot contamination on the performance of massive MIMO systems, particularly on achievable rates. Next, we categorize the different proposed mitigation techniques for pilot contamination using the following taxonomy: pilot-based approach and subspace-based approach. Finally, we highlight the open issues, such as training overhead, deployment scenario, computational complexity, use of channel reciprocity, and conclude with broader perspective and a look at future trends in pilot contamination in massive MIMO systems.
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paper_title: Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

paper_content:

A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
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paper_title: Network MIMO with Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation and Reduced-Complexity Scheduling

paper_content:

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.
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paper_title: On the Number of RF Chains and Phase Shifters, and Scheduling Design With Hybrid Analog–Digital Beamforming

paper_content:

This paper considers hybrid beamforming (HB) for downlink multiuser massive multiple-input multiple-output (MIMO) systems with frequency selective channels. The proposed HB design employs sets of digitally controlled phase (fixed phase) paired phase shifters (PSs) and switches. For this system, first we determine the required number of radio frequency (RF) chains and PSs such that the proposed HB achieves the same performance as that of the digital beamforming (DB) which utilizes $N$ (number of transmitter antennas) RF chains. We show that the performance of the DB can be achieved with our HB just by utilizing $r_t$ RF chains and $2r_t(N-r_t + \text{1})$ PSs, where $r_t \leq N$ is the rank of the combined digital precoder matrices of all subcarriers. Second, we provide a simple and novel approach to reduce the number of PSs with only a negligible performance degradation. Numerical results reveal that only ${20}{-}{40}$ PSs per RF chain are sufficient for practically relevant parameter settings. Finally, for the scenario where the deployed number of RF chains $(N_a) $ is less than $r_t$ , we propose a simple user scheduling algorithm to select the best set of users in each subcarrier. Simulation results validate theoretical expressions, and demonstrate the superiority of the proposed HB design over the existing HB designs in both flat fading and frequency selective channels.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: Low-Complexity Downlink User Selection for Massive MIMO Systems

paper_content:

In this paper, we propose a pair of low-complexity user selection schemes with zero-forcing precoding for multiuser massive multiple-input–multiple-output downlink systems, in which the base station is equipped with a large-scale antenna array. First, we derive approximations of the ergodic sum rates of the systems invoking the conventional random user selection (RUS) and the location-dependent user selection (LUS). Then, the optimal number of simultaneously served user equipments (UEs),i.e., $K^\ast$ , is investigated to maximize the sum rate approximations. Upon exploiting $K^\ast$ , we develop two user selection schemes, namely, $K^\ast$ -RUS and $K^\ast$ -LUS, where $K^\ast$ UEs are selected either randomly or based on their locations. Both the proposed schemes are independent of the instantaneous channel state information of small-scale fading, therefore enjoying the same extremely low computational complexity as that of the conventional RUS scheme. Moreover, both of our proposed schemes achieve significant sum rate improvement over the conventional RUS. In addition, it is worth noting that, like the conventional RUS, the $K^\ast$ -RUS achieves good fairness among UEs.
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paper_title: Scaling up MIMO: Opportunities and Challenges with Very Large Arrays

paper_content:

Multiple-input multiple-output (MIMO) technology is maturing and is being incorporated into emerging wireless broadband standards like long-term evolution (LTE) [1]. For example, the LTE standard allows for up to eight antenna ports at the base station. Basically, the more antennas the transmitter/receiver is equipped with, and the more degrees of freedom that the propagation channel can provide, the better the performance in terms of data rate or link reliability. More precisely, on a quasi static channel where a code word spans across only one time and frequency coherence interval, the reliability of a point-to-point MIMO link scales according to Prob(link outage) ` SNR-ntnr where nt and nr are the numbers of transmit and receive antennas, respectively, and signal-to-noise ratio is denoted by SNR. On a channel that varies rapidly as a function of time and frequency, and where circumstances permit coding across many channel coherence intervals, the achievable rate scales as min(nt, nr) log(1 + SNR). The gains in multiuser systems are even more impressive, because such systems offer the possibility to transmit simultaneously to several users and the flexibility to select what users to schedule for reception at any given point in time [2].
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paper_title: Joint Spatial Division and Multiplexing—The Large-Scale Array Regime

paper_content:

We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink/downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users.
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paper_title: User selection schemes in multiple antenna broadcast channels with guaranteed performance

paper_content:

Recently, user selection algorithms in combination with linear pre- coding have been proposed that achieve the same scaling as the sum capacity of the MIMO BC. In this work, we study the properties of four user selection algorithms in conjunction with beamforming that guarantee certain SINR requirements under transmit power minimization. It is shown that for a large number of transmit antennas, the norm-based user selection performs close to the optimum. The results are illustrated by various numerical simulations.
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paper_title: What Will 5G Be?

paper_content:

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
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paper_title: Exploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems

paper_content:

In the design of narrowband multi-antenna systems, a limiting factor is the amount of channel state information (CSI) available at the transmitter. This is especially evident in multi-user systems, where the spatial user separability determines the multiplexing gain, but it is also important for transmission-rate adaptation in single-user systems. To limit the feedback load, the unknown and multi-dimensional channel needs to be represented by a limited number of bits. When combined with long-term channel statistics, the norm of the channel matrix has been shown to provide substantial CSI that permits efficient user selection, linear precoder design, and rate adaptation. Herein, we consider quantized feedback of the squared Frobenius norm in a Rayleigh fading environment with arbitrary spatial correlation. The conditional channel statistics are characterized and their moments are derived for both identical, distinct, and sets of repeated eigenvalues. These results are applied for minimum mean square error (MMSE) estimation of signal and interference powers in single- and multi-user systems, for the purpose of reliable rate adaptation and resource allocation. The problem of efficient feedback quantization is discussed and an entropy-maximizing framework is developed where the post-user-selection distribution can be taken into account in the design of the quantization levels. The analytic results of this paper are directly applicable in many widely used communication techniques, such as space-time block codes, linear precoding, space division multiple access (SDMA), and scheduling.
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paper_title: Optimal User-Cell Association for Massive MIMO Wireless Networks

paper_content:

The use of a very large number of antennas at each base station site (referred to as"Massive MIMO") is one of the most promising approaches to cope with the predicted wireless data traffic explosion. In combination with Time Division Duplex and with simple per-cell processing, it achieves large throughput per cell, low latency, and attractive power efficiency performance. Following the current wireless technology trend of moving to higher frequency bands and denser small cell deployments, a large number of antennas can be implemented within a small form factor even in small cell base stations. In a heterogeneous network formed by large (macro) and small cell BSs, a key system optimization problem consists of"load balancing", that is, associating users to BSs in order to avoid congested hot-spots and/or under-utilized infrastructure. In this paper, we consider the user-BS association problem for a massive MIMO heterogeneous network. We formulate the problem as a network utility maximization, and provide a centralized solution in terms of the fraction of transmission resources (time-frequency slots) over which each user is served by a given BS. Furthermore, we show that such a solution is physically realizable, i.e., there exists a sequence of integer scheduling configurations realizing (by time-sharing) the optimal fractions. While this solution is optimal, it requires centralized computation. Then, we also consider decentralized user-centric schemes, formulated as non-cooperative games where each user makes individual selfish association decisions based only on its local information. We identify a class of schemes such that their Nash equilibrium is very close to the global centralized optimum. Hence, these user-centric algorithms are attractive not only for their simplicity and fully decentralized implementation, but also because they operate near the system"social"optimum.
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paper_title: Massive MIMO and mmWave for 5G Wireless HetNet: Potential Benefits and Challenges

paper_content:

There has been active research worldwide to develop the next-generation, i.e., fifth-generation (5G), wireless network. The 5G network is expected to support a significantly large amount of mobile data traffic and a huge number of wireless connections and achieve better costand energy-efficiency as well as quality of service (QoS) in terms of communication delay, reliability, and security. To this end, the 5G wireless network should exploit the potential of new developments, including superdense and heterogeneous deployment of cells and massive antenna arrays [i.e., massive multiple-input, multiple-output (MIMO) technologies] and utilization of higher frequencies, particularly millimeter-wave (mmWave) frequencies. This article discusses the potential benefits and challenges of the 5G wireless heterogeneous network (HetNet) that incorporates massive MIMO and mmWave technologies.
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paper_title: Optimizing client association for load balancing and fairness in millimeter-wave wireless networks

paper_content:

Millimeter-wave communications in the 60-GHz band are considered one of the key technologies for enabling multigigabit wireless access. However, the special characteristics of such a band pose major obstacles to the optimal utilization of the wireless resources, where the problem of efficient client association to access points (APs) is of vital importance. In this paper, the client association in 60-GHz wireless access networks is investigated. The AP utilization and the quality of the rapidly vanishing communication links are the control parameters. Because of the tricky nonconvex and combinatorial nature of the client association optimization problem, a novel solution method is developed to guarantee balanced and fair resource allocation. A new distributed, lightweight, and easy-to-implement association algorithm, based on Lagrangian duality theory and subgradient methods, is proposed. It is shown that the algorithm is asymptotically optimal, that is, the relative duality gap diminishes to zero as the number of clients increases .
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paper_title: Millimeter Wave Cellular Networks: A MAC Layer Perspective

paper_content:

The millimeter-wave (mmWave) frequency band is seen as a key enabler of multigigabit wireless access in future cellular networks. In order to overcome the propagation challenges, mmWave systems use a large number of antenna elements both at the base station and at the user equipment, which leads to high directivity gains, fully directional communications, and possible noise-limited operations. The fundamental differences between mmWave networks and traditional ones challenge the classical design constraints, objectives, and available degrees of freedom. This paper addresses the implications that highly directional communication has on the design of an efficient medium access control (MAC) layer. The paper discusses key MAC layer issues, such as synchronization, random access, handover, channelization, interference management, scheduling, and association. This paper provides an integrated view on MAC layer issues for cellular networks, identifies new challenges and tradeoffs, and provides novel insights and solution approaches.
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

paper_content:

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: Joint Precoding and Load Balancing Optimization for Energy-Efficient Heterogeneous Networks

paper_content:

This paper considers a downlink heterogeneous network, where different types of multiantenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS operation mode are jointly optimized for improving the network energy efficiency. We minimize the weighted total power consumption while satisfying quality-of-service constraints at the users. This problem is nonconvex, but we prove that for each BS mode combination, the considered problem has a hidden convexity structure. Thus, the optimal solution is obtained by an exhaustive search over all possible BS mode combinations. Furthermore, by iterative convex approximations of the nonconvex objective function, a heuristic algorithm is proposed to obtain a suboptimal solution of low complexity. We show that although multicell joint transmission is allowed, in most cases, it is optimal for each user to be served by a single BS. The optimal BS association condition is parameterized, which reveals how it is impacted by different system parameters. Simulation results indicate that putting a BS into sleep mode by proper load balancing is an important solution for energy savings.
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paper_title: On limits of wireless communications in a fading environment when using multiple antennas

paper_content:

This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. ::: ::: We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.
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paper_title: Hierarchical Interference Mitigation for Massive MIMO Cellular Networks

paper_content:

We propose a hierarchical interference mitigation scheme for massive MIMO cellular networks. The MIMO precoder at each base station (BS) is partitioned into an inner precoder and an outer precoder. The inner precoder controls the intra-cell interference and is adaptive to local channel state information (CSI) at each BS (CSIT). The outer precoder controls the inter-cell interference and is adaptive to channel statistics. Such hierarchical precoding structure reduces the number of pilot symbols required for CSI estimation in massive MIMO downlink and is robust to the backhaul latency. We study joint optimization of the outer precoders, the user selection, and the power allocation to maximize a general concave utility which has no closed-form expression. We first apply random matrix theory to obtain an approximated problem with closed-form objective. We show that the solution of the approximated problem is asymptotically optimal with respect to the original problem as the number of antennas per BS grows large. Then using the hidden convexity of the problem, we propose an iterative algorithm to find the optimal solution for the approximated problem. We also obtain a low complexity algorithm with provable convergence. Simulations show that the proposed design has significant gain over various state-of-the-art baselines.
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paper_title: Uplink Scheduling in LTE and LTE-Advanced: Tutorial, Survey and Evaluation Framework

paper_content:

The choice of OFDM-based multi-carrier access techniques for LTE marked a fundamental and farsighted parting from preceding 3GPP networks. With OFDMA in the downlink and SC-FDMA in the uplink, LTE possesses a robust and adaptive multiple access scheme that facilitates many physical layer enhancements. Despite this flexibility, scheduling in LTE is a challenging functionality to design, especially in the uplink. Resource allocation in LTE is made complex, especially when considering its target packet-based services and mobility profiles, both current and emerging, in addition to the use of several physical layer enhancements. In this paper, we offer a tutorial on scheduling in LTE and its successor LTE-Advanced. We also survey representative schemes in the literature that have addressed the scheduling problem, and offer an evaluation methodology to be used as a basis for comparison between scheduling proposals in the literature.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: On the Capacity of MIMO Broadcast Channels With Partial Side Information

paper_content:

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.
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paper_title: On the balance of multiuser diversity and spatial multiplexing gain in random beamforming

paper_content:

This paper is concerned with the problem of exploiting spatial multiplexing gain through opportunistic beamforming with multiple random beams. The base station transmits multiple pilot sequences using orthogonal beams, and each user feeds the channel gain of each beam back. Then, the base station selects the subset of users and beams for which the sum-rate is maximized. We aim to exploit spatial multiplexing gain in a controlled fashion, i.e., the number of beams used for data transmission is chosen depending on the available multiuser diversity in the system. Two schemes are proposed: dynamic Orthonormal Random Beamforming with Systematic Beam Selection (ORBF/SBS), for which the number of beams used for data transmission is dynamically changed from one fading block to another so that the sum-rate is maximized; and static ORBF/SBS, which selects a fixed number of beams for a given signal-to-noise ratio and user number. The static scheme achieves the sum-rate of the dynamic one up to a small gap with much reduced computational and feedback complexity. We derive an approximate expression for the sum-rate achieved by the dynamic scheme, and provide insight into the optimal data stream number in the static scheme by means of asymptotical results. Computer simulations are provided to evaluate the performance of the proposed schemes.
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paper_title: How much feedback is multi-user diversity really worth?

paper_content:

Wireless scheduling algorithms can extract multi-user diversity (MUDiv) via prioritizing the users with best current channel conditions. One drawback of MUDiv is the required feedback carrying the instantaneous channel rates from from all active subscribers to the access point/base station. This paper shows that this feedback load is, for the most part, unjustified. To alleviate this problem, we propose a technique allowing to dramatically reduce the feedback (by up to 90%) needs while preserving the essential of the scheme performance. We provide a theoretical analysis of the feedback load as function of the system's ergodic and outage capacity for both the traditional MUDiv scheme and the new scheme.
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paper_title: Opportunistic Two-Stage Feedback and Scheduling for MIMO Downlink Systems

paper_content:

We propose an opportunistic two-stage feedback and scheduling algorithm that is based upon zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) to reduce its feedback load. In an SUS algorithm, a base station schedules semi-orthogonal users using the feedback of all users' channel information. However, such feedback overhead significantly increases with the number of users. To reduce the feedback load of ZFBF-SUS systems, the proposed two-stage feedback scheme opportunistically and separately exploits the signal-to-interference-plus-noise ratio and orthogonality in each stage such that only a fraction of users feed back their channel information. Based on this opportunistic feedback scheme, we decouple the entire process of the SUS into two sub-processes. The proposed two-stage feedback and scheduling scheme effectively exclude the inappropriate users for ZFBF transmission in both feedback and scheduling periods, and thus save the scarce resources consumed for the feedback process. We derive an analytical expression for the average number of feedback bits of the proposed system and optimize it in an averaged sense. Further, the sum-rate of the proposed system is theoretically investigated. Both analytical and simulation results show that the proposed algorithm achieves the performance of conventional ZFBF-SUS systems with a significantly reduced number of feedback bits.
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paper_title: Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems with Multi-Antenna Users

paper_content:

In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than N, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and/or to enable interference-aware receive combining. In this paper, we try to answer the question if the N data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user-the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.
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paper_title: Acquiring Partial CSI for Spatially Selective Transmission by Instantaneous Channel Norm Feedback

paper_content:

In the design of next-generation multiuser communication systems, multiple-antenna transmission is an essential part providing additional spatial degrees of freedom and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. Herein, we show that the Euclidean norm of the instantaneous channel, when combined with long-term channel statistics provides sufficient information for the transmitter to efficiently utilize multiuser diversity in time, frequency, and space. We consider the downlink of a communication system where the base station has multiple transmit antennas whereas each user terminal has a single receive antenna. The CSI provided by channel statistics and feedback of the norm of the instantaneous channel vector is studied in depth for correlated Rayleigh and Ricean fading channels, within a minimum mean-square error (MMSE) estimation framework. An asymptotic analysis (high instantaneous SNR) is presented which shows that channel realizations with large channel norm provide additional spatial CSI at the transmitter. This makes the proposed scheme ideal for multiuser diversity transmission schemes, where resources are only allocated to users experiencing favorable channel conditions.
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paper_title: Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels

paper_content:

In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total system-wide feedback load, is it preferable to get low-rate/coarse channel feedback from a large number of receivers or high-rate/high-quality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multi-user diversity to be exploited, while high-rate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining high-quality feedback, and that obtaining near-perfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users.
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: Spatial Transmission Mode Switching in Multiuser MIMO-OFDM Systems With User Fairness

paper_content:

Multiantenna radio systems allow accessing the channel in diversity or spatial multiplexing (SMUX) mode. Adequate switching between these modes according to current channel conditions was shown to yield significant performance improvements while requiring little feedback from the receiving side. We present a transmission concept for the downlink of a multiuser multiple-input-multiple-output orthogonal frequency-division-multiplexing (MU-MIMO-OFDM) system aiming at high user rates with limited feedback demands. An extended score-based scheduling (SB) approach ensures fair-resource allocation to the users, whereas transmission mode switching is used to guarantee high user rates. The degree of fairness of the scheduler can be adapted by adequately configuring a weighting function for the scores. Comparison with single-mode schemes reveals substantial throughput gains of the adaptive switching concept. Furthermore, targeting maximum throughput, we show that a considerable proportion of the capacity of the MIMO broadcast channel (BC) can be achieved with a comparatively low amount of required feedback.
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paper_title: Downlink SDMA with Limited Feedback in Interference-Limited Wireless Networks

paper_content:

The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that single-stream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks.
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paper_title: Two-Phase Multiuser Scheduling for Multiantenna Downlinks Exploiting Reduced Finite-Rate Feedback

paper_content:

This paper considers a multiantenna system with an M -antenna base station and K single antenna users, employing zero-forcing beamforming (ZFBF) and a finite-rate feedback strategy. We study scheduling to select KS users for transmit beamforming. To reduce the feedback requirement, we propose a two-phase scheduling scheme that exploits quantized channel direction information (CDI) from only a small subset of the overall users, as well as a 1-bit signal-to-interference-plus-noise ratio (SINR) indicator feedback per user. In the proposed scheme, we introduce a newly defined expression for evaluating SINR that extends the existing SINR approximation for KS = M to a more general case with arbitrary KS ? M. Asymptotic analysis reveals that the proposed two-phase scheduling is asymptotically optimal for large user numbers. Through numerical simulations, we also show that the proposed scheme requires less feedback than conventional schemes, whereas the resulting sum rate loss due to the reduced feedback is negligible. Moreover, we find that the choice of KS < M, instead of a full-multiplexing case with KS = M, for scheduling may achieve a better tradeoff between performance and feedback requirement in systems where fewer bits are utilized for feeding back CDI.
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paper_title: On beamforming with finite rate feedback in multiple-antenna systems

paper_content:

We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t-1)2/sup -B/t-1/, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.
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paper_title: Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider a downlink channel where a base station equipped with M transmit antennas communicates with K ≥ M single-antenna receivers and has partial channel knowledge obtained via a limited rate feedback channel. We propose scalar feedback metrics that provide an estimate of the received signal-to-noise plus interference ratio (SINR), which are combined with efficient user selection algorithms and zero-forcing beamforming. The asymptotic system sum rate for large K is analyzed and numerical results are provided, showing the performance of each metric in different scenarios.
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paper_title: A comparison of scheduling strategies for MIMO broadcast channel with limited feedback on OFDM systems

paper_content:

We consider a multiuser downlink transmission from a base station with multiple antennas (MIMO) to mobile terminals (users) with a single antenna, using orthogonal frequency division multiplexing (OFDM). Channel conditions are reported by a feedback from users with limited rate, and the base station schedules transmissions and beamforms signals to users. We show that an important set of schedulers using a general utility function can be reduced to a scheduler maximizing the weighted sum rate of the system. For this case we then focus on scheduling methods with many users and OFDM subcarriers. Various scheduling strategies are compared in terms of achieved throughput and computational complexity and a good tradeoff is identified in greedy and semiorthogonal user selection algorithms. In the greedy selection algorithm, users are selected one by one as long as the throughput increases, while in the semiorthogonal approach users are selected based on the channel correlation. An extension of these approaches from a flat-fading channel to OFDM is considered and simplifications that may be useful for a large number of subcarriers are presented. Results are reported for a typical cellular transmission of the long-term evolution (LTE) of 3GPP.
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paper_title: Multi-mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

paper_content:

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.
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paper_title: Two-Stage Channel Quantization for Scheduling and Beamforming in Network MIMO Systems: Feedback Design and Scaling Laws

paper_content:

This paper proposes an efficient two-stage channel quantization and feedback scheme for the downlink limited-feedback network multiple-input multiple-output (MIMO) system. In the first stage, the users report their best set of base-station antenna and physical resource block combinations, and the base-stations schedule the best user for each antenna in each resource block. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. This paper proposes an analytical framework to show that, under a total feedback budget of B bits, the number of bits assigned to the second feedback stage should scale as log B, and in quantizing channel vectors from different base-stations, each user should allocate feedback bits in proportion to the channel magnitudes in dB scale. Under these optimized bit allocations, the overall sum rate of the system is shown to scale double-logarithmically with B, linearly with the total number of antennas, and logarithmically with transmit power, thus achieving both multiuser diversity and spatial multiplexing gains under limited feedback. Finally, realistic wireless propagation model of an urban small-cell deployment is used to show that the proposed scheme can approach the performance of a network MIMO system with full channel state information with only modest amount of channel feedback.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

paper_content:

In this paper, we tackle the problem of semidistributed user selection with distributed linear precoding for sum-rate maximization in multiuser multicell systems. A set of adjacent base stations (BSs) forms a cluster to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling, and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to nonintended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, namely, distributed zero forcing and distributed virtual signal-to-interference-plus-noise ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First, we investigate how the signal-to-noise ratio regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the BSs.
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paper_title: Coordinated beamforming with limited feedback in the MIMO broadcast channel

paper_content:

In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.
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paper_title: Multi-Antenna Downlink Channels with Limited Feedback and User Selection

paper_content:

We analyze the sum-rate performance of a multi- antenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load.
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paper_title: Enhanced Limited Feedback Schemes for DL MU-MIMO ZF Precoding

paper_content:

This paper proposes new limited-feedback Channel State Information (CSI) calculation schemes for Zero Forcing (ZF)-precoded downlink Multi-User Multiple-Input Multiple-Output (MU-MIMO) systems. It is a common understanding that the feedback quantized by the codebook limits the performance of MU-MIMO. In this paper, through a quasi-ZF or a quasi-Minimum Mean-Squared Error (MMSE) weight, the channel matrix is transferred to one of the codebook vectors, based on which, the CSI is calculated. Thus, the quantization error is minimized. Meanwhile, the selection for the codebook vector guarantees the maximizing of the estimated Signal to Interference plus Noise Ratio (SINR). We verify that the proposed scheme obtains accurate feedback information, and the predicted weight can be the same as the optimal linear decoder as if the receiver knew all the precoder information that is fed-forward from the BS, as long as the number of antennas for each receiver equals that for the transmitter, and equals that for the total transmit data streams. Compared to the commonly used Precoding Matrix Index (PMI) based method, which uses rank-one single user (SU)-MIMO feedback, simulation results show that the proposed schemes achieve higher sum capacities in different scenarios. Moreover, since the weight can be directly used as the decoder, the feed-forward overhead is reduced.
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paper_title: MU-MISO Transmission with Limited Feedback

paper_content:

Downlink multi-user transmission techniques that allow several users to be served simultaneously in frequency and time have been recognized as a promising means to increase system capacity. However they require accurate channel state information (CSI) at the base station (BS) such that appropriate signal processing can be performed to separate multiple users in the space domain. In practice however, CSI cannot be perfectly known to the BS due to the capacity-limited feedback channel in FDD systems for instance. In this letter we investigate multiuser multiple-input single-output (MU-MISO) transmission with limited feedback. In particular we identify the useful information that the BS needs to deal with inter-user interference and a codebook design is derived accordingly. In addition, an adaptive threshold-based feedback approach is proposed, where only users with good feedback quality are allowed to do feedback. It is shown that the adaptive scheme can effectively improve the system performance given a fixed number of feedback bits.
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paper_title: MIMO Broadcast Channels with Spatial Heterogeneity

paper_content:

We develop a realistic model for multiple-input multiple-output (MIMO) broadcast channels, where each randomly located user's average SNR depends on its distance from the transmitter. With perfect channel state information at the transmitter (CSIT), the average sum capacity is proven to scale for many users like αM/2 log K instead of M log log K, where α, M, and K denote the path loss exponent, the number of transmit antennas, and the number of users in a cell. With only partial CSIT, the sum capacity at high SNR eventually saturates due to interference, and the saturation value scales for large B like MB/M-1, where B denotes the quantization resolution for channel feedback.
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paper_title: Downlink Multiuser MIMO Systems With Adaptive Feedback Rate

paper_content:

In this paper, an efficient channel feedback scheme for downlink multiuser multiple-input-multiple-output (MU-MIMO) systems is proposed. The objective of the new feedback design is to adaptively control the feedback rate of each user, depending on the individual channel status, while the overall sum feedback rate is kept the same. The proposed channel feedback scheme is composed of two stages: 1) the common channel feedback stage of all users and 2) the user-specific channel feedback stage of the selected users. We present a low-complexity algorithm to determine the individual feedback rates of users, which utilizes convex optimization, followed by iterative steepest descent direction searching. Numerical results show that zero-forcing beamforming (ZFBF), combined with the proposed channel feedback scheme, considerably outperforms ZFBF with conventional channel feedback schemes.
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paper_title: Grassmannian beamforming for multiple-input multiple-output wireless systems

paper_content:

Multiple-input multiple-output (MIMO) wireless systems provides capacity much larger than that provided by traditional single-input single-output (SISO) wireless systems. Beamforming is a low complexity technique that increases the receive signal-to-noise ratio (SNR), however, it requires channel knowledge. Since in practice channel knowledge at the transmitter is difficult to realize, we propose a technique where the receiver designs the beamforming vector and sends it to the transmitter by transmitting a label in a finite set, or codebook, of beamforming vectors. A codebook design method for quantized versions of maximum ratio transmission, equal gain transmission, and generalized selection diversity with maximum ratio combining at the receiver is presented. The codebook design criterion exploits the quantization problem's relationship with Grassmannian line packing. Systems using the beamforming codebooks are shown to have a diversity order of the product of the number of transmit and the number of receive antennas. Monte Carlo simulations compare the performance of systems using this new codebook method with the performance of systems using previously proposed quantized and unquantized systems.
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paper_title: MIMO broadcast channels with finite rate feedback

paper_content:

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where the receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. Simple expressions for the capacity degradation due to finite rate feedback as well as the required increases in feedback load per mobile as a function of the number of access point antennas and the system SNR are provided.
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paper_title: How Many Users should be Turned On in a Multi-Antenna Broadcast Channel

paper_content:

This paper considers broadcast channels with L antennas at the base station and m single-antenna users, where each user has perfect channel knowledge and the base station obtains channel information through a finite rate feedback. The key observation of this paper is that the optimal number of on-users (users turned on), say s, is a function of signal-to-noise ratio (SNR) and other system parameters. Towards this observation, we use asymptotic analysis to guide the design of feedback and transmission strategies. As L, m and the feedback rates approach infinity linearly, we derive the asymptotic optimal feedback strategy and a realistic criterion to decide which users should be turned on. Define the corresponding asymptotic throughput per antenna as the spatial efficiency. It is a function of the number of on-users s, and therefore, s should be appropriately chosen. Based on the above asymptotic results, we also develop a scheme for a system with finite many antennas and users. Compared with other works where s is presumed constant, our scheme achieves a significant gain by choosing the appropriate s. Furthermore, our analysis and scheme is valid for heterogeneous systems where different users may have different path loss coefficients and feedback rates.
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paper_title: Performance of Orthogonal Beamforming for SDMA With Limited Feedback

paper_content:

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.
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paper_title: On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

paper_content:

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.
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paper_title: Enhanced multiuser random beamforming: dealing with the not so large number of users case

paper_content:

We consider the downlink of a wireless system with an M-antenna base station and K single-antenna users. A limited feedback-based scheduling and precoding scenario is considered that builds on the multiuser random beamforming (RBF). Such a scheme was shown to yield the same capacity scaling, in terms of multiplexing and multiuser diversity gain, as the optimal full CSIT-based (channel state information at transmitter) precoding scheme, in the large number of users K regime. Unfortunately, for more practically relevant (low to moderate) K values, RBF yields degraded performance. In this work, we investigate solutions to this problem. We introduce a two-stage framework that decouples the scheduling and beamforming problems. In our scenario, RBF is exploited to identify good, spatially separable, users in a first stage. In the second stage, the initial random beams are refined based on the available feedback to offer improved performance toward the selected users. Specifically, we propose beam power control techniques that do not change the direction of the second-stage beams, offering feedback reduction and performance tradeoffs. The common feature of these schemes is to restore robustness of RBF with respect to sparse network settings (low K), at the cost of moderate complexity increase.
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paper_title: A New Approach to User Scheduling in Massive Multi-User MIMO Broadcast Channels

paper_content:

In this paper, a new user-scheduling-and-beamforming method is proposed for multi-user massive multiple-input multiple-output (massive MIMO) broadcast channels in the context of two-stage beamforming. The key ideas of the proposed scheduling method are 1) to use a set of orthogonal reference beams and construct a double cone around each reference beam to select `nearly-optimal' semi-orthogonal users based only on channel quality indicator (CQI) feedback and 2) to apply post-user-selection beam refinement with zero-forcing beamforming (ZFBF) based on channel state information (CSI) feedback only from the selected users. It is proved that the proposed scheduling-and-beamforming method is asymptotically optimal as the number of users increases. Furthermore, the proposed scheduling-and-beamforming method almost achieves the performance of the existing semi-orthogonal user selection with ZFBF (SUS-ZFBF) that requires full CSI feedback from all users, with significantly reduced feedback overhead which is even less than that required by random beamforming.
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paper_title: Multiuser multi-antenna systems with limited feedback

paper_content:

The use of multiple antennas has been recognized as a key technology to significantly improve the spectral efficiency of next-generation, multiuser wireless communication networks. In multiuser multiple-input multiple-output (MIMO) networks, the spatial degrees of freedom offered by multiple antennas can be advantageously exploited to enhance the system capacity, by scheduling multiple users simultaneously by means of spatial division multiple access (SDMA). A linear increase in throughput, proportional to the number of transmit antennas, can be achieved even by using linear precoding strategies if combined with efficiently designed scheduling protocols. However, these promising gains come under the often unrealistic assumption of close-to-perfect channel state information at the transmitter (CSIT). Therefore, at the heart of the downlink resource allocation problem lies that of feedback acquisition. In this thesis, we focus on linear beamforming techniques relying on low-rate partial CSIT. Several methods that allow the base station (BS) to live well even with coarse, limited channel knowledge are identified. One first key idea is based on splitting the design between the scheduling and the final beam design stages, thus taking profit from the fact the number of users to be served at each scheduling slot is much smaller than the total number of active users. This two-stage approach is applied to a scenario in which random beamforming (RBF) is exploited to identify good, spatially separable, users in the first stage. In the second stage, several refinement strategies, including beam power control and beam selection, are proposed, offering various feedback reduction and significant sum rate gains, even in sparse network settings (low to moderate number of users). In channels that exhibit some form of correlation, either in temporal or in spatial domain, we point out that significant useful information for the SDMA scheduler lies hidden in the channel structure. We show how memory-based RBF can exploit channel redundancy in order to achieve throughput close to that of optimum unitary beamforming with full CSIT for slow time-varying channels. In spatially correlated channels, long-term statistical CSIT, which can be easily obtained with negligible per-slot or no feedback overhead, reveals information about the mean spatial separability of users. A maximum likelihood (ML) channel estimation framework is proposed, which effectively combines slowly varying statistical CSIT with instantaneous low-rate channel quality information (CQI). User selection and beamforming techniques suitable for such settings are also proposed. It is demonstrated that in systems with reasonably limited angle spread at the BS, feeding back a single scalar CQI parameter per user is sufficient to perform SDMA scheduling and beamforming with near optimum performance. Limited feedback strategies utilizing vector quantization codebooks are also investigated. In particular, the problem of efficient, sum-rate maximizing CQI design is addressed and several scalar feedback metrics are proposed. These metrics are built upon inter-user interference bounds and can be interpreted as reliable estimates of the received signal-to-interference-plus-noise ratio (SINR) at the receiver side. It is shown that scalar CQI feedback combined with channel directional information (CDI), zero-forcing beamforming, and greedy user selection algorithms can achieve a significant fraction of the capacity of the full CSIT case by exploiting multiuser diversity. An efficient technique that provides the BS the flexibility to switch from multiuser (SDMA) to single-user (TDMA) transmission is provided, exhibiting linear sum-rate growth at any range of signal-to-noise ratio (SNR). Further feedback compression can be achieved if the CSIT information utilized by the scheduler is represented by ranking-based feedback. We show that an integer value is often sufficient in order to identify users with favorable channel conditions. In parallel, it equalizes the channel access probability in networks where users' channels are not necessarily identically distributed and mobile terminals experience unequal average SNRs due to different distances from the BS and the corresponding different path losses (near-far effects).
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paper_title: Scheduling Methods with MIMO Interference Alignment for Mutually Interfering Broadcast Channels

paper_content:

In this paper, we investigate an interference alignment (IA) technique introduced by Cadambe and Jafar in mutually interfering broadcast channels (IFBCs). First, we study the spatial multiplexing gain (SMG) for the 3-cell IFBC where all base stations and mobile users are equipped with multiple antennas. To achieve the derived optimal SMG, we extend the IA algorithm designed for K-user multi-input multi-output (MIMO) interference channels (IFCs) to the IFBC. In this paper, we present the IA scheme in conjunction with user selection which outperforms the time division multiple access (TDMA) technique in the IFBC environment. The optimal scheduling method capitalizes on multiuser diversity to achieve a significant fraction of sum capacity by using an exhaustive search algorithm. Since the computational complexity of the optimal scheduling method is prohibitive, a reduced complexity suboptimal scheduling method is proposed based on a coordinate ascent approach. Simulation results confirm that the reduced complexity scheduling algorithm achieves the sum rate close to the optimal algorithm with much reduced complexity.
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paper_title: An Overview of Massive MIMO: Benefits and Challenges

paper_content:

Massive multiple-input multiple-output (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of state-of-the-art research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of non-orthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient single-carrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.
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paper_title: Round-Robin Scheduling for Orthogonal Beamforming with Limited Feedback

paper_content:

We propose a round-robin scheduling algorithm for orthogonal beamforming with a strict signal to interference-plus-noise ratio (SINR) constraint and limited feedback. The presented algorithm aims at scheduling the users at identical slots over different blocks, in order to reduce the necessary scheduling overhead, and to minimize the maximum delay between serving the same user. Thus, the presented algorithm is especially suited for real-time multimedia traffic. The algorithm allocates the users using orthogonal beamforming based on the quantized feedback provided by the users. The quantized feedback consists of the estimated power that is necessary to fulfill a predefined SINR constraint. Further, we propose an algorithm to design codebooks to quantize the estimated power. Using the feedback, the base station redistributes power from users with spare power to users that lack power so that they fulfill their SINR constraints. The performance of the algorithm is demonstrated through simulations.
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paper_title: Optimal Resource Allocation for Multiuser MIMO-OFDM Systems With User Rate Constraints

paper_content:

With the proliferation of wireless services, personal connectivity is quickly becoming ubiquitous. As the user population demands greater multimedia interactivity, data rate requirements are set to soar. Future wireless systems, e.g., multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), need to cater to not only a burgeoning subscriber pool but also to a higher throughput per user. Furthermore, resource allocation for multiuser MIMO-OFDM systems is vital for the optimization of the subcarrier and power allocations to improve overall system performance. Using convex optimization techniques, this paper proposes an efficient solution to minimize the total transmit power subject to each user's data rate requirement. Using a Lagrangian dual decomposition, the complexity is reduced from one that is exponential in the number of subcarriers M to one that is only linear in M. To keep the complexity low, linear beamforming is incorporated at both the transmitter and the receiver. Although frequency-flat fading has been known to plague OFDM resource allocation systems, a modification, i.e., dual proportional fairness, seamlessly handles flat or partially frequency-selective fading. Due to the nonconvexity of the optimization problem, the proposed solution is not guaranteed to be optimal. However, for a realistic number of subcarriers, the duality gap is practically zero, and optimal resource allocation can be evaluated efficiently. Simulation results show large performance gains over a fixed subcarrier allocation.
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paper_title: Robust multi-user opportunistic beamforming for sparse networks

paper_content:

A scheme exploiting reduced feedback for the purpose of opportunistic multi-user beamforming is proposed. The scheme builds on recent promising advances realized in the area of multi-user downlink precoding and scheduling based on partial transmitter channel state information (CSIT) using random beamforming-based SDMA. Although random precoding followed by SDMA scheduling is optimal within the set of unitary precoders, it is only so in the asymptotic number of users K. For-practically relevant-sparse networks (i.e., with low to moderate number of users) random beam-forming SDMA yields severely degraded performance. In this work we present a scheme allowing to restore robustness with respect to cell sparsity. The core idea here is to preserve the low complexity low feedback advantage of random opportunistic beamforming in selecting a target group of users, while much more efficient beamforming schemes can be used to serve the group of users once it has been identified. We propose different designs, optimal and suboptimal, based upon variable levels of feedback requirement. We show substantial gain over opportunistic beamforming for a range of K.
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paper_title: Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels

paper_content:

In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total system-wide feedback load, is it preferable to get low-rate/coarse channel feedback from a large number of receivers or high-rate/high-quality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multi-user diversity to be exploited, while high-rate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining high-quality feedback, and that obtaining near-perfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users.
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: Spatial Transmission Mode Switching in Multiuser MIMO-OFDM Systems With User Fairness

paper_content:

Multiantenna radio systems allow accessing the channel in diversity or spatial multiplexing (SMUX) mode. Adequate switching between these modes according to current channel conditions was shown to yield significant performance improvements while requiring little feedback from the receiving side. We present a transmission concept for the downlink of a multiuser multiple-input-multiple-output orthogonal frequency-division-multiplexing (MU-MIMO-OFDM) system aiming at high user rates with limited feedback demands. An extended score-based scheduling (SB) approach ensures fair-resource allocation to the users, whereas transmission mode switching is used to guarantee high user rates. The degree of fairness of the scheduler can be adapted by adequately configuring a weighting function for the scores. Comparison with single-mode schemes reveals substantial throughput gains of the adaptive switching concept. Furthermore, targeting maximum throughput, we show that a considerable proportion of the capacity of the MIMO broadcast channel (BC) can be achieved with a comparatively low amount of required feedback.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.
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paper_title: Two-Phase Multiuser Scheduling for Multiantenna Downlinks Exploiting Reduced Finite-Rate Feedback

paper_content:

This paper considers a multiantenna system with an M -antenna base station and K single antenna users, employing zero-forcing beamforming (ZFBF) and a finite-rate feedback strategy. We study scheduling to select KS users for transmit beamforming. To reduce the feedback requirement, we propose a two-phase scheduling scheme that exploits quantized channel direction information (CDI) from only a small subset of the overall users, as well as a 1-bit signal-to-interference-plus-noise ratio (SINR) indicator feedback per user. In the proposed scheme, we introduce a newly defined expression for evaluating SINR that extends the existing SINR approximation for KS = M to a more general case with arbitrary KS ? M. Asymptotic analysis reveals that the proposed two-phase scheduling is asymptotically optimal for large user numbers. Through numerical simulations, we also show that the proposed scheme requires less feedback than conventional schemes, whereas the resulting sum rate loss due to the reduced feedback is negligible. Moreover, we find that the choice of KS < M, instead of a full-multiplexing case with KS = M, for scheduling may achieve a better tradeoff between performance and feedback requirement in systems where fewer bits are utilized for feeding back CDI.
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paper_title: Memory-based opportunistic multi-user beamforming

paper_content:

A scheme exploiting memory in opportunistic multiuser beamforming is proposed. The scheme builds on recent advances realized in M. Sharif and B. Hassibi, 2005, in the area of multi-user downlink preceding and scheduling based on partial transmitter channel state information (CSIT). Although the preceding and scheduling done in M. Sharif and B. Hassibi, 2005 is optimal within the set of unitary precoders, it is only so asymptotically for large number of users. Secondly, this scheme is unable to exploit potential time correlation of the channel. In this paper, we show (1) that exploiting memory in the transmitter allows to fill the gap to optimality for fixed (even low) number of users for time correlated channels, (2) how such schemes can be extended to take fairness into account in the proportional fair sense
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paper_title: Fundamental Limits in MIMO Broadcast Channels

paper_content:

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system parameters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.
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paper_title: Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization

paper_content:

Block diagonalization (BD) is a preceding technique that eliminates inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. With the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission, the number of simultaneously supportable users with BD is limited by the ratio of the number of basestation transmit antennas to the number of user receive antennas. In a downlink MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput The brute-force search for the optimal user set, however, is computationally prohibitive. We propose two low-complexity suboptimal user selection algorithms for multiuser MIMO systems with BD. Both algorithms aim to select a subset of users such that the total throughput is nearly maximized. The first user selection algorithm greedily maximizes the total throughput, whereas the criterion of the second algorithm is based on the channel energy. We show that both algorithms have linear complexity in the total number of users and achieve around 95% of the total throughput of the complete search method in simulations
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paper_title: Multiuser MIMO User Selection Based on Chordal Distance

paper_content:

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.
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paper_title: Efficient Margin Adaptive Scheduling for MIMO-OFDMA Systems

paper_content:

In this paper we address the problem of margin adaptive scheduling in the downlink of an orthogonal frequency division multiple access (OFDMA) multiple-input multiple-output (MIMO) system. Optimal resource allocation in MIMO systems requires the joint optimization of: a) linear transmit and receive spatial filters, b) channel assignment and c) power allocation. This problem is not convex and its complexity becomes thus intractable already for small sets of users and subcarriers. To reduce the complexity of the problem at hand, we propose a novel heuristic strategy that partitions the users in different groups according to their average channel quality and addresses the original problem by solving a succession of lower-complexity allocation problems. The spatial dimension is employed to prevent multiple access interference from hindering the performance of the sequential allocation. To further reduce the complexity burden we introduce a linear programming formulation in combination with a waterfilling-based strategy to allocate channels and power to the groups of users. Numerical results and evaluation of the computational complexity show that, though suboptimal, in most cases the proposed algorithm manages to exploit in an original way the inherent multi-user diversity of multi-carrier systems to ease the task of resource allocation with a very limited performance loss from the theoretic optimum.
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paper_title: CDF Scheduling Methods for Finite Rate Multiuser Systems With Limited Feedback

paper_content:

In this work, simple and practical CDF scheduling methods are developed that preserve the virtues of CDF scheduling, namely fairness and effective use of multiuser diversity. They are the accelerated extended CDF scheduling (AeCS), modified non-parametric CDF scheduling (modified NPCS), and the CDF scheduling with optimized Quantizers (CSwQ) methods. The developed methods do not need a priori knowledge of the channel distribution and can work effectively in systems that support discrete number of transmission rates and are constrained by limited feedback resources. They exploit the limited feedback resource for their scheduling decisions and transmission rate selections and learn the distribution of channel quality information of each user, as needed, to best exploit multiuser diversity. The CSwQ method is shown to have desirable properties in terms of both system throughput and power savings. Analytical results for the system throughput and power savings of the CSwQ method are developed that are valid for a finite number of observation samples. Then, through numerical simulations, the developed methods are shown to effectively save transmit power and achieve high system throughput. In addition, they converge rapidly with the number of data samples to the ideal case wherein perfect knowledge of the channel CDF is assumed.
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paper_title: On the Capacity of MIMO Broadcast Channels With Partial Side Information

paper_content:

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.
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paper_title: On the balance of multiuser diversity and spatial multiplexing gain in random beamforming

paper_content:

This paper is concerned with the problem of exploiting spatial multiplexing gain through opportunistic beamforming with multiple random beams. The base station transmits multiple pilot sequences using orthogonal beams, and each user feeds the channel gain of each beam back. Then, the base station selects the subset of users and beams for which the sum-rate is maximized. We aim to exploit spatial multiplexing gain in a controlled fashion, i.e., the number of beams used for data transmission is chosen depending on the available multiuser diversity in the system. Two schemes are proposed: dynamic Orthonormal Random Beamforming with Systematic Beam Selection (ORBF/SBS), for which the number of beams used for data transmission is dynamically changed from one fading block to another so that the sum-rate is maximized; and static ORBF/SBS, which selects a fixed number of beams for a given signal-to-noise ratio and user number. The static scheme achieves the sum-rate of the dynamic one up to a small gap with much reduced computational and feedback complexity. We derive an approximate expression for the sum-rate achieved by the dynamic scheme, and provide insight into the optimal data stream number in the static scheme by means of asymptotical results. Computer simulations are provided to evaluate the performance of the proposed schemes.
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paper_title: Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

paper_content:

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC.
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paper_title: Large deviation delay analysis of queue-aware multi-user MIMO systems with two timescale mobile-driven feedback

paper_content:

Multi-user multi-input-multi-output (MU-MIMO) systems usually require users to feedback the channel state information (CSI) for scheduling. Most of the existing literature on the reduced feedback user scheduling focused on the throughput performance and the queueing delay was usually ignored. As the delay is important for real-time applications, it is desirable to have a low feedback queue-aware user scheduling algorithm for MU-MIMO systems. This paper proposes a two timescale queue-aware user scheduling algorithm, which consists of a queue-aware mobile-driven feedback filtering stage and a SINR-based user scheduling stage. The feedback policy is obtained by solving a queue-weighted optimization problem. In addition, we evaluate the associated queueing delay performance by using the large deviation analysis. The large deviation decay rate for the proposed algorithm is shown to be much larger than the CSI-only scheduling algorithm. Numerical results demonstrate the large performance gain of the proposed algorithm over the CSI-only algorithm, while the proposed one requires only a small amount of feedback.
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paper_title: A User Selection Algorithm Using Angle between Subspaces for Downlink MU-MIMO Systems

paper_content:

One of major issues in the efficient use of radio resource for multiuser multiple-input/multiple-output (MU-MIMO) systems is the selection of users to achieve the maximum system throughput. The optimal user selection algorithm, which requires exhaustive search, is prohibitive due to its high computational complexity where Block diagonalization (BD) method is applied and known as a suboptimal precoding technique for downlink MU-MIMO systems, which intents to perfectly eliminate inter-user interference. In this paper, we propose efficient, iterative user selection algorithms with low complexity, where the product of eigenvalues of effective channels is utilized as a selection metric by applying the concept of principal angles between subspaces. And, we further examined the applicability of the proposed algorithms to limited feedback systems and proportional fair (PF) scheduling. Through computational complexity analysis, we show that the proposed algorithm has low complexity with a little loss in throughput. Simulation results validate that the proposed algorithm achieves almost the same system throughput by a capacity-based algorithm under high SNR regime with considerable reduction in complexity.
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paper_title: On the Performance of Random Beamforming in Sparse Millimeter Wave Channels

paper_content:

The performance of random beamforming (RBF) with partial channel state information (CSI) feedback is investigated here for millimeter wave (mmWave) multiuser multiple-input single-output (MU-MISO) downlink systems using the uniform random multipath (UR-MP) channel model. In particular, the required number of users in the cell for RBF to yield linear sum rate scaling with respect to the number of transmit antennas is identified under the UR-MP channel model for different levels of channel sparsity. Then, the problem of user scheduling in MU-MISO downlink is considered when the number of users in the cell is not sufficiently large (sparse user regime) for the system to operate in the identified sufficient user regime. By exploiting the sparsity of mmWave radio channels, several user scheduling algorithms based on beam aggregation with reasonable amount of feedback are proposed for the sparse user regime. Our numerical results show that the proposed algorithms yield very good sum-rate performance in sparse mmWave channels.
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paper_title: Multiple-antenna techniques for wireless communications - a comprehensive literature survey

paper_content:

The use of multiple antennas for wireless communication systems has gained overwhelming interest during the last decade - both in academia and industry. Multiple antennas can be utilized in order to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. With an enormous amount of yearly publications, the field of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly. To date, there are numerous papers on the performance limits of MIMO systems, and an abundance of transmitter and receiver concepts has been proposed. The objective of this literature survey is to provide non-specialists working in the general area of digital communications with a comprehensive overview of this exciting research field. To this end, the last ten years of research efforts are recapitulated, with focus on spatial multiplexing and spatial diversity techniques. In particular, topics such as transmitter and receiver structures, channel coding, MIMO techniques for frequency-selective fading channels, diversity reception and space-time coding techniques, differential and non-coherent schemes, beamforming techniques and closed-loop MIMO techniques, cooperative diversity schemes, as well as practical aspects influencing the performance of multiple-antenna systems are addressed. Although the list of references is certainly not intended to be exhaustive, the publications cited will serve as a good starting point for further reading.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Space Division Multiple Access with a Sum Feedback Rate Constraint

paper_content:

On a multi-antenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.
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paper_title: Fundamentals of Wireless Communication

paper_content:

1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.
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paper_title: Traffic-Aware Training and Scheduling for MISO Wireless Downlink Systems

paper_content:

In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback/training decision. This should be leveraged in future communication systems.
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paper_title: Network MIMO with Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation and Reduced-Complexity Scheduling

paper_content:

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.
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paper_title: An improved partial CSIT random beamforming for multibeam satellite systems

paper_content:

A novel multiple input multiple output (MIMO) transmitting scheme is presented for multibeam satellite systems, where the objective is to increase the system sum rate, availability and variance performance.
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paper_title: Opportunistic beamforming based on multiple weighting vectors

paper_content:

In order to improve the throughput of the opportunistic beamforming, the authors generalize the opportunistic beamforming by using multiple random weighting vectors at each time slot. The base station chooses the best weighting vector and performs the opportunistic beamforming with this optimum vector. For the case of equally strong independent fast Rayleigh fading channels, the throughput of the proposed scheme is analytically approximated and the optimum number of random weighting vectors per time slot is obtained. Numerical results demonstrate that the proposed scheme considerably improves the throughput compared to the conventional opportunistic beamforming for a low/realistic number of users.
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paper_title: Adaptive Modulation in PU2RC Systems with Finite Rate Feedback

paper_content:

This paper addresses a per user unitary precoding and rate control (PU 2 RC) system with adaptive multi-level quadrature amplitude modulation (QAM) modulation, where both the PU 2 RC operation and adaptive modulation are based on finite rate feedback. The system supports two transmission modes (single user transmit beamforming and multiuser transmission with orthogonal beamforming), and switches between the two modes to maximize the average throughput. We first study single user transmit beamforming, and derive closed-form expressions for the average throughput and bit-error rate (BER) with outdated channel information. Then, multiuser transmission with orthogonal beamforming is investigated. We analyze the throughput and BER performance without feedback delay in the normal signal noise ratio (SNR) regime, and the performance with feedback delay in the interference-limited regime. Simulation results demonstrate the effect of time delay, and the preferred regions of the single user transmission mode and multiuser transmission mode.
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paper_title: Joint Beamforming and Scheduling for a Multi-Antenna Downlink with Imperfect Transmitter Channel Knowledge

paper_content:

We consider the downlink of a wireless system where the base-station has M ges 1 antennas and K user terminals have one antenna each. We study the weighted rate sum maximization in the case of non-perfect Channel State Information at the Transmitter (CSIT). Some relevant downlink optimization problems, such as the stabilization of the transmission queues under random packet arrivals and the proportional fair scheduling for infinite backlogged systems, can be solved as special cases of the proposed problem. We restrict the transmitter strategy to be based on Gaussian coding and beamforming. Even under this simplifying condition, the problem at hand is non-convex and it does not appear to lend itself to a simple algorithmic solution. Therefore, we introduce some approximations that yield a definition of signal-to-interference plus noise ratio (SINR) commonly used in the classical array- processing/beamforming literature. For the simpler (but still non-convex) approximated problem, we propose a powerful heuristic solution based on greedy user selection and a gradient iteration that converges to a local maximum of the objective function. This method yields very competitive results with relatively low computational complexity. Extensive simulations show that, in the case of perfect CSIT, the proposed heuristic scheme performs very closely to the optimal (dirty-paper coding) strategy while, in the case of non-perfect CSIT, it significantly outperforms previously proposed suboptimal approaches, such as random beamforming and approximated zero-forcing with greedy user selection.
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paper_title: Low Complexity Scheduling and Beamforming for Multiuser MIMO Systems

paper_content:

The problem of joint scheduling and beam-forming for a multiple antenna broadcast channel with partial channel state information at the transmitter (CSIT) is considered. We show how long-term statistical channel knowledge can be efficiently combined with instantaneous low-rate feedback for user selection and linear beamforming. A low complexity algorithm based on an estimate (bound) of the multiuser interference is proposed. Our scheme is shown to exhibit significant throughput gain over opportunistic techniques, approaching the sum rate of full CSIT for small angle spreads.
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paper_title: How much feedback is multi-user diversity really worth?

paper_content:

Wireless scheduling algorithms can extract multi-user diversity (MUDiv) via prioritizing the users with best current channel conditions. One drawback of MUDiv is the required feedback carrying the instantaneous channel rates from from all active subscribers to the access point/base station. This paper shows that this feedback load is, for the most part, unjustified. To alleviate this problem, we propose a technique allowing to dramatically reduce the feedback (by up to 90%) needs while preserving the essential of the scheme performance. We provide a theoretical analysis of the feedback load as function of the system's ergodic and outage capacity for both the traditional MUDiv scheme and the new scheme.
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paper_title: User Scheduling for Heterogeneous Multiuser MIMO Systems: A Subspace Viewpoint

paper_content:

In downlink multiuser multiple-input-multiple-output (MU-MIMO) systems, users are practically heterogeneous. However, many existing user-scheduling algorithms are designed with an implicit assumption that users are homogeneous. In this paper, we revisit the problem by exploring the characteristics of heterogeneous users from a subspace viewpoint. With an objective of minimizing interference nonorthogonality among users, three new angular-based user-scheduling criteria are proposed. While the first criterion is heuristically determined by identifying the incapability of the largest principal angle to characterize subspace correlation and, hence, interference nonorthogonality between users, the second and third criteria are derived by using the sum rate capacity bounds with block diagonalization and the change in capacity by adding a new user into an existing user subset, respectively. Aiming to capture fairness among heterogeneous users while maintaining multiuser diversity gain, two new hybrid user-scheduling algorithms, whose computational complexities are only linearly proportional to the number of users, are proposed. We show by simulations the effectiveness of our proposed user-scheduling criteria and algorithms with respect to those commonly used in a homogeneous environment.
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paper_title: Opportunistic beamforming using dumb antennas

paper_content:

An important means to cope with fading in wireless channels is the use of diversity. Diversity can be obtained over time (interleaving of coded bits), frequency (combining of multipaths in CDMA systems) and space (multiple antennas). The basic idea is to improve performance by creating several independent signal paths between the transmitter and the receiver. In this paper, we propose a scheme that induces random fading when the environment has little scattering and/or the fading is slow. We focus on the downlink of a cellular system. We use multiple antennas at the base-station to transmit the same signal from each antenna modulated by a gain whose phase and magnitude is changing in time in a controlled but pseudo random fashion.
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paper_title: MIMO Broadcast Scheduling with Limited Feedback

paper_content:

We consider multiuser scheduling with limited feedback of partial channel state information in MIMO broadcast channels. By using spatial multiplexing at the base station (BS) and antenna selection for each user, we propose a multiuser scheduling method that allocates independent information streams from all M transmit antennas to the M most favorable users with the highest signal-to-interference-plus-noise ratio (SINR). A close approximation of the achievable sum-rate throughput for the proposed method is obtained and shown to match the simulation results very well. Moreover, two reduced feedback scheduling approaches are proposed. In the first approach, which we shall refer to as selected feedback scheduling, the users are selected based on their SINR compared to a predesigned threshold. Only those selected users are allowed to feed back limited information to the BS. The resultant feedback load and achievable throughput are derived. It will then be demonstrated that with a proper choice of the threshold, the feedback load can be greatly reduced with a negligible performance loss. The second reduced feedback scheduling approach employs quantization for each user, in which only few bits of quantized SINR are fed back to the BS. Performance analysis will show that even with only 1-bit quantization, the proposed quantized feedback scheduling approach can exploit the multiuser diversity at the expense of slight decrease of throughput.
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paper_title: Opportunistic Space-Division Multiple Access With Beam Selection

paper_content:

In this paper, a novel transmission technique for the multiple-input multiple-output (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple sets of randomly chosen orthogonal beamforming vectors. Each user sends the index of the best beamforming vector and the corresponding signal-to-interference-plus-noise ratio for that set of orthogonal vectors back to the base station. The base station opportunistically determines the users and corresponding orthogonal vectors that maximize the sum capacity. Based on the capacity expressions, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20% gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100% gain (for a large number of users) over conventional opportunistic beamforming when the number of transmit antennas is four.
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paper_title: Performance of Orthogonal Beamforming for SDMA With Limited Feedback

paper_content:

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.
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paper_title: Scheduling for Multiuser MIMO Downlink Channels with Ranking-Based Feedback

paper_content:

We consider a multi-antenna broadcast channel with more single-antenna receivers than transmit antennas and partial channel state information at the transmitter (CSIT). We propose a novel type of CSIT representation for the purpose of user selection, coined as ranking-based feedback. Each user calculates and feeds back the rank, an integer between 1 and W + 1, of its instantaneous channel quality information (CQI) among a set of W past CQI measurements. Apart from reducing significantly the required feedback load, ranking-based feedback enables the transmitter to select users that are on the highest peak (quantile) with respect to their own channel distribution, independently of the distribution of other users. It can also be shown that this feedback metric can restore temporal fairness in heterogeneous networks, in which users' channels are not identically distributed and mobile terminals experience different average signal-to-noise ratio (SNR). The performance of a system that performs user selection using ranking-based CSIT in the context of random opportunistic beamforming is analyzed, and we provide design guidelines on the number of required past CSIT samples and the impact of finite W on average throughput. Simulation results show that feedback reduction of order of 40-50% can be achieved with negligible decrease in system throughput.
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paper_title: Exploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems

paper_content:

In the design of narrowband multi-antenna systems, a limiting factor is the amount of channel state information (CSI) available at the transmitter. This is especially evident in multi-user systems, where the spatial user separability determines the multiplexing gain, but it is also important for transmission-rate adaptation in single-user systems. To limit the feedback load, the unknown and multi-dimensional channel needs to be represented by a limited number of bits. When combined with long-term channel statistics, the norm of the channel matrix has been shown to provide substantial CSI that permits efficient user selection, linear precoder design, and rate adaptation. Herein, we consider quantized feedback of the squared Frobenius norm in a Rayleigh fading environment with arbitrary spatial correlation. The conditional channel statistics are characterized and their moments are derived for both identical, distinct, and sets of repeated eigenvalues. These results are applied for minimum mean square error (MMSE) estimation of signal and interference powers in single- and multi-user systems, for the purpose of reliable rate adaptation and resource allocation. The problem of efficient feedback quantization is discussed and an entropy-maximizing framework is developed where the post-user-selection distribution can be taken into account in the design of the quantization levels. The analytic results of this paper are directly applicable in many widely used communication techniques, such as space-time block codes, linear precoding, space division multiple access (SDMA), and scheduling.
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paper_title: Enhanced multiuser random beamforming: dealing with the not so large number of users case

paper_content:

We consider the downlink of a wireless system with an M-antenna base station and K single-antenna users. A limited feedback-based scheduling and precoding scenario is considered that builds on the multiuser random beamforming (RBF). Such a scheme was shown to yield the same capacity scaling, in terms of multiplexing and multiuser diversity gain, as the optimal full CSIT-based (channel state information at transmitter) precoding scheme, in the large number of users K regime. Unfortunately, for more practically relevant (low to moderate) K values, RBF yields degraded performance. In this work, we investigate solutions to this problem. We introduce a two-stage framework that decouples the scheduling and beamforming problems. In our scenario, RBF is exploited to identify good, spatially separable, users in a first stage. In the second stage, the initial random beams are refined based on the available feedback to offer improved performance toward the selected users. Specifically, we propose beam power control techniques that do not change the direction of the second-stage beams, offering feedback reduction and performance tradeoffs. The common feature of these schemes is to restore robustness of RBF with respect to sparse network settings (low K), at the cost of moderate complexity increase.
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paper_title: Training and Feedback Optimization for Multiuser MIMO Downlink

paper_content:

We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over time-frequency blocks that span a coherent time x a coherence bandwidth. In closed-loop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In open-loop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use closed-form lower bounds and tight approximations of the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three time-frequency block models inspired by actual systems, we provide useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.
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paper_title: Optimal Resource Allocation for Multiuser MIMO-OFDM Systems With User Rate Constraints

paper_content:

With the proliferation of wireless services, personal connectivity is quickly becoming ubiquitous. As the user population demands greater multimedia interactivity, data rate requirements are set to soar. Future wireless systems, e.g., multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), need to cater to not only a burgeoning subscriber pool but also to a higher throughput per user. Furthermore, resource allocation for multiuser MIMO-OFDM systems is vital for the optimization of the subcarrier and power allocations to improve overall system performance. Using convex optimization techniques, this paper proposes an efficient solution to minimize the total transmit power subject to each user's data rate requirement. Using a Lagrangian dual decomposition, the complexity is reduced from one that is exponential in the number of subcarriers M to one that is only linear in M. To keep the complexity low, linear beamforming is incorporated at both the transmitter and the receiver. Although frequency-flat fading has been known to plague OFDM resource allocation systems, a modification, i.e., dual proportional fairness, seamlessly handles flat or partially frequency-selective fading. Due to the nonconvexity of the optimization problem, the proposed solution is not guaranteed to be optimal. However, for a realistic number of subcarriers, the duality gap is practically zero, and optimal resource allocation can be evaluated efficiently. Simulation results show large performance gains over a fixed subcarrier allocation.
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paper_title: Robust multi-user opportunistic beamforming for sparse networks

paper_content:

A scheme exploiting reduced feedback for the purpose of opportunistic multi-user beamforming is proposed. The scheme builds on recent promising advances realized in the area of multi-user downlink precoding and scheduling based on partial transmitter channel state information (CSIT) using random beamforming-based SDMA. Although random precoding followed by SDMA scheduling is optimal within the set of unitary precoders, it is only so in the asymptotic number of users K. For-practically relevant-sparse networks (i.e., with low to moderate number of users) random beam-forming SDMA yields severely degraded performance. In this work we present a scheme allowing to restore robustness with respect to cell sparsity. The core idea here is to preserve the low complexity low feedback advantage of random opportunistic beamforming in selecting a target group of users, while much more efficient beamforming schemes can be used to serve the group of users once it has been identified. We propose different designs, optimal and suboptimal, based upon variable levels of feedback requirement. We show substantial gain over opportunistic beamforming for a range of K.
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paper_title: Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels

paper_content:

In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total system-wide feedback load, is it preferable to get low-rate/coarse channel feedback from a large number of receivers or high-rate/high-quality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multi-user diversity to be exploited, while high-rate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining high-quality feedback, and that obtaining near-perfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users.
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paper_title: Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling

paper_content:

Joint Spatial Division and Multiplexing (JSDM) is a downlink multiuser MIMO scheme recently proposed by the authors in order to enable “massive MIMO” gains and simplified system operations for Frequency Division Duplexing (FDD) systems. The key idea lies in partitioning the users into groups with approximately similar channel covariance eigenvectors and serving these groups by using two-stage downlink precoding scheme obtained as the concatenation of a pre-beamforming matrix, that depends only on the channel second-order statistics, with a multiuser MIMO linear precoding matrix, which is a function of the effective channels including pre-beamforming. The role of pre-beamforming is to reduce the dimensionality of the effective channel by exploiting the near-orthogonality of the eigenspaces of the channel covariances of the different user groups. This paper is an extension of our initial work on JSDM, and addresses some important practical issues. First, we focus on the regime of finite number of antennas and large number of users and show that JSDM with simple opportunistic user selection is able to achieve the same scaling law of the system capacity with full channel state information. Next, we consider the large-system regime (both antennas and users growing large) and propose a simple scheme for user grouping in a realistic setting where users have different angles of arrival and angular spreads. Finally, we propose a low-overhead probabilistic scheduling algorithm that selects the users at random with probabilities derived from large-system random matrix analysis. Since only the pre-selected users are required to feedback their channel state information, the proposed scheme realizes important savings in the CSIT feedback.
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paper_title: Two-Phase Multiuser Scheduling for Multiantenna Downlinks Exploiting Reduced Finite-Rate Feedback

paper_content:

This paper considers a multiantenna system with an M -antenna base station and K single antenna users, employing zero-forcing beamforming (ZFBF) and a finite-rate feedback strategy. We study scheduling to select KS users for transmit beamforming. To reduce the feedback requirement, we propose a two-phase scheduling scheme that exploits quantized channel direction information (CDI) from only a small subset of the overall users, as well as a 1-bit signal-to-interference-plus-noise ratio (SINR) indicator feedback per user. In the proposed scheme, we introduce a newly defined expression for evaluating SINR that extends the existing SINR approximation for KS = M to a more general case with arbitrary KS ? M. Asymptotic analysis reveals that the proposed two-phase scheduling is asymptotically optimal for large user numbers. Through numerical simulations, we also show that the proposed scheme requires less feedback than conventional schemes, whereas the resulting sum rate loss due to the reduced feedback is negligible. Moreover, we find that the choice of KS < M, instead of a full-multiplexing case with KS = M, for scheduling may achieve a better tradeoff between performance and feedback requirement in systems where fewer bits are utilized for feeding back CDI.
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paper_title: Multiuser Diversity - Multiplexing Tradeoff in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider joint scheduling and beamforming in a broadcast channel with multiple antennas at the transmitter and a single antenna at the mobile receiver. Perfect channel knowledge is assumed to be available at the receiver while the transmitter is provided with partial channel state information (CSIT) through a limited rate feedback channel. Each user feeds back quantized information regarding the channel vector direction (from a codebook) and a quantized (scalar) channel quality indicator. We identify the tradeoff between multiuser diversity and spatial multiplexing gain given a limited amount of feedback bits. Scaling laws of the above parameters are derived in order to achieve a target rate performance. Our results reveal useful design guidelines for the split of feedback bits for channel quantization and channel quality.
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paper_title: Fundamental Limits in MIMO Broadcast Channels

paper_content:

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system parameters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.
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paper_title: Efficient Margin Adaptive Scheduling for MIMO-OFDMA Systems

paper_content:

In this paper we address the problem of margin adaptive scheduling in the downlink of an orthogonal frequency division multiple access (OFDMA) multiple-input multiple-output (MIMO) system. Optimal resource allocation in MIMO systems requires the joint optimization of: a) linear transmit and receive spatial filters, b) channel assignment and c) power allocation. This problem is not convex and its complexity becomes thus intractable already for small sets of users and subcarriers. To reduce the complexity of the problem at hand, we propose a novel heuristic strategy that partitions the users in different groups according to their average channel quality and addresses the original problem by solving a succession of lower-complexity allocation problems. The spatial dimension is employed to prevent multiple access interference from hindering the performance of the sequential allocation. To further reduce the complexity burden we introduce a linear programming formulation in combination with a waterfilling-based strategy to allocate channels and power to the groups of users. Numerical results and evaluation of the computational complexity show that, though suboptimal, in most cases the proposed algorithm manages to exploit in an original way the inherent multi-user diversity of multi-carrier systems to ease the task of resource allocation with a very limited performance loss from the theoretic optimum.
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paper_title: On the Capacity of MIMO Broadcast Channels With Partial Side Information

paper_content:

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.
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paper_title: Multi-mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

paper_content:

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.
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paper_title: On the balance of multiuser diversity and spatial multiplexing gain in random beamforming

paper_content:

This paper is concerned with the problem of exploiting spatial multiplexing gain through opportunistic beamforming with multiple random beams. The base station transmits multiple pilot sequences using orthogonal beams, and each user feeds the channel gain of each beam back. Then, the base station selects the subset of users and beams for which the sum-rate is maximized. We aim to exploit spatial multiplexing gain in a controlled fashion, i.e., the number of beams used for data transmission is chosen depending on the available multiuser diversity in the system. Two schemes are proposed: dynamic Orthonormal Random Beamforming with Systematic Beam Selection (ORBF/SBS), for which the number of beams used for data transmission is dynamically changed from one fading block to another so that the sum-rate is maximized; and static ORBF/SBS, which selects a fixed number of beams for a given signal-to-noise ratio and user number. The static scheme achieves the sum-rate of the dynamic one up to a small gap with much reduced computational and feedback complexity. We derive an approximate expression for the sum-rate achieved by the dynamic scheme, and provide insight into the optimal data stream number in the static scheme by means of asymptotical results. Computer simulations are provided to evaluate the performance of the proposed schemes.
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paper_title: Two-Stage Channel Quantization for Scheduling and Beamforming in Network MIMO Systems: Feedback Design and Scaling Laws

paper_content:

This paper proposes an efficient two-stage channel quantization and feedback scheme for the downlink limited-feedback network multiple-input multiple-output (MIMO) system. In the first stage, the users report their best set of base-station antenna and physical resource block combinations, and the base-stations schedule the best user for each antenna in each resource block. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. This paper proposes an analytical framework to show that, under a total feedback budget of B bits, the number of bits assigned to the second feedback stage should scale as log B, and in quantizing channel vectors from different base-stations, each user should allocate feedback bits in proportion to the channel magnitudes in dB scale. Under these optimized bit allocations, the overall sum rate of the system is shown to scale double-logarithmically with B, linearly with the total number of antennas, and logarithmically with transmit power, thus achieving both multiuser diversity and spatial multiplexing gains under limited feedback. Finally, realistic wireless propagation model of an urban small-cell deployment is used to show that the proposed scheme can approach the performance of a network MIMO system with full channel state information with only modest amount of channel feedback.
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paper_title: Large deviation delay analysis of queue-aware multi-user MIMO systems with two timescale mobile-driven feedback

paper_content:

Multi-user multi-input-multi-output (MU-MIMO) systems usually require users to feedback the channel state information (CSI) for scheduling. Most of the existing literature on the reduced feedback user scheduling focused on the throughput performance and the queueing delay was usually ignored. As the delay is important for real-time applications, it is desirable to have a low feedback queue-aware user scheduling algorithm for MU-MIMO systems. This paper proposes a two timescale queue-aware user scheduling algorithm, which consists of a queue-aware mobile-driven feedback filtering stage and a SINR-based user scheduling stage. The feedback policy is obtained by solving a queue-weighted optimization problem. In addition, we evaluate the associated queueing delay performance by using the large deviation analysis. The large deviation decay rate for the proposed algorithm is shown to be much larger than the CSI-only scheduling algorithm. Numerical results demonstrate the large performance gain of the proposed algorithm over the CSI-only algorithm, while the proposed one requires only a small amount of feedback.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Space Division Multiple Access with a Sum Feedback Rate Constraint

paper_content:

On a multi-antenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.
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paper_title: Limited feedback design for MIMO broadcast channels with ARQ mechanism

paper_content:

We investigate the design of a limited feedback mechanism for multiple-input-multiple-output (MIMO) broadcast systems that are equipped with automatic repeat request (ARQ) capabilities. Given multiple antennas at the base-station (BS) and single antenna subscribers, we focus on maximizing the ergodic system sum capacity and propose an adaptive feedback bit allocation scheme under the constraint of total feedback bandwidth. Furthermore, we develop two efficient feedback allocation schemes based on asymptotic analysis. We present simulation results that verify the effectiveness of the proposed adaptive allocation schemes.
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paper_title: Downlink Multiuser MIMO Systems With Adaptive Feedback Rate

paper_content:

In this paper, an efficient channel feedback scheme for downlink multiuser multiple-input-multiple-output (MU-MIMO) systems is proposed. The objective of the new feedback design is to adaptively control the feedback rate of each user, depending on the individual channel status, while the overall sum feedback rate is kept the same. The proposed channel feedback scheme is composed of two stages: 1) the common channel feedback stage of all users and 2) the user-specific channel feedback stage of the selected users. We present a low-complexity algorithm to determine the individual feedback rates of users, which utilizes convex optimization, followed by iterative steepest descent direction searching. Numerical results show that zero-forcing beamforming (ZFBF), combined with the proposed channel feedback scheme, considerably outperforms ZFBF with conventional channel feedback schemes.
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paper_title: MIMO Broadcast Scheduling with Limited Feedback

paper_content:

We consider multiuser scheduling with limited feedback of partial channel state information in MIMO broadcast channels. By using spatial multiplexing at the base station (BS) and antenna selection for each user, we propose a multiuser scheduling method that allocates independent information streams from all M transmit antennas to the M most favorable users with the highest signal-to-interference-plus-noise ratio (SINR). A close approximation of the achievable sum-rate throughput for the proposed method is obtained and shown to match the simulation results very well. Moreover, two reduced feedback scheduling approaches are proposed. In the first approach, which we shall refer to as selected feedback scheduling, the users are selected based on their SINR compared to a predesigned threshold. Only those selected users are allowed to feed back limited information to the BS. The resultant feedback load and achievable throughput are derived. It will then be demonstrated that with a proper choice of the threshold, the feedback load can be greatly reduced with a negligible performance loss. The second reduced feedback scheduling approach employs quantization for each user, in which only few bits of quantized SINR are fed back to the BS. Performance analysis will show that even with only 1-bit quantization, the proposed quantized feedback scheduling approach can exploit the multiuser diversity at the expense of slight decrease of throughput.
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paper_title: Scheduling for Multiuser MIMO Downlink Channels with Ranking-Based Feedback

paper_content:

We consider a multi-antenna broadcast channel with more single-antenna receivers than transmit antennas and partial channel state information at the transmitter (CSIT). We propose a novel type of CSIT representation for the purpose of user selection, coined as ranking-based feedback. Each user calculates and feeds back the rank, an integer between 1 and W + 1, of its instantaneous channel quality information (CQI) among a set of W past CQI measurements. Apart from reducing significantly the required feedback load, ranking-based feedback enables the transmitter to select users that are on the highest peak (quantile) with respect to their own channel distribution, independently of the distribution of other users. It can also be shown that this feedback metric can restore temporal fairness in heterogeneous networks, in which users' channels are not identically distributed and mobile terminals experience different average signal-to-noise ratio (SNR). The performance of a system that performs user selection using ranking-based CSIT in the context of random opportunistic beamforming is analyzed, and we provide design guidelines on the number of required past CSIT samples and the impact of finite W on average throughput. Simulation results show that feedback reduction of order of 40-50% can be achieved with negligible decrease in system throughput.
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paper_title: On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

paper_content:

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.
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paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

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This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
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paper_title: Networked MIMO with clustered linear precoding

paper_content:

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination to enhance the sum rate and limited inter-cluster coordination to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.
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paper_title: Solution of the multiuser downlink beamforming problem with individual SINR constraints

paper_content:

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.
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paper_title: Multi-Cell MIMO Cooperative Networks: A New Look at Interference

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This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.
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paper_title: Multiuser MIMO Scheduling for LTE-A Downlink Cellular Networks

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In this paper, we investigate multiuser MIMO scheduling in LTE downlink cellular networks. We formulate the downlink LTE-A MIMO scheduling as a weighted sum rate maximization problem by allocating the RBs to users or user pairs subject to some constraints in LTE-A. We develop a low-complexity MU-MIMO scheduling and resource allocation algorithm and propose an adaptive switching approach between SU-MIMO and MU-MIMO to improve network performance. System-level simulation results demonstrate significantly performance improvement of the proposed MU-MIMO scheduling algorithm and the adaptive switching algorithm.
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paper_title: Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

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A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
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paper_title: Network MIMO with Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation and Reduced-Complexity Scheduling

paper_content:

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.
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paper_title: Enhanced Limited Feedback Schemes for DL MU-MIMO ZF Precoding

paper_content:

This paper proposes new limited-feedback Channel State Information (CSI) calculation schemes for Zero Forcing (ZF)-precoded downlink Multi-User Multiple-Input Multiple-Output (MU-MIMO) systems. It is a common understanding that the feedback quantized by the codebook limits the performance of MU-MIMO. In this paper, through a quasi-ZF or a quasi-Minimum Mean-Squared Error (MMSE) weight, the channel matrix is transferred to one of the codebook vectors, based on which, the CSI is calculated. Thus, the quantization error is minimized. Meanwhile, the selection for the codebook vector guarantees the maximizing of the estimated Signal to Interference plus Noise Ratio (SINR). We verify that the proposed scheme obtains accurate feedback information, and the predicted weight can be the same as the optimal linear decoder as if the receiver knew all the precoder information that is fed-forward from the BS, as long as the number of antennas for each receiver equals that for the transmitter, and equals that for the total transmit data streams. Compared to the commonly used Precoding Matrix Index (PMI) based method, which uses rank-one single user (SU)-MIMO feedback, simulation results show that the proposed schemes achieve higher sum capacities in different scenarios. Moreover, since the weight can be directly used as the decoder, the feed-forward overhead is reduced.
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paper_title: Adaptive Modulation in PU2RC Systems with Finite Rate Feedback

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This paper addresses a per user unitary precoding and rate control (PU 2 RC) system with adaptive multi-level quadrature amplitude modulation (QAM) modulation, where both the PU 2 RC operation and adaptive modulation are based on finite rate feedback. The system supports two transmission modes (single user transmit beamforming and multiuser transmission with orthogonal beamforming), and switches between the two modes to maximize the average throughput. We first study single user transmit beamforming, and derive closed-form expressions for the average throughput and bit-error rate (BER) with outdated channel information. Then, multiuser transmission with orthogonal beamforming is investigated. We analyze the throughput and BER performance without feedback delay in the normal signal noise ratio (SNR) regime, and the performance with feedback delay in the interference-limited regime. Simulation results demonstrate the effect of time delay, and the preferred regions of the single user transmission mode and multiuser transmission mode.
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paper_title: Dynamic Multi-User MIMO scheduling with limited feedback in LTE-Advanced

paper_content:

Multi-User MIMO (MU-MIMO) systems have gained numerous attention from researchers in the past decade due to its substantial gains in the system throughput. Most of the initial research assumes the knowledge of perfect channel state information at the transmitter (CSIT). However, this is considered impractical and research over the past few years has been focused on receivers feeding back limited information to the transmitter. In this work, we consider a transparent MU-MIMO system model with limited feedback. We propose a general framework for dynamic MU-MIMO scheduling with the capability to switch between Single-User MIMO mode and (Multi-Rank) Multi-User MIMO mode without users feeding back additional multi-user information. Specifically, this is done by each user carefully estimating its CQI under the hypothesis of Multi-Rank MultiUser MIMO transmission and taking advantage of the codebook structure. We consider the sum rate of the system assuming each user uses ML and LMMSE receiver and show that our proposed scheduler, with significantly reduced feedback load, outperforms the best-companion user pairing.
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paper_title: Learning-Based Adaptive Transmission for Limited Feedback Multiuser MIMO-OFDM

paper_content:

Performing link adaptation in a multiantenna and multiuser system is challenging because of the coupling between precoding, user selection, spatial mode selection and use of limited feedback about the channel. The problem is exacerbated by the difficulty of selecting the proper modulation and coding scheme when using orthogonal frequency division multiplexing (OFDM). This paper presents a data-driven approach to link adaptation for multiuser multiple input mulitple output (MIMO) OFDM systems. A machine learning classifier is used to select the modulation and coding scheme, taking as input the SNR values in the different subcarriers and spatial streams. A new approximation is developed to estimate the unknown interuser interference due to the use of limited feedback. This approximation allows to obtain SNR information at the transmitter with a minimum communication overhead. A greedy algorithm is used to perform spatial mode and user selection with affordable complexity, without resorting to an exhaustive search. The proposed adaptation is studied in the context of the IEEE 802.11ac standard, and is shown to schedule users and adjust the transmission parameters to the channel conditions as well as to the rate of the feedback channel.
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paper_title: MU-MIMO MAC Protocols for Wireless Local Area Networks: A Survey

paper_content:

As wireless devices boom and bandwidth-hungry applications (e.g., video and cloud uploading) get popular, today's wireless local area networks (WLANs) become not only crowded but also stressed at throughput. Multiuser multiple-input–multiple-output (MU-MIMO), an advanced form of MIMO, has gained attention due to its huge potential in improving the performance of WLANs. This paper surveys random access-based medium access control (MAC) protocols for MU-MIMO-enabled WLANs. It first provides background information about the evolution and the fundamental MAC schemes of IEEE 802.11 Standards and Amendments, and then identifies the key requirements of designing MU-MIMO MAC protocols for WLANs. After this, the most representative MU-MIMO MAC proposals in the literature are overviewed by benchmarking their MAC procedures and examining the key components, such as the channel state information acquisition, decoding/precoding, and scheduling schemes. Classifications and discussions on important findings of the surveyed MAC protocols are provided, based on which, the research challenges for designing effective MU-MIMO MAC protocols, as well as the envisaged MAC's role in the future heterogeneous networks, are highlighted.
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paper_title: Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization

paper_content:

Block diagonalization (BD) is a preceding technique that eliminates inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. With the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission, the number of simultaneously supportable users with BD is limited by the ratio of the number of basestation transmit antennas to the number of user receive antennas. In a downlink MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput The brute-force search for the optimal user set, however, is computationally prohibitive. We propose two low-complexity suboptimal user selection algorithms for multiuser MIMO systems with BD. Both algorithms aim to select a subset of users such that the total throughput is nearly maximized. The first user selection algorithm greedily maximizes the total throughput, whereas the criterion of the second algorithm is based on the channel energy. We show that both algorithms have linear complexity in the total number of users and achieve around 95% of the total throughput of the complete search method in simulations
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

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In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Managing downlink multi-user MIMO transmission using group membership

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Advances in digital communications and signal processing have enabled the adaptation of advanced communication techniques in wireless LAN (WLAN) standards. Among those advanced techniques, multiple-input-multipleoutput (MIMO) is now part of the high throughput (HT) WLAN standard, a.k.a. IEEE 802.11n. With the completion of the IEEE 802.11n specification, the IEEE 802.11 working group (WG) is now working on a new amendment to achieve very high throughput (VHT) in the gigabit range.. The move to higher data rates is enabled by introducing wider bandwidth, downlink multi-user MIMO (MU-MIMO), and higher modulation and coding schemes (MCS). This paper focuses the use of group membership and identifiers for managing downlink transmissions using MU-MIMO. Downlink MU-MIMO allows a WLAN access point to transmit to multiple stations simultaneously. Group Membership and identifiers are used to signal target stations together with their positions and the number of spatial streams intended for each of them in the downlink transmission. A description of the Group ID concept and its application to the VHT specification is discussed here. A method for assigning stations' position to Group IDs is introduced and its performance is examined.
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paper_title: Recent Advances in Radio Resource Management for Heterogeneous LTE/LTE-A Networks

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As heterogeneous networks (HetNets) emerge as one of the most promising developments toward realizing the target specifications of Long Term Evolution (LTE) and LTE-Advanced (LTE-A) networks, radio resource management (RRM) research for such networks has, in recent times, been intensively pursued. Clearly, recent research mainly concentrates on the aspect of interference mitigation. Other RRM aspects, such as radio resource utilization, fairness, complexity, and QoS, have not been given much attention. In this paper, we aim to provide an overview of the key challenges arising from HetNets and highlight their importance. Subsequently, we present a comprehensive survey of the RRM schemes that have been studied in recent years for LTE/LTE-A HetNets, with a particular focus on those for femtocells and relay nodes. Furthermore, we classify these RRM schemes according to their underlying approaches. In addition, these RRM schemes are qualitatively analyzed and compared to each other. We also identify a number of potential research directions for future RRM development. Finally, we discuss the lack of current RRM research and the importance of multi-objective RRM studies.
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paper_title: Novel scheduling strategy for downlink multiuser MIMO system: Particle swarm optimization

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In this paper the scheduling problem in downlink multiuser MIMO system is described as an optimization problem and particle swarm optimization (PSO) algorithm is introduced to address such problem. Two PSO scheduling methods with different objective functions applicable to different requirements on capacity and complexity are investigated. One is the capacity based PSO(C-PSO) scheduling method aiming at achieving the near optimal capacity; and the other is the lower bound of eigenvalue based PSO (LBE-PSO) scheduling method with the purpose of reducing computational complexity and at the same time achieving as large as possible capacity gain. Furthermore, convergence analysis of PSO from both the particle and the velocity aspects is also presented to derive the convergent condition, which is validated by several examples of different parameter values. Simulation results reveal that the C-PSO can obtain nearly the same capacity as the exhaustive search method with lower complexity, while the LBE-PSO provides a viable approach by striking a better tradeoff between capacity and computational complexity.
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paper_title: On the Performance, Complexity, and Fairness of Suboptimal Resource Allocation for Multiuser MIMO–OFDMA Systems

paper_content:

The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) is a promising solution to the flexible and spectrally efficient provision of data services in future wireless communication systems. However, adaptive resource allocation (RA) in frequency, time, and space in multiuser MIMO-OFDMA systems is very complex due to the inclusion of the space dimension and the large number of resources to be managed. Indeed, an optimal RA for maximizing the sum rate is usually too complex for practical application, and suboptimal strategies are required. In this paper, the performance, complexity, and fairness of suboptimal RA strategies aiming at the maximization of the sum rate are investigated. A model for suboptimal RA strategies is proposed, and two new RA strategies are introduced. The proposed strategies are compared in terms of the sum rate, complexity, and throughput fairness and are shown to present better performance-complexity and performance-fairness tradeoffs than some existing suboptimal strategies, as well as to achieve almost the same sum rate as that obtained through an exhaustive search.
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paper_title: User Selection With Zero-Forcing Beamforming Achieves the Asymptotically Optimal Sum Rate

paper_content:

In this paper, we propose a generalized greedy (G-greedy) algorithm based on zero-forcing beamforming (ZFBF) for the multiple-input multiple-output (MIMO) broadcast channel. This algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations. As previous results only give the scaling law of the sum rate of dirty paper coding (DPC), with the help of the G-greedy structure, we are able to obtain the exact limit of the DPC sum rate for a large number of users. We also prove that the difference between the sum rates obtained by G-greedy user selection and by DPC goes to zero as the number of users increases. In addition to this, we investigate one particular greedy user selection scheme called sequential water-filling (SWF). For this algorithm, a complexity reduction is achieved by an iterative procedure based on an LQ decomposition, which converts the calculation of the Moore-Penrose matrix inverse to one vector-matrix multiplication. A sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction. With the help of the G-greedy algorithm, we prove that SWF achieves the full DPC sum rate for a large number of users. For a moderate number of users, simulation demonstrates that, compared with other user selection algorithms, SWF achieves a higher sum rate that is close to the maximal sum rate achievable by ZFBF with the same order of complexity.
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paper_title: Efficient Scheduling Algorithms for Multiantenna CDMA Systems

paper_content:

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.
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paper_title: Adaptive radio resource allocation for downlink OFDMA/SDMA systems with multimedia traffic

paper_content:

This paper proposes an adaptive radio resource allocation (ARRA) algorithm for downlink OFDMA/SDMA systems with multimedia traffic. Considering multiple service classes and diverse QoS requirements of multimedia traffic, the ARRA algorithm is designed with the goal to maximize spectrum efficiency and to fulfill quality of service (QoS) requirements. It is composed of two parts, a dynamic priority adjustment (DPA) scheme and a priority-based greedy (PBG) scheme. The DPA adopts a type of time-to-expiration to indicate the degree of user's urgency, and dynamically gives high priorities to urgent users. The PBG allocates the radio resource iteratively, based on a cost value, to maximize the system throughput while allocating enough resource to high-priority users. Simulation results show that the ARRA algorithm outperforms conventional algorithms in terms of system throughput and satisfaction extent of QoS requirements; it can sustain users' QoS requirements up till a traffic load of 0.8, while the conventional algorithms cannot guarantee QoS requirements after a traffic load of 0.3.
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paper_title: On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm

paper_content:

This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple "beams" directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail so-called Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DP-based scheme proposed by Tu and Blum. We also propose another user-selection method of the same computational complexity based on simple zero-forcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum's scheme and, thus, offers an attractive alternative to DP-based schemes.
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paper_title: User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming

paper_content:

In this paper, we propose a greedy user selection with swap (GUSS) algorithm based on zero-forcing beamforming for multiuser multiple-input-multiple-output (MIMO) downlink channels. Existing user selection algorithms such as zero forcing with selection (ZFS) have the flaws of “redundant users” and “local optimum,” which compromise the achieved sum rate. GUSS improves the performance by adding the “delete” and “swap” operations to the user selection procedure of ZFS to eliminate “redundant users” and escape from “local optimum,” respectively. In addition, an effective-channel-vector-based effective-channel-gain-updating scheme is proposed to reduce the complexity of GUSS. With the help of this updating scheme, GUSS has the same order of complexity as ZFS with only a linear increment. Simulation results indicate that over the range of transmit signal-to-noise ratios (SNRs) considered, on average, the sum rate of GUSS reaches 99.3% of the upper bound that is achieved by exhaustive search, with only 1.51 to 2.29 times the complexity of ZFS.
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paper_title: Hierarchical Interference Mitigation for Massive MIMO Cellular Networks

paper_content:

We propose a hierarchical interference mitigation scheme for massive MIMO cellular networks. The MIMO precoder at each base station (BS) is partitioned into an inner precoder and an outer precoder. The inner precoder controls the intra-cell interference and is adaptive to local channel state information (CSI) at each BS (CSIT). The outer precoder controls the inter-cell interference and is adaptive to channel statistics. Such hierarchical precoding structure reduces the number of pilot symbols required for CSI estimation in massive MIMO downlink and is robust to the backhaul latency. We study joint optimization of the outer precoders, the user selection, and the power allocation to maximize a general concave utility which has no closed-form expression. We first apply random matrix theory to obtain an approximated problem with closed-form objective. We show that the solution of the approximated problem is asymptotically optimal with respect to the original problem as the number of antennas per BS grows large. Then using the hidden convexity of the problem, we propose an iterative algorithm to find the optimal solution for the approximated problem. We also obtain a low complexity algorithm with provable convergence. Simulations show that the proposed design has significant gain over various state-of-the-art baselines.
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paper_title: Low complexity greedy, genetic and hybrid user scheduling algorithms for multiuser MIMO systems with successive zero‐forcing

paper_content:

In this paper, we consider low complexity user scheduling algorithms for multiuser multiple-input multiple-output systems employing successive zero-forcing precoding. Optimal scheduling involves an exhaustive search (ES), which is prohibitively complex. Greedy algorithms (GrAs) with heuristic scheduling metrics achieve performance close to that of the ES. Meanwhile, genetic algorithms (GAs) are a rapid suboptimal option of optimising utility (e.g. scheduling) metrics. Herein, we evaluate the performance and complexity of greedy and genetic scheduling algorithms for successive zero-forcing. We also propose and evaluate two hybrid algorithms combining the traits of the GrA and GA. The algorithms' performance is assessed through a series of computer simulations. We demonstrate both the GrA and GA achieve a near-optimal sum rate with low complexity, whereas the hybrid algorithms further enhance the GrA and GA performance without an increase in the order of complexity.Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: Scheduling Methods with MIMO Interference Alignment for Mutually Interfering Broadcast Channels

paper_content:

In this paper, we investigate an interference alignment (IA) technique introduced by Cadambe and Jafar in mutually interfering broadcast channels (IFBCs). First, we study the spatial multiplexing gain (SMG) for the 3-cell IFBC where all base stations and mobile users are equipped with multiple antennas. To achieve the derived optimal SMG, we extend the IA algorithm designed for K-user multi-input multi-output (MIMO) interference channels (IFCs) to the IFBC. In this paper, we present the IA scheme in conjunction with user selection which outperforms the time division multiple access (TDMA) technique in the IFBC environment. The optimal scheduling method capitalizes on multiuser diversity to achieve a significant fraction of sum capacity by using an exhaustive search algorithm. Since the computational complexity of the optimal scheduling method is prohibitive, a reduced complexity suboptimal scheduling method is proposed based on a coordinate ascent approach. Simulation results confirm that the reduced complexity scheduling algorithm achieves the sum rate close to the optimal algorithm with much reduced complexity.
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paper_title: Scheduling for Multiuser MIMO Broadcast Systems: Transmit or Receive Beamforming?

paper_content:

In this paper, we present an approximation formula and the close-form expression for the sum rate of the transmit and the receive zero-forcing (ZF) multiple-input multiple-output (MIMO) broadcast systems with user selection, respectively. Instead of assuming a large number of users to obtain a scaling law as most current work, we derive the sum rate formulas of the ZF MIMO broadcast systems with a small number of scheduled users. By analysis and simulations, we find that when taking the variations of feedback channel into account, the receive ZF MIMO broadcast system is more robust to feedback errors and can deliver equal or even higher sum rate than the transmit ZF MIMO broadcast system. We discuss whether a feedback channel is suitable to send channel state information (CSI) for calculating transmit antenna beamforming weights, or suitable to send CSI for selecting users in the receive ZF MIMO broadcast system. Our results show that as the variation of feedback channel errors increases from 0.5 to 1.5, the receive ZF 3 × 3 MIMO broadcast system can provide 36% to 116% higher sum rate than the transmit ZF 3 × 3 MIMO broadcast system in the case of 20 users at signal to noise ratio (SNR) equal to 20 dB. Providing that more feedback bandwidth and an error-free feedback channel are available, the transmit ZF MIMO broadcast system can achieve higher sum rate than the receive ZF MIMO broadcast system.
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paper_title: Decremental User Selection for Large-Scale Multi-User MIMO Downlink with Zero-Forcing Beamforming

paper_content:

This paper proposes a decremental user selection algorithm based on zero-forcing beamforming when the number of users K in the network is smaller than the number of antennas M at a base station. The algorithm is specifically designed for large-scale multi-user multiple-input multiple-output (MIMO) downlink channels. While previous user selection algorithms are based on incremental search that starts from an empty user set, our proposed delete the minimum lambda (DML) algorithm starts by selecting all users and then deleting one user per iteration. DML substantially reduces the computational complexity as the cardinality of the final user set is close to K. Simulation results indicate that on average DML achieves an equal or higher sum rate performance than previous algorithms with greatly reduced complexity of O(MK2).
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

paper_content:

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.
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paper_title: Simplified Semi-Orthogonal User Selection for MU-MIMO Systems with ZFBF

paper_content:

In this letter, we simplify the well-known semi-orthogonal user selection (SUS) algorithm for the multi-user multiple-input multiple-output (MU-MIMO) system with zero-forcing beamforming (ZFBF). Compared with the original SUS algorithm, the proposed user selection algorithm achieves the same performance, but with significantly less complexity. Simulation results show that the proposed algorithm can make a good tradeoff between performance and complexity for the MU-MIMO system with ZFBF.
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paper_title: Sum Rates, Rate Allocation, and User Scheduling for Multi-User MIMO Vector Perturbation Precoding

paper_content:

This paper considers the multiuser multiple-input multiple-output (MIMO) broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via vector perturbation. We derive expressions for the sum rate in terms of the average energy of the precoded vector, and use this to derive a high signal-to-noise ratio (SNR) closed-form upper bound, which we show to be tight via simulation. We also propose a modification to vector perturbation where different rates can be allocated to different users. We conclude that for vector perturbation precoding most of the sum rate gains can be achieved by reducing the rate allocation problem to the user selection problem. We then propose a low-complexity user selection algorithm that attempts to maximize the high-SNR sum rate upper bound. Simulations show that the algorithm outperforms other user selection algorithms of similar complexity.
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paper_title: Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization

paper_content:

Block diagonalization (BD) is a preceding technique that eliminates inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. With the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission, the number of simultaneously supportable users with BD is limited by the ratio of the number of basestation transmit antennas to the number of user receive antennas. In a downlink MIMO system with a large number of users, the basestation may select a subset of users to serve in order to maximize the total throughput The brute-force search for the optimal user set, however, is computationally prohibitive. We propose two low-complexity suboptimal user selection algorithms for multiuser MIMO systems with BD. Both algorithms aim to select a subset of users such that the total throughput is nearly maximized. The first user selection algorithm greedily maximizes the total throughput, whereas the criterion of the second algorithm is based on the channel energy. We show that both algorithms have linear complexity in the total number of users and achieve around 95% of the total throughput of the complete search method in simulations
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paper_title: Multiuser MIMO User Selection Based on Chordal Distance

paper_content:

Multiuser MIMO (MU-MIMO) systems have advantages over single-user MIMO systems in terms of system performance. In MU-MIMO systems, inter-user interference needs to be dealt with especially when linear processing is used. The block diagonalization (BD) method is one of techniques that are widely used to eliminate the inter-user interference. In a cellular system where there are many users, the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell. In this paper, we propose a low complexity MU-MIMO scheduling scheme using BD with chordal distance. For a large number of users, the optimal scheduling technique needs an exhaustive search, which is impractical. One of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users. Simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms.
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paper_title: Efficient Margin Adaptive Scheduling for MIMO-OFDMA Systems

paper_content:

In this paper we address the problem of margin adaptive scheduling in the downlink of an orthogonal frequency division multiple access (OFDMA) multiple-input multiple-output (MIMO) system. Optimal resource allocation in MIMO systems requires the joint optimization of: a) linear transmit and receive spatial filters, b) channel assignment and c) power allocation. This problem is not convex and its complexity becomes thus intractable already for small sets of users and subcarriers. To reduce the complexity of the problem at hand, we propose a novel heuristic strategy that partitions the users in different groups according to their average channel quality and addresses the original problem by solving a succession of lower-complexity allocation problems. The spatial dimension is employed to prevent multiple access interference from hindering the performance of the sequential allocation. To further reduce the complexity burden we introduce a linear programming formulation in combination with a waterfilling-based strategy to allocate channels and power to the groups of users. Numerical results and evaluation of the computational complexity show that, though suboptimal, in most cases the proposed algorithm manages to exploit in an original way the inherent multi-user diversity of multi-carrier systems to ease the task of resource allocation with a very limited performance loss from the theoretic optimum.
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paper_title: A comparison of scheduling strategies for MIMO broadcast channel with limited feedback on OFDM systems

paper_content:

We consider a multiuser downlink transmission from a base station with multiple antennas (MIMO) to mobile terminals (users) with a single antenna, using orthogonal frequency division multiplexing (OFDM). Channel conditions are reported by a feedback from users with limited rate, and the base station schedules transmissions and beamforms signals to users. We show that an important set of schedulers using a general utility function can be reduced to a scheduler maximizing the weighted sum rate of the system. For this case we then focus on scheduling methods with many users and OFDM subcarriers. Various scheduling strategies are compared in terms of achieved throughput and computational complexity and a good tradeoff is identified in greedy and semiorthogonal user selection algorithms. In the greedy selection algorithm, users are selected one by one as long as the throughput increases, while in the semiorthogonal approach users are selected based on the channel correlation. An extension of these approaches from a flat-fading channel to OFDM is considered and simplifications that may be useful for a large number of subcarriers are presented. Results are reported for a typical cellular transmission of the long-term evolution (LTE) of 3GPP.
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paper_title: Optimal downlink space-time scheduling design with convex utility functions-multiple-antenna systems with orthogonal spatial multiplexing

paper_content:

It is well known that link level throughput could be significantly increased by using multiple antennae at the transmitter and receiver without increasing the bandwidth and power budget. However, optimizing the link level performance of multiple-antenna systems does not always imply achieving system level optimization. Therefore, cross-layer optimization across the link layer and the scheduling layer is very important to fully exploit the temporal and spatial dimensions of the communication channel. In this paper, we consider the optimal downlink space-time scheduling design for a general class of convex utility functions. The access point or base station is equipped with n/sub T/ transmit antennas. There are K mobiles in the system with a single receive antenna. For practical reasons, we assume zero-forcing processing at the physical layer of the base station and mobile. We will apply the design framework to two common utility functions, namely the maximum throughput and the proportional fair. The cross-layer scheduling design is a mixed convex and combinatorial optimization problem and the search space of the optimal solution is enormous. Greedy algorithm, which has been widely used in today's wireless data systems (3G1X, high data rate system (HDR), Universal Mobile Terrestrial Service), is optimal when n/sub T/=1. However, we found that there is a large performance penalty of greedy algorithms (relative to optimal performance) when n/sub T/>1 and this motivates the search for more efficient heuristics. In this paper, we will address genetic-based heuristics and discuss their complexity-performance tradeoff.
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paper_title: On the balance of multiuser diversity and spatial multiplexing gain in random beamforming

paper_content:

This paper is concerned with the problem of exploiting spatial multiplexing gain through opportunistic beamforming with multiple random beams. The base station transmits multiple pilot sequences using orthogonal beams, and each user feeds the channel gain of each beam back. Then, the base station selects the subset of users and beams for which the sum-rate is maximized. We aim to exploit spatial multiplexing gain in a controlled fashion, i.e., the number of beams used for data transmission is chosen depending on the available multiuser diversity in the system. Two schemes are proposed: dynamic Orthonormal Random Beamforming with Systematic Beam Selection (ORBF/SBS), for which the number of beams used for data transmission is dynamically changed from one fading block to another so that the sum-rate is maximized; and static ORBF/SBS, which selects a fixed number of beams for a given signal-to-noise ratio and user number. The static scheme achieves the sum-rate of the dynamic one up to a small gap with much reduced computational and feedback complexity. We derive an approximate expression for the sum-rate achieved by the dynamic scheme, and provide insight into the optimal data stream number in the static scheme by means of asymptotical results. Computer simulations are provided to evaluate the performance of the proposed schemes.
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paper_title: Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

paper_content:

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC.
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paper_title: Downlink Scheduling via Genetic Algorithms for Multiuser Single-Carrier and Multicarrier MIMO Systems With Dirty Paper Coding

paper_content:

Multiple-input-multiple-output (MIMO) systems are of interest for meeting the expected demand for higher data rates and lower delays in future wireless packet data systems. In such systems, it is optimal to simultaneously transmit to multiple users compared with a single user in a single-input-single-output system. In addition, multicarrier systems are of interest to combat frequency-selective fading that is experienced over the larger bandwidth that these future broadband systems will use. The use of dirty paper coding further complicates the matter, because the order in which the users are encoded will affect the rates that they can achieve. A well-designed cross-layer scheduling algorithm must take into account the multiple dimensions of this resource-allocation problem and other quality-of-service (QoS) parameters to fully exploit the communications channel. The scheduling problem is often expressed in terms of optimizing some utility function. Unfortunately, the search space for this optimization problem is extremely large, which prohibits an optimal exhaustive search. To this end, we investigate the use of genetic algorithms to reduce the complexity of the scheduling. This paper builds upon prior work that implements scheduling via genetic algorithms in the context of single-carrier systems using zero-forcing beamforming (ZFB). In this paper, we investigate how the genetic algorithm can be adapted to account for the effect of encoding order on the scheduling and how the scheduling can be extended to a multicarrier system. In particular, we investigate the maximum throughput and proportionally fair scheduling criteria. We demonstrate that the performance of the genetic algorithm is near optimal compared with an exhaustive search at a greatly reduced computational complexity. Furthermore, in the case of a multicarrier orthogonal frequency-division multiplexing (OFDM) system, an increase in capacity is shown relative to the single-carrier case.
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paper_title: System evaluation of optimal downlink beamforming with congestion control in wireless communication

paper_content:

We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: A User Selection Algorithm Using Angle between Subspaces for Downlink MU-MIMO Systems

paper_content:

One of major issues in the efficient use of radio resource for multiuser multiple-input/multiple-output (MU-MIMO) systems is the selection of users to achieve the maximum system throughput. The optimal user selection algorithm, which requires exhaustive search, is prohibitive due to its high computational complexity where Block diagonalization (BD) method is applied and known as a suboptimal precoding technique for downlink MU-MIMO systems, which intents to perfectly eliminate inter-user interference. In this paper, we propose efficient, iterative user selection algorithms with low complexity, where the product of eigenvalues of effective channels is utilized as a selection metric by applying the concept of principal angles between subspaces. And, we further examined the applicability of the proposed algorithms to limited feedback systems and proportional fair (PF) scheduling. Through computational complexity analysis, we show that the proposed algorithm has low complexity with a little loss in throughput. Simulation results validate that the proposed algorithm achieves almost the same system throughput by a capacity-based algorithm under high SNR regime with considerable reduction in complexity.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA

paper_content:

In this paper, we propose a low-complexity fair scheduling algorithm for wireless multiuser MIMO communication systems in which users are multiplexed via time-, frequency-, and space-division multiple access (SDMA) schemes. In such systems, the transmission quality considerably degrades if users with spatially correlated channels are to be served at the same time and frequency. The approach presented here works with both zero- and nonzero-forcing SDMA precoding schemes by deciding, for each time and frequency slot, which users are to be served in order to maximize the precoding performance. The number of users is not a fixed parameter of the algorithm (as often assumed for other schedulers present in the literature), but it is also adjusted in accordance to the channel conditions. While smaller SDMA groups allow us to transmit with a higher average power per user, larger groups lead to higher multiplexing gains. Our algorithm ProSched is based on a novel interpretation of the precoding process using orthogonal projections which permit us to estimate the precoding results of all user combinations of interest with significantly reduced complexity. In addition, the possible user combinations are efficiently treated with the help of a tree-based sorting algorithm. The ProSched takes advantage of a perfect channel state information, when available, or, alternatively, of second-order channel statistics. The individual-user quality-of-service requirements can be considered in the decision-making process. The effectiveness of the algorithm is illustrated with simulations based on the IlmProp channel model, which features realistic correlation in space, time, and frequency.
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paper_title: Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

paper_content:

In this paper, we tackle the problem of semidistributed user selection with distributed linear precoding for sum-rate maximization in multiuser multicell systems. A set of adjacent base stations (BSs) forms a cluster to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling, and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to nonintended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, namely, distributed zero forcing and distributed virtual signal-to-interference-plus-noise ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First, we investigate how the signal-to-noise ratio regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the BSs.
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paper_title: Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search

paper_content:

We consider a multi-user MIMO downlink system employing zero-forcing beamforming (ZFBF) as a spatial multiplexing strategy, and propose low-complexity user subset selection methods based on a clique (fully connected subgraph) search. The proposed algorithms, maximum weighted clique (MWC)-ZFBF and greedy weighted clique (GWC)-ZFBF, are shown to achieve the asymptotic sum-capacity of MIMO downlink channels as the number of users goes to infinity. Thus, clique search based ZFBF is an appealing strategy in MIMO downlink systems with a large number of users.
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paper_title: Convex approximation techniques for joint multiuser downlink beamforming and admission control

paper_content:

Multiuser downlink beamforming under quality of service (QoS) constraints has attracted considerable interest in years, because it is particularly appealing from a network operator's perspective (e.g., UMTS, 802.16e). When there are many co-channel users and/or the service constraints are stringent, the problem becomes infeasible and some form of admission control is necessary. We advocate a cross-layer approach to joint multiuser transmit beamforming and admission control, aiming to maximize the number of users that can be served at their desired QoS. It is shown that the core problem is NP-hard, yet amenable to convex approximation tools. Two computationally efficient convex approximation algorithms are proposed: one is based on semidefinite relaxation of an equivalent problem reformulation; the other takes a penalized second-order cone approach. Their performance is assessed in a range of experiments, using both simulated and measured channel data. In all experiments considered, the proposed algorithms work remarkably well in terms of the attained performance-complexity trade-off, consistently exhibiting close to optimal performance at an affordable computational complexity.
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paper_title: Iterative Precoder Design and User Scheduling for Block-Diagonalized Systems

paper_content:

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices.
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paper_title: Joint User Scheduling and Adaptive Intercell Interference Cancelation for MISO Downlink Cellular Systems

paper_content:

Recently, an adaptive intercell interference (ICI) mitigation technique has been proposed for downlink cellular systems as a means to increase throughput with low system complexity. However, in the prior work, the issue of intercell user scheduling has not been considered. In this paper, we study multiple-input-single-output (MISO) downlink cellular systems that jointly design adaptive ICI cancelation (ICIC) and intercell user scheduling assuming that partial channel state information (CSI) is shared among base stations (BSs). Since the optimal solution would require high complexity, we investigate a new low-complexity algorithm that selects the best users and their beamforming strategies in terms of maximizing the weighted sum rate (WSR). To this end, we first develop a simple threshold criterion for each user to decide the preferred beamforming strategy based on the derivation of the expected signal-to-interference-plus-noise ratio (SINR). Then, according to users' feedback about their decisions, a successive user and beamforming selection algorithm is performed at the BSs. From simulation results, we show that, combined with proportional fair scheduling, the proposed scheme provides excellent throughput performance with very low computational complexity and the amount of inter-BS CSI exchange. Furthermore, we discuss an extension of the proposed scheme to limited feedback systems and observe that our algorithm also provides similar advantages over conventional schemes with quantized feedback.
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paper_title: Efficient Sum Rate Maximization and Resource Allocation in Block-Diagonalized Space-Division Multiplexing

paper_content:

For space-division multiplexing (SDM) via block diagonalization on multiuser multiple-input multiple-output (MIMO) wireless downlink, it is shown that receive antenna selection (RAS) is necessary for maximizing the achievable sum rate. This is true even when all receive antennas are equipped with radio frequency (RF) chains and RAS reduces the upper bound on the broadcast sum capacity, and when the orthogonalized channels use optimal processing. Similarly, spatial-mode selection (SMS) is necessary for sum rate maximization when receive-weight matrices are used for spatial-mode allocation. RAS/SMS may release transmission resources that can fully be utilized via additional user scheduling to yield further sum rate gains. Optimal user selection for sum rate maximization is subsumed within an exhaustive RAS/SMS process for multiantenna terminals, and both selection processes become identical for single-antenna terminals. RAS/SMS thus helps reduce the performance gap from the optimal sum capacity even for small user pool sizes. A block antenna/mode selection approach is introduced to help overcome the drawbacks of existing algorithms. Since RAS/SMS involves antenna/mode ranking, a systematic method for resource allocation with sum rate loss minimization is inherently provided. This way, a streamlined process that combines user selection, RAS/SMS, and resource allocation is developed for sum rate maximization of block-diagonalized SDM.
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paper_title: Multimode Transmission for Multiuser MIMO Systems With Block Diagonalization

paper_content:

A low-complexity multimode transmission technique for downlink multiuser multiple-input-multiple-output (MIMO) systems with block diagonalization (BD) is proposed. The proposed technique adaptively configures the number of data streams for each user by adjusting its number of active receive antenna and switching between single-stream beamforming and multistream spatial multiplexing, as a means to exploit the multimode switching diversity. We consider a highly loaded system where there are a large number of users, hence a subset of users need to be selected. Joint user and antenna selection has been proposed as a multiuser multimode switching technique, where the optimal subset of receive antennas and users are chosen to maximize the sum throughput. The brute-force search, however, is prohibitively complicated. In this paper, two low-complexity near-optimal user/antenna selection algorithms are developed. The first algorithm aims at maximizing a capacity lower bound, derived in terms of the sum Frobenius norm of the channel, while the second algorithm greedily maximizes the sum capacity. We analytically evaluate the complexity of the proposed algorithms and show that it is orders of magnitude lower than that of the exhaustive search. Simulation results demonstrate that the proposed algorithms achieve up to 98% of the sum throughput of the exhaustive search, for most system configurations, while the complexity is substantially reduced.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

paper_content:

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: An efficient greedy scheduler for zero-forcing dirty-paper coding

paper_content:

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.
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paper_title: On the user selection for MIMO broadcast channels

paper_content:

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.
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paper_title: Downlink Multiuser MIMO Systems With Adaptive Feedback Rate

paper_content:

In this paper, an efficient channel feedback scheme for downlink multiuser multiple-input-multiple-output (MU-MIMO) systems is proposed. The objective of the new feedback design is to adaptively control the feedback rate of each user, depending on the individual channel status, while the overall sum feedback rate is kept the same. The proposed channel feedback scheme is composed of two stages: 1) the common channel feedback stage of all users and 2) the user-specific channel feedback stage of the selected users. We present a low-complexity algorithm to determine the individual feedback rates of users, which utilizes convex optimization, followed by iterative steepest descent direction searching. Numerical results show that zero-forcing beamforming (ZFBF), combined with the proposed channel feedback scheme, considerably outperforms ZFBF with conventional channel feedback schemes.
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paper_title: Low-Complexity Downlink User Selection for Massive MIMO Systems

paper_content:

In this paper, we propose a pair of low-complexity user selection schemes with zero-forcing precoding for multiuser massive multiple-input–multiple-output downlink systems, in which the base station is equipped with a large-scale antenna array. First, we derive approximations of the ergodic sum rates of the systems invoking the conventional random user selection (RUS) and the location-dependent user selection (LUS). Then, the optimal number of simultaneously served user equipments (UEs),i.e., $K^\ast$ , is investigated to maximize the sum rate approximations. Upon exploiting $K^\ast$ , we develop two user selection schemes, namely, $K^\ast$ -RUS and $K^\ast$ -LUS, where $K^\ast$ UEs are selected either randomly or based on their locations. Both the proposed schemes are independent of the instantaneous channel state information of small-scale fading, therefore enjoying the same extremely low computational complexity as that of the conventional RUS scheme. Moreover, both of our proposed schemes achieve significant sum rate improvement over the conventional RUS. In addition, it is worth noting that, like the conventional RUS, the $K^\ast$ -RUS achieves good fairness among UEs.
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paper_title: User Scheduling for Heterogeneous Multiuser MIMO Systems: A Subspace Viewpoint

paper_content:

In downlink multiuser multiple-input-multiple-output (MU-MIMO) systems, users are practically heterogeneous. However, many existing user-scheduling algorithms are designed with an implicit assumption that users are homogeneous. In this paper, we revisit the problem by exploring the characteristics of heterogeneous users from a subspace viewpoint. With an objective of minimizing interference nonorthogonality among users, three new angular-based user-scheduling criteria are proposed. While the first criterion is heuristically determined by identifying the incapability of the largest principal angle to characterize subspace correlation and, hence, interference nonorthogonality between users, the second and third criteria are derived by using the sum rate capacity bounds with block diagonalization and the change in capacity by adding a new user into an existing user subset, respectively. Aiming to capture fairness among heterogeneous users while maintaining multiuser diversity gain, two new hybrid user-scheduling algorithms, whose computational complexities are only linearly proportional to the number of users, are proposed. We show by simulations the effectiveness of our proposed user-scheduling criteria and algorithms with respect to those commonly used in a homogeneous environment.
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paper_title: Adaptive scheduling for MIMO wireless networks: cross-layer approach and application to HSDPA

paper_content:

In this paper, we consider the scheduling problem in multiple-input multiple-output (MIMO) wireless networks. The main important characteristic of an optimal scheduler is to maximize throughput while servicing users in a fair manner. Herein, we formulate MIMO scheduling as a generalized assignment problem (GAP) and propose a general solution for the GAP, namely, a cross-layer MIMO scheduler (CMS), which uses a novel adaptive proportional fairness (APF) mapping approach in conjunction with a new fast transmit antenna selection (FTAS) technique, to determine the set of users to transmit to and the antenna over which the data associated to each user should be transmitted. The proposed scheduler is applied for packet transmission in high-speed downlink packet access (HSDPA), taking advantage of the use of adaptive modulation and coding while coping with the constraints on the maximum number of simultaneous codes a user equipment can support, the limited uplink signalling, and the absence of fast power control. Numerical results show that the proposed CMS provides up to 70% increase in total throughput compared to other scheduling schemes
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paper_title: Maximum product of effective channel gains: an innovative user selection algorithm for downlink multi-user multiple input and multiple output

paper_content:

Recently, zero-forcing beamforming has been widely used for multiple-input and multiple-output broadcast channels, because it could provide suboptimal capacity with low complexity. To increase the sum data rate, a good user selection algorithm is attractive. In this paper, a new user selection algorithm named maximum product of effective channel gains is presented. The proposed algorithm is described mathematically, and the lower bound of the sum capacity is demonstrated to be proportional to the product of effective channel gains. Our simulation results show that maximum product of effective channel gains can achieve higher sum rate compared with the classical algorithm, semi-orthogonal user selection, with the same complexity order, especially when the signal-to-noise ratio is high; in addition, the complexity of the proposed algorithm is superior to minimum of the Frobenius norm of the pseudo-inverse algorithm. Meanwhile, the number of users that can be served simultaneously is equal to the number of transmission antennas, which is the maximum performance that can be achieved.Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: Capacity Maximization for Zero-Forcing MIMO-OFDMA Downlink Systems with Multiuser Diversity

paper_content:

This paper considers the optimal resource allocation for a multiuser MIMO-OFDMA downlink system using zero-forcing SDMA, with the objective of maximizing the system capacity. We provide the general mathematical formulation of the capacity maximization problem whose resource allocation includes user selection, power allocation and receive signal subspace selection. While the optimal solution of this problem is difficult to obtain, we consider two special cases: user selection based only and antenna selection based only optimization, and develop the optimal solution by reformulating the combinatorial optimization problem into a convex problem. Our proposed algorithms for these special cases can be extended to develop a suboptimal algorithm for the original general optimization problem which allows subspace selection. Moreover, we develop reduced-complexity algorithms for these problems which incur negligible capacity loss. Numerical results and analysis are provided to evaluate the system capacity and to study the effect of the number of users and the receive antennas per user on the performance. Comparisons on the capacity achieved by user selection only, antenna selection only and suboptimal subspace selection are discussed
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paper_title: Transmit Selection Diversity for Unitary Precoded Multiuser Spatial Multiplexing Systems With Linear Receivers

paper_content:

Multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference. In such a system, the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain. This paper proposes two precoding methods that use extra transmit antennas, beyond the minimum required, to provide additional degrees of diversity. The approach taken is to solve for a unitary transmit precoder, under a zero interuser interference constraint, that minimizes an upper bound on the symbol error rate (SER) for each user. Solutions where all transmit antennas are employed, as well as subsets of antennas (to reduce analog components), are described. Numerical results confirm a dramatic improvement in terms of SER and mutual information over single-user multiple-input multiple-output (MIMO) methods and static allocation methods. For example, the proposed techniques achieve a signal-to-noise ratio (SNR) improvement of 6-10 dB at an uncoded SER of 10-3, with only one extra transmit antenna
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paper_title: Leakage-based user scheduling in MU-MIMO broadcast channel

paper_content:

This paper investigates user scheduling in multi-user MIMO broadcast channel. We propose a leakagebased user scheduling scheme, in which a user’s leakage power to other users is an important factor to determine whether the user should be selected. The accuracy of closed-form solution of SLNR (signal to leakage plus noise ratio) makes the proposed scheme outperform the traditional scheduling method based on SINR (signal to interference plus noise ratio). The proposed algorithms can work in case of perfect or limited feedback of CSI (channel state information) at transmitter, and the advantage is verified with numerical results. A tradeoff relation among feedback bits number, active user number and transmit/receive antennas number is analyzed, which serves as a system design guideline.
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paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

paper_content:

This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
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paper_title: Resource Allocation and Link Adaptation in LTE and LTE Advanced: A Tutorial

paper_content:

Resource allocation and link adaptation in Long-Term Evolution (LTE) and LTE Advanced are discussed with focus on the location and formatting of the pertinent reference and control signals, as well as the decisions they enable. In particular, after reviewing the units for resource allocation and the time-frequency resource grid, the enabled resource-allocation modes and their purposes are reviewed. A detailed description of the way the resource allocations are encoded under these different modes is also given. Similarly, the various methods of link adaptation, including power control and rate control, both through the use of adaptive modulation and coding and hybrid automatic repeat request, are reviewed. The control signaling encoding for link adaptation is provided in detail, as is the encoding of channel state feedback for the purposes of link adaptation and resource allocation.
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paper_title: Downlink Packet Scheduling in LTE Cellular Networks: Key Design Issues and a Survey

paper_content:

Future generation cellular networks are expected to provide ubiquitous broadband access to a continuously growing number of mobile users. In this context, LTE systems represent an important milestone towards the so called 4G cellular networks. A key feature of LTE is the adoption of advanced Radio Resource Management procedures in order to increase the system performance up to the Shannon limit. Packet scheduling mechanisms, in particular, play a fundamental role, because they are responsible for choosing, with fine time and frequency resolutions, how to distribute radio resources among different stations, taking into account channel condition and QoS requirements. This goal should be accomplished by providing, at the same time, an optimal trade-off between spectral efficiency and fairness. In this context, this paper provides an overview on the key issues that arise in the design of a resource allocation algorithm for LTE networks. It is intended for a wide range of readers as it covers the topic from basics to advanced aspects. The downlink channel under frequency division duplex configuration is considered as object of our study, but most of the considerations are valid for other configurations as well. Moreover, a survey on the most recent techniques is reported, including a classification of the different approaches presented in literature. Performance comparisons of the most well-known schemes, with particular focus on QoS provisioning capabilities, are also provided for complementing the described concepts. Thus, this survey would be useful for readers interested in learning the basic concepts before going into the details of a particular scheduling strategy, as well as for researchers aiming at deepening more specific aspects.
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paper_title: Low RF-Complexity Technologies for 5G Millimeter-Wave MIMO Systems with Large Antenna Arrays

paper_content:

Millimeter-wave (mmWave) MIMO with large antenna array has attracted considerable interests from academic and industry, as it can simultaneously provide wider bandwidth and higher spectrum efficiency. However, with hundreds of antennas employed at mmWave frequencies, the number of radio frequency (RF) chains required by mmWave MIMO is also huge, leading to unaffordable hardware cost and energy consumption in practice. In this paper, we review low RFcomplexity technologies to solve this bottleneck in mmWave MIMO systems.We first describe the evolution of low RF-complexity technologies from cellular frequencies to mmWave frequencies. Then, we discuss two attractive low RF-complexity technologies for mmWave MIMO systems in detail, i.e., hybrid precoding and beamspace MIMO, including their fundamental principles, application advantages, and design challenges. We compare the performance of these two low RF-complexity technologies to draw some insights about how they should be employed in practical mmWave MIMO systems. Finally, we conclude this paper by highlighting the potential opportunities in this emerging research direction.
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paper_title: Beamforming for Millimeter Wave Communications: An Inclusive Survey

paper_content:

The remarkable growth of wireless data traffic in recent times has driven the need to explore suitable regions in the radio spectrum to meet the projected requirements. In pursuance of this, millimeter wave communications have received considerable attention in the research fraternity. Due to the high path and penetration losses at millimeter wavelengths, antenna beamforming assumes a pivotal role in establishing and maintaining a robust communication link. Beamforming for millimeter wave communications poses a multitude of diverse challenges due to the large channel bandwidth, unique channel characteristics, and hardware constraints. In this paper, we track the evolution and advancements in antenna beamforming for millimeter wave communications in the context of the distinct requirements for indoor and outdoor communication scenarios. We expand the scope of discussion by including the developments in radio frequency system design and implementation for millimeter wave beamforming. We explore the suitability of millimeter wave beamforming methods, both, existing and proposed till midyear 2015, and identify the exciting new prospects unfolding in this domain.
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paper_title: Efficient MAC protocol for JT CoMP in small cells

paper_content:

In this paper, we investigate an efficient MAC protocol for interference coordination in small cells embedded in a macro-cell mobile network. We perform joint transmission (JT)-coordinated multi-point (CoMP), where cells in the cluster include adjacent macro-cells as suggested by the small-cell terminal. Most gains compared to uncoordinated transmission come from selecting the right users in these macro-cells. For minimizing the feedback overhead, we propose successive channel state information (CSI) requests. Thereby we replace users in the set until all of them experience consistently enhanced performance when using JT-CoMP. Gains can be further increased by MIMO mode switching in each cell and frequency-selective scheduling. We tested our algorithms over coherently measured multi-cell channels in the LTE-Advanced testbed in Berlin where small cells were embedded at several places. Using these algorithms, performance becomes comparable to a popular bound assuming no more intra-cluster interference while feedback overhead and complexity are substantially reduced.
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paper_title: MIMO Downlink Scheduling with Non-Perfect Channel State Knowledge

paper_content:

Downlink scheduling schemes are well-known and widely investigated under the assumption that the channel state is perfectly known to the scheduler. In the multiuser MIMO (broadcast) case, downlink scheduling in the presence of non-perfect channel state information (CSI) is only scantly treated. In this paper we provide a general framework that addresses the problem systematically. Also, we illuminate the key role played by the channel state prediction error: our scheme treats in a fundamentally different way users with small channel prediction error ("predictable" users) and users with large channel prediction error ("non-predictable" users), and can be interpreted as a near-optimal opportunistic time-sharing strategy between MIMO downlink beamforming to predictable users and space-time coding to non-predictable users. Our results, based on a realistic MIMO channel model used in 3GPP standardization, show that the proposed algorithms can significantly outperform a conventional "mismatched" scheduling scheme that treats the available CSI as if it was perfect.
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paper_title: Learning-Based Adaptive Transmission for Limited Feedback Multiuser MIMO-OFDM

paper_content:

Performing link adaptation in a multiantenna and multiuser system is challenging because of the coupling between precoding, user selection, spatial mode selection and use of limited feedback about the channel. The problem is exacerbated by the difficulty of selecting the proper modulation and coding scheme when using orthogonal frequency division multiplexing (OFDM). This paper presents a data-driven approach to link adaptation for multiuser multiple input mulitple output (MIMO) OFDM systems. A machine learning classifier is used to select the modulation and coding scheme, taking as input the SNR values in the different subcarriers and spatial streams. A new approximation is developed to estimate the unknown interuser interference due to the use of limited feedback. This approximation allows to obtain SNR information at the transmitter with a minimum communication overhead. A greedy algorithm is used to perform spatial mode and user selection with affordable complexity, without resorting to an exhaustive search. The proposed adaptation is studied in the context of the IEEE 802.11ac standard, and is shown to schedule users and adjust the transmission parameters to the channel conditions as well as to the rate of the feedback channel.
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paper_title: User scheduling for massive MIMO OFDMA systems with hybrid analog-digital beamforming

paper_content:

This paper proposes a new user scheduling and sub-carrier allocation algorithm for multiuser downlink massive multiple input multiple output (MIMO) orthogonal frequency division multiple access (OFDMA) systems with hybrid analogdigital beamforming (HB). We assume that the transmitter having N antennas is serving K i decentralized single antenna receivers by sub-carrier i. The scheduling algorithm leverages the solutions of the digital beamforming (DB) result and is designed to maximize the total sum rate of all sub-carriers under per carrier power constraint. For this system and problem setup, the proposed algorithm is explained as follows: First, we express the HB matrix of sub-carrier i as a product of AB i , where the high dimensional matrix A ∈ CN×Na is common to all subcarriers whereas, B i ∈ CNa×Ki is a low dimensional matrix which is designed for sub-carrier i, and Na is the number of RF chains satisfying N ≥ Na ≥ K i . Second, we compute A as the first Na eigenvectors of the left singular value decomposition of the combined DB precoder matrices of sub-carriers having the highest sum rate. Finally, for fixed A, we compute Bi and its corresponding users such that the total sum rate of all sub-carriers is maximized. The performance of the proposed scheduling is studied analytically. Furthermore, the superiority of the proposed algorithm over that of the existing one is quantified analytically and demonstrated by computer simulations.
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paper_title: High SNR Analysis for MIMO Broadcast Channels: Dirty Paper Coding Versus Linear Precoding

paper_content:

In this correspondence, we compare the achievable throughput for the optimal strategy of dirty paper coding (DPC) to that achieved with suboptimal and lower complexity linear precoding techniques (zero-forcing and block diagonalization). Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR. Furthermore, the difference is not affected by asymmetric channel behavior when each user has a different average SNR. Weighted sum rate maximization is also considered. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate.
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paper_title: Enhanced multiuser random beamforming: dealing with the not so large number of users case

paper_content:

We consider the downlink of a wireless system with an M-antenna base station and K single-antenna users. A limited feedback-based scheduling and precoding scenario is considered that builds on the multiuser random beamforming (RBF). Such a scheme was shown to yield the same capacity scaling, in terms of multiplexing and multiuser diversity gain, as the optimal full CSIT-based (channel state information at transmitter) precoding scheme, in the large number of users K regime. Unfortunately, for more practically relevant (low to moderate) K values, RBF yields degraded performance. In this work, we investigate solutions to this problem. We introduce a two-stage framework that decouples the scheduling and beamforming problems. In our scenario, RBF is exploited to identify good, spatially separable, users in a first stage. In the second stage, the initial random beams are refined based on the available feedback to offer improved performance toward the selected users. Specifically, we propose beam power control techniques that do not change the direction of the second-stage beams, offering feedback reduction and performance tradeoffs. The common feature of these schemes is to restore robustness of RBF with respect to sparse network settings (low K), at the cost of moderate complexity increase.
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paper_title: Networked MIMO with clustered linear precoding

paper_content:

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination to enhance the sum rate and limited inter-cluster coordination to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.
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paper_title: Adaptive radio resource allocation for downlink OFDMA/SDMA systems with multimedia traffic

paper_content:

This paper proposes an adaptive radio resource allocation (ARRA) algorithm for downlink OFDMA/SDMA systems with multimedia traffic. Considering multiple service classes and diverse QoS requirements of multimedia traffic, the ARRA algorithm is designed with the goal to maximize spectrum efficiency and to fulfill quality of service (QoS) requirements. It is composed of two parts, a dynamic priority adjustment (DPA) scheme and a priority-based greedy (PBG) scheme. The DPA adopts a type of time-to-expiration to indicate the degree of user's urgency, and dynamically gives high priorities to urgent users. The PBG allocates the radio resource iteratively, based on a cost value, to maximize the system throughput while allocating enough resource to high-priority users. Simulation results show that the ARRA algorithm outperforms conventional algorithms in terms of system throughput and satisfaction extent of QoS requirements; it can sustain users' QoS requirements up till a traffic load of 0.8, while the conventional algorithms cannot guarantee QoS requirements after a traffic load of 0.3.
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paper_title: Practical algorithms for a family of waterfilling solutions

paper_content:

Many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure; the classical example is the capacity-achieving solution for a frequency-selective channel. For simple waterfilling solutions with a single waterlevel and a single constraint (typically, a power constraint), some algorithms have been proposed in the literature to compute the solutions numerically. However, some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints. For such cases, it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure. In addition, a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing. The purpose of this paper is twofold. On the one hand, it overviews the waterfilling results existing in the literature from a unified viewpoint. On the other hand, it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice; to be more precise, it provides a practical algorithm to evaluate numerically a general waterfilling solution, which includes the currently existing waterfilling solutions and others that may possibly appear in future problems.
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paper_title: Solution of the multiuser downlink beamforming problem with individual SINR constraints

paper_content:

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.
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paper_title: Multiuser MIMO Scheduling for LTE-A Downlink Cellular Networks

paper_content:

In this paper, we investigate multiuser MIMO scheduling in LTE downlink cellular networks. We formulate the downlink LTE-A MIMO scheduling as a weighted sum rate maximization problem by allocating the RBs to users or user pairs subject to some constraints in LTE-A. We develop a low-complexity MU-MIMO scheduling and resource allocation algorithm and propose an adaptive switching approach between SU-MIMO and MU-MIMO to improve network performance. System-level simulation results demonstrate significantly performance improvement of the proposed MU-MIMO scheduling algorithm and the adaptive switching algorithm.
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paper_title: Optimizing User Selection Schemes in Vector Broadcast Channels

paper_content:

In this paper, we focus on the ergodic downlink sum-rate performance of a system consisting of a set of heterogeneous users. We study three user selection schemes to group near-orthogonal users for simultaneous transmission. The first scheme is a random selection policy that achieves fairness, but does not exploit multi-user diversity. The second scheme is a greedy selection policy that fully exploits multi-user diversity, but does not achieve fairness, and the third scheme achieves fairness while partially exploiting multi-user diversity. We also consider two beamforming methods for data transmission, namely, maximum-ratio transmission and zero-forcing beamforming. In all scheduling schemes studied in the paper, there is a key parameter that controls the degrees of orthogonality of channel directions between co-scheduled users. We focus on optimally setting this parameter for each scheduling scheme such that the ergodic downlink sum-rate is maximized. To this end, we derive analytical expressions for the ergodic downlink sum-rate considering each scheduling scheme. Numerical results are also presented to provide further insights.
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paper_title: Fast Algorithms and Performance Bounds for Sum Rate Maximization in Wireless Networks

paper_content:

Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying the solutions to two related problems, sum rate maximization using an SIR approximation and max-min weighted SIR optimization. We also show that these two problems can be solved very efficiently, using much faster algorithms than the existing ones in the literature. Furthermore, using a new parameterization of the sum rate maximization problem, we obtain a characterization of the power controlled rate region and its convexity property in various asymptotic regimes. Engineering implications are discussed for IEEE 802.11 networks.
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paper_title: Scheduling Methods with MIMO Interference Alignment for Mutually Interfering Broadcast Channels

paper_content:

In this paper, we investigate an interference alignment (IA) technique introduced by Cadambe and Jafar in mutually interfering broadcast channels (IFBCs). First, we study the spatial multiplexing gain (SMG) for the 3-cell IFBC where all base stations and mobile users are equipped with multiple antennas. To achieve the derived optimal SMG, we extend the IA algorithm designed for K-user multi-input multi-output (MIMO) interference channels (IFCs) to the IFBC. In this paper, we present the IA scheme in conjunction with user selection which outperforms the time division multiple access (TDMA) technique in the IFBC environment. The optimal scheduling method capitalizes on multiuser diversity to achieve a significant fraction of sum capacity by using an exhaustive search algorithm. Since the computational complexity of the optimal scheduling method is prohibitive, a reduced complexity suboptimal scheduling method is proposed based on a coordinate ascent approach. Simulation results confirm that the reduced complexity scheduling algorithm achieves the sum rate close to the optimal algorithm with much reduced complexity.
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paper_title: Academic Press Library in Signal Processing : Communications and Radar Signal Processing

paper_content:

This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: Quickly grasp a new area of research Understand the underlying principles of a topic and its applicationAscertain how a topic relates to other areas and learn of the research issues yet to be resolvedQuick tutorial reviews of important and emerging topics of research in communications and radar engineeringPresents core principles in signal processing theory and shows their applicationReference content on core principles, technologies, algorithms and applications Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
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paper_title: Round-Robin Scheduling for Orthogonal Beamforming with Limited Feedback

paper_content:

We propose a round-robin scheduling algorithm for orthogonal beamforming with a strict signal to interference-plus-noise ratio (SINR) constraint and limited feedback. The presented algorithm aims at scheduling the users at identical slots over different blocks, in order to reduce the necessary scheduling overhead, and to minimize the maximum delay between serving the same user. Thus, the presented algorithm is especially suited for real-time multimedia traffic. The algorithm allocates the users using orthogonal beamforming based on the quantized feedback provided by the users. The quantized feedback consists of the estimated power that is necessary to fulfill a predefined SINR constraint. Further, we propose an algorithm to design codebooks to quantize the estimated power. Using the feedback, the base station redistributes power from users with spare power to users that lack power so that they fulfill their SINR constraints. The performance of the algorithm is demonstrated through simulations.
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paper_title: Packet Scheduling and Fairness for Multiuser MIMO Systems

paper_content:

This paper investigates the network resource allocation in multiuser downlink wireless systems where the base station and the mobile stations are equipped with multiple antennas to provide fair and efficient transmission services to the mobile users. We focus on packet scheduling, given that it has a significant impact on the overall performance of a multiple-input-multiple-output (MIMO) system. Most previous schedulers designed at the packet level do not take into account the traffic characteristics (different packet lengths and the arrival process parameters); consequently, they fall short of simultaneously providing fairness and a low average packet transmission delay. We are making use of a flexible packet transmission algorithm at the medium access control (MAC) layer to develop and propose a novel scheduler, which is referred to as MIMO packet-based proportional fairness (MP-PF). The new scheduler is designed with the goal of providing high performance in terms of a low average packet transmission delay and time and service fairness among the users based on the concept of proportional fairness. The scheduler also conserves work and takes into consideration the packet length, the user queue length, the user transmission rate (related to its channel quality), and the service guarantees for heterogeneous users. The well-known ideal service fair scheduler called max-min can also significantly be improved using our framework by taking into consideration the traffic characteristics. We also provide an analysis for the fairness of the new scheduler in terms of time and service allocation, which is the key contribution of this paper. Simulations that consider the traffic characteristics and the mobility of users show the relatively low average packet transmission delay and demonstrate the time and service fairness capabilities of MP-PF, compared with other well-known MIMO schedulers.
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paper_title: Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels

paper_content:

In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total system-wide feedback load, is it preferable to get low-rate/coarse channel feedback from a large number of receivers or high-rate/high-quality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multi-user diversity to be exploited, while high-rate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining high-quality feedback, and that obtaining near-perfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users.
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paper_title: Antenna Combining for the MIMO Downlink Channel

paper_content:

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.
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paper_title: ⋄ Convex Optimization,

paper_content:

Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.
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paper_title: Weighted max-min fair beamforming, power control, and scheduling for a MISO downlink

paper_content:

In this paper, we consider the joint beamforming, power control and scheduling problem in a multiple-input single- output (MISO) downlink for maximizing the minimum weighted rate among all users. We solve this problem by formulating it as a convex optimization problem whose function evaluations require maximization of a difference of convex functions (D.C. Programming). We also propose a simpler heuristic that finds the best policy under restricted set of power vectors. We then compare the performance of these policies against the dirty paper coding (DPC) policy to quantify the performance gap between an optimal point-to-point coding approach and an optimal joint encoding/decoding approach.
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paper_title: Efficient Metrics for Scheduling in MIMO Broadcast Channels with Limited Feedback

paper_content:

We consider a downlink channel where a base station equipped with M transmit antennas communicates with K ≥ M single-antenna receivers and has partial channel knowledge obtained via a limited rate feedback channel. We propose scalar feedback metrics that provide an estimate of the received signal-to-noise plus interference ratio (SINR), which are combined with efficient user selection algorithms and zero-forcing beamforming. The asymptotic system sum rate for large K is analyzed and numerical results are provided, showing the performance of each metric in different scenarios.
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paper_title: Stability and Delay of Zero-Forcing SDMA With Limited Feedback

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This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor M >; 1. For given M → 1, the number of feedback bits per mobile is proved to be O(-log2(1-1/M)) .
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paper_title: Multi-mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

paper_content:

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.
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paper_title: Joint Antenna Beamforming, Multiuser Scheduling, and Power Allocation for Hierarchical Cellular Systems

paper_content:

Cognitive radio (CR) is concretely embodied in hierarchical cellular systems by deploying an underlying microcellular system to reuse the underutilized spectrum of a macrocellular system. One of the key challenges to the success of hierarchical cellular systems is to manage the intercell interference between the macrocell and the microcell and to maximize the spectrum efficiency. In this paper, antenna beamforming, power allocation, and multiuser scheduling are jointly designed to opportunistically utilize the macrocell's uplink spectrum in serving multiple secondary microcellular users concurrently. The joint design of antenna beamforming, power allocation, and scheduling with the objective of maximizing the sum rate is indeed a mixed-integer nonlinear programming NP-hard problem. The proposed simpler iterative subgradient projection and semidefinite programming approach can obtain better performance than the conventional zero-forcing beamforming. Furthermore, unlike the optimal singular value decomposition (SVD) beamforming that requires all users to have channel knowledge at the receiver for cooperation, the proposed joint design methodology requires no channel knowledge at the receiver and can outperform the SVD beamforming without user scheduling. When considering both implementation complexity and performance enhancement issues, the proposed joint power allocation, multiuser scheduling, and antenna beamforming technique can help provide important insights into the design of interference management techniques for hierarchical CR systems.
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paper_title: An Effective Inter-Cell Interference Coordination Scheme for Downlink CoMP in LTE-A Systems

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Coordinated multi-point (CoMP) has been adopted in 3GPP LTE-Advanced to improve the coverage of high data rates. Downlink CoMP is mainly categorized into joint transmission (JT) and coordinated beamforming (CB). Previous research shows that JT does not benefit cell average throughput. Moreover, traditional CB algorithms are based on iterative evaluation, resulting in very high computational complexity. To address these issues, in this paper, we propose an effective inter-cell interference coordination scheme for downlink CoMP, which includes two phases. Firstly, in order to improve the performance of all user equipments (UEs), cell edge UEs employ JT, while CB is adopted by both cell edge and cell center UEs. Secondly, we design linear CB precoders by maximizing a signal to leakage and noise ratio (SLNR) metric, so as to reduce processing complexity. System-level simulations validate that, in contrast to non-CoMP, the proposed scheme brings a cell average spectral efficiency (SE) gain up to 21.50% and a cell edge SE gain up to 119.2%.
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paper_title: System evaluation of optimal downlink beamforming with congestion control in wireless communication

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We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.
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paper_title: An Efficient Transmission Strategy for the Multicarrier Multiuser MIMO Downlink

paper_content:

A new transmission strategy that consists of a spatial scheduling algorithm and two precoding algorithms is developed for multicarrier multiuser (MU) multiple-input-multiple-output (MIMO) systems. The scheduling algorithm, which is called efficient multicarrier ProSched (EMC-ProSched), adopts a novel and effective scheduling metric for each user and can efficiently search for a suitable group of users to be served at the same time on the same frequency. Two precoding techniques are then designed to handle different antenna configurations. For the case where the number of transmit antennas at the base station (BS) is not smaller than the total number of receive antennas at the user terminals (UTs), the linear-precoding-based geometric mean decomposition (LP-GMD) algorithm is proposed. It suppresses the MU interference (MUI) and enables an effective implementation of the same modulation and coding scheme (MCS) on all spatial streams of each user. Consequently, smaller signaling overhead is required compared with the case where a different MCS is applied on each spatial stream. When the total number of receive antennas at the UTs exceeds the number of transmit antennas at the BS, we propose the low-complexity coordinated beamforming (LoCCoBF) algorithm to accomplish the goal of the MUI mitigation and to achieve a high capacity. A system-level simulator with a link-to-system interface is further developed under the framework of the IEEE 802.11ac standard to evaluate the performance of the proposed transmission strategy. The simulation results indicate that a promising performance can be achieved by employing the proposed transmission strategy.
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paper_title: Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

paper_content:

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.
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paper_title: Convex approximation techniques for joint multiuser downlink beamforming and admission control

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Multiuser downlink beamforming under quality of service (QoS) constraints has attracted considerable interest in years, because it is particularly appealing from a network operator's perspective (e.g., UMTS, 802.16e). When there are many co-channel users and/or the service constraints are stringent, the problem becomes infeasible and some form of admission control is necessary. We advocate a cross-layer approach to joint multiuser transmit beamforming and admission control, aiming to maximize the number of users that can be served at their desired QoS. It is shown that the core problem is NP-hard, yet amenable to convex approximation tools. Two computationally efficient convex approximation algorithms are proposed: one is based on semidefinite relaxation of an equivalent problem reformulation; the other takes a penalized second-order cone approach. Their performance is assessed in a range of experiments, using both simulated and measured channel data. In all experiments considered, the proposed algorithms work remarkably well in terms of the attained performance-complexity trade-off, consistently exhibiting close to optimal performance at an affordable computational complexity.
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paper_title: Coordinated beamforming with limited feedback in the MIMO broadcast channel

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In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.
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paper_title: Network MIMO with Linear Zero-Forcing Beamforming: Large System Analysis, Impact of Channel Estimation and Reduced-Complexity Scheduling

paper_content:

We consider the downlink of a multicell system with multiantenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general “fairness” requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Intercluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio. In particular, for the per-base station power constraint, we find new results in random matrix theory, yielding the squared Frobenius norm of submatrices of the Moore-Penrose pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the cooperation cluster, user distribution, and path-loss coefficients. The analysis is extended to the case of nonideal Channel State Information at the Transmitters obtained through explicit downlink channel training and uplink feedback. Specifically, our results illuminate the trade-off between the benefit of a larger number of cooperating antennas and the cost of estimating higher-dimensional channel vectors. Furthermore, our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large-system results, depending on the desired fairness criterion. The proposed scheme performs close to the optimal (finite-dimensional) opportunistic user selection while requiring significantly less channel state feedback, since only a small fraction of preselected users must feed back their channel state information.
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paper_title: Coordinated user scheduling in the multi-cell MIMO downlink

paper_content:

We propose a novel, coordinated user scheduling (CUS) algorithm for inter-cell interference (ICI) mitigation in the downlink of a multi-cell multi-user MIMO system. In the proposed algorithm, ICI mitigation is performed through the exchange of necessary channel state information (CSI) among the base stations, and the revision of the scheduling decisions and beamformer designs at each base station. Furthermore, ICI mitigation is performed only for the cell-edge users so that the amount of inter-base station signaling overhead is minimized. Our simulation results demonstrate that the proposed coordination scheduling algorithm significantly improves the cell-edge users' throughput compared to conventional systems with only a negligible amount of CSI sharing among the base stations and a relatively small throughput loss for the cell-interior users.
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paper_title: New Beamforming Techniques Based on Virtual SINR Maximization for Coordinated Multi-Cell Transmission

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In this paper, we propose new beamforming techniques based on virtual signal-to-interference-plus-noise ratio (VSINR) for weighted sum-rate (WSR) maximization in coordinated multi-cell transmission. In earlier works based on the VSINR maximization, the parameters which control the interference power and the noise variance were set to fixed values regardless of channel realizations and the signal-to-noise ratio level. In order to obtain an improved WSR performance, we propose a method which adaptively adjusts the parameters after establishing a connection between the WSR and VSINR. Our proposed method can be applied to the cases of various coordination levels among base stations. To address practical implementation issues, a decentralized implementation of the beamforming techniques is also proposed based on local channel state information. Numerical results confirm that the proposed centralized schemes provide near-optimal WSR performance and the proposed decentralized methods show a negligible performance loss compared to the centralized algorithms with reduced system complexity.
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paper_title: Cooperative Multicell Precoding: Rate Region Characterization and Distributed Strategies With Instantaneous and Statistical CSI

paper_content:

Base station cooperation is an attractive way of increasing the spectral efficiency in multiantenna communication. By serving each terminal through several base stations in a given area, intercell interference can be coordinated and higher performance achieved, especially for terminals at cell edges. Most previous work in the area has assumed that base stations have common knowledge of both data dedicated to all terminals and full or partial channel state information (CSI) of all links. Herein, we analyze the case of distributed cooperation where each base station has only local CSI, either instantaneous or statistical. In the case of instantaneous CSI, the beamforming vectors that can attain the outer boundary of the achievable rate region are characterized for an arbitrary number of multiantenna transmitters and single-antenna receivers. This characterization only requires local CSI and justifies distributed precoding design based on a novel virtual signal-to-interference noise ratio (SINR) framework, which can handle an arbitrary SNR and achieves the optimal multiplexing gain. The local power allocation between terminals is solved heuristically. Conceptually, analogous results for the achievable rate region characterization and precoding design are derived in the case of local statistical CSI. The benefits of distributed cooperative transmission are illustrated numerically, and it is shown that most of the performance with centralized cooperation can be obtained using only local CSI.
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paper_title: Adaptive Modulation in PU2RC Systems with Finite Rate Feedback

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This paper addresses a per user unitary precoding and rate control (PU 2 RC) system with adaptive multi-level quadrature amplitude modulation (QAM) modulation, where both the PU 2 RC operation and adaptive modulation are based on finite rate feedback. The system supports two transmission modes (single user transmit beamforming and multiuser transmission with orthogonal beamforming), and switches between the two modes to maximize the average throughput. We first study single user transmit beamforming, and derive closed-form expressions for the average throughput and bit-error rate (BER) with outdated channel information. Then, multiuser transmission with orthogonal beamforming is investigated. We analyze the throughput and BER performance without feedback delay in the normal signal noise ratio (SNR) regime, and the performance with feedback delay in the interference-limited regime. Simulation results demonstrate the effect of time delay, and the preferred regions of the single user transmission mode and multiuser transmission mode.
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paper_title: Dynamic Multi-User MIMO scheduling with limited feedback in LTE-Advanced

paper_content:

Multi-User MIMO (MU-MIMO) systems have gained numerous attention from researchers in the past decade due to its substantial gains in the system throughput. Most of the initial research assumes the knowledge of perfect channel state information at the transmitter (CSIT). However, this is considered impractical and research over the past few years has been focused on receivers feeding back limited information to the transmitter. In this work, we consider a transparent MU-MIMO system model with limited feedback. We propose a general framework for dynamic MU-MIMO scheduling with the capability to switch between Single-User MIMO mode and (Multi-Rank) Multi-User MIMO mode without users feeding back additional multi-user information. Specifically, this is done by each user carefully estimating its CQI under the hypothesis of Multi-Rank MultiUser MIMO transmission and taking advantage of the codebook structure. We consider the sum rate of the system assuming each user uses ML and LMMSE receiver and show that our proposed scheduler, with significantly reduced feedback load, outperforms the best-companion user pairing.
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paper_title: Low Complexity Scheduling and Beamforming for Multiuser MIMO Systems

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The problem of joint scheduling and beam-forming for a multiple antenna broadcast channel with partial channel state information at the transmitter (CSIT) is considered. We show how long-term statistical channel knowledge can be efficiently combined with instantaneous low-rate feedback for user selection and linear beamforming. A low complexity algorithm based on an estimate (bound) of the multiuser interference is proposed. Our scheme is shown to exhibit significant throughput gain over opportunistic techniques, approaching the sum rate of full CSIT for small angle spreads.
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paper_title: Joint User Scheduling and Adaptive Intercell Interference Cancelation for MISO Downlink Cellular Systems

paper_content:

Recently, an adaptive intercell interference (ICI) mitigation technique has been proposed for downlink cellular systems as a means to increase throughput with low system complexity. However, in the prior work, the issue of intercell user scheduling has not been considered. In this paper, we study multiple-input-single-output (MISO) downlink cellular systems that jointly design adaptive ICI cancelation (ICIC) and intercell user scheduling assuming that partial channel state information (CSI) is shared among base stations (BSs). Since the optimal solution would require high complexity, we investigate a new low-complexity algorithm that selects the best users and their beamforming strategies in terms of maximizing the weighted sum rate (WSR). To this end, we first develop a simple threshold criterion for each user to decide the preferred beamforming strategy based on the derivation of the expected signal-to-interference-plus-noise ratio (SINR). Then, according to users' feedback about their decisions, a successive user and beamforming selection algorithm is performed at the BSs. From simulation results, we show that, combined with proportional fair scheduling, the proposed scheme provides excellent throughput performance with very low computational complexity and the amount of inter-BS CSI exchange. Furthermore, we discuss an extension of the proposed scheme to limited feedback systems and observe that our algorithm also provides similar advantages over conventional schemes with quantized feedback.
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paper_title: MIMO wireless linear precoding

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This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues. The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation. It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding. A precoded system structure is then described, involving an encoder and a linear precoder. Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios.
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paper_title: Multimode Transmission for Multiuser MIMO Systems With Block Diagonalization

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A low-complexity multimode transmission technique for downlink multiuser multiple-input-multiple-output (MIMO) systems with block diagonalization (BD) is proposed. The proposed technique adaptively configures the number of data streams for each user by adjusting its number of active receive antenna and switching between single-stream beamforming and multistream spatial multiplexing, as a means to exploit the multimode switching diversity. We consider a highly loaded system where there are a large number of users, hence a subset of users need to be selected. Joint user and antenna selection has been proposed as a multiuser multimode switching technique, where the optimal subset of receive antennas and users are chosen to maximize the sum throughput. The brute-force search, however, is prohibitively complicated. In this paper, two low-complexity near-optimal user/antenna selection algorithms are developed. The first algorithm aims at maximizing a capacity lower bound, derived in terms of the sum Frobenius norm of the channel, while the second algorithm greedily maximizes the sum capacity. We analytically evaluate the complexity of the proposed algorithms and show that it is orders of magnitude lower than that of the exhaustive search. Simulation results demonstrate that the proposed algorithms achieve up to 98% of the sum throughput of the exhaustive search, for most system configurations, while the complexity is substantially reduced.
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paper_title: Utilizing the Spatial Information Provided by Channel Norm Feedback in SDMA Systems

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To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.
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paper_title: User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

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The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.
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paper_title: Elements of Information Theory

paper_content:

Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
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paper_title: Complete Characterization of the Pareto Boundary for the MISO Interference Channel

paper_content:

In this correspondence, we study the achievable rate region of the multiple-input single-output (MISO) interference channel, under the assumption that all receivers treat the interference as additive Gaussian noise. Our main result is an explicit parametrization of the Pareto boundary for an arbitrary number of users and antennas. The parametrization describes the boundary in terms of a low-dimensional manifold. For the two-user case we show that a single real-valued parameter per user is sufficient to achieve all points on the Pareto boundary and that any point on the Pareto boundary corresponds to beamforming vectors that are linear combinations of the zero-forcing (ZF) and maximum-ratio transmission (MRT) beamformers. We further specialize the results to the MISO broadcast channel (BC). A numerical example illustrates the result.
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paper_title: Spatial scheduling in multiuser wireless systems: from power allocation to admission control

paper_content:

Given a zero forcing transmit beamforming, we focus on how the multi-antenna access point distributes the scarce resource (power) among the single-antenna terminals. Since there is a clear trade-off between the satisfaction of the individual needs and the global performance of the cell, several criteria are proposed, ranging from a classical physical layer point of view of capacity (rate) maximization to bit error rate (BER)-based cost functions, which are closer to the second layer of the protocol stack. Between two traditional techniques, namely the uniform power allocation and the equal BER and rate, a new one is proposed, which ultimately provides an intermediate performance. Then, we add BER (or signal to noise ratio) constraints so that the admission control problem has to be solved. Among traditional options, we propose a new mechanism to balance the above-mentioned trade-off between the total performance and the particular user behavior. The results in terms of fairness are presented by a mean vs. variance plot and by the Gini plot
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paper_title: MIMO broadcast channels with finite rate feedback

paper_content:

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where the receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. Simple expressions for the capacity degradation due to finite rate feedback as well as the required increases in feedback load per mobile as a function of the number of access point antennas and the system SNR are provided.
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paper_title: Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms

paper_content:

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones. This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions. The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
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paper_title: User selection schemes in multiple antenna broadcast channels with guaranteed performance

paper_content:

Recently, user selection algorithms in combination with linear pre- coding have been proposed that achieve the same scaling as the sum capacity of the MIMO BC. In this work, we study the properties of four user selection algorithms in conjunction with beamforming that guarantee certain SINR requirements under transmit power minimization. It is shown that for a large number of transmit antennas, the norm-based user selection performs close to the optimum. The results are illustrated by various numerical simulations.
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paper_title: Transmit Selection Diversity for Unitary Precoded Multiuser Spatial Multiplexing Systems With Linear Receivers

paper_content:

Multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference. In such a system, the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain. This paper proposes two precoding methods that use extra transmit antennas, beyond the minimum required, to provide additional degrees of diversity. The approach taken is to solve for a unitary transmit precoder, under a zero interuser interference constraint, that minimizes an upper bound on the symbol error rate (SER) for each user. Solutions where all transmit antennas are employed, as well as subsets of antennas (to reduce analog components), are described. Numerical results confirm a dramatic improvement in terms of SER and mutual information over single-user multiple-input multiple-output (MIMO) methods and static allocation methods. For example, the proposed techniques achieve a signal-to-noise ratio (SNR) improvement of 6-10 dB at an uncoded SER of 10-3, with only one extra transmit antenna
---
paper_title: The impact of space division multiplexing on resource allocation: a unified treatment of TDMA, OFDMA and CDMA

paper_content:

Space division multiple access (SDMA) with an antenna array at the transmitter is a promising means for increasing system capacity and supporting rate-demanding services. However, the presence of an antenna array at the physical layer raises significant issues at higher layers. In this paper, we attempt to capture the impact of SDMA on access layer channel allocation, reflected on channel reuse. This impact obtains different twists in TDMA, CDMA and OFDMA due to the different nature of co-channel and cross-channel interference and the different interaction of user spatial channel characteristics with system channels, namely time slots, codes and subcarriers. We consider these access schemes in a generalized unified framework and propose heuristic algorithms for channel allocation, downlink beamforming and transmit power control so as to increase total provisioned system rate and provide QoS to users in the form of minimum rate guarantees. We study the class of greedy algorithms that rely on criteria such as induced or received interference and signal-to-interference ratio (SIR), and a class of SIR balancing algorithms. Results show superior performance for SIR balancing resource allocation and expose the performance benefits of cross-layer design.
---
paper_title: Leakage-based user scheduling in MU-MIMO broadcast channel

paper_content:

This paper investigates user scheduling in multi-user MIMO broadcast channel. We propose a leakagebased user scheduling scheme, in which a user’s leakage power to other users is an important factor to determine whether the user should be selected. The accuracy of closed-form solution of SLNR (signal to leakage plus noise ratio) makes the proposed scheme outperform the traditional scheduling method based on SINR (signal to interference plus noise ratio). The proposed algorithms can work in case of perfect or limited feedback of CSI (channel state information) at transmitter, and the advantage is verified with numerical results. A tradeoff relation among feedback bits number, active user number and transmit/receive antennas number is analyzed, which serves as a system design guideline.
---
paper_title: A survey of energy-efficient wireless communications

paper_content:

Reducing energy consumption in wireless communications has attracted increasing attention recently. Advanced physical layer techniques such as multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM), cognitive radio, network coding, cooperative communication, etc.; new network architectures such as heterogeneous networks, distributed antennas, multi-hop cellulars, etc.; as well as radio and network resource management schemes such as various cross-layer optimization algorithms, dynamic power saving, multiple radio access technologies coordination, etc. have been proposed to address this issue. In this article, we overview these technologies and present the state-of-the-art on each aspect. Some challenges that need to be solved in the area are also described.
---
paper_title: Millimeter Wave Cellular Networks: A MAC Layer Perspective

paper_content:

The millimeter-wave (mmWave) frequency band is seen as a key enabler of multigigabit wireless access in future cellular networks. In order to overcome the propagation challenges, mmWave systems use a large number of antenna elements both at the base station and at the user equipment, which leads to high directivity gains, fully directional communications, and possible noise-limited operations. The fundamental differences between mmWave networks and traditional ones challenge the classical design constraints, objectives, and available degrees of freedom. This paper addresses the implications that highly directional communication has on the design of an efficient medium access control (MAC) layer. The paper discusses key MAC layer issues, such as synchronization, random access, handover, channelization, interference management, scheduling, and association. This paper provides an integrated view on MAC layer issues for cellular networks, identifies new challenges and tradeoffs, and provides novel insights and solution approaches.
---
paper_title: Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO

paper_content:

What would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a “massive MIMO” fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.
---
paper_title: 4G: LTE/LTE-Advanced for Mobile Broadband

paper_content:

Based on the bestseller "3G Evolution - HSPA and LTE for mobile broadband" and reflecting the ongoing success of LTE throughout the world, this book focuses on LTE with full updates including LTE-Advanced to provide a complete picture of the LTE system. Overview and detailed explanations are given for the latest LTE standards for radio interface architecture, the physical layer, access procedures, broadcast, relaying, spectrum and RF characteristics, and system performance. Key technologies presented include multi-carrier transmission, advanced single-carrier transmission, advanced receivers, OFDM, MIMO and adaptive antenna solutions, advanced radio resource management and protocols, and different radio network architectures. Their role and use in the context of mobile broadband access in general is explained. Both a high-level overview and more detailed step-by-step explanations of the LTE/LTE-Advanced implementation are given. An overview of other related systems such as GSM/EDGE, HSPA, CDMA2000, and WIMAX is also provided. This book is a 'must-have' resource for engineers and other professionals in the telecommunications industry, working with cellular or wireless broadband technologies, giving an understanding of how to utilize the new technology in order to stay ahead of the competition. The authors of the book all work at Ericsson Research and have been deeply involved in 3G and 4G development and standardisation since the early days of 3G research. They are leading experts in the field and are today still actively contributing to the standardisation of LTE within 3GPP. Includes full details of the latest additions to the LTE Radio Access standards and technologies up to and including 3GPP Release 10Clear explanations of the role of the underlying technologies for LTE, including OFDM and MIMO Full coverage of LTE-Advanced, including LTE carrier aggregation, extended multi-antenna transmission, relaying functionality and heterogeneous deploymentsLTE radio interface architecture, physical layer, access procedures, MBMS, RF characteristics and system performance covered in detail
---
paper_title: Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics in 5G Systems

paper_content:

The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by delivering a Wi-Fi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years [1], as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate requirements specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological preparations for fifth-generation (5G) networks: higher peak rates, improved coverage with uniform user experience, higher reliability and lower latency, better energy efficiency (EE), lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the existence of multiple objectives and tradeoffs between them.
---
paper_title: What Will 5G Be?

paper_content:

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
---
paper_title: Multi-Cell Coordinated Scheduling and MIMO in LTE

paper_content:

This paper provides an overview of multi-cell coordinated scheduling and multiple-input multiple-output (MIMO) techniques in LTE. We first discuss single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) for LTE and identify potential techniques for further improving the performance of LTE, such as enhanced channel state information feedback and adaptive switching between SU-MIMO and MU-MIMO. Then, we address inter-cell interference mitigation techniques for downlink and uplink, respectively. Finally, potential research challenges and topics in the area are discussed.
---
paper_title: Full dimension mimo (FD-MIMO): the next evolution of MIMO in LTE systems

paper_content:

Full dimension MIMO has attracted significant attention in the wireless industry and academia in the past few years as a candidate technology for the next generation evolution toward beyond fourth generation and fifth generation cellular systems. FD-MIMO utilizes a large number of antennas placed in a 2D antenna array panel for realizing spatially separated transmission links to a large number of mobile stations. The arrangement of these antennas on a 2D panel allows the extension of spatial separation to the elevation domain as well as the traditional azimuth domain. This article discusses features and performance benefits of FD-MIMO along with the ongoing standardization efforts in 3GPP to incorporate FD-MIMO features in the next evolution of LTE. Furthermore, a design of a 2D antenna array, which plays a key role in the implementation of FD-MIMO, is also discussed. Finally, in order to demonstrate the performance benefits of FD-MIMO, system-level evaluation results are provided.
---
paper_title: 5G Network Capacity: Key Elements and Technologies

paper_content:

It has been projected that, in the next decade, a mobile traffic increase on the order of 1,000 times is expected compared to what we experience today. To meet that dramatic traffic growth, next-generation mobile networks are also expected to achieve a 1,000-fold capacity increase compared to the current generation of wireless network deployments. In this article, we discuss how such capacity growth could be achieved in a ten-year time frame. We discuss the techniques that we expect to have the highest opportunity for increasing the system capacity and estimate their gains based on analysis and simulation. We observe that the main driver of capacity growth is expected to come from network architecture advancements, with heterogeneous networks and convergence of information and communication technology being two of the key techniques. We also estimate that the air-interface evolution would focus not only on improving the link and system spectrum efficiency but also on facilitating the required network efficiency improvements. This article provides insights into the communication technology evolution and can be used as a guideline for technology development toward the fifth generation (5G).
---
paper_title: Survey of Large-Scale MIMO Systems

paper_content:

The escalating teletraffic growth imposed by the proliferation of smartphones and tablet computers outstrips the capacity increase of wireless communications networks. Furthermore, it results in substantially increased carbon dioxide emissions. As a powerful countermeasure, in the case of full-rank channel matrices, MIMO techniques are potentially capable of linearly increasing the capacity or decreasing the transmit power upon commensurately increasing the number of antennas. Hence, the recent concept of large-scale MIMO (LS-MIMO) systems has attracted substantial research attention and been regarded as a promising technique for next-generation wireless communications networks. Therefore, this paper surveys the state of the art of LS-MIMO systems. First, we discuss the measurement and modeling of LS-MIMO channels. Then, some typical application scenarios are classified and analyzed. Key techniques of both the physical and network layers are also detailed. Finally, we conclude with a range of challenges and future research topics.
---
paper_title: Full dimension MIMO for LTE-Advanced and 5G

paper_content:

Elevation beamforming and Full Dimension MIMO (FD-MIMO) has been an active area of research and standardization in 3GPP LTE-Advanced. In an FD-MIMO system, a base station with 2-dimensional (2D) active array supports multi-user joint elevation and azimuth beamforming (a.k.a. 3D beamfoming), which results in much higher cell capacity compared to conventional systems. Recent study has shown that with these new FD-MIMO technologies, we can achieve promising 3–5× gain in both cell capacity as well as cell-edge throughput. In this paper, we will provide a brief summary of recent 3GPP activities, including the recently completed 3D channel model, ongoing study on FD-MIMO scenarios, antenna/RF (radio frequency) transceiver architectures, as well as potential network performance benefits. In addition, we also discuss some methods for reducing CSI (channel state information) feedback overhead and ensuring efficient operation of large size FD-MIMO for both TDD and FDD systems.
---
paper_title: 4G: LTE/LTE-Advanced for Mobile Broadband

paper_content:

Based on the bestseller "3G Evolution - HSPA and LTE for mobile broadband" and reflecting the ongoing success of LTE throughout the world, this book focuses on LTE with full updates including LTE-Advanced to provide a complete picture of the LTE system. Overview and detailed explanations are given for the latest LTE standards for radio interface architecture, the physical layer, access procedures, broadcast, relaying, spectrum and RF characteristics, and system performance. Key technologies presented include multi-carrier transmission, advanced single-carrier transmission, advanced receivers, OFDM, MIMO and adaptive antenna solutions, advanced radio resource management and protocols, and different radio network architectures. Their role and use in the context of mobile broadband access in general is explained. Both a high-level overview and more detailed step-by-step explanations of the LTE/LTE-Advanced implementation are given. An overview of other related systems such as GSM/EDGE, HSPA, CDMA2000, and WIMAX is also provided. This book is a 'must-have' resource for engineers and other professionals in the telecommunications industry, working with cellular or wireless broadband technologies, giving an understanding of how to utilize the new technology in order to stay ahead of the competition. The authors of the book all work at Ericsson Research and have been deeply involved in 3G and 4G development and standardisation since the early days of 3G research. They are leading experts in the field and are today still actively contributing to the standardisation of LTE within 3GPP. Includes full details of the latest additions to the LTE Radio Access standards and technologies up to and including 3GPP Release 10Clear explanations of the role of the underlying technologies for LTE, including OFDM and MIMO Full coverage of LTE-Advanced, including LTE carrier aggregation, extended multi-antenna transmission, relaying functionality and heterogeneous deploymentsLTE radio interface architecture, physical layer, access procedures, MBMS, RF characteristics and system performance covered in detail
---
paper_title: MIMO wireless linear precoding

paper_content:

This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues. The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation. It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding. A precoded system structure is then described, involving an encoder and a linear precoder. Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios.
---
paper_title: User selection and power schedule for downlink non-orthogonal multiple access (NOMA) system

paper_content:

As a promising multiple access techniques for 5th generation (5G) wireless systems, non-orthogonal multiple access (NOMA) has received many attentions recently. In this paper, we study the NOMA based downlink multi-user beamforming system, where the base station (BS) tries to transmit information to multiple user clusters and each beam serves one user cluster compromising of two users simultaneously. User selection algorithm is proposed to reduce the interference and improve the system information rate. Moreover, we also provide the user power schedule scheme to guarantee the advantage of the proposed NOMA downlink multi-user beamforming system. Simulation results show that the proposed user selection algorithm and the power schedule scheme can improve the sum-rate of NOMA based downlink multi-user system.
---
paper_title: Beamforming for Millimeter Wave Communications: An Inclusive Survey

paper_content:

The remarkable growth of wireless data traffic in recent times has driven the need to explore suitable regions in the radio spectrum to meet the projected requirements. In pursuance of this, millimeter wave communications have received considerable attention in the research fraternity. Due to the high path and penetration losses at millimeter wavelengths, antenna beamforming assumes a pivotal role in establishing and maintaining a robust communication link. Beamforming for millimeter wave communications poses a multitude of diverse challenges due to the large channel bandwidth, unique channel characteristics, and hardware constraints. In this paper, we track the evolution and advancements in antenna beamforming for millimeter wave communications in the context of the distinct requirements for indoor and outdoor communication scenarios. We expand the scope of discussion by including the developments in radio frequency system design and implementation for millimeter wave beamforming. We explore the suitability of millimeter wave beamforming methods, both, existing and proposed till midyear 2015, and identify the exciting new prospects unfolding in this domain.
---
paper_title: Cell-Free Massive MIMO Versus Small Cells

paper_content:

A Cell-Free Massive MIMO (multiple-input multiple-output) system comprises a very large number of distributed access points (APs)which simultaneously serve a much smaller number of users over the same time/frequency resources based on directly measured channel characteristics. The APs and users have only one antenna each. The APs acquire channel state information through time-division duplex operation and the reception of uplink pilot signals transmitted by the users. The APs perform multiplexing/de-multiplexing through conjugate beamforming on the downlink and matched filtering on the uplink. Closed-form expressions for individual user uplink and downlink throughputs lead to max-min power control algorithms. Max-min power control ensures uniformly good service throughout the area of coverage. A pilot assignment algorithm helps to mitigate the effects of pilot contamination, but power control is far more important in that regard. ::: Cell-Free Massive MIMO has considerably improved performance with respect to a conventional small-cell scheme, whereby each user is served by a dedicated AP, in terms of both 95%-likely per-user throughput and immunity to shadow fading spatial correlation. Under uncorrelated shadow fading conditions, the cell-free scheme provides nearly 5-fold improvement in 95%-likely per-user throughput over the small-cell scheme, and 10-fold improvement when shadow fading is correlated.
---
paper_title: A flexible 100-antenna testbed for Massive MIMO

paper_content:

Massive multiple-input multiple-output (MIMO) is one of the main candidates to be included in the fifth generation (5G) cellular systems. For further system development it is desirable to have real-time testbeds showing possibilities and limitations of the technology. In this paper we describe the Lund University Massive MIMO testbed — LuMaMi. It is a flexible testbed where the base station operates with up to 100 coherent radio-frequency transceiver chains based on software radio technology. Orthogonal Frequency Division Multiplex (OFDM) based signaling is used for each of the 10 simultaneous users served in the 20 MHz bandwidth. Real time MIMO precoding and decoding is distributed across 50 Xilinx Kintex-7 FPGAs with PCI-Express interconnects. The unique features of this system are: (i) high throughput processing of 384 Gbps of real time baseband data in both the transmit and receive directions, (ii) low-latency architecture with channel estimate to precoder turnaround of less than 500 micro seconds, and (iii) a flexible extension up to 128 antennas. We detail the design goals of the testbed, discuss the signaling and system architecture, and show initial measured results for a uplink Massive MIMO over-the-air transmission from four single-antenna UEs to 100 BS antennas.
---
paper_title: Massive MIMO and mmWave for 5G Wireless HetNet: Potential Benefits and Challenges

paper_content:

There has been active research worldwide to develop the next-generation, i.e., fifth-generation (5G), wireless network. The 5G network is expected to support a significantly large amount of mobile data traffic and a huge number of wireless connections and achieve better costand energy-efficiency as well as quality of service (QoS) in terms of communication delay, reliability, and security. To this end, the 5G wireless network should exploit the potential of new developments, including superdense and heterogeneous deployment of cells and massive antenna arrays [i.e., massive multiple-input, multiple-output (MIMO) technologies] and utilization of higher frequencies, particularly millimeter-wave (mmWave) frequencies. This article discusses the potential benefits and challenges of the 5G wireless heterogeneous network (HetNet) that incorporates massive MIMO and mmWave technologies.
---
paper_title: Design of Energy- and Cost-Efficient Massive MIMO Arrays

paper_content:

Large arrays of radios have been exploited for beamforming and null steering in both radar and communication applications, but cost and form factor limitations have precluded their use in commercial systems. This paper discusses how to build arrays that enable multiuser massive multiple-input–multiple-output (MIMO) and aggressive spatial multiplexing with many users sharing the same spectrum. The focus of the paper is the energy- and cost-efficient realization of these arrays in order to enable new applications. Distributed algorithms for beamforming are proposed, and the optimum array size is considered as a function of the performance of the receiver, transmitter, frequency synthesizer, and signal distribution within the array. The effects of errors such as phase noise and synchronization skew across the array are analyzed. The paper discusses both RF frequencies below 10 GHz, where fully digital techniques are preferred, and operation at millimeter (mm)-wave bands where a combination of digital and analog techniques are needed to keep cost and power low.
---
paper_title: Millimeter Wave Cellular Networks: A MAC Layer Perspective

paper_content:

The millimeter-wave (mmWave) frequency band is seen as a key enabler of multigigabit wireless access in future cellular networks. In order to overcome the propagation challenges, mmWave systems use a large number of antenna elements both at the base station and at the user equipment, which leads to high directivity gains, fully directional communications, and possible noise-limited operations. The fundamental differences between mmWave networks and traditional ones challenge the classical design constraints, objectives, and available degrees of freedom. This paper addresses the implications that highly directional communication has on the design of an efficient medium access control (MAC) layer. The paper discusses key MAC layer issues, such as synchronization, random access, handover, channelization, interference management, scheduling, and association. This paper provides an integrated view on MAC layer issues for cellular networks, identifies new challenges and tradeoffs, and provides novel insights and solution approaches.
---
paper_title: Five Disruptive Technology Directions for 5G

paper_content:

New research directions will lead to fundamental changes in the design of future 5th generation (5G) cellular networks. This paper describes five technologies that could lead to both architectural and component disruptive design changes: device-centric architectures, millimeter Wave, Massive-MIMO, smarter devices, and native support to machine-2-machine. The key ideas for each technology are described, along with their potential impact on 5G and the research challenges that remain.
---
paper_title: Point-to-multipoint in-band mmwave backhaul for 5G networks

paper_content:

Cost-effective and scalable wireless backhaul solutions are essential for realizing the 5G vision of providing gigabits per second anywhere. Not only is wireless backhaul essential to support network densification based on small cell deployments, but also for supporting very low latency inter-BS communication to deal with intercell interference. Multiplexing backhaul and access on the same frequency band (in-band wireless backhaul) has obvious cost benefits from the hardware and frequency reuse perspective, but poses significant technology challenges. We consider an in-band solution to meet the backhaul and inter-BS coordination challenges that accompany network densification. Here, we present an analysis to persuade the readers of the feasibility of in-band wireless backhaul, discuss realistic deployment and system assumptions, and present a scheduling scheme for inter- BS communications that can be used as a baseline for further improvement. We show that an inband wireless backhaul for data backhauling and inter-BS coordination is feasible without significantly hurting the cell access capacities.
---
paper_title: Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO

paper_content:

What would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a “massive MIMO” fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.
---
paper_title: Beamforming for Millimeter Wave Communications: An Inclusive Survey

paper_content:

The remarkable growth of wireless data traffic in recent times has driven the need to explore suitable regions in the radio spectrum to meet the projected requirements. In pursuance of this, millimeter wave communications have received considerable attention in the research fraternity. Due to the high path and penetration losses at millimeter wavelengths, antenna beamforming assumes a pivotal role in establishing and maintaining a robust communication link. Beamforming for millimeter wave communications poses a multitude of diverse challenges due to the large channel bandwidth, unique channel characteristics, and hardware constraints. In this paper, we track the evolution and advancements in antenna beamforming for millimeter wave communications in the context of the distinct requirements for indoor and outdoor communication scenarios. We expand the scope of discussion by including the developments in radio frequency system design and implementation for millimeter wave beamforming. We explore the suitability of millimeter wave beamforming methods, both, existing and proposed till midyear 2015, and identify the exciting new prospects unfolding in this domain.
---
paper_title: What Will 5G Be?

paper_content:

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
---
paper_title: Three Practical Aspects of Massive MIMO: Intermittent User Activity, Pilot Synchronism, and Asymmetric Deployment

paper_content:

This paper considers three aspects of Massive MIMO (multiple- input multiple-output) communication networks that have received little attention in previous works, but are important to understand when designing and implementing this promising wireless technology. First, we analyze how bursty data traffic behaviors affect the system. Using a probabilistic model for intermittent user activity, we show that the spectral efficiency (SE) scales gracefully with reduced user activity. Then, we make an analytic comparison between synchronous and asynchronous pilot signaling, and prove that the choice between these has no impact on the SE. Finally, we provide an analytical and numerical study of the SE achieved with random network deployment.
---

Title: An Overview on Resource Allocation Techniques for Multi-User MIMO Systems

Section 1: Introduction
Description 1: Explain the importance and challenges of resource allocation in MU-MIMO systems, introduce fundamental concepts, and provide an overview of the research scope.

Section 2: Contributions of the Survey
Description 2: Summarize the contributions of the survey, including classifications of precoding schemes, optimization criteria, and scheduling algorithms.

Section 3: Multiple Antenna Systems
Description 3: Describe the basic principles of MIMO systems, including spatial diversity and spatial multiplexing techniques.

Section 4: Multiuser MIMO
Description 4: Discuss the specifics of MU-MIMO, including downlink (Broadcast Channel) and uplink (Multiple Access Channel) distinctions, and the duality between them.

Section 5: The Need of User Scheduling
Description 5: Highlight the necessity and objectives of user scheduling in MU-MIMO systems, and introduce the general optimization problem.

Section 6: The Need of CSI Availability
Description 6: Explain the importance of Channel State Information (CSI) in MU-MIMO systems and describe the methods for CSI acquisition and feedback.

Section 7: MU-MIMO Channel and System Models
Description 7: Introduce common MU-MIMO channel and system models including single and multiple transmitter scenarios, along with interference management techniques.

Section 8: MU-MIMO Precoding
Description 8: Provide a classification and detailed description of different precoding techniques used in MU-MIMO systems, including both linear and non-linear methods.

Section 9: Spatial Compatibility Metrics
Description 9: Explain the metrics used to quantify spatial compatibility among users for efficient scheduling in MU-MIMO systems.

Section 10: System Optimization Criteria
Description 10: Describe different optimization criteria used in MU-MIMO systems, including PHY layer and cross-layer design considerations for resource allocation.

Section 11: MU-MIMO Scheduling
Description 11: Classify and discuss various scheduling algorithms for MU-MIMO systems, including heuristic, classical optimization, and metaheuristic approaches.

Section 12: MU-MIMO Scheduling with Partial CSIT
Description 12: Outline the techniques and challenges associated with scheduling in MU-MIMO systems when partial Channel State Information at the Transmitter (CSIT) is available.

Section 13: Power Allocation
Description 13: Detail the strategies for power allocation in MU-MIMO systems, discussing the trade-offs and methods used to optimize performance metrics.

Section 14: Final Remarks
Description 14: Summarize the state-of-the-art research on MU-MIMO systems, discuss open challenges, and outline future research directions in resource allocation and scheduling.

Section 15: Heterogeneous Networks
Description 15: Discuss the challenges and solutions for implementing MU-MIMO in heterogeneous network scenarios, addressing network densification and joint resource allocation issues.

Section 16: Massive MIMO and Millimeter Waves
Description 16: Explore the role and challenges of massive MIMO and mmWave technologies in future wireless networks.

Section 17: Summary of Asymptotic Analysis and Scaling Laws
Description 17: Provide an overview of asymptotic analysis and scaling laws for MU-MIMO system performance metrics based on system parameters.