An overview of transmission theory and techniques of large-scale antenna systems for 5G wireless communications
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paper_title: On Capacity of Large-Scale MIMO Multiple Access Channels with Distributed Sets of Correlated Antennas

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In this paper, a deterministic equivalent of ergodic sum rate and an algorithm for evaluating the capacity-achieving input covariance matrices for the uplink large-scale multiple-input multiple-output (MIMO) antenna channels are proposed. We consider a large-scale MIMO system consisting of multiple users and one base station with several distributed antenna sets. Each link between a user and an antenna set forms a two-sided spatially correlated MIMO channel with line-of-sight (LOS) components. Our derivations are based on novel techniques from large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the terminals approach to infinity with a fixed ratio. The deterministic equivalent results (the deterministic equivalent of ergodic sum rate and the capacity-achieving input covariance matrices) are easy to compute and shown to be accurate for realistic system dimensions. In addition, they are shown to be invariant to several types of fading distribution.
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paper_title: Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?

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We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.
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paper_title: Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems

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A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.
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paper_title: A free deterministic equivalent for the capacity of MIMO MAC with distributed antenna sets

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In this paper, we propose a free deterministic equivalent for the capacity analysis of multi-input multi-output (MIMO) multiple access channel (MAC) with distributed antenna sets. In the analysis, we use the operator-valued free probability framework, which is much more straightforward than the widely used methods, i.e., the Bai and Silverstein method and the Gaussian method. By replacing independent random Gaussian variables with freely independent circular entries, we obtain the free deterministic equivalent of our channel model. To evaluate the capacity, we use the Shannon transform of the free deterministic equivalent to approximate that of the channel model. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.
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paper_title: Spectral efficiency of multi-cell multi-user DAS with pilot contamination

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The spectral efficiency of multi-cell multi-user distributed antenna system with imperfect channel state information (CSI) is studied in this paper. First, considering the pilot contamination and minimum mean-squared-error (MMSE) channel estimation, the equivalent channel model is presented and the sum-rate of the uplink transmission is derived. Under a physical channel model, the equivalent channel model can be seen as a special case of the joint correlated MIMO channel model proposed by Gao [1]. Then, the closed-form approximation of the spectral efficiency is derived. The spectral efficiency of the system with large number of antennas is also studied. Finally, the theoretical results are compared with Monte-Carlo simulation, and the performances of DAS and co-located massive MIMO are also compared. It is shown that similar to the systems with perfect CSIs, DAS still has large performance gains compared with massive MIMO.
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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: Downlink spectral efficiency of multi-cell multi-user large-scale DAS with pilot contamination

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In this paper, the downlink spectral efficiency of multi-cell multi-user large-scale distributed antenna systems (DASs) is studied in the presence of pilot contamination. Based on the properties of Gamma distribution, the closed-form expression is derived for the downlink achievable rate with maximum ratio transmission (MRT). The ultimate rate is also given when the ratio of the total number of base station (BS) antennas to the number of users goes to infinity. Finally, the results are validated via numerical simulations. It is shown that the closed-form expression is very accurate, and the downlink achievable rate of large-scale DAS is much larger than that of co-located massive multiple-input multiple-output (MIMO) with the same antenna configuration.
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paper_title: Uplink sum-rate analysis of multi-cell multi-user massive MIMO system

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In this paper, the uplink sum-rate of the multi-cell multi-user massive MIMO system is studied under correlated Rayleigh fading channels. First, by considering pilot contamination effect, the equivalent system model of the massive MIMO is given with MMSE channel estimation. Then, the lower bound of the sum-rate is derived, and its asymptotical performance is studied when the base station antenna number goes to infinity. The result is general and is very accurate under the physical channel models.
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paper_title: Performance Analysis and Location Optimization for Massive MIMO Systems with Circularly Distributed Antennas

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In this paper, we analyze the achievable rate of the uplink of a single-cell multi-user distributed massive multiple-input-multiple-output (MIMO) system. The multiple users are equipped with single antenna and the base station (BS) is equipped with a large number of distributed antennas. We derive an analytical expression for the asymptotic ergodic achievable rate of the system under zero-forcing (ZF) detector. In particular, we consider circular antenna array, where the distributed BS antennas are located evenly on a circle, and derive an analytical expression and closed-form tight bounds for the achievable rate of an arbitrarily located user. Subsequently, closed-form bounds on the average achievable rate per user are obtained under the assumption that the users are uniformly located in the cell. Based on the bounds, we can understand the behavior of the system rate with respect to different parameters and find the optimal location of the circular BS antenna array that maximizes the average rate. Numerical results are provided to assess our analytical results and examine the impact of the number and the location of the BS antennas, the transmit power, and the path-loss exponent on system performance. It is shown that circularly distributed massive MIMO system largely outperforms centralized massive MIMO system.
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paper_title: Area Spectral Efficiency and Area Energy Efficiency of Massive MIMO Cellular Systems

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This paper investigates the performance of massive multiple-input multiple-output (MIMO) cellular systems with pilot contamination. We derive a closed-form approximation of the area spectral efficiency (ASE) for uplink multicell multiuser massive MIMO systems by using a uniformly distributed user location model. Considering a practical power consumption model, we obtain the area energy efficiency (AEE) in a cell. The theoretical results of ASE and AEE can be used to investigate some system parameters of massive MIMO cellular systems, such as the number of antennas at the base station, the number of users, and the number of symbols over which the channel remains constant. We also study the optimal pilot-to-data power ratio for both ASE maximization and AEE maximization.
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paper_title: Analyzing Uplink SINR and Rate in Massive MIMO Systems Using Stochastic Geometry

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This paper proposes a stochastic geometry framework to analyze the SINR and rate performance in a large-scale uplink massive MIMO network. Based on the model, expressions are derived for spatial average SINR distributions over user and base station distributions with maximum ratio combining (MRC) and zero-forcing (ZF) receivers. We show that using massive MIMO, the uplink SINR in certain urban marco-cell scenarios is limited by interference. In the interference-limited regime, the results reveal that for MRC receivers, a super-linear (polynomial) scaling law between the number of base station antennas and scheduled users per cell preserves the uplink SIR distribution, while a linear scaling applies to ZF receivers. ZF receivers are shown to outperform MRC receivers in the SIR coverage, and the performance gap is quantified in terms of the difference in the number of antennas to achieve the same SIR distribution. Numerical results verify the analysis. It is found that the optimal compensation fraction in fractional power control to optimize rate is generally different for MRC and ZF receivers. Besides, simulations show that the scaling results derived from the proposed framework apply to the networks where base stations are distributed according to a hexagonal lattice.
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paper_title: On the Design of Large Scale Wireless Systems

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In this paper, we consider the downlink of large OFDMA-based networks and study their performance bounds as a function of the number of - transmitters B, users K, and resource-blocks N. Here, a resource block is a collection of subcarriers such that all such collections, that are disjoint have associated independently fading channels. In particular, we analyze the expected achievable sum-rate as a function of above variables and derive novel upper and lower bounds for a general spatial geometry of transmitters, a truncated path-gain model, and a variety of fading models. We establish the associated scaling laws for dense and extended networks, and propose design guidelines for the regulators to guarantee various QoS constraints and, at the same time, maximize revenue for the service providers. Thereafter, we develop a distributed resource allocation scheme that achieves the same sum-rate scaling as that of the proposed upper bound for a wide range of K, B, N. Based on it, we compare low-powered peer-to-peer networks to high-powered single-transmitter networks and give an additional design principle. Finally, we also show how our results can be extended to the scenario where each of the B transmitters have M (>;1) co-located antennas.
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paper_title: Ergodic capacity analysis of downlink distributed antenna systems using stochastic geometry

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This paper studies the ergodic capacity of a multicell distributed antenna system (DAS), where remote antenna ports are spread within each cell to cooperatively transmit to user terminals. Unlike most prior studies which assume the antenna ports to be deployed at fixed locations, this paper assumes the antenna ports to be distributed as a spatial Poisson point process (PPP) to account for the fact that in practice the antenna ports are randomly placed to cover wherever the dead spots are. We first model DAS within each cell as a downlink multiple-input single-output (MISO) channel with per-antenna power constraint while accounting for inter-cell (inter-cluster) interference. Two DAS layouts are considered: the “regular” layout where the antenna ports are randomly deployed within regular cellular boundary to serve a given user, and the “user-centric” layout where the antenna ports are distributed over a wide area and the users choose the surrounding antenna ports to form a “virtual cell” as its own serving antenna subset. Using the tool of stochastic geometry, we analytically derive efficiently computable ergodic capacity expressions for the two layouts of DAS. Using these expressions, the cell-edge capacity of DAS under the regular layout is shown to be upper-bounded by α/2, where α is the pathloss exponent. Numerical results show that the proposed analytical model can accurately model the first layout, and can well approximate the second layout when the serving radius of users is not large. Compared to the traditional cellular system where all antennas are co-located at the cell center, DAS has better cell-edge performance. Further, the user-centric DAS has higher capacity than the DAS under regular layout.
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paper_title: A Tractable Approach to Coverage and Rate in Cellular Networks

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Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.
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paper_title: A Stochastic Geometry Framework for Analyzing Pairwise-Cooperative Cellular Networks

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Cooperation in cellular networks is a promising scheme to improve system performance, especially for cell-edge users. In this work, stochastic geometry is used to analyze cooperation models where the positions of base stations follow a Poisson point process distribution and where Voronoi cells define the planar areas associated with them. For the service of each user, either one or two base stations are involved. If two, these cooperate by exchange of user data and channel related information with conferencing over some backhaul link. Our framework generally allows for variable levels of channel information at the transmitters. This paper is focused on a case of limited information based on Willems' encoding. The total per-user transmission power is split between the two transmitters and a common message is encoded. The decision for a user to choose service with or without cooperation is directed by a family of geometric policies, depending on its relative position to its two closest base stations. An exact expression of the network coverage probability is derived. Numerical evaluation shows average coverage benefits of up to 17% compared to the non-cooperative case. Various other network problems of cellular cooperation, like the fully adaptive case, can be analyzed within our framework.
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paper_title: Spectral Efficiency of Distributed MIMO Cellular Systems in a Composite Fading Channel

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In this paper, accurate approximations of the spectral efficiency are presented for co-located multiple-input multiple-output (C-MIMO) and distributed MIMO (D-MIMO) cellular systems in the composite channel model, which includes path loss, shadow fading, and multipath fading. Firstly, conditioned on the desired user position, the analytical approximations of the mean and variance of the mutual information are derived for C-MIMO and D-MIMO at high SNR. Because the exact distribution of the mutual information in a composite Rayleigh- lognormal environment is difficult to analyze, we apply Gaussian approximation to the distribution of the mutual information. Then, the growth in ergodic capacity and outage capacity of a D-MIMO channel with the number of antennas as well as the variance of the shadow fading is well understood. Assuming that the users are randomly distributed in the cell, the closed-form expressions for the mean spectral efficiency and mean outage spectral efficiency are derived. Finally, the numerical results are presented which validate the analytical results.
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paper_title: Performance analysis for range expansion in heterogeneous networks

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In this paper, the uplink and downlink performance of a two-tier heterogeneous network (HetNet) with range expansion (RE) is analyzed. Different from previous works, base stations (BSs) are modeled as a spatial Poisson point process. This model can not only capture the irregularity of the BS deployment but also lead to closed form expressions. With the analytical results, the impacts of several key parameters on the coverage and throughput performance are investigated. Our results justifies the effectiveness of RE and Pico deployment. Based on our analyses, certain attention should be made on the RE design to balance the uplink and downlink performance. Our analyses are corroborated by simulations and can thus serve as a flexible and quick guidance for system design without complicated and time-consuming system-level platform construction and simulation.
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paper_title: On the impact of hardware impairments on massive MIMO

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Massive multi-user (MU) multiple-input multiple-output (MIMO) systems are one possible key technology for next generation wireless communication systems. Claims have been made that massive MU-MIMO will increase both the radiated energy efficiency as well as the sum-rate capacity by orders of magnitude, because of the high transmit directivity. However, due to the very large number of transceivers needed at each base-station (BS), a successful implementation of massive MU-MIMO will be contingent on of the availability of very cheap, compact and power-efficient radio and digital-processing hardware. This may in turn impair the quality of the modulated radio frequency (RF) signal due to an increased amount of power-amplifier distortion, phase-noise, and quantization noise. In this paper, we examine the effects of hardware impairments on a massive MU-MIMO single-cell system by means of theory and simulation. The simulations are performed using simplified, well-established statistical hardware impairment models as well as more sophisticated and realistic models based upon measurements and electromagnetic antenna array simulations.
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paper_title: Coordinated Multi-Point Transmission Strategies for TDD Systems with Non-Ideal Channel Reciprocity

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This paper studies transmission strategies for downlink time division duplex coordinated multi-point (CoMP) systems with non-ideal uplink-downlink channel reciprocity, where several multi-antenna base stations (BSs) jointly serve multiple single-antenna users. Due to the inherent antenna calibration errors among different BSs, the uplink-downlink channels are no longer reciprocal such that the channel information at the BSs is with multiplicative noises. To mitigate the performance degradation caused by the imperfect channels, we employ a weighted sum rate estimate as the objective function for robust precoder design. To show the impact of data sharing on the performance of CoMP under the non-ideal channel reciprocity, we provide a unified framework for designing precoder for CoMP systems with different amount of data sharing. The optimal parametric linear precoder structure that maximizes the weighted sum rate estimate under per-BS power constraints is characterized, based on which a closed-form robust signal-to-leakage-plus-noise ratio (SLNR) precoder is proposed to exploit the statistics of the calibration errors. Simulation results show that the proposed precoder in conjunction with user scheduling provides substantial performance gain over Non-CoMP transmission and the CoMP transmission with non-robust precoders.
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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: JMB: scaling wireless capacity with user demands

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We present joint multi-user beamforming (JMB), a system that enables independent access points (APs) to beamform their signals, and communicate with their clients on the same channel as if they were one large MIMO transmitter. The key enabling technology behind JMB is a new low-overhead technique for synchronizing the phase of multiple transmitters in a distributed manner. The design allows a wireless LAN to scale its throughput by continually adding more APs on the same channel. JMB is implemented and tested with both software radio clients and off-the-shelf 802.11n cards, and evaluated in a dense congested deployment resembling a conference room. Results from a 10-AP software-radio testbed show a linear increase in network throughput with a median gain of 8.1 to 9.4x. Our results also demonstrate that JMB's joint multi-user beamforming can provide throughput gains with unmodified 802.11n cards.
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paper_title: Uplink Sum-Rate Analysis of Massive MIMO System with Pilot Contamination and CSI Delay

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We consider multi-cell multi-user massive MIMO system under correlated Rayleigh fading channels. Taking pilot contamination and CSI delay into consideration, we derive the equivalent channel model with MMSE channel estimation and one-tap prediction. Employing this equivalent channel model, the lower bound of the uplink sum-rate is derived, and its asymptotical performance is studied when the base station antenna number goes without bound. We find that if we schedule the $$k$$ k -th user of all cells who have the same prediction coefficient, the uplink sum-rate is the same as the one with no CSI delay when the number of BS antennas goes without bound at a much greater rate than the number of users. Simulation results show that the asymptotic approximation has good performance for large $$M$$ M , and suggest that large antenna array can compensate for the decay due to CSI delay. Simulation results also verify our guess that CSI delay does not necessarilly decrease the uplink sum-rate due to the impact of pilot contamination.
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paper_title: Widely linear block-diagonalization type precoding in massive mimo systems with IQ imbalance

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In this paper, we propose widely-linear blockdiagonalization (BD) type precoding techniques to alleviate the impact of IQ imbalance in the downlink Massive multi-input multi-output (MIMO) systems. We first introduce a real-valued signal model and then develop widely-linear BD (WL-BD) type precoding algorithms, i.e., WL-BD, widely linear regularized BD (WL-RBD) and widely linear simplified generalized MMSE channel inversion (WL-S-GMI). We also present analysis of the sum-rate and multiplexing gain achieved by the proposed WLBD for scenarios with and without IQ imbalance. Numerical results verify the analysis and show that WL-BD type precoding methods significantly outperform their conventional counterparts with IQ imbalance and approach the ideal case.
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paper_title: Mixed-ADC Massive MIMO Detectors: Performance Analysis and Design Optimization

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The hardware cost and power consumption of a massive multiple-input multiple-output (MIMO) system can be remarkably reduced by using a very low-resolution analog-to-digital converter (ADC) unit in each antenna. However, such a pure low-resolution ADC architecture complicates parameter estimation problems. These issues can be resolved and the potential of a pure low-resolution ADC architecture can be achieved by applying a mixed ADC architecture, whose antennas are equipped with low-precision ADCs, while few antennas are composed of high-precision ADCs. In this paper, a unified framework is presented to develop a family of detectors on a massive MIMO uplink system through probabilistic Bayesian inference. Our basic setup comprises an optimal detector, which is developed to provide a minimum mean-squared-error estimate on data symbols. Considering that highly nonlinear steps are involved in quantization, we also investigate the potential for complexity reduction on an optimal detector by postulating a common pseudo-quantization noise model. We provide asymptotic performance expressions, including mean squared error and bit error rate for optimal and suboptimal MIMO detectors. These expressions can be evaluated rapidly and efficiently. Thus, they can be used for system design optimization.
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paper_title: Noncoherent Trellis Coded Quantization: A Practical Limited Feedback Technique for Massive MIMO Systems

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Accurate channel state information (CSI) is essential for attaining beamforming gains in single-user (SU) multiple-input multiple-output (MIMO) and multiplexing gains in multi-user (MU) MIMO wireless communication systems. State-of-the-art limited feedback schemes, which rely on pre-defined codebooks for channel quantization, are only appropriate for a small number of transmit antennas and low feedback overhead. In order to scale informed transmitter schemes to emerging massive MIMO systems with a large number of transmit antennas at the base station, one common approach is to employ time division duplexing (TDD) and to exploit the implicit feedback obtained from channel reciprocity. However, most existing cellular deployments are based on frequency division duplexing (FDD), hence it is of great interest to explore backwards compatible massive MIMO upgrades of such systems. For a fixed feedback rate per antenna, the number of codewords for quantizing the channel grows exponentially with the number of antennas, hence generating feedback based on look-up from a standard vector quantized codebook does not scale. In this paper, we propose noncoherent trellis-coded quantization (NTCQ), whose encoding complexity scales linearly with the number of antennas. The approach exploits the duality between source encoding in a Grassmannian manifold (for finding a vector in the codebook which maximizes beamforming gain) and noncoherent sequence detection (for maximum likelihood decoding subject to uncertainty in the channel gain). Furthermore, since noncoherent detection can be realized near-optimally using a bank of coherent detectors, we obtain a low-complexity implementation of NTCQ encoding using an off-the-shelf Viterbi algorithm applied to standard trellis coded quantization. We also develop advanced NTCQ schemes which utilize various channel properties such as temporal/spatial correlations. Monte Carlo simulation results show the proposed NTCQ and its extensions can achieve near-optimal performance with moderate complexity and feedback overhead.
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paper_title: Pilot Reuse for Massive MIMO Transmission over Spatially Correlated Rayleigh Fading Channels

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We propose pilot reuse (PR) in single cell for massive multiuser multiple-input multiple-output (MIMO) transmission to reduce the pilot overhead. For spatially correlated Rayleigh fading channels, we establish a relationship between channel spatial correlations and channel power angle spectrum when the base station antenna number tends to infinity. With this channel model, we show that sum mean square error (MSE) of channel estimation can be minimized provided that channel angle of arrival intervals of the user terminals reusing the pilots are non-overlapping, which shows feasibility of PR over spatially correlated massive MIMO channels with constrained channel angular spreads. Since channel estimation performance might degrade due to PR, we also develop the closed-form robust multiuser uplink receiver and downlink precoder that minimize sum MSE of signal detection, and reveal a duality between them. Subsequently, we investigate pilot scheduling, which determines the PR pattern, under two minimum MSE related criteria, and propose a low complexity pilot scheduling algorithm, which relies on the channel statistics only. Simulation results show that the proposed PR scheme provides significant performance gains over the conventional orthogonal training scheme in terms of net spectral efficiency.
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paper_title: Large-Scale Multi-User Distributed Antenna System for 5G Wireless Communications

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In this paper, we study the large-scale multi-user distributed antenna system (DAS) for hot-spot coverage in the future 5G wireless network. Firstly, the multi- user system model of large- scale DAS is introduced and a simple random pilot reuse scheme is presented to reduce the overhead of pilot. Then, the sum-rate of system is derived, and its asymptotical performance is studied when the number of antennas goes to infinity. Moreover, an attractive method for large-scale DAS using matrix sparsification is presented to simplify the signal processing, which is of great significance for the future research. Finally, we study the detection bit error ratio (BER) and area spectral efficiency of large-scale DAS.
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paper_title: Pilot scheduling schemes for multi-cell massive multiple-input–multiple-output transmission

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This study addresses the pilot scheduling problem in multiuser multi-cell massive multiple-input–multiple-output (MIMO) systems, aiming at mitigating the inter-cell interference (pilot contamination), which constitutes a bottleneck of the system performance. First, the authors investigate the pilot reuse and scheduling problem in cellular systems with unlimited number of base station antennas, only considering the large fading coefficients. Three low-complexity pilot scheduling schemes are then proposed by maximising the system achievable sum rate, including the greedy algorithm, the tabu search (TS) algorithm and the greedy TS algorithm. Second, they investigate the pilot reuse problem among the inter-cell user terminals (UTs) under spatially correlated channels for massive MIMO transmission, trying to distinguish UTs sharing the same time-frequency resources from the spatial domain. A closed-form expression of the non-asymptotic downlink achievable rate is derived by exploiting the second-order channel statistical information. On the basis of the degree of the UTs’ covariance matrices overlap with each other, they further propose a spatial orthogonality-based greedy pilot scheduling algorithm. The proposed approaches can provide much better performance in the presence of pilot contamination. Theoretical analysis and numerical results both verify the effectiveness of the proposed algorithms.
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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: A Coordinated Approach to Channel Estimation in Large-scale Multiple-antenna Systems

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This paper addresses the problem of channel estimation in multi-cell interference-limited cellular networks. We consider systems employing multiple antennas and are interested in both the finite and large-scale antenna number regimes (so-called "massive MIMO"). Such systems deal with the multi-cell interference by way of per-cell beamforming applied at each base station. Channel estimation in such networks, which is known to be hampered by the pilot contamination effect, constitutes a major bottleneck for overall performance. We present a novel approach which tackles this problem by enabling a low-rate coordination between cells during the channel estimation phase itself. The coordination makes use of the additional second-order statistical information about the user channels, which are shown to offer a powerful way of discriminating across interfering users with even strongly correlated pilot sequences. Importantly, we demonstrate analytically that in the large-number-of-antennas regime, the pilot contamination effect is made to vanish completely under certain conditions on the channel covariance. Gains over the conventional channel estimation framework are confirmed by our simulations for even small antenna array sizes.
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paper_title: On massive MIMO performance with semi-orthogonal pilot-assisted channel estimation

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With the rapidly increasing demand for high-speed data transmission and a growing number of terminals, massive multiple-input multiple-output (MIMO) has been shown promising to meet the challenges owing to its high spectrum efficiency. Although massive MIMO can efficiently improve the system performance, usage of orthogonal pilots and growing terminals causes large resource consumption especially when the coherence interval is short. This paper proposes a semi-orthogonal pilot design with simultaneous data and pilot transmission. In the proposed technique, we exploit the asymptotic channel orthogonality in massive MIMO systems, with which a successive interference cancellation (SIC)-based channel estimation is applied to mitigate the mutual interference between data and pilot. We derived the theoretical expressions of the achievable rates in massive MIMO systems with our proposed pilot design. Further discussion on performance verifies the superiority of our proposed pilot design for high or low signal-to-noise-ratios (SNRs) with any coherence interval length. And simulation results show that the proposed pilot design can achieve a significant performance improvement with reduced pilot resource consumption compared with the conventional orthogonal pilots.
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paper_title: Pilot decontamination in massive MIMO systems: Exploiting channel sparsity with pilot assignment

paper_content:

This paper deals with the pilot contamination problem for massive MIMO systems. Considering the sparse nature of channel impulse response inherent in wideband systems, the paths of channels of the desired and interference users hardly arrive at the same time, which allows most paths of desired channel to be distinguishable from the paths of interference channels in time-domain. Based on this observation, we first estimate the power delay profile (PDP) of the desired channel with the contaminated channel estimate, from which we acquire the delay of each path of the desired channel. By extracting the corresponding channel components from the contaminated channel estimate, a clean channel estimate can be obtained. To reduce the impact of pilot contamination on the estimated PDP, we propose a pilot assignment method among adjacent cells to randomize the interference over successive uplink frames. Simulation results demonstrate substantial sum rate gain of the proposed approach over existing methods.
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paper_title: Inter-Cell Interference in Noncooperative TDD Large Scale Antenna Systems

paper_content:

In this paper we study the performance of cellular networks when their base stations have an unlimited number of antennas. In previous work, the asymptotic behavior of the signal to interference plus nose ratio (SINR) was obtained. We revisit these results by deriving the rigorous expression for the SINR of both downlink and uplink in the scenario of infinite number of antennas. We show that the contamination of the channel estimates happens whenever a pilot sequence is received at a base station simultaneously with non-orthogonal signals coming from other users. We propose a method to avoid such simultaneous transmissions from adjacent cells, thus significantly decreasing interference. We also investigate the effects of power allocation in this interference-limited scenario, and show that it results in gains of over 15dB in the signal to interference ratio for the scenario simulated here. The combination of these two techniques results in rate gains of about 18 times in our simulations.
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paper_title: Fractional Pilot Reuse in Massive MIMO Systems

paper_content:

Pilot contamination is known to be one of the main impairments for massive MIMO multi-cell communications. Inspired by the concept of fractional frequency reuse and by recent contributions on pilot reutilization among non-adjacent cells, we propose a new pilot allocation scheme to mitigate this effect. The key idea is to allow users in neighboring cells that are closest to their base stations to reuse the same pilot sequences. Focusing on the uplink, we obtain expressions for the overall spectral efficiency per cell for different linear combining techniques at the base station and use them to obtain both the optimal pilot reuse parameters and the optimal number of scheduled users. Numerical results show a remarkable improvement in terms of spectral efficiency with respect to the existing techniques.
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paper_title: Downlink Training Techniques for FDD Massive MIMO Systems: Open-Loop and Closed-Loop Training with Memory

paper_content:

The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD massive MIMO be used for training signal transmissions and channel state information (CSI) feedback. To reduce the overhead of the downlink training phase, we propose practical open-loop and closed-loop training frameworks in this paper. We assume the base station and the user share a common set of training signals in advance. In open-loop training, the base station transmits training signals in a round-robin manner, and the user successively estimates the current channel using long-term channel statistics such as temporal and spatial correlations and previous channel estimates. In closed-loop training, the user feeds back the best training signal to be sent in the future based on channel prediction and the previously received training signals. With a small amount of feedback from the user to the base station, closed-loop training offers better performance in the data communication phase, especially when the signal-to-noise ratio is low, the number of transmit antennas is large, or prior channel estimates are not accurate at the beginning of the communication setup, all of which would be mostly beneficial for massive MIMO systems.
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paper_title: Structured Compressive Sensing Based Superimposed Pilot Design in Downlink Large-Scale MIMO Systems

paper_content:

Large-scale multiple-input multiple-output (MIMO) with high spectrum and energy efficiency is a very promising key technology for future 5G wireless communications. For large-scale MIMO systems, accurate channel state information (CSI) acquisition is a challenging problem, especially when each user has to distinguish and estimate numerous channels coming from a large number of transmit antennas in the downlink. Unlike the conventional orthogonal pilots whose pilot overhead prohibitively increases with the number of transmit antennas, we propose a spectrum-efficient superimposed pilot design for downlink large-scale MIMO scenarios, where frequency-domain pilots of different transmit antennas occupy the completely same subcarriers in the freqency domain. Meanwhile, spatial-temporal common sparsity of large-scale MIMO channels motivates us to exploit the emerging theory of structured compressive sensing (CS) for reliable MIMO channel estimation, which is realized by the proposed structured subspace pursuit (SSP) algorithm to simultaneously recover multiple channels with low pilot overhead. Simulation results demonstrate that the proposed scheme performs well and can approach the performance bound.
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paper_title: Spatially Common Sparsity Based Adaptive Channel Estimation and Feedback for FDD Massive MIMO

paper_content:

This paper proposes a spatially common sparsity based adaptive channel estimation and feedback scheme for frequency division duplex based massive multi-input multi-output (MIMO) systems, which adapts training overhead and pilot design to reliably estimate and feed back the downlink channel state information (CSI) with significantly reduced overhead. Specifically, a non-orthogonal downlink pilot design is first proposed, which is very different from standard orthogonal pilots. By exploiting the spatially common sparsity of massive MIMO channels, a compressive sensing (CS) based adaptive CSI acquisition scheme is proposed, where the consumed time slot overhead only adaptively depends on the sparsity level of the channels. Additionally, a distributed sparsity adaptive matching pursuit algorithm is proposed to jointly estimate the channels of multiple subcarriers. Furthermore, by exploiting the temporal channel correlation, a closed-loop channel tracking scheme is provided, which adaptively designs the non-orthogonal pilot according to the previous channel estimation to achieve an enhanced CSI acquisition. Finally, we generalize the results of the multiple-measurement-vectors case in CS and derive the Cramer-Rao lower bound of the proposed scheme, which enlightens us to design the non-orthogonal pilot signals for the improved performance. Simulation results demonstrate that the proposed scheme outperforms its counterparts, and it is capable of approaching the performance bound.
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paper_title: Sparse Reconstruction Using Distribution Agnostic Bayesian Matching Pursuit

paper_content:

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator.
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paper_title: Distributed Compressive CSIT Estimation and Feedback for FDD Multi-user Massive MIMO Systems

paper_content:

To fully utilize the spatial multiplexing gains or array gains of massive MIMO, the channel state information must be obtained at the transmitter side (CSIT). However, conventional CSIT estimation approaches are not suitable for FDD massive MIMO systems because of the overwhelming training and feedback overhead. In this paper, we consider multi-user massive MIMO systems and deploy the compressive sensing (CS) technique to reduce the training as well as the feedback overhead in the CSIT estimation. The multi-user massive MIMO systems exhibits a hidden joint sparsity structure in the user channel matrices due to the shared local scatterers in the physical propagation environment. As such, instead of naively applying the conventional CS to the CSIT estimation, we propose a distributed compressive CSIT estimation scheme so that the compressed measurements are observed at the users locally, while the CSIT recovery is performed at the base station jointly. A joint orthogonal matching pursuit recovery algorithm is proposed to perform the CSIT recovery, with the capability of exploiting the hidden joint sparsity in the user channel matrices. We analyze the obtained CSIT quality in terms of the normalized mean absolute error, and through the closed-form expressions, we obtain simple insights into how the joint channel sparsity can be exploited to improve the CSIT recovery performance.
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paper_title: Blind pilot decontamination

paper_content:

A subspace projection to improve channel estimation in massive multi-antenna systems is proposed and analyzed. Together with power-controlled hand-off, it can mitigate the pilot contamination problem without the need for coordination among cells. The proposed method is blind in the sense that it does not require pilot data to find the appropriate subspace. It is based on the theory of large random matrices that predicts that the eigenvalue spectra of large sample covariance matrices can asymptotically decompose into disjoint bulks as the matrix size grows large. Random matrix and free probability theory are utilized to predict under which system parameters such a bulk decomposition takes place. Simulation results are provided to confirm that the proposed method outperforms conventional linear channel estimation if bulk separation occurs.
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paper_title: Pilot decontamination in massive MIMO systems: Exploiting channel sparsity with pilot assignment

paper_content:

This paper deals with the pilot contamination problem for massive MIMO systems. Considering the sparse nature of channel impulse response inherent in wideband systems, the paths of channels of the desired and interference users hardly arrive at the same time, which allows most paths of desired channel to be distinguishable from the paths of interference channels in time-domain. Based on this observation, we first estimate the power delay profile (PDP) of the desired channel with the contaminated channel estimate, from which we acquire the delay of each path of the desired channel. By extracting the corresponding channel components from the contaminated channel estimate, a clean channel estimate can be obtained. To reduce the impact of pilot contamination on the estimated PDP, we propose a pilot assignment method among adjacent cells to randomize the interference over successive uplink frames. Simulation results demonstrate substantial sum rate gain of the proposed approach over existing methods.
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paper_title: Low-complexity Subspace Tracking Based Channel Estimation Method for OFDM Systems In Time-Varying Channels

paper_content:

In this paper, a group of low-complexity subspace tracking based pilot-aided channel estimation methods for orthogonal frequency-division multiplexing (OFDM) systems is studied. These methods are based on a parametric channel model where the channel response is characterized as a collection of sparse propagation paths. Considering the slow variations of the channel correlation matrix's signal subspace, we first translate the estimation of channel parameters into an unconstrained minimization problem. Then, to solve this minimization problem, a novel Kalman-filter based subspace tracking method is proposed, which employs the constant signal subspace to construct state equation and measurement equation. In contrast, other two adaptive filters, LMS and RLS, are applied and evaluated. These three methods constitute a group of low-complexity subsapce tracking schemes. It is shown that the proposed Kalman filter method is able to effectively track the time-varying channels, and outperforms LMS and RLS methods with large Doppler frequency spread.
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paper_title: EVD-based channel estimation in multicell multiuser MIMO systems with very large antenna arrays

paper_content:

This paper considers multicell multiuser MIMO systems with very large antenna arrays at the base station. We propose an eigenvalue-decomposition-based approach to channel estimation, that estimates the channel blindly from the received data. The approach exploits the asymptotic orthogonality of the channel vectors in very large MIMO systems. We show that the channel to each user can be estimated from the covariance matrix of the received signals, up to a remaining scalar multiplicative ambiguity. A short training sequence is required to resolve this ambiguity. Furthermore, to improve the performance of our approach, we combine it with the iterative least-square with projection (ILSP) algorithm. Numerical results verify the effectiveness of our channel estimation approach.
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paper_title: Channel Acquisition for Massive MIMO-OFDM With Adjustable Phase Shift Pilots

paper_content:

We propose adjustable phase shift pilots (APSPs) for channel acquisition in wideband massive multiple-input multiple-output (MIMO) systems employing orthogonal frequency division multiplexing (OFDM) to reduce the pilot overhead. Based on a physically motivated channel model, we first establish a relationship between channel space-frequency correlations and the channel power angle-delay spectrum in the massive antenna array regime, which reveals the channel sparsity in massive MIMO-OFDM. With this channel model, we then investigate channel acquisition, including channel estimation and channel prediction, for massive MIMO-OFDM with APSPs. We show that channel acquisition performance in terms of sum mean square error can be minimized if the user terminals' channel power distributions in the angle-delay domain can be made nonoverlapping with proper pilot phase shift scheduling. A simplified pilot phase shift scheduling algorithm is developed based on this optimal channel acquisition condition. The performance of APSPs is investigated for both one symbol and multiple symbol data models. Simulations demonstrate that the proposed APSP approach can provide substantial performance gains in terms of achievable spectral efficiency over the conventional phase shift orthogonal pilot approach in typical mobility scenarios.
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paper_title: Data-aided channel estimation in large antenna systems

paper_content:

This paper is concerned with a uplink scheme for multicell large antenna systems. We study a channel estimation technique where partially decoded data is used to estimate the channel. We show that there are two types of interference components in this scheme that do not vanish even when the number of antennas grows to infinity. The first type, referred to as cross-contamination, is due to the correlation among the data signals from different users. The second type, referred to as self-contamination, is due to the dependency between the channel estimate and the estimation error. Cross contamination is in principle similar to pilot contamination in a conventional pilot-based channel estimation scheme, while self-contamination is unique for the data-aided scheme. For efficient use of the channel, the data part in a signaling frame is typically much longer than the pilot part for a practical system. Consequently, compared with pilot signals, data signals naturally have lower cross correlation. This fact reduces the cross-contamination effect in the data-aided scheme. Furthermore, self-contamination can be effectively suppressed by iterative processing. These results are confirmed by both analyses and simulations.
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paper_title: On composite channel estimation in wireless massive MIMO systems

paper_content:

A multiuser MIMO (MU-MIMO) TDD system in which the base station (BS) uses a large scale antenna array to communicate with single-antenna mobile users is considered. We present novel schemes to estimate both large-scale and small-scale fading coefficients by uplink pilot sequences. The large-scale fading coefficients (LSFCs) are usually ignored or assumed perfectly known and almost all MIMO channel state information (CSI) estimation studies deal solely with small-scale fading coefficients (SSFCs). We propose low complexity algorithms that give reliable estimates for both FCs. The LSFC estimator takes advantage of the excess spatial samples received and the channel hardening effect while the SSFC estimator is based on a rank-reduction approach. Our estimators require a low training overhead and both analysis and numerical experiments prove that they offer superior mean-squared error performance.
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paper_title: Pilot-based channel estimation for OFDM systems by tracking the delay-subspace

paper_content:

In orthogonal frequency division multiplexing (OFDM) systems over fast-varying fading channels, channel estimation and tracking is generally carried out by transmitting known pilot symbols in given positions of the frequency-time grid. The traditional approach consists of two steps. First, the least-squares (LS) estimate is obtained over the pilot subcarriers. Then, this preliminary estimate is interpolated/smoothed over the entire frequency-time grid. In this paper, we propose to add an intermediate step, whose purpose is to increase the accuracy of the estimate over the pilot subcarriers. The presented techniques are based on the observation that the wireless radio channel can be parametrized as a combination of paths, each characterized by a delay and a complex amplitude. The amplitudes show fast temporal variations due to the mobility of terminals while the delays (and their associated delay-subspace) are almost constant over a large number of OFDM symbols. We propose to track the delay-subspace by a subspace tracking algorithm and the amplitudes by the least mean square algorithm (or modifications of the latter). The approach can be extended to multiple input multiple output OFDM or multicarrier code-division multiple-access systems. Analytical results and simulations prove the relevant benefits of the novel structure.
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paper_title: Efficient Coordinated Recovery of Sparse Channels in Massive MIMO

paper_content:

This paper addresses the problem of estimating sparse channels in massive MIMO-OFDM systems. Most wireless channels are sparse in nature with large delay spread. In addition, these channels as observed by multiple antennas in a neighborhood have approximately common support. The sparsity and common support properties are attractive when it comes to the efficient estimation of large number of channels in massive MIMO systems. Moreover, to avoid pilot contamination and to achieve better spectral efficiency, it is important to use a small number of pilots. We present a novel channel estimation approach which utilizes the sparsity and common support properties to estimate sparse channels and require a small number of pilots. Two algorithms based on this approach have been developed which perform Bayesian estimates of sparse channels even when the prior is non-Gaussian or unknown. Neighboring antennas share among each other their beliefs about the locations of active channel taps to perform estimation. The coordinated approach improves channel estimates and also reduces the required number of pilots. Further improvement is achieved by the data-aided version of the algorithm. Extensive simulation results are provided to demonstrate the performance of the proposed algorithms.
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paper_title: DoA estimation and capacity analysis for 2D active massive MIMO systems

paper_content:

Mobile data traffic is expected to have an exponential growth in the future. In order to meet the challenge as well as the form factor limitation on the base station, two-dimensional (2D) “massive MIMO” has been proposed as one of the enabling technologies for future wireless systems. In 2D “massive MIMO” systems, a base station will rely on the uplink sounding signals to figure out the downlink spatial channel information to perform MIMO precoding. Accordingly, direction-of-arrival (DoA) estimation of the underlying three-dimensional (3D) channel at the base station becomes essential for 2D “massive MIMO” systems to realize the predicted capacity gains. In this paper, we will analyze the performance of DoA estimation based on ESPRIT methods and study its impact on the capacity of 2D “massive MIMO” systems. To be specific, for ESPRIT-type algorithms, we will derive the closed-form expressions for the mean square errors of the elevation and azimuth angle estimations. These results will be used to obtain design intuitions for 2D antenna arrays at the base station as well as the capacity of the underlying 2D “massive MIMO” systems.
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paper_title: Sparse channel estimation based on compressed sensing for massive MIMO systems

paper_content:

The sparse channel estimation which sufficiently exploits the inherent sparsity of wireless channels, is capable of improving the channel estimation performance with less pilot overhead. To reduce the pilot overhead in massive MIMO systems, sparse channel estimation exploring the joint channel sparsity is first proposed, where the channel estimation is modeled as a joint sparse recovery problem. Then the block coherence of MIMO channels is analyzed for the proposed model, which shows that as the number of antennas at the base station grows, the probability of joint recovery of the positions of nonzero channel entries will increase. Furthermore, an improved algorithm named block optimized orthogonal matching pursuit (BOOMP) is also proposed to obtain an accurate channel estimate for the model. Simulation results verify our analysis and show that the proposed scheme exploring joint channel sparsity substantially outperforms the existing methods using individual sparse channel estimation.
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paper_title: Relative channel reciprocity calibration in MIMO/TDD systems

paper_content:

Channel state information at the transmitter (CSIT) can greatly improve the capacity of a wireless MIMO communication system. In a time division duplex (TDD) system CSIT can be obtained by exploiting the reciprocity of the wireless channel. This however requires calibration of the radio frequency (RF) chains of the receiver and the transmitter, which are in general not reciprocal. In this paper we investigate different methods for relative calibration in the presence of frequency offsets between transmitter and receiver. We show results of theses calibration methods with real two-directional channel measurements, which were performed using the Eure-com MIMO Openair Sounder (EMOS). We demonstrate that in a single-user MIMO channel and for low signal-to-noise (SNR) ratios, the relative calibration method can increase the capacity close to the theoretical limit.
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paper_title: Argos: practical many-antenna base stations

paper_content:

Multi-user multiple-input multiple-output theory predicts manyfold capacity gains by leveraging many antennas on wireless base stations to serve multiple clients simultaneously through multi-user beamforming (MUBF). However, realizing a base station with a large number antennas is non-trivial, and has yet to be achieved in the real-world. We present the design, realization, and evaluation of Argos, the first reported base station architecture that is capable of serving many terminals simultaneously through MUBF with a large number of antennas (M >> 10). Designed for extreme flexibility and scalability, Argos exploits hierarchical and modular design principles, properly partitions baseband processing, and holistically considers real-time requirements of MUBF. Argos employs a novel, completely distributed, beamforming technique, as well as an internal calibration procedure to enable implicit beamforming with channel estimation cost independent of the number of base station antennas. We report an Argos prototype with 64 antennas and capable of serving 15 clients simultaneously. We experimentally demonstrate that by scaling from 1 to 64 antennas the prototype can achieve up to 6.7 fold capacity gains while using a mere 1/64th of the transmission power.
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paper_title: Analyzing Uplink SINR and Rate in Massive MIMO Systems Using Stochastic Geometry

paper_content:

This paper proposes a stochastic geometry framework to analyze the SINR and rate performance in a large-scale uplink massive MIMO network. Based on the model, expressions are derived for spatial average SINR distributions over user and base station distributions with maximum ratio combining (MRC) and zero-forcing (ZF) receivers. We show that using massive MIMO, the uplink SINR in certain urban marco-cell scenarios is limited by interference. In the interference-limited regime, the results reveal that for MRC receivers, a super-linear (polynomial) scaling law between the number of base station antennas and scheduled users per cell preserves the uplink SIR distribution, while a linear scaling applies to ZF receivers. ZF receivers are shown to outperform MRC receivers in the SIR coverage, and the performance gap is quantified in terms of the difference in the number of antennas to achieve the same SIR distribution. Numerical results verify the analysis. It is found that the optimal compensation fraction in fractional power control to optimize rate is generally different for MRC and ZF receivers. Besides, simulations show that the scaling results derived from the proposed framework apply to the networks where base stations are distributed according to a hexagonal lattice.
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paper_title: Impact of RF mismatches on the performance of massive MIMO systems with ZF precoding

paper_content:

Thanks to the channel reciprocity, the time division duplex (TDD) operation is more preferred in massive multiple-input multiple-output (MIMO) systems. Avoiding the heavy feedback of downlink channel state information (CSI) from the user equipment (UE) to the base station (BS), the uplink CSI can be exploited for the downlink precoding. However, due to the mismatches of the radio frequency (RF) circuits at both sides of the link, the whole communication channels are usually not symmetric in practical systems. This paper is focused on the RF mismatches at the UEs and the BS for the multi-user massive MIMO systems with zero forcing (ZF) precoding. The closed-form expressions of the ergodic sum-rates are derived for evaluating the impact of RF mismatches on the system performance. Theoretical analysis and simulation results show that the RF mismatches at the UEs only lead to a negligible performance loss. However, it is imperative to perform reciprocity calibration at the BS, because the RF mismatches at the BS contribute to the inter-user interference (IUI) and result in a severe system performance degradation.
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paper_title: Effectiveness of implicit beamforming using calibration technique in massive MIMO system

paper_content:

This paper describes the effectiveness of implicit beamforming which enables the transmission without the channel state information (CSI) feedback in massive MIMO system. First, we explain the CSI feedback scheme from the terminal stations to base station gives a very large overhead. The calibration technique, which compensate the difference of complex amplitudes between transmitters and receivers for the implicit beamforming, is next introduced. Finally, the throughput by the IEEE802.11ac based massive MIMO transmission with and without CSI feedback is clarified when considering Medium Access Control efficiency.
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paper_title: Mutual Coupling Calibration for Multiuser Massive MIMO Systems

paper_content:

Massive multiple-input multiple-output (MIMO) is a promising technique to greatly increase the spectral efficiency and may be adopted by the next generation mobile communication systems. Base stations (BSs) equipped with large-scale antennas can serve multiple users simultaneously by exploiting the downlink precoding in time division duplex (TDD) mode. However, channel state information (CSI) of uplink transmissions cannot be simply used for downlink precoding, because the gain mismatches of the transceiver radio frequency (RF) circuits disable the channel reciprocity. In this paper, we focus on antenna calibration for massive MIMO systems with maximal ratio transmit (MRT) precoding to solve the channel nonreciprocity problem. A new calibration method, called mutual coupling calibration, is proposed by using the effect of mutual coupling between adjacent antennas. By exploiting this method, the BS can perform the calibration without extra hardware circuit and users’ involvement. We also build up the model of calibration error and derive the closed-form expressions of the ergodic sum-rates for evaluating the impact of calibration error on system performance. Simulation results verify the high calibration accuracy of the proposed method and show the significant improvement of system performance by performing antenna calibration.
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paper_title: Hardware-impairment compensation for enabling distributed large-scale MIMO

paper_content:

Distributed large-scale MIMO is a promising option for coping with the projected explosion in mobile traffic. It involves multiple Access Points (APs) that are connected to a central server via wired backhaul and act as a distributed MIMO transmitter, serving multiple users via spatial precoding. As is well known, large downlink (DL) spectral efficiencies can be achieved with TDD operation, pilots sent in the uplink (UL), and DL-UL channel reciprocity. With APs made of inexpensive hardware and connected via, e.g., Ethernet, synchronization and reciprocity calibration are the main hurdle for implementing a truly distributed MU-MIMO system. This work studies mechanisms for RF calibration that can enable distributed high-performing large-scale MIMO operation. We propose methods for relative calibration of the APs in order to ensure TDD reciprocity while not relying on an explicitly self-calibrating RF design. As our analysis and simulations suggest, the proposed methods significantly outperform existing self calibration methods without requiring additional signaling overhead and can enable TDD reciprocity for calibration of non-colocated networks.
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paper_title: Scalable Synchronization and Reciprocity Calibration for Distributed Multiuser MIMO

paper_content:

Large-scale distributed Multiuser MIMO (MU-MIMO) is a promising wireless network architecture that combines the advantages of"massive MIMO"and"small cells."It consists of several Access Points (APs) connected to a central server via a wired backhaul network and acting as a large distributed antenna system. We focus on the downlink, which is both more demanding in terms of traffic and more challenging in terms of implementation than the uplink. In order to enable multiuser joint precoding of the downlink signals, channel state information at the transmitter side is required. We consider Time Division Duplex (TDD), where the {\em downlink} channels can be learned from the user uplink pilot signals, thanks to channel reciprocity. Furthermore, coherent multiuser joint precoding is possible only if the APs maintain a sufficiently accurate relative timing and phase synchronization. AP synchronization and TDD reciprocity calibration are two key problems to be solved in order to enable distributed MU-MIMO downlink. In this paper, we propose novel over-the-air synchronization and calibration protocols that scale well with the network size. The proposed schemes can be applied to networks formed by a large number of APs, each of which is driven by an inexpensive 802.11-grade clock and has a standard RF front-end, not explicitly designed to be reciprocal. Our protocols can incorporate, as a building block, any suitable timing and frequency estimator. Here we revisit the problem of joint ML timing and frequency estimation and use the corresponding Cramer-Rao bound to evaluate the performance of the synchronization protocol. Overall, the proposed synchronization and calibration schemes are shown to achieve sufficient accuracy for satisfactory distributed MU-MIMO performance.
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paper_title: Large-Scale Antenna Systems With UL/DL Hardware Mismatch: Achievable Rates Analysis and Calibration

paper_content:

This paper studies the impact of hardware mismatch (HM) between the base station (BS) and the user equipment (UE) in the downlink (DL) of large-scale antenna systems. Analytical expressions to predict the achievable rates are derived for different precoding methods, i.e., matched filter (MF) and regularized zero-forcing (RZF), using large system analysis techniques. Furthermore, the upper bounds on achievable rates of MF and RZF with HM are investigated, which are related to the statistics of the circuit gains of the mismatched hardware. Moreover, we present a study of HM calibration, where we take zero-forcing (ZF) precoding as an example to compare two HM calibration schemes, i.e., Pre-precoding Calibration (Pre-Cal) and Post-precoding Calibration (Post-Cal). The analysis shows that Pre-Cal outperforms Post-Cal schemes. Monte-Carlo simulations are carried out, and numerical results demonstrate the correctness of the analysis.
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paper_title: Spectral efficiency of multi-cell multi-user DAS with pilot contamination

paper_content:

The spectral efficiency of multi-cell multi-user distributed antenna system with imperfect channel state information (CSI) is studied in this paper. First, considering the pilot contamination and minimum mean-squared-error (MMSE) channel estimation, the equivalent channel model is presented and the sum-rate of the uplink transmission is derived. Under a physical channel model, the equivalent channel model can be seen as a special case of the joint correlated MIMO channel model proposed by Gao [1]. Then, the closed-form approximation of the spectral efficiency is derived. The spectral efficiency of the system with large number of antennas is also studied. Finally, the theoretical results are compared with Monte-Carlo simulation, and the performances of DAS and co-located massive MIMO are also compared. It is shown that similar to the systems with perfect CSIs, DAS still has large performance gains compared with massive MIMO.
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paper_title: Message Passing Algorithm for Distributed Downlink Regularized Zero-Forcing Beamforming with Cooperative Base Stations

paper_content:

Base station (BS) cooperation can turn unwanted interference to useful signal energy for enhancing system performance. In the cooperative downlink, zero-forcing beamforming (ZFBF) with a simple scheduler is well known to obtain nearly the performance of the capacity-achieving dirty-paper coding. However, the centralized ZFBF approach is prohibitively complex as the network size grows. In this paper, we devise message passing algorithms for realizing the regularized ZFBF (RZFBF) in a distributed manner using belief propagation. In the proposed methods, the overall computational cost is decomposed into many smaller computation tasks carried out by groups of neighboring BSs and communication is only required between neighboring BSs. More importantly, some exchanged messages can be computed based on channel statistics rather than instantaneous channel state information, leading to significant reduction in computational complexity. Simulation results demonstrate that the proposed algorithms converge quickly to the exact RZFBF and much faster compared to conventional methods.
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paper_title: Large-Scale Multi-User Distributed Antenna System for 5G Wireless Communications

paper_content:

In this paper, we study the large-scale multi-user distributed antenna system (DAS) for hot-spot coverage in the future 5G wireless network. Firstly, the multi- user system model of large- scale DAS is introduced and a simple random pilot reuse scheme is presented to reduce the overhead of pilot. Then, the sum-rate of system is derived, and its asymptotical performance is studied when the number of antennas goes to infinity. Moreover, an attractive method for large-scale DAS using matrix sparsification is presented to simplify the signal processing, which is of great significance for the future research. Finally, we study the detection bit error ratio (BER) and area spectral efficiency of large-scale DAS.
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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: Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?

paper_content:

We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.
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paper_title: Linear Precoding Based on Polynomial Expansion: Large-Scale Multi-Cell MIMO Systems

paper_content:

Large-scale MIMO systems can yield a substantial improvements in spectral efficiency for future communication systems. Due to the finer spatial resolution and array gain achieved by a massive number of antennas at the base station, these systems have shown to be robust to inter-user interference and the use of linear precoding appears to be asymptotically optimal. However, from a practical point of view, most precoding schemes exhibit prohibitively high computational complexity as the system dimensions increase. For example, the near-optimal regularized zero forcing (RZF) precoding requires the inversion of a large matrix. To solve this issue, we propose in this paper to approximate the matrix inverse by a truncated polynomial expansion (TPE), where the polynomial coefficients are optimized to maximize the system performance. This technique has been recently applied in single cell scenarios and it was shown that a small number of coefficients is sufficient to reach performance similar to that of RZF, while it was not possible to surpass RZF. In a realistic multi-cell scenario involving large-scale multi-user MIMO systems, the optimization of RZF precoding has, thus far, not been feasible. This is mainly attributed to the high complexity of the scenario and the non-linear impact of the necessary regularizing parameters. On the other hand, the scalar coefficients in TPE precoding give hope for possible throughput optimization. To this end, we exploit random matrix theory to derive a deterministic expression of the asymptotic signal-to-interference-and-noise ratio for each user based on channel statistics. We also provide an optimization algorithm to approximate the coefficients that maximize the network-wide weighted max-min fairness. The optimization weights can be used to mimic the user throughput distribution of RZF precoding. Using simulations, we compare the network throughput of the proposed TPE precoding with that of the suboptimal RZF scheme and show that our scheme can achieve higher throughput using a TPE order of only 5.
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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: Beam Division Multiple Access Transmission for Massive MIMO Communications

paper_content:

We study multicarrier multiuser multiple-input multiple-output (MU-MIMO) systems, in which the base station employs an asymptotically large number of antennas. We analyze a fully correlated channel matrix and provide a beam domain channel model, where the channel gains are independent of sub-carriers. For this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate, based on which, we develop asymptotically necessary and sufficient conditions for optimal downlink transmission that require only statistical channel state information at the transmitter. Furthermore, we propose a beam division multiple access (BDMA) transmission scheme that simultaneously serves multiple users via different beams. By selecting users within non-overlapping beams, the MU-MIMO channels can be equivalently decomposed into multiple single-user MIMO channels; this scheme significantly reduces the overhead of channel estimation, as well as, the processing complexity at transceivers. For BDMA transmission, we work out an optimal pilot design criterion to minimize the mean square error (MSE) and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. Simulations demonstrate the near-optimal performance of BDMA transmission and the advantages of the proposed pilot sequences.
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paper_title: Message Passing Algorithm for Distributed Downlink Regularized Zero-Forcing Beamforming with Cooperative Base Stations

paper_content:

Base station (BS) cooperation can turn unwanted interference to useful signal energy for enhancing system performance. In the cooperative downlink, zero-forcing beamforming (ZFBF) with a simple scheduler is well known to obtain nearly the performance of the capacity-achieving dirty-paper coding. However, the centralized ZFBF approach is prohibitively complex as the network size grows. In this paper, we devise message passing algorithms for realizing the regularized ZFBF (RZFBF) in a distributed manner using belief propagation. In the proposed methods, the overall computational cost is decomposed into many smaller computation tasks carried out by groups of neighboring BSs and communication is only required between neighboring BSs. More importantly, some exchanged messages can be computed based on channel statistics rather than instantaneous channel state information, leading to significant reduction in computational complexity. Simulation results demonstrate that the proposed algorithms converge quickly to the exact RZFBF and much faster compared to conventional methods.
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paper_title: Large-Scale Multi-User Distributed Antenna System for 5G Wireless Communications

paper_content:

In this paper, we study the large-scale multi-user distributed antenna system (DAS) for hot-spot coverage in the future 5G wireless network. Firstly, the multi- user system model of large- scale DAS is introduced and a simple random pilot reuse scheme is presented to reduce the overhead of pilot. Then, the sum-rate of system is derived, and its asymptotical performance is studied when the number of antennas goes to infinity. Moreover, an attractive method for large-scale DAS using matrix sparsification is presented to simplify the signal processing, which is of great significance for the future research. Finally, we study the detection bit error ratio (BER) and area spectral efficiency of large-scale DAS.
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paper_title: Channel Hardening-Exploiting Message Passing (CHEMP) Receiver in Large-Scale MIMO Systems

paper_content:

In this paper, we propose a multiple-input multiple-output (MIMO) receiver algorithm that exploits channel hardening that occurs in large MIMO channels. Channel hardening refers to the phenomenon where the off-diagonal terms of the matrix become increasingly weaker compared to the diagonal terms as the size of the channel gain matrix increases. Specifically, we propose a message passing detection (MPD) algorithm which works with the real-valued matched filtered received vector (whose signal term becomes, where is the transmitted vector), and uses a Gaussian approximation on the off-diagonal terms of the matrix. We also propose a simple estimation scheme which directly obtains an estimate of (instead of an estimate of), which is used as an effective channel estimate in the MPD algorithm. We refer to this receiver as the channel hardening-exploiting message passing (CHEMP) receiver. The proposed CHEMP receiver achieves very good performance in large-scaleMIMO systems (e.g., in systems with 16 to 128 uplink users and 128 base station antennas). For the considered large MIMO settings, the complexity of the proposed MPD algorithm is almost the same as or less than that of the minimum mean square error (MMSE) detection. This is because the MPD algorithm does not need a matrix inversion. It also achieves a significantly better performance compared to MMSE and other message passing detection algorithms using MMSE estimate of. Further, we design optimized irregular low density parity check (LDPC) codes specific to the considered large MIMO channel and the CHEMP receiver through EXIT chart matching. The LDPC codes thus obtained achieve improved coded bit error rate performance compared to off-the-shelf irregular LDPC codes.
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paper_title: Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method for Uplink Multiuser Large-Scale MIMO Systems

paper_content:

For uplink large-scale MIMO systems, minimum mean square error (MMSE) algorithm is near-optimal but involves matrix inversion with high complexity. In this paper, we propose to exploit the Gauss-Seidel (GS) method to iteratively realize the MMSE algorithm without the complicated matrix inversion. To further accelerate the convergence rate and reduce the complexity, we propose a diagonal-approximate initial solution to the GS method, which is much closer to the final solution than the traditional zero-vector initial solution. We also propose a approximated method to compute log-likelihood ratios (LLRs) for soft channel decoding with a negligible performance loss. The analysis shows that the proposed GS-based algorithm can reduce the computational complexity from O(K^3) to O(K^2), where K is the number of users. Simulation results verify that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm, and achieves the near-optimal performance of the classical MMSE algorithm with a small number of iterations.
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paper_title: New Iterative Detector of MIMO Transmission Using Sparse Decomposition

paper_content:

This paper addresses the problem of decoding in large-scale multiple-input–multiple-output (MIMO) systems. In this case, the optimal maximum-likelihood (ML) detector becomes impractical due to an exponential increase in the complexity with the signal and the constellation dimensions. This paper introduces an iterative decoding strategy with a tolerable complexity order. We consider a MIMO system with finite constellation and model it as a system with sparse signal sources. We propose an ML relaxed detector that minimizes the Euclidean distance with the received signal while preserving a constant $\ell_{1} $ -norm of the decoded signal. We also show that the detection problem is equivalent to a convex optimization problem, which is solvable in polynomial time. Two applications are proposed, and simulation results illustrate the efficiency of the proposed detector.
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paper_title: Chunk-based resource allocation in OFDMA systems - part I: chunk allocation

paper_content:

In this paper, throughput performance analysis of the chunk-based subcarrier allocation is presented by considering the average bit-error-rate (BER) constraint over a chunk in downlink multiuser orthogonal frequency division multiplexing (OFDM) transmission. The outage probabilities per subcarrier are compared between the average BER-constraint based chunk allocation and the average signal-to-noise-ratio (SNR) based chunk allocation. The effects of system parameters, such as the number of users, the number of subcarriers per chunk, and the coherence bandwidth, are evaluated. The numerical results show that, when the chunk bandwidth is smaller than the coherence bandwidth, the average downlink throughput of the chunk-based subcarrier allocation is very close to that of the single-subcarrier-based allocation. When the number of users is small, the average throughput increases dramatically with increasing the number of users due to multiuser diversity, whereas when the number of users is large, the multiuser diversity gain is saturated. The effective throughput of the average BER-constraint based chunk allocation is higher than that of the average SNR based chunk allocation, especially when the number of users is large or when the ratio of the chunk bandwidth to the coherence bandwidth is large.
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paper_title: An improved dynamic clustering algorithm for multi-user distributed antenna system

paper_content:

The multi-user distributed antenna system (MUDAS) is considered as a promising technology in the future wireless communication. Compared to the multi-user centralized antenna system (CAS), MU-DAS can improve the spectral efficiency significantly. One most attractive feature is that the implementation of the MU-DAS can be reduced by using the clustering approach of the remote antenna units (RAUs). However, the cluster algorithm of DAS has been only partially investigated. In this paper, a novel dynamic clustering algorithm for MU-DAS is presented. The objective of this algorithm is to maximize the total system capacity by using the full channel state information (CSI) or partial CSI. Simulation results show that our approach yields significant capacity gains when compared with some proposed clustering algorithms, and also the implementation complexity of the proposed algorithm remains very low.
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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: Sparse Beamforming and User-Centric Clustering for Downlink Cloud Radio Access Network

paper_content:

This paper considers a downlink cloud radio access network (C-RAN) in which all the base-stations (BSs) are connected to a central computing cloud via digital backhaul links with finite capacities. Each user is associated with a user-centric cluster of BSs; the central processor shares the user's data with the BSs in the cluster, which then cooperatively serve the user through joint beamforming. Under this setup, this paper investigates the user scheduling, BS clustering, and beamforming design problem from a network utility maximization perspective. Differing from previous works, this paper explicitly considers the per-BS backhaul capacity constraints. We formulate the network utility maximization problem for the downlink C-RAN under two different models depending on whether the BS clustering for each user is dynamic or static over different user scheduling time slots. In the former case, the user-centric BS cluster is dynamically optimized for each scheduled user along with the beamforming vector in each time-frequency slot, whereas in the latter case, the user-centric BS cluster is fixed for each user and we jointly optimize the user scheduling and the beamforming vector to account for the backhaul constraints. In both cases, the nonconvex per-BS backhaul constraints are approximated using the reweighted l 1 -norm technique. This approximation allows us to reformulate the per-BS backhaul constraints into weighted per-BS power constraints and solve the weighted sum rate maximization problem through a generalized weighted minimum mean square error approach. This paper shows that the proposed dynamic clustering algorithm can achieve significant performance gain over existing naive clustering schemes. This paper also proposes two heuristic static clustering schemes that can already achieve a substantial portion of the gain.
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paper_title: Dynamic Nested Clustering for Parallel PHY-Layer Processing in Cloud-RANs

paper_content:

Featured by centralized processing and cloud based infrastructure, Cloud Radio Access Network (C-RAN) is a promising solution to achieving an unprecedented system capacity in future wireless cellular networks. The huge capacity gain mainly comes from the centralized and coordinated signal processing at the cloud server. However, full-scale coordination in a large-scale C-RAN requires the processing of very large channel matrices, leading to high computational complexity and channel estimation overhead. To tackle this challenge, we establish a unified theoretical framework for dynamic clustering by exploiting the near-sparsity of large C-RAN channel matrices. Based on this framework, we propose a dynamic nested clustering (DNC) algorithm that greatly improves the system scalability in terms of baseband-processing and channel-estimation complexity. With the proposed DNC algorithm, we show that the computational complexity (i.e., the computation time with serial processing) for the optimal linear detector is significantly reduced from $O(N^3)$ to $O(N^2)$ , where $N$ is the number of remote radio heads (RRHs) in the C-RAN. Moreover, the proposed DNC algorithm is also amenable to parallel processing, which further reduces the computation time to $O(N^{\frac{42}{23}})$ .
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paper_title: Beam Division Multiple Access Transmission for Massive MIMO Communications

paper_content:

We study multicarrier multiuser multiple-input multiple-output (MU-MIMO) systems, in which the base station employs an asymptotically large number of antennas. We analyze a fully correlated channel matrix and provide a beam domain channel model, where the channel gains are independent of sub-carriers. For this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate, based on which, we develop asymptotically necessary and sufficient conditions for optimal downlink transmission that require only statistical channel state information at the transmitter. Furthermore, we propose a beam division multiple access (BDMA) transmission scheme that simultaneously serves multiple users via different beams. By selecting users within non-overlapping beams, the MU-MIMO channels can be equivalently decomposed into multiple single-user MIMO channels; this scheme significantly reduces the overhead of channel estimation, as well as, the processing complexity at transceivers. For BDMA transmission, we work out an optimal pilot design criterion to minimize the mean square error (MSE) and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. Simulations demonstrate the near-optimal performance of BDMA transmission and the advantages of the proposed pilot sequences.
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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 utility principle access control for beyond 3G mobile system

paper_content:

With current research focusing on beyond 3G (B3G)/4G mobile systems, many advanced techniques are investigated by world-wide research institutes and standard organization, such as multi input multi output (MIMO), orthogonal frequency division multiplex (OFDM), and multi-antenna distributed cellular network architecture. Based on these novel techniques, the radio resource management (RRM) strategies, such as access control, also need to be developed. This paper proposes the maximum utility principle access control (MUPAC) basing on Dijkstra's Shortest Path Algorithm for multi-antenna cellular network architectures. In the accessing process of the proposed algorithm, the shortest path in Dijkstra's Algorithm is replaced by the cost of accessing process, which is represented by utility function. Taking Generalized Distributed Cellular Architecture—Group Cell as an example, MUPAC is described in details with the utility function, maximum utility principle, flow chart of accessing process. Performance evaluation and analyses verify the merits of MUPAC algorithm in improving system capacity, accessing success probability, and efficiency of system resources usage. Copyright © 2007 John Wiley & Sons, Ltd.
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paper_title: Chunk-Based Resource Allocation in OFDMA Systems—Part II: Joint Chunk, Power and Bit Allocation

paper_content:

By grouping a number of adjacent subcarriers into a chunk, resource allocation can be carried out chunk by chunk in orthogonal frequency division multiple access (OFDMA) systems. Chunk-based resource allocation is an effective approach to reduce the complexity of resource allocation in OFDMA systems. In this paper, a chunk-based resource allocation scheme, i.e. joint chunk, power and bit allocation, is proposed and analyzed by maximizing the throughput under a total transmit power constraint. A scaling factor is introduced to achieve optimal allocation. Considering the digital nature of bits per symbol per subcarrier (bits/symbol/subcarrier), a digitization process is proposed to digitize the theoretically allocated bits/symbol/subcarrier to integer. System parameters, such as the power constraint, number of users, coherence bandwidth, number of subcarriers and number of chunks, are introduced and their impacts on the average throughput are studied. The performance of the dynamic power allocation scheme is compared with the fixed power allocation scheme. The numerical results show that the theoretical throughput of the fixed power allocation scheme is quite close to that of the dynamic power allocation scheme. However, when the digital nature of bits/symbol/subcarrier is considered, the average throughput of the dynamic power allocation outperforms the fixed power allocation scheme.
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paper_title: An Uplink Capacity Analysis of the Distributed Antenna System (DAS): From Cellular DAS to DAS with Virtual Cells

paper_content:

Performance of cellular networks is severely limited by intense inter-cell interference due to aggressive frequency reuse among cells. How to characterize the dependency of inter-cell interference on positions of BS antennas and users is a key question for the capacity analysis of cellular systems, which unfortunately remains elusive. In this paper, a comparative study on the uplink ergodic sum capacity of cellular systems is presented, where L_c BS antennas are either co-located at the cell center or uniformly distributed within each cell. With a large number of users, the inter-cell interference density is shown to be inversely proportional to L_c if the co-located antenna (CA) layout is adopted. With the distributed antenna (DA) layout, it scales in the order of L_{c}^{-\frac α{2}}, where α is the path-loss factor, and is much lower than that in the CA case when L_c is large. Substantial gains on the uplink sum capacity are achieved by the DA layout thanks to the reduction of inter-cell interference level. The analysis also reveals that the inter-cell interference density of each BS antenna is sensitive to its position. With the DA layout, BS antennas at cell boundary areas suffer from much higher inter-cell interference than those at the cell center, which may exacerbate the performance disparity of users in cellular systems. To tackle the cell-edge problem, a distributed antenna system (DAS) is further considered, where L BS antennas are distributed over a wide area, and each user chooses Vl L surrounding BS antennas as its virtual cell, i.e., its own serving BS antenna set. A uniform inter-cell interference density is shown to be achieved thanks to the adaptive formation of virtual cells. More importantly, by the use of virtual cell, the number of users served by each BS antenna decreases with an increasing L, implying that much of the signal processing and information exchange can be performed in a local and distributed way. The uplink ergodic sum capacity and the ergodic rate with orthogonal access of DASs with V=1 are further derived, and shown to be close to each other even with a large L. It is in sharp contrast to cellular systems where a significant tradeoff between performance and complexity has to be made when the number of BS antennas is large.
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paper_title: Capacity analysis of interlaced clustering in a distributed antenna system

paper_content:

Low signal strength and high interference lead to significantly reduced data-rates at the cell edge. With rising demand for spectrum and systems moving closer to universal frequency reuse, the problem has become more pronounced. Techniques like Fractional Frequency Reuse boost the edgeuser performance at the cost of the spectral efficiency and are therefore sub-optimal. In this paper we investigate interlaced clustering as a solution to the edge user problem for a general distributed cellular transmission system, and explore a multicell Distributed Antenna System as a particular example. In interlaced clustering, different parts of the spectrum use coverage patterns that are spatially shifted (by less than a cell size) replicas of each other. An information theoretic analysis is presented to characterize the proportional fairness boundary point of the achievable rate region. In the process, the joint resource allocation problem is formulated and shown to be convex. As opposed to using interior point methods which are relatively slower, the current paper proposes a novel gradientsearch algorithm to solve the resource allocation problem. It is demonstrated that fractional frequency reuse can in fact be represented as a special (albeit sub-optimal) case of interlaced clustering. Simulation results show that interlaced clustering can boost the edge-user rates by a factor of 2 with negligible degradation of rates in the cell interior. Results also show that interlaced clustering outperforms the edge-user rates achieved with fractional frequency reuse by a factor of 1∶5. The theoretical results are validated by comparing performance to a practical proportional fairness scheduler.
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Title: An overview of transmission theory and techniques of large-scale antenna systems for 5G wireless communications

Section 1: Introduction
Description 1: Provide an overview of the increasing demand for mobile data traffic, challenges with 4G systems, and the potential and challenges of 5G with LSAS.

Section 2: Spectral efficiency analysis of LSAS
Description 2: Discuss the theoretical analysis of spectral efficiency, including capacity analysis, system-level spectral efficiency, and future research directions.

Section 3: Theoretical analysis of spectral efficiency
Description 3: Explore the mathematical models and equations for analyzing spectral efficiency and their implications for LSAS performance.

Section 4: System-level spectral efficiency
Description 4: Examine methods and approaches to study system-level spectral efficiency and the impact of various system parameters.

Section 5: Topics for future research
Description 5: Identify areas requiring further research, particularly focusing on pilot contamination, hardware non-idealities, and high mobility scenarios.

Section 6: CSI acquisition in LSAS
Description 6: Analyze the challenges and techniques for Channel State Information (CSI) acquisition, including pilot design, channel estimation methods, and reciprocity calibration for TDD systems.

Section 7: Pilot design
Description 7: Delve into the different methods of pilot design, including orthogonal and non-orthogonal techniques, and their impact on pilot overhead and efficiency.

Section 8: Channel estimation methods
Description 8: Discuss various methods for channel estimation, including exploiting sparsity, compress sensing, and blind channel estimation.

Section 9: Reciprocity calibration for TDD systems
Description 9: Investigate methods to calibrate RF mismatches and ensure reciprocity in TDD systems for LSAS.

Section 10: Transmission methods of multi-user LSAS
Description 10: Overview the methods for uplink and downlink transmission in multi-user LSAS, focusing on capacity-approaching transceivers and low-complexity solutions.

Section 11: SDMA based on statistical CSI
Description 11: Review Space Division Multiple Access (SDMA) techniques utilizing statistical CSI for efficient multi-user transmission.

Section 12: Downlink transmission in large-scale DAS
Description 12: Explore methods for downlink transmission in distributed antenna systems, leveraging sparsity to reduce complexity.

Section 13: Low-complexity receivers
Description 13: Examine receiver technologies that balance performance and computational complexity, specifically within interference-limited LSAS.

Section 14: Resource allocation in LSAS
Description 14: Discuss strategies for optimizing spatial and power resources and user grouping in LSAS, with a focus on low-complexity solutions.

Section 15: Conclusion
Description 15: Summarize key findings, state-of-the-art progress, and the future potential of LSAS technologies in the context of 5G communications.