Wideband spectrum sensing for cognitive radio networks: a survey
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paper_title: On capacity of cognitive radio networks with average interference power constraints

paper_content:

Cognitive radio (CR) has been considered as a promising technology to improve the spectrum utilization. In this paper we analyze the capacity of a CR network with average received interference power constraints. Under the assumptions of uniform node placements and a simple power control scheme, the maximum transmit power of a target CR transmitter is characterized by its cumulative distribution function (CDF). We study two CR scenarios for future applications. The first scenario is called the CR based central access network, which aims at providing broadband access to CR devices. In the second scenario, the so-called CR assisted virtual multiple-input multiple-output (MIMO) network, CR is used to improve the access capability of a cellular system. The uplink ergodic channel capacities of both scenarios are derived and analyzed with an emphasis on understanding the impact of numbers of primary users and CR users on the capacity. Numerical and simulation results suggest that the CR based central access network is more suitable for less-populated rural areas where a relatively low density of primary receivers is expected; while the CR assisted virtual MIMO network performs better in urban environments with a dense population of mobile CR users.
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paper_title: Computationally Tractable Model of Energy Detection Performance over Slow Fading Channels

paper_content:

Energy detection (ED) has been widely used for detecting unknown deterministic signals in many wireless communication applications, e.g., cognitive radio, and ultra-wideband (UWB). However, the performance analysis of ED over slow fading channels is cumbersome, because it is difficult to derive closed-form expressions for the average probability of detection involving the generalised Marcum Q-function and the log-normal distribution. In this letter, we derive an approximation of the average probability of detection over a slow fading channel by replacing the log-normal distribution with a Wald distribution. In addition, we analyze the detection performance of the ED using a square-law combining scheme over multiple independent and identically distributed slow fading channels.
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paper_title: Computationally Tractable Model of Energy Detection Performance over Slow Fading Channels

paper_content:

Energy detection (ED) has been widely used for detecting unknown deterministic signals in many wireless communication applications, e.g., cognitive radio, and ultra-wideband (UWB). However, the performance analysis of ED over slow fading channels is cumbersome, because it is difficult to derive closed-form expressions for the average probability of detection involving the generalised Marcum Q-function and the log-normal distribution. In this letter, we derive an approximation of the average probability of detection over a slow fading channel by replacing the log-normal distribution with a Wald distribution. In addition, we analyze the detection performance of the ED using a square-law combining scheme over multiple independent and identically distributed slow fading channels.
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paper_title: A Wavelet Approach to Wideband Spectrum Sensing for Cognitive Radios

paper_content:

In cognitive radio networks, the first cognitive task preceding any form of dynamic spectrum management is the sensing and identification of spectrum holes in wireless environments. This paper develops a wavelet approach to efficient spectrum sensing of wideband channels. The signal spectrum over a wide frequency band is decomposed into elementary building blocks of subbands that are well characterized by local irregularities in frequency. As a powerful mathematical tool for analyzing singularities and edges, the wavelet transform is employed to detect and estimate the local spectral irregular structure, which carries important information on the frequency locations and power spectral densities of the subbands. Along this line, a couple of wideband spectrum sensing techniques are developed based on the local maxima of the wavelet transform modulus and the multi-scale wavelet products. The proposed sensing techniques provide an effective radio sensing architecture to identify and locate spectrum holes in the signal spectrum.
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paper_title: Filter Bank Spectrum Sensing for Cognitive Radios

paper_content:

The primary task in any cognitive radio (CR) network is to dynamically explore the radio spectrum and reliably determine portion(s) of the frequency band that may be used for the communication link(s). Accordingly, each CR node in the network has to be equipped with a spectrum analyzer. In this paper, we propose filter banks as a tool for spectrum sensing in CR systems. Various choices of filter banks are suggested and their performance are evaluated theoretically and through numerical examples. Moreover, the proposed spectrum analyzer is contrasted with the Thomson's multitaper (MT) method - a method that in the recent literature has been recognized as the best choice for spectrum sensing in CR systems. A novel derivation of the MT method that facilitates our comparisons as well as reveals an important aspect of the MT method that has been less emphasized in the recent literature is also presented.
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paper_title: Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio Networks

paper_content:

Spectrum sensing is an essential functionality that enables cognitive radios to detect spectral holes and to opportunistically use under-utilized frequency bands without causing harmful interference to legacy (primary) networks. In this paper, a novel wideband spectrum sensing technique referred to as multiband joint detection is introduced, which jointly detects the primary signals over multiple frequency bands rather than over one band at a time. Specifically, the spectrum sensing problem is formulated as a class of optimization problems, which maximize the aggregated opportunistic throughput of a cognitive radio system under some constraints on the interference to the primary users. By exploiting the hidden convexity in the seemingly nonconvex problems, optimal solutions can be obtained for multiband joint detection under practical conditions. The situation in which individual cognitive radios might not be able to reliably detect weak primary signals due to channel fading/shadowing is also considered. To address this issue by exploiting the spatial diversity, a cooperative wideband spectrum sensing scheme refereed to as spatial-spectral joint detection is proposed, which is based on a linear combination of the local statistics from multiple spatially distributed cognitive radios. The cooperative sensing problem is also mapped into an optimization problem, for which suboptimal solutions can be obtained through mathematical transformation under conditions of practical interest. Simulation results show that the proposed spectrum sensing schemes can considerably improve system performance. This paper establishes useful principles for the design of distributed wideband spectrum sensing algorithms in cognitive radio networks.
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paper_title: Cyclic Feature Detection With Sub-Nyquist Sampling for Wideband Spectrum Sensing

paper_content:

For cognitive radio networks, efficient and robust spectrum sensing is a crucial enabling step for dynamic spectrum access. Cognitive radios need to not only rapidly identify spectrum opportunities over very wide bandwidth, but also make reliable decisions in noise-uncertain environments. Cyclic spectrum sensing techniques work well under noise uncertainty, but require high-rate sampling which is very costly in the wideband regime. This paper develops robust and compressive wideband spectrum sensing techniques by exploiting the unique sparsity property of the two-dimensional cyclic spectra of communications signals. To do so, a new compressed sensing framework is proposed for extracting useful second-order statistics of wideband random signals from digital samples taken at sub-Nyquist rates. The time-varying cross-correlation functions of these compressive samples are formulated to reveal the cyclic spectrum, which is then used to simultaneously detect multiple signal sources over the entire wide band. Because the proposed wideband cyclic spectrum estimator utilizes all the cross-correlation terms of compressive samples to extract second-order statistics, it is also able to recover the power spectra of stationary signals as a special case, permitting lossless rate compression even for non-sparse signals. Simulation results demonstrate the robustness of the proposed spectrum sensing algorithms against both sampling rate reduction and noise uncertainty in wireless networks.
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paper_title: Distributed Compressive Spectrum Sensing in Cooperative Multihop Cognitive Networks

paper_content:

In wideband cognitive radio (CR) networks, spectrum sensing is an essential task for enabling dynamic spectrum sharing, but entails several major technical challenges: very high sampling rates required for wideband processing, limited power and computing resources per CR, frequency-selective wireless fading, and interference due to signal leakage from other coexisting CRs. In this paper, a cooperative approach to wideband spectrum sensing is developed to overcome these challenges. To effectively reduce the data acquisition costs, a compressive sampling mechanism is utilized which exploits the signal sparsity induced by network spectrum under-utilization. To collect spatial diversity against wireless fading, multiple CRs collaborate during the sensing task by enforcing consensus among local spectral estimates; accordingly, a decentralized consensus optimization algorithm is derived to attain high sensing performance at a reasonable computational cost and power overhead. To identify spurious spectral estimates due to interfering CRs, the orthogonality between the spectrum of primary users and that of CRs is imposed as constraints for consensus optimization during distributed collaborative sensing. These decentralized techniques are developed for both cases of with and without channel knowledge. Simulations testify the effectiveness of the proposed cooperative sensing approach in multi-hop CR networks.
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paper_title: Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

paper_content:

Wideband analog signals push contemporary analog-to-digital conversion (ADC) systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the band limit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its band limit in hertz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W hertz. In contrast to Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system's performance that supports the empirical observations.
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paper_title: Wideband Spectrum Sensing with Sub-Nyquist Sampling in Cognitive Radios

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Multi-rate asynchronous sub-Nyquist sampling (MASS) is proposed for wideband spectrum sensing. Corresponding spectral recovery conditions are derived and the probability of successful recovery is given. Compared to previous approaches, MASS offers lower sampling rate, and is an attractive approach for cognitive radio networks.
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paper_title: Perfect Reconstruction Formulas and Bounds on Aliasing Error in Sub-Nyquist Nonuniform Sampling of Multiband Signals

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We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class /spl Bscr/(/spl Fscr/) of multiband signals with spectral support /spl Fscr/, at rates arbitrarily close to the Landau (1969) minimum rate equal to the Lebesgue measure of /spl Fscr/, even when /spl Fscr/ does not tile R under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band-limited to the "span of /spl Fscr/" (the smallest interval containing /spl Fscr/) which is a bigger class than the valid signals /spl Bscr/(/spl Fscr/), band-limited to /spl Fscr/. We also examine the performance of the reconstruction system when the input contains additive sample noise.
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Title: Wideband Spectrum Sensing for Cognitive Radio Networks: A Survey

Section 1: INTRODUCTION
Description 1: This section introduces the importance of radio frequency spectrum, discusses cognitive radio technologies, and outlines the need for wideband spectrum sensing.

Section 2: ABSTRACT
Description 2: This section provides an overview of the survey, summarizing the focus on wideband spectrum sensing algorithms and highlighting key techniques and challenges.

Section 3: NARROWBAND SPECTRUM SENSING
Description 3: This section reviews traditional narrowband spectrum sensing techniques, including matched filtering, energy detection, and cyclostationary feature detection, and discusses their limitations.

Section 4: WIDEBAND SPECTRUM SENSING
Description 4: This section explains the concept of wideband spectrum sensing, differentiates it from narrowband sensing, and categorizes the wideband sensing techniques into Nyquist and sub-Nyquist approaches.

Section 5: NYQUIST WIDEBAND SENSING
Description 5: This section discusses Nyquist rate wideband sensing techniques, including multiband joint detection, wavelet-based spectrum sensing, superheterodyne techniques, and filter bank methods.

Section 6: SUB-NYQUIST WIDEBAND SENSING
Description 6: This section explores sub-Nyquist wideband sensing approaches such as compressive sensing and multichannel sub-Nyquist sampling techniques, including their advantages and inherent challenges.

Section 7: OPEN RESEARCH CHALLENGES
Description 7: This section identifies and discusses key research challenges in implementing wideband spectrum sensing, such as sparse basis selection, adaptive wideband sensing, and cooperative wideband sensing.

Section 8: CONCLUDING REMARKS
Description 8: This section provides concluding thoughts, summarizing the survey's key points and emphasizing the importance and potential of wideband spectrum sensing for cognitive radio networks.