A review on spectrum sensing for cognitive radio: challenges and solutions
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paper_title: Optimum Active Array Processing Structure and Space-Time Factorability

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An active array processor is concerned with the problem of detecting a signal echo, reflected from a target, in the presence of reverberation (clutter). The processor can also be used to estimate target range and bearing. It is a priori not evident whether the optimum (likelihood ratio) detector can be factored into spatial and temporal operations, thus resulting in a simpler processor implementation. This paper studies this problem for a linear continuous array in a reverberation-limited environment. Conditions on signal, reverberation, and array parameters are derived under which the optimum detector is factorable. The validity of using factorability as a criterion of signal design is briefly examined. Finally, the relationship between space-time factorability and range-bearing estimates is pointed out.
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paper_title: Spectrum Survey in Singapore: Occupancy Measurements and Analyses

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We study the 24-hour spectrum usage pattern in Singapore in the frequency bands ranging from 80 MHz to 5850 MHz. The objectives are to find how the scarce radio spectrum allocated to different services is utilized in Singapore and identify the bands that could be accessed for future opportunistic use due to their low or no active utilization. The results from the spectrum measurements taken over 12 weekday periods reveal that a significant amount of spectrum in Singapore has very low occupancy all the time. The occupancy is quantified as the amount of spectrum detected above a certain received power threshold. The outcome of this study suggests that Singapore has a great potential for employing emerging spectrum sharing technology such as the cognitive radio technology to accommodate enormous demands for future wireless services. However, this study of spectrum survey is preliminary in its nature and future long term studies need to be performed to determine any potential secondary usage on those channels that have low or no active utilization.
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paper_title: Cooperative Sensing for Primary Detection in Cognitive Radio

paper_content:

One of the main requirements of cognitive radio systems is the ability to reliably detect the presence of licensed primary transmissions. Previous works on the problem of detection for cognitive radio have suggested the necessity of user cooperation in order to be able to detect at the low signal-to-noise ratios experienced in practical situations. We consider a system of cognitive radio users who cooperate with each other in trying to detect licensed transmissions. Assuming that the cooperating nodes use identical energy detectors, we model the received signals as correlated log-normal random variables and study the problem of fusing the decisions made by the individual nodes. We design a linear-quadratic (LQ) fusion strategy based on a deflection criterion for this problem, which takes into account the correlation between the nodes. Using simulations we show that when the observations at the sensors are correlated, the LQ detector significantly outperforms the counting rule, which is the fusion rule that is obtained by ignoring the correlation.
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paper_title: NeXt generation/dynamic spectrum access/cognitive Radio Wireless Networks: A Survey

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Today's wireless networks are characterized by a fixed spectrum assignment policy. However, a large portion of the assigned spectrum is used sporadically and geographical variations in the utilization of assigned spectrum ranges from 15% to 85% with a high variance in time. The limited available spectrum and the inefficiency in the spectrum usage necessitate a new communication paradigm to exploit the existing wireless spectrum opportunistically. This new networking paradigm is referred to as NeXt Generation (xG) Networks as well as Dynamic Spectrum Access (DSA) and cognitive radio networks. The term xG networks is used throughout the paper. The novel functionalities and current research challenges of the xG networks are explained in detail. More specifically, a brief overview of the cognitive radio technology is provided and the xG network architecture is introduced. Moreover, the xG network functions such as spectrum management, spectrum mobility and spectrum sharing are explained in detail. The influence of these functions on the performance of the upper layer protocols such as routing and transport are investigated and open research issues in these areas are also outlined. Finally, the cross-layer design challenges in xG networks are discussed.
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paper_title: Cluster-Based Cooperative Spectrum Sensing in Cognitive Radio Systems

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In cognitive radio systems, secondary users can be coordinated to perform cooperative spectrum sensing so as to detect the primary user more accurately. However, when the sensing observations are forwarded to a common receiver through fading channels, the sensing performance can be severely degraded. In this paper, we propose a cluster-based cooperative spectrum sensing method to improve the sensing performance. By separating all the secondary users into a few clusters and selecting the most favorable user in each cluster to report to the common receiver, the proposed method can exploit the user selection diversity so that the sensing performance can be enhanced. Furthermore, decision fusion and energy fusion are both studied and the analytical performance results are given. Numerical results show that the sensing performance is improved significantly as opposed to conventional spectrum sensing.
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paper_title: Maximum-Minimum Eigenvalue Detection for Cognitive Radio

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Sensing (signal detection) is a fundamental problem in cognitive radio. In this paper, a new method is proposed based on the eigenvalues of the covariance matrix of the received signal. It is shown that the ratio of the maximum eigenvalue to the minimum eigenvalue can be used to detect the signal existence. Based on some latest random matrix theories (RMT), we can quantize the ratio and find the threshold. The probability of false alarm is also found by using the RMT. The proposed method overcomes the noise uncertainty difficulty while keeps the advantages of the energy detection. The method can be used for various sensing applications without knowledge of the signal, the channel and noise power. Simulations based on randomly generated signals and captured ATSC DTV signals are presented to verify the methods.
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paper_title: White-Space Sensing Device for Detecting Vacant Channels in TV Bands

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Measurements performed at several locations clearly show that frequency spectrum is under-utilized. Cognitive radio is a strong candidate to ensure better spectrum utilization by providing access in an opportunistic manner. Simulations performed on the algorithm that we proposed show promising results in sensing vacant channels in TV bands. Here we present the work, which implements the algorithm on a real-time prototype, and measure its sensing performance in actual environments. Results show that our algorithm is robust under realistic conditions. This confirmation will give much needed confidence in the capability of cognitive radio systems to detect the operation of primary users and protect their use of spectrum.
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paper_title: Optimal Linear Cooperation for Spectrum Sensing in Cognitive Radio Networks

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Cognitive radio technology has been proposed to improve spectrum efficiency by having the cognitive radios act as secondary users to opportunistically access under-utilized frequency bands. Spectrum sensing, as a key enabling functionality in cognitive radio networks, needs to reliably detect signals from licensed primary radios to avoid harmful interference. However, due to the effects of channel fading/shadowing, individual cognitive radios may not be able to reliably detect the existence of a primary radio. In this paper, we propose an optimal linear cooperation framework for spectrum sensing in order to accurately detect the weak primary signal. Within this framework, spectrum sensing is based on the linear combination of local statistics from individual cognitive radios. Our objective is to minimize the interference to the primary radio while meeting the requirement of opportunistic spectrum utilization. We formulate the sensing problem as a nonlinear optimization problem. By exploiting the inherent structures in the problem formulation, we develop efficient algorithms to solve for the optimal solutions. To further reduce the computational complexity and obtain solutions for more general cases, we finally propose a heuristic approach, where we instead optimize a modified deflection coefficient that characterizes the probability distribution function of the global test statistics at the fusion center. Simulation results illustrate significant cooperative gain achieved by the proposed strategies. The insights obtained in this paper are useful for the design of optimal spectrum sensing in cognitive radio networks.
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paper_title: Cognitive radio: making software radios more personal

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Software radios are emerging as platforms for multiband multimode personal communications systems. Radio etiquette is the set of RF bands, air interfaces, protocols, and spatial and temporal patterns that moderate the use of the radio spectrum. Cognitive radio extends the software radio with radio-domain model-based reasoning about such etiquettes. Cognitive radio enhances the flexibility of personal services through a radio knowledge representation language. This language represents knowledge of radio etiquette, devices, software modules, propagation, networks, user needs, and application scenarios in a way that supports automated reasoning about the needs of the user. This empowers software radios to conduct expressive negotiations among peers about the use of radio spectrum across fluents of space, time, and user context. With RKRL, cognitive radio agents may actively manipulate the protocol stack to adapt known etiquettes to better satisfy the user's needs. This transforms radio nodes from blind executors of predefined protocols to radio-domain-aware intelligent agents that search out ways to deliver the services the user wants even if that user does not know how to obtain them. Software radio provides an ideal platform for the realization of cognitive radio.
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paper_title: TV white-space sensing prototype

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Measurements performed at several locations clearly show that frequency spectrum is under-utilized. Cognitive radio (CR) is a strong candidate to ensure better spectrum utilization by providing access in an opportunistic manner, i.e., when the spectrum is temporary or spatially unutilized (a.k.a. white-space). The key enabling technology for realizing better frequency spectrum utilization in CR system is spectrum sensing. In particular, spectrum sensing in television (TV) bands is of great interest due to the potential availability of spectrum as a result of the planned migration of analog TV broadcasting to digital TV broadcasting. In this paper, we present the TV white-space prototype that we developed to detect vacant spectrum in TV bands. The prototype is implemented on a real-time platform and tested in practical environments. Results show that our prototype is able to detect vacant channels up to sensitivities from -116 to -120 dBm under realistic conditions. This confirmation will give the much needed confidence in the capability of CR systems to detect the operation of primary users and protect their use of spectrum. Copyright © 2008 John Wiley & Sons, Ltd.
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paper_title: Cognitive radio: brain-empowered wireless communications

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Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a software-defined radio, is defined as an intelligent wireless communication system that is aware of its environment and uses the methodology of understanding-by-building to learn from the environment and adapt to statistical variations in the input stimuli, with two primary objectives in mind: /spl middot/ highly reliable communication whenever and wherever needed; /spl middot/ efficient utilization of the radio spectrum. Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks. 1) Radio-scene analysis. 2) Channel-state estimation and predictive modeling. 3) Transmit-power control and dynamic spectrum management. This work also discusses the emergent behavior of cognitive radio.
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paper_title: Spectral correlation based signal detection method for spectrum sensing in IEEE 802.22 WRAN systems

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In this paper, signal detection methods for spectrum sensing in IEEE 802.22 wireless RAN systems are discussed. As most of the manmade signals can be treated as a cyclostationary random process, the spectral correlation function is effective for the detection of these signals. In WRAN systems, due to the specific detection environment, the computational complexity of the spectral correlation based method is significantly reduced. Peak detection in the high SNR environment together with contour figure based unique patterns search method in the low SNR environment are proposed for the primary user signal detection.
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paper_title: Spectrum sensing in cognitive radio networks: requirements, challenges and design trade-offs

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Opportunistic unlicensed access to the (temporarily) unused frequency bands across the licensed radio spectrum is currently being investigated as a means to increase the efficiency of spectrum usage. Such opportunistic access calls for implementation of safeguards so that ongoing licensed operations are not compromised. Among different candidates, sensing-based access, where the unlicensed users transmit if they sense the licensed band to be free, is particularly appealing due to its low deployment cost and its compatibility with the legacy licensed systems. The ability to reliably and autonomously identify unused frequency bands is envisaged as one of the main functionalities of cognitive radios. In this article we provide an overview of the regulatory requirements and major challenges associated with the practical implementation of spectrum sensing functionality in cognitive radio systems. Furthermore, we outline different design trade-offs that have to be made in order to enhance various aspects of the system's performance.
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paper_title: Covariance Based Signal Detections for Cognitive Radio

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Sensing (signal detection) is a fundamental problem in cognitive radio. The statistical covariances of signal and noise are usually different. In this paper, this property is used to differentiate signal from noise. The sample covariance matrix of the received signal is computed and transformed based on the receiving filter. Then two detection methods are proposed based on the transformed sample covariance matrix. One is the covariance absolute value (CAV) detection and the other is the covariance Frobenius norm (CFN) detection. Theoretical analysis and threshold setting for the algorithms are discussed. Both methods do not need any information of the signal, the channel and noise power as a priori. Simulations based on captured ATSC DTV signals are presented to verify the methods.
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paper_title: Cooperative Spectrum Sensing in Cognitive Radio, Part II: Multiuser Networks

paper_content:

In cognitive radio networks, cognitive (unlicensed) users need to continuously monitor spectrum for the presence of primary (licensed) users. In this paper, we illustrate the benefits of cooperation in cognitive radio. We show that by allowing the cognitive users operating in the same band to cooperate we can reduce the detection time and thus increase the overall agility. We first consider a two-user cognitive radio network and show how the inherent asymmetry in the network can be exploited to increase the agility. We show that our cooperation scheme increases the agility of the cognitive users by as much as 35%. We then extend our cooperation scheme to multicarrier networks with two users per carrier and analyze asymptotic agility gain. In Part II of our paper [1], we investigate multiuser single carrier networks. We develop a decentralized cooperation protocol which ensures agility gain for arbitrarily large cognitive network population.
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paper_title: Exploitation of spectral redundancy in cyclostationary signals

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It is shown that the cyclostationarity attribute, as it is reflected in the periodicities of (second-order) moments of the signal, can be interpreted in terms of the property that allows generation of spectral lines from the signal by putting it through a (quadratic) nonlinear transformation. The fundamental link between the spectral-line generation property and the statistical property called spectral correlation, which corresponds to the correlation that exists between the random fluctuations of components of the signal residing in distinct spectral bands, is explained. The effects on the spectral-correlation characteristics of some basic signal processing operations, such as filtering, product modulation, and time sampling, are examined. It is shown how to use these results to derive the spectral-correlation characteristics for various types of man-made signals. Some ways of exploiting the inherent spectral redundancy associated with spectral correlation to perform various signal processing tasks involving detection and estimation of highly corrupted man-made signals are described. >
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paper_title: Cramer-Rao bounds for estimating range, velocity, and direction with an active array

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We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model. Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional (3-D) array with isotropic sensors in spatially white noise and show that it is a function of the array geometry only through the "moments of inertia" of the array. The volume of the confidence region for the target's location is proposed as a measure of accuracy. For this measure, we show that the highest (and lowest) target location accuracy is achieved if the target lies along one of the principal axes of inertia of the array. Finally, we compare the location accuracies of several array geometries.
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paper_title: Signature Based Spectrum Sensing Algorithms for IEEE 802.22 WRAN

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Spectral sensing for the presence of ATSC DTV signals in VHF/UHF TV bands under a very low SNR environment is one of the core technologies in IEEE 802.22 WRAN. There are multiple signatures embedded in the ATSC DTV signals and these signatures can be utilized to perform spectrum sensing. Signature-based spectrum sensing algorithms have an advantage in that when the signals other than noise are detected, we are almost sure that they are signals we want to detect. Thus, in this paper, several signature based spectrum sensing algorithms are presented. The false alarm rate for detectors employing different algorithms is analytically derived. The operating characteristic curves for different detectors are determined from computer simulations using ATSC A/74 DTV signal captures as a test database.
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paper_title: Cooperative Sensing among Cognitive Radios

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Cognitive Radios have been advanced as a technology for the opportunistic use of under-utilized spectrum since they are able to sense the spectrum and use frequency bands if no Primary user is detected. However, the required sensitivity is very demanding since any individual radio might face a deep fade. We propose light-weight cooperation in sensing based on hard decisions to mitigate the sensitivity requirements on individual radios. We show that the "link budget" that system designers have to reserve for fading is a significant function of the required probability of detection. Even a few cooperating users (~10-20) facing independent fades are enough to achieve practical threshold levels by drastically reducing individual detection requirements. Hard decisions perform almost as well as soft decisions in achieving these gains. Cooperative gains in a environment where shadowing is correlated, is limited by the cooperation footprint (area in which users cooperate). In essence, a few independent users are more robust than many correlated users. Unfortunately, cooperative gain is very sensitive to adversarial/failing Cognitive Radios. Radios that fail in a known way (always report the presence/absence of a Primary user) can be compensated for by censoring them. On the other hand, radios that fail in unmodeled ways or may be malicious, introduce a bound on achievable sensitivity reductions. As a rule of thumb, if we believe that 1/N users can fail in an unknown way, then the cooperation gains are limited to what is possible with N trusted users.
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paper_title: Cognitive radios for spectrum sharing

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Wireless systems require spectrum to operate, but interference is likely if radios in physical proximity simultaneously operate on the same band. Therefore, spectrum is a potentially scarce resource; across the planet today, spectrum is regulated so that most bands are allocated exclusively to a single system licensed to use that band in any given location. However, such static spectrum allocation policies lead to significant underuse of spectrum [1]. This can be viewed as a kind of regulatory overhead that is paid to get reliable operation. With frequency-agile radios becoming commercially feasible within the next 5-10 years, Cognitive Radio is about making such radios smart enough to share spectrum and reduce the regulatory overhead. This is an impending wireless revolution that draws upon many signal-processing areas including robust detection, sensor networks, as well as the design of incentives and waveforms. This is a short column touching on the issues; further technical details/references can be found in [2].
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paper_title: SNR Walls for Signal Detection

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This paper considers the detection of the presence/absence of signals in uncertain low SNR environments. Small modeling uncertainties are unavoidable in any practical system and so robustness to them is a fundamental performance metric. The impact of these modeling uncertainties can be quantified by the position of the "SNR wall" below which a detector will fail to be robust, no matter how long it can observe the channel. We propose simple mathematical models for the uncertainty in the noise and fading processes. These are used to show what aspects of the model lead to SNR walls for differing levels of knowledge of the signal to be detected. These results have implications for wireless spectrum regulators. The context is opportunistically sharing spectrum with primary users that must be detected in order to avoid causing harmful interference on a channel. Ideally, a secondary system would be able to detect primaries robustly without having to know much about their signaling strategies. We argue that the tension between primary and secondary users is captured by the technical question of computing the optimal tradeoff between the primary user's capacity and the secondary user's sensing robustness as quantified by the SNR wall. This is an open problem, but we compute this tradeoff for some simple detectors.
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paper_title: Spectral Correlation of Modulated Signals: Part II--Digital Modulation

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As a continuation of Part I, the spectral correlation function is presented for a variety of types of digitally modulated signals. These include digital pulse-amplitude, pulse-width, and pulse-position modulation, and various types of phase-shift keying and frequency-shift keying. The magnitudes of the spectral correlation functions are graphed as the heights of surfaces above a bifrequency plane, and these graphs are used as visual aids for comparison and contrast of the spectral correlation properties of different modulation types.
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paper_title: Radiometric detection of spreadspectrum signals in noise of uncertain power

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The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval. >
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paper_title: Distributed Detection and Data Fusion

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1 Introduction.- 1.1 Distributed Detection Systems.- 1.2 Outline of the Book.- 2 Elements of Detection Theory.- 2.1 Introduction.- 2.2 Bayesian Detection Theory.- 2.3 Minimax Detection.- 2.4 Neyman-Pearson Test.- 2.5 Sequential Detection.- 2.6 Constant False Alarm Rate (CFAR) Detection.- 2.7 Locally Optimum Detection.- 3 Distributed Bayesian Detection: Parallel Fusion Network.- 3.1 Introduction.- 3.2 Distributed Detection Without Fusion.- 3.3 Design of Fusion Rules.- 3.4 Detection with Parallel Fusion Network.- 4 Distributed Bayesian Detection: Other Network Topologies.- 4.1 Introduction.- 4.2 The Serial Network.- 4.3 Tree Networks.- 4.4 Detection Networks with Feedback.- 4.5 Generalized Formulation for Detection Networks.- 5 Distributed Detection with False Alarm Rate Constraints.- 5.1 Introduction.- 5.2 Distributed Neyman-Pearson Detection.- 5.3 Distributed CFAR Detection.- 5.4 Distributed Detection of Weak Signals.- 6 Distributed Sequential Detection.- 6.1 Introduction.- 6.2 Sequential Test Performed at the Sensors.- 6.3 Sequential Test Performed at the Fusion Center.- 7 Information Theory and Distributed Hypothesis Testing.- 7.1 Introduction.- 7.2 Distributed Detection Based on Information Theoretic Criterion.- 7.3 Multiterminal Detection with Data Compression.- Selected Bibliography.
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paper_title: Cooperative Spectrum Sensing in Cognitive Radio, Part I: Two User Networks

paper_content:

In cognitive radio networks, cognitive (unlicensed) users need to continuously monitor spectrum for the presence of primary (licensed) users. In this paper, we illustrate the benefits of cooperation in cognitive radio. We show that by allowing the cognitive users operating in the same band to cooperate we can reduce the detection time and thus increase the overall agility. We first consider a two-user cognitive radio network and show how the inherent asymmetry in the network can be exploited to increase the agility. We show that our cooperation scheme increases the agility of the cognitive users by as much as 35%. We then extend our cooperation scheme to multicarrier networks with two users per carrier and analyze asymptotic agility gain. In Part II of our paper [1], we investigate multiuser single carrier networks. We develop a decentralized cooperation protocol which ensures agility gain for arbitrarily large cognitive network population.
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paper_title: Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices

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Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. These techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far are based on asymptotical assumptions, due to the difficulties in characterizing the exact eigenvalues ratio distribution. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then applied to calculate the decision sensing threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial improvement compared to the other eigenvalue-based algorithms.
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paper_title: Spectrum-Sensing Algorithms for Cognitive Radio Based on Statistical Covariances

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Spectrum sensing, i.e., detecting the presence of primary users in a licensed spectrum, is a fundamental problem in cognitive radio. Since the statistical covariances of the received signal and noise are usually different, they can be used to differentiate the case where the primary user's signal is present from the case where there is only noise. In this paper, spectrum-sensing algorithms are proposed based on the sample covariance matrix calculated from a limited number of received signal samples. Two test statistics are then extracted from the sample covariance matrix. A decision on the signal presence is made by comparing the two test statistics. Theoretical analysis for the proposed algorithms is given. Detection probability and the associated threshold are found based on the statistical theory. The methods do not need any information about the signal, channel, and noise power a priori. In addition, no synchronization is needed. Simulations based on narrow-band signals, captured digital television (DTV) signals, and multiple antenna signals are presented to verify the methods.
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paper_title: A Wavelet Approach to Wideband Spectrum Sensing for Cognitive Radios

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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: Blindly Combined Energy Detection for Spectrum Sensing in Cognitive Radio

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In this letter, a method is proposed to optimally combine the received signal samples in space and time based on the principle of maximizing the signal-to-noise ratio (SNR). After the combining, energy detection (ED) is used. However, optimal combining needs information of the source signal and channel, which is usually unknown. To overcome this difficulty, a method is proposed to blindly combine the signal samples. Similar to energy detection, blindly combined energy detection (BCED) does not need any information of the source signal and the channel a priori. BCED can be much better than ED for highly correlated signals, and most importantly, it does not need noise power estimation and overcomes ED's susceptibility to noise uncertainty. Also, perfect synchronization is not required. Simulations based on wireless microphone signals and randomly generated signals are presented to verify the methods.
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paper_title: Soft Combination and Detection for Cooperative Spectrum Sensing in Cognitive Radio Networks

paper_content:

In this letter, we consider cooperative spectrum sensing based on energy detection in cognitive radio networks. Soft combination of the observed energies from different cognitive radio users is investigated. Based on the Neyman-Pearson criterion, we obtain an optimal soft combination scheme that maximizes the detection probability for a given false alarm probability. Encouraged by the performance gain of soft combination, we further propose a new softened hard combination scheme with two-bit overhead for each user and achieve a good tradeoff between detection performance and complexity.
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paper_title: Asymptotics of eigenbased collaborative sensing

paper_content:

In this contribution, we propose a new technique for collaborative sensing based on the analysis of the normalized (by the trace) largest eigenvalues of the sample covariance matrix. Assuming that several base stations are cooperating and without the knowledge of the noise variance, the test is able to determine the presence of mobile users in a network when only few samples are available. Unlike previous heuristic techniques, we show that the test has roots within the Generalized Likelihood Ratio Test and provide an asymptotic random matrix analysis enabling to determine adequate threshold detection values (probability of false alarm). Simulations sustain our theoretical claims.
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paper_title: MIMO radar: an idea whose time has come

paper_content:

It has recently been shown that multiple-input multiple-output (MIMO) antenna systems have the potential to improve dramatically the performance of communication systems over single antenna systems. Unlike beamforming, which presumes a high correlation between signals either transmitted or received by an array, the MIMO concept exploits the independence between signals at the array elements. In conventional radar, target scintillations are regarded as a nuisance parameter that degrades radar performance. The novelty of MIMO radar is that it takes the opposite view; namely, it capitalizes on target scintillations to improve the radar's performance. We introduce the MIMO concept for radar. The MIMO radar system under consideration consists of a transmit array with widely-spaced elements such that each views a different aspect of the target. The array at the receiver is a conventional array used for direction finding (DF). The system performance analysis is carried out in terms of the Cramer-Rao bound of the mean-square error in estimating the target direction. It is shown that MIMO radar leads to significant performance improvement in DF accuracy.
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paper_title: Fundamental limits on detection in low SNR under noise uncertainty

paper_content:

In this paper we consider the problem of detecting whether a frequency band is being used by a known primary user. We derive fundamental bounds on detection performance in low SNR in the presence of noise uncertainty - the noise is assumed to be white, but we know its distribution only to within a particular set. For clarity of analysis, we focus on primary transmissions that are BPSK-modulated random data without any pilot tones or training sequences. The results should all generalize to more general primary transmissions as long as no deterministic component is present. Specifically, we show that for every 'moment detector' there exists an SNR below which detection becomes impossible in the presence of noise uncertainty. In the neighborhood of that SNR wall, we show how the sample complexity of detection approaches infinity. We also show that if our radio has a finite dynamic range (upper and lower limits to the voltages we can quantize), then at low enough SNR, any detector can be rendered useless even under moderate noise uncertainty.
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paper_title: Optimization for Cooperative Sensing in Cognitive Radio Networks

paper_content:

In cognitive radio networks, the secondary users can use the frequency bands when the primary users are not present. Hence secondary users need to constantly sense the presence of the primary users. When the primary users are detected, the secondary users have to vacate that channel. This makes the probability of detection important to the primary users as it indicates their protection level from secondary users. When the secondary users detect the presence of a primary user which is in fact not there, it is referred to as false alarm. The probability of false alarm is important to the secondary users as it determines their usage of an unoccupied channel. Depending on whose interest is of priority, either a targeted probability of detection or false alarm shall be set. After setting one of the probabilities, the other can be optimized through cooperative sensing. In this paper, we show that cooperating all secondary users in the network does not necessary achieve the optimum performance, but instead, it is achieved by cooperating a certain number of users with the highest primary user's signal to noise ratio. Computer simulations have shown that the Pd can increase from 92.03% to 99.88% and Pf can decrease from 6.02% to 0.06% in a network with 200 users.
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paper_title: Coherent Detection for MIMO Radars

paper_content:

Superiority of multiple-input multiple-output (MIMO) radars over conventional phased array radars has been recently shown in many aspects. MIMO radars have better detection performance and can extract target information more precisely than phased array radars. In this paper, the problem of target detection using temporal coherent pulse terrain is considered for MIMO radars. We have introduced a structure that is suitable for coherent processing. Based on this structure, we have formulated this problem as a hypothesis test. One decision rule is developed for detection of target with unknown amplitude embedded in additive white gaussian noise (AWGN) with known power using the generalized likelihood ratio test (GLRT). Another adaptive scheme for the case of unknown power is presented. We have also proposed an ad-hoc constant false alarm rate (CFAR) detector against AWGN with unknown power. Performance of these detectors have been evaluated analytically. The results show the superiority of the MIMO radars with temporal coherent processing over the conventional phased arrays.
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paper_title: Eigenvalue-based spectrum sensing algorithms for cognitive radio

paper_content:

Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.
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paper_title: Cooperative Sensing for Primary Detection in Cognitive Radio

paper_content:

One of the main requirements of cognitive radio systems is the ability to reliably detect the presence of licensed primary transmissions. Previous works on the problem of detection for cognitive radio have suggested the necessity of user cooperation in order to be able to detect at the low signal-to-noise ratios experienced in practical situations. We consider a system of cognitive radio users who cooperate with each other in trying to detect licensed transmissions. Assuming that the cooperating nodes use identical energy detectors, we model the received signals as correlated log-normal random variables and study the problem of fusing the decisions made by the individual nodes. We design a linear-quadratic (LQ) fusion strategy based on a deflection criterion for this problem, which takes into account the correlation between the nodes. Using simulations we show that when the observations at the sensors are correlated, the LQ detector significantly outperforms the counting rule, which is the fusion rule that is obtained by ignoring the correlation.
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paper_title: Cluster-Based Cooperative Spectrum Sensing in Cognitive Radio Systems

paper_content:

In cognitive radio systems, secondary users can be coordinated to perform cooperative spectrum sensing so as to detect the primary user more accurately. However, when the sensing observations are forwarded to a common receiver through fading channels, the sensing performance can be severely degraded. In this paper, we propose a cluster-based cooperative spectrum sensing method to improve the sensing performance. By separating all the secondary users into a few clusters and selecting the most favorable user in each cluster to report to the common receiver, the proposed method can exploit the user selection diversity so that the sensing performance can be enhanced. Furthermore, decision fusion and energy fusion are both studied and the analytical performance results are given. Numerical results show that the sensing performance is improved significantly as opposed to conventional spectrum sensing.
---
paper_title: Optimal Linear Cooperation for Spectrum Sensing in Cognitive Radio Networks

paper_content:

Cognitive radio technology has been proposed to improve spectrum efficiency by having the cognitive radios act as secondary users to opportunistically access under-utilized frequency bands. Spectrum sensing, as a key enabling functionality in cognitive radio networks, needs to reliably detect signals from licensed primary radios to avoid harmful interference. However, due to the effects of channel fading/shadowing, individual cognitive radios may not be able to reliably detect the existence of a primary radio. In this paper, we propose an optimal linear cooperation framework for spectrum sensing in order to accurately detect the weak primary signal. Within this framework, spectrum sensing is based on the linear combination of local statistics from individual cognitive radios. Our objective is to minimize the interference to the primary radio while meeting the requirement of opportunistic spectrum utilization. We formulate the sensing problem as a nonlinear optimization problem. By exploiting the inherent structures in the problem formulation, we develop efficient algorithms to solve for the optimal solutions. To further reduce the computational complexity and obtain solutions for more general cases, we finally propose a heuristic approach, where we instead optimize a modified deflection coefficient that characterizes the probability distribution function of the global test statistics at the fusion center. Simulation results illustrate significant cooperative gain achieved by the proposed strategies. The insights obtained in this paper are useful for the design of optimal spectrum sensing in cognitive radio networks.
---
paper_title: Cooperative Spectrum Sensing in Cognitive Radio, Part II: Multiuser Networks

paper_content:

In cognitive radio networks, cognitive (unlicensed) users need to continuously monitor spectrum for the presence of primary (licensed) users. In this paper, we illustrate the benefits of cooperation in cognitive radio. We show that by allowing the cognitive users operating in the same band to cooperate we can reduce the detection time and thus increase the overall agility. We first consider a two-user cognitive radio network and show how the inherent asymmetry in the network can be exploited to increase the agility. We show that our cooperation scheme increases the agility of the cognitive users by as much as 35%. We then extend our cooperation scheme to multicarrier networks with two users per carrier and analyze asymptotic agility gain. In Part II of our paper [1], we investigate multiuser single carrier networks. We develop a decentralized cooperation protocol which ensures agility gain for arbitrarily large cognitive network population.
---
paper_title: Cooperative Covariance and Eigenvalue Based Detections for Robust Sensing

paper_content:

Spectrum sensing is a fundamental problem in cognitive radio. As a result, it has been reborn as a very active research area in recent years despite its long history. Although various sensing methods have been proposed, their robustness at very low signal-to-noise ratio (SNR) and uncertain noise/interference environment is generally not satisfactory. In this paper, the concept of robust sensing is discussed first. Subsequently the cooperative covariance and eigenvalue based detections are proposed for robust spectrum sensing. It is proved mathematically that under some conditions the proposed methods are robust to uncertain and unpredictable noise and interference. The performances of the methods are also verified by simulations.
---
paper_title: Cooperative Sensing among Cognitive Radios

paper_content:

Cognitive Radios have been advanced as a technology for the opportunistic use of under-utilized spectrum since they are able to sense the spectrum and use frequency bands if no Primary user is detected. However, the required sensitivity is very demanding since any individual radio might face a deep fade. We propose light-weight cooperation in sensing based on hard decisions to mitigate the sensitivity requirements on individual radios. We show that the "link budget" that system designers have to reserve for fading is a significant function of the required probability of detection. Even a few cooperating users (~10-20) facing independent fades are enough to achieve practical threshold levels by drastically reducing individual detection requirements. Hard decisions perform almost as well as soft decisions in achieving these gains. Cooperative gains in a environment where shadowing is correlated, is limited by the cooperation footprint (area in which users cooperate). In essence, a few independent users are more robust than many correlated users. Unfortunately, cooperative gain is very sensitive to adversarial/failing Cognitive Radios. Radios that fail in a known way (always report the presence/absence of a Primary user) can be compensated for by censoring them. On the other hand, radios that fail in unmodeled ways or may be malicious, introduce a bound on achievable sensitivity reductions. As a rule of thumb, if we believe that 1/N users can fail in an unknown way, then the cooperation gains are limited to what is possible with N trusted users.
---
paper_title: Distributed Detection and Data Fusion

paper_content:

1 Introduction.- 1.1 Distributed Detection Systems.- 1.2 Outline of the Book.- 2 Elements of Detection Theory.- 2.1 Introduction.- 2.2 Bayesian Detection Theory.- 2.3 Minimax Detection.- 2.4 Neyman-Pearson Test.- 2.5 Sequential Detection.- 2.6 Constant False Alarm Rate (CFAR) Detection.- 2.7 Locally Optimum Detection.- 3 Distributed Bayesian Detection: Parallel Fusion Network.- 3.1 Introduction.- 3.2 Distributed Detection Without Fusion.- 3.3 Design of Fusion Rules.- 3.4 Detection with Parallel Fusion Network.- 4 Distributed Bayesian Detection: Other Network Topologies.- 4.1 Introduction.- 4.2 The Serial Network.- 4.3 Tree Networks.- 4.4 Detection Networks with Feedback.- 4.5 Generalized Formulation for Detection Networks.- 5 Distributed Detection with False Alarm Rate Constraints.- 5.1 Introduction.- 5.2 Distributed Neyman-Pearson Detection.- 5.3 Distributed CFAR Detection.- 5.4 Distributed Detection of Weak Signals.- 6 Distributed Sequential Detection.- 6.1 Introduction.- 6.2 Sequential Test Performed at the Sensors.- 6.3 Sequential Test Performed at the Fusion Center.- 7 Information Theory and Distributed Hypothesis Testing.- 7.1 Introduction.- 7.2 Distributed Detection Based on Information Theoretic Criterion.- 7.3 Multiterminal Detection with Data Compression.- Selected Bibliography.
---
paper_title: Cooperative Spectrum Sensing in Cognitive Radio, Part I: Two User Networks

paper_content:

In cognitive radio networks, cognitive (unlicensed) users need to continuously monitor spectrum for the presence of primary (licensed) users. In this paper, we illustrate the benefits of cooperation in cognitive radio. We show that by allowing the cognitive users operating in the same band to cooperate we can reduce the detection time and thus increase the overall agility. We first consider a two-user cognitive radio network and show how the inherent asymmetry in the network can be exploited to increase the agility. We show that our cooperation scheme increases the agility of the cognitive users by as much as 35%. We then extend our cooperation scheme to multicarrier networks with two users per carrier and analyze asymptotic agility gain. In Part II of our paper [1], we investigate multiuser single carrier networks. We develop a decentralized cooperation protocol which ensures agility gain for arbitrarily large cognitive network population.
---
paper_title: Soft Combination and Detection for Cooperative Spectrum Sensing in Cognitive Radio Networks

paper_content:

In this letter, we consider cooperative spectrum sensing based on energy detection in cognitive radio networks. Soft combination of the observed energies from different cognitive radio users is investigated. Based on the Neyman-Pearson criterion, we obtain an optimal soft combination scheme that maximizes the detection probability for a given false alarm probability. Encouraged by the performance gain of soft combination, we further propose a new softened hard combination scheme with two-bit overhead for each user and achieve a good tradeoff between detection performance and complexity.
---
paper_title: Optimization for Cooperative Sensing in Cognitive Radio Networks

paper_content:

In cognitive radio networks, the secondary users can use the frequency bands when the primary users are not present. Hence secondary users need to constantly sense the presence of the primary users. When the primary users are detected, the secondary users have to vacate that channel. This makes the probability of detection important to the primary users as it indicates their protection level from secondary users. When the secondary users detect the presence of a primary user which is in fact not there, it is referred to as false alarm. The probability of false alarm is important to the secondary users as it determines their usage of an unoccupied channel. Depending on whose interest is of priority, either a targeted probability of detection or false alarm shall be set. After setting one of the probabilities, the other can be optimized through cooperative sensing. In this paper, we show that cooperating all secondary users in the network does not necessary achieve the optimum performance, but instead, it is achieved by cooperating a certain number of users with the highest primary user's signal to noise ratio. Computer simulations have shown that the Pd can increase from 92.03% to 99.88% and Pf can decrease from 6.02% to 0.06% in a network with 200 users.
---
paper_title: An Introduction to Signal Detection and Estimation

paper_content:

Preface I. Introduction II. Elements of Hypothesis Testing III. Signal Detection in Discrete Time IV. Elements of Parameter Estimation V. Elements of Signal Estimation VI. Signal Detection in Continuous Time VII. Signal Estimation in Continuous Time References Index
---
paper_title: Study on Cooperative Sensing in Cognitive Radio based AD-HOC Network

paper_content:

In this paper, we propose a soft decision based cooperative sensing method for cognitive radio (CR) in ad-hoc networks. A CR can sense a surrounding radio environment and adapt to the environment by the reconfigurability to achieve more effective frequency utilization. Observing the environment, CR should detect presence or absence of primary user and exploits this information to opportunistically provide communication among secondary users while performance of primary user should not be deteriorated by the secondary users. Because of multi- path fading or shadowing, the detection of primary users may be significantly difficult. For this problem, cooperative sensing (CS), where gathered observations obtained by multiple users is utilized to achieve higher performance of detection, has been investigated. We propose a soft decision based CS where test statistic used in traditional single user energy detection is treated as soft decision information. The detector is designed analytically, i.e., the statistic of the performance, detection probability and given false alarm, can be obtained analytically. By computer simulations, we have presented as follows; validity of analysis and that the CS has better performance compared to non-cooperative sensing. In addition, we have presented the detection performance of cooperative sensing when there are considerable differences regarding signal to noise ratio among users.
---
paper_title: Radiometric detection of spreadspectrum signals in noise of uncertain power

paper_content:

The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval. >
---
paper_title: Soft Combination and Detection for Cooperative Spectrum Sensing in Cognitive Radio Networks

paper_content:

In this letter, we consider cooperative spectrum sensing based on energy detection in cognitive radio networks. Soft combination of the observed energies from different cognitive radio users is investigated. Based on the Neyman-Pearson criterion, we obtain an optimal soft combination scheme that maximizes the detection probability for a given false alarm probability. Encouraged by the performance gain of soft combination, we further propose a new softened hard combination scheme with two-bit overhead for each user and achieve a good tradeoff between detection performance and complexity.
---
paper_title: MIMO radar: an idea whose time has come

paper_content:

It has recently been shown that multiple-input multiple-output (MIMO) antenna systems have the potential to improve dramatically the performance of communication systems over single antenna systems. Unlike beamforming, which presumes a high correlation between signals either transmitted or received by an array, the MIMO concept exploits the independence between signals at the array elements. In conventional radar, target scintillations are regarded as a nuisance parameter that degrades radar performance. The novelty of MIMO radar is that it takes the opposite view; namely, it capitalizes on target scintillations to improve the radar's performance. We introduce the MIMO concept for radar. The MIMO radar system under consideration consists of a transmit array with widely-spaced elements such that each views a different aspect of the target. The array at the receiver is a conventional array used for direction finding (DF). The system performance analysis is carried out in terms of the Cramer-Rao bound of the mean-square error in estimating the target direction. It is shown that MIMO radar leads to significant performance improvement in DF accuracy.
---
paper_title: Coherent Detection for MIMO Radars

paper_content:

Superiority of multiple-input multiple-output (MIMO) radars over conventional phased array radars has been recently shown in many aspects. MIMO radars have better detection performance and can extract target information more precisely than phased array radars. In this paper, the problem of target detection using temporal coherent pulse terrain is considered for MIMO radars. We have introduced a structure that is suitable for coherent processing. Based on this structure, we have formulated this problem as a hypothesis test. One decision rule is developed for detection of target with unknown amplitude embedded in additive white gaussian noise (AWGN) with known power using the generalized likelihood ratio test (GLRT). Another adaptive scheme for the case of unknown power is presented. We have also proposed an ad-hoc constant false alarm rate (CFAR) detector against AWGN with unknown power. Performance of these detectors have been evaluated analytically. The results show the superiority of the MIMO radars with temporal coherent processing over the conventional phased arrays.
---
paper_title: Maximum-Minimum Eigenvalue Detection for Cognitive Radio

paper_content:

Sensing (signal detection) is a fundamental problem in cognitive radio. In this paper, a new method is proposed based on the eigenvalues of the covariance matrix of the received signal. It is shown that the ratio of the maximum eigenvalue to the minimum eigenvalue can be used to detect the signal existence. Based on some latest random matrix theories (RMT), we can quantize the ratio and find the threshold. The probability of false alarm is also found by using the RMT. The proposed method overcomes the noise uncertainty difficulty while keeps the advantages of the energy detection. The method can be used for various sensing applications without knowledge of the signal, the channel and noise power. Simulations based on randomly generated signals and captured ATSC DTV signals are presented to verify the methods.
---
paper_title: Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices

paper_content:

Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. These techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far are based on asymptotical assumptions, due to the difficulties in characterizing the exact eigenvalues ratio distribution. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then applied to calculate the decision sensing threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial improvement compared to the other eigenvalue-based algorithms.
---
paper_title: Blindly Combined Energy Detection for Spectrum Sensing in Cognitive Radio

paper_content:

In this letter, a method is proposed to optimally combine the received signal samples in space and time based on the principle of maximizing the signal-to-noise ratio (SNR). After the combining, energy detection (ED) is used. However, optimal combining needs information of the source signal and channel, which is usually unknown. To overcome this difficulty, a method is proposed to blindly combine the signal samples. Similar to energy detection, blindly combined energy detection (BCED) does not need any information of the source signal and the channel a priori. BCED can be much better than ED for highly correlated signals, and most importantly, it does not need noise power estimation and overcomes ED's susceptibility to noise uncertainty. Also, perfect synchronization is not required. Simulations based on wireless microphone signals and randomly generated signals are presented to verify the methods.
---
paper_title: Soft Combination and Detection for Cooperative Spectrum Sensing in Cognitive Radio Networks

paper_content:

In this letter, we consider cooperative spectrum sensing based on energy detection in cognitive radio networks. Soft combination of the observed energies from different cognitive radio users is investigated. Based on the Neyman-Pearson criterion, we obtain an optimal soft combination scheme that maximizes the detection probability for a given false alarm probability. Encouraged by the performance gain of soft combination, we further propose a new softened hard combination scheme with two-bit overhead for each user and achieve a good tradeoff between detection performance and complexity.
---
paper_title: Asymptotics of eigenbased collaborative sensing

paper_content:

In this contribution, we propose a new technique for collaborative sensing based on the analysis of the normalized (by the trace) largest eigenvalues of the sample covariance matrix. Assuming that several base stations are cooperating and without the knowledge of the noise variance, the test is able to determine the presence of mobile users in a network when only few samples are available. Unlike previous heuristic techniques, we show that the test has roots within the Generalized Likelihood Ratio Test and provide an asymptotic random matrix analysis enabling to determine adequate threshold detection values (probability of false alarm). Simulations sustain our theoretical claims.
---
paper_title: Eigenvalue-based spectrum sensing algorithms for cognitive radio

paper_content:

Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.
---
paper_title: Maximum-Minimum Eigenvalue Detection for Cognitive Radio

paper_content:

Sensing (signal detection) is a fundamental problem in cognitive radio. In this paper, a new method is proposed based on the eigenvalues of the covariance matrix of the received signal. It is shown that the ratio of the maximum eigenvalue to the minimum eigenvalue can be used to detect the signal existence. Based on some latest random matrix theories (RMT), we can quantize the ratio and find the threshold. The probability of false alarm is also found by using the RMT. The proposed method overcomes the noise uncertainty difficulty while keeps the advantages of the energy detection. The method can be used for various sensing applications without knowledge of the signal, the channel and noise power. Simulations based on randomly generated signals and captured ATSC DTV signals are presented to verify the methods.
---
paper_title: Covariance Based Signal Detections for Cognitive Radio

paper_content:

Sensing (signal detection) is a fundamental problem in cognitive radio. The statistical covariances of signal and noise are usually different. In this paper, this property is used to differentiate signal from noise. The sample covariance matrix of the received signal is computed and transformed based on the receiving filter. Then two detection methods are proposed based on the transformed sample covariance matrix. One is the covariance absolute value (CAV) detection and the other is the covariance Frobenius norm (CFN) detection. Theoretical analysis and threshold setting for the algorithms are discussed. Both methods do not need any information of the signal, the channel and noise power as a priori. Simulations based on captured ATSC DTV signals are presented to verify the methods.
---
paper_title: Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices

paper_content:

Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. These techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far are based on asymptotical assumptions, due to the difficulties in characterizing the exact eigenvalues ratio distribution. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then applied to calculate the decision sensing threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial improvement compared to the other eigenvalue-based algorithms.
---
paper_title: Spectrum-Sensing Algorithms for Cognitive Radio Based on Statistical Covariances

paper_content:

Spectrum sensing, i.e., detecting the presence of primary users in a licensed spectrum, is a fundamental problem in cognitive radio. Since the statistical covariances of the received signal and noise are usually different, they can be used to differentiate the case where the primary user's signal is present from the case where there is only noise. In this paper, spectrum-sensing algorithms are proposed based on the sample covariance matrix calculated from a limited number of received signal samples. Two test statistics are then extracted from the sample covariance matrix. A decision on the signal presence is made by comparing the two test statistics. Theoretical analysis for the proposed algorithms is given. Detection probability and the associated threshold are found based on the statistical theory. The methods do not need any information about the signal, channel, and noise power a priori. In addition, no synchronization is needed. Simulations based on narrow-band signals, captured digital television (DTV) signals, and multiple antenna signals are presented to verify the methods.
---
paper_title: Asymptotics of eigenbased collaborative sensing

paper_content:

In this contribution, we propose a new technique for collaborative sensing based on the analysis of the normalized (by the trace) largest eigenvalues of the sample covariance matrix. Assuming that several base stations are cooperating and without the knowledge of the noise variance, the test is able to determine the presence of mobile users in a network when only few samples are available. Unlike previous heuristic techniques, we show that the test has roots within the Generalized Likelihood Ratio Test and provide an asymptotic random matrix analysis enabling to determine adequate threshold detection values (probability of false alarm). Simulations sustain our theoretical claims.
---
paper_title: Eigenvalue-based spectrum sensing algorithms for cognitive radio

paper_content:

Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.
---
paper_title: Exploitation of spectral redundancy in cyclostationary signals

paper_content:

It is shown that the cyclostationarity attribute, as it is reflected in the periodicities of (second-order) moments of the signal, can be interpreted in terms of the property that allows generation of spectral lines from the signal by putting it through a (quadratic) nonlinear transformation. The fundamental link between the spectral-line generation property and the statistical property called spectral correlation, which corresponds to the correlation that exists between the random fluctuations of components of the signal residing in distinct spectral bands, is explained. The effects on the spectral-correlation characteristics of some basic signal processing operations, such as filtering, product modulation, and time sampling, are examined. It is shown how to use these results to derive the spectral-correlation characteristics for various types of man-made signals. Some ways of exploiting the inherent spectral redundancy associated with spectral correlation to perform various signal processing tasks involving detection and estimation of highly corrupted man-made signals are described. >
---
paper_title: Spectral Correlation of Modulated Signals: Part II--Digital Modulation

paper_content:

As a continuation of Part I, the spectral correlation function is presented for a variety of types of digitally modulated signals. These include digital pulse-amplitude, pulse-width, and pulse-position modulation, and various types of phase-shift keying and frequency-shift keying. The magnitudes of the spectral correlation functions are graphed as the heights of surfaces above a bifrequency plane, and these graphs are used as visual aids for comparison and contrast of the spectral correlation properties of different modulation types.
---
paper_title: Optimal Linear Cooperation for Spectrum Sensing in Cognitive Radio Networks

paper_content:

Cognitive radio technology has been proposed to improve spectrum efficiency by having the cognitive radios act as secondary users to opportunistically access under-utilized frequency bands. Spectrum sensing, as a key enabling functionality in cognitive radio networks, needs to reliably detect signals from licensed primary radios to avoid harmful interference. However, due to the effects of channel fading/shadowing, individual cognitive radios may not be able to reliably detect the existence of a primary radio. In this paper, we propose an optimal linear cooperation framework for spectrum sensing in order to accurately detect the weak primary signal. Within this framework, spectrum sensing is based on the linear combination of local statistics from individual cognitive radios. Our objective is to minimize the interference to the primary radio while meeting the requirement of opportunistic spectrum utilization. We formulate the sensing problem as a nonlinear optimization problem. By exploiting the inherent structures in the problem formulation, we develop efficient algorithms to solve for the optimal solutions. To further reduce the computational complexity and obtain solutions for more general cases, we finally propose a heuristic approach, where we instead optimize a modified deflection coefficient that characterizes the probability distribution function of the global test statistics at the fusion center. Simulation results illustrate significant cooperative gain achieved by the proposed strategies. The insights obtained in this paper are useful for the design of optimal spectrum sensing in cognitive radio networks.
---
paper_title: Cooperative Covariance and Eigenvalue Based Detections for Robust Sensing

paper_content:

Spectrum sensing is a fundamental problem in cognitive radio. As a result, it has been reborn as a very active research area in recent years despite its long history. Although various sensing methods have been proposed, their robustness at very low signal-to-noise ratio (SNR) and uncertain noise/interference environment is generally not satisfactory. In this paper, the concept of robust sensing is discussed first. Subsequently the cooperative covariance and eigenvalue based detections are proposed for robust spectrum sensing. It is proved mathematically that under some conditions the proposed methods are robust to uncertain and unpredictable noise and interference. The performances of the methods are also verified by simulations.
---
paper_title: Distributed Detection and Data Fusion

paper_content:

1 Introduction.- 1.1 Distributed Detection Systems.- 1.2 Outline of the Book.- 2 Elements of Detection Theory.- 2.1 Introduction.- 2.2 Bayesian Detection Theory.- 2.3 Minimax Detection.- 2.4 Neyman-Pearson Test.- 2.5 Sequential Detection.- 2.6 Constant False Alarm Rate (CFAR) Detection.- 2.7 Locally Optimum Detection.- 3 Distributed Bayesian Detection: Parallel Fusion Network.- 3.1 Introduction.- 3.2 Distributed Detection Without Fusion.- 3.3 Design of Fusion Rules.- 3.4 Detection with Parallel Fusion Network.- 4 Distributed Bayesian Detection: Other Network Topologies.- 4.1 Introduction.- 4.2 The Serial Network.- 4.3 Tree Networks.- 4.4 Detection Networks with Feedback.- 4.5 Generalized Formulation for Detection Networks.- 5 Distributed Detection with False Alarm Rate Constraints.- 5.1 Introduction.- 5.2 Distributed Neyman-Pearson Detection.- 5.3 Distributed CFAR Detection.- 5.4 Distributed Detection of Weak Signals.- 6 Distributed Sequential Detection.- 6.1 Introduction.- 6.2 Sequential Test Performed at the Sensors.- 6.3 Sequential Test Performed at the Fusion Center.- 7 Information Theory and Distributed Hypothesis Testing.- 7.1 Introduction.- 7.2 Distributed Detection Based on Information Theoretic Criterion.- 7.3 Multiterminal Detection with Data Compression.- Selected Bibliography.
---
paper_title: Soft Combination and Detection for Cooperative Spectrum Sensing in Cognitive Radio Networks

paper_content:

In this letter, we consider cooperative spectrum sensing based on energy detection in cognitive radio networks. Soft combination of the observed energies from different cognitive radio users is investigated. Based on the Neyman-Pearson criterion, we obtain an optimal soft combination scheme that maximizes the detection probability for a given false alarm probability. Encouraged by the performance gain of soft combination, we further propose a new softened hard combination scheme with two-bit overhead for each user and achieve a good tradeoff between detection performance and complexity.
---
paper_title: Optimization for Cooperative Sensing in Cognitive Radio Networks

paper_content:

In cognitive radio networks, the secondary users can use the frequency bands when the primary users are not present. Hence secondary users need to constantly sense the presence of the primary users. When the primary users are detected, the secondary users have to vacate that channel. This makes the probability of detection important to the primary users as it indicates their protection level from secondary users. When the secondary users detect the presence of a primary user which is in fact not there, it is referred to as false alarm. The probability of false alarm is important to the secondary users as it determines their usage of an unoccupied channel. Depending on whose interest is of priority, either a targeted probability of detection or false alarm shall be set. After setting one of the probabilities, the other can be optimized through cooperative sensing. In this paper, we show that cooperating all secondary users in the network does not necessary achieve the optimum performance, but instead, it is achieved by cooperating a certain number of users with the highest primary user's signal to noise ratio. Computer simulations have shown that the Pd can increase from 92.03% to 99.88% and Pf can decrease from 6.02% to 0.06% in a network with 200 users.
---
paper_title: Maximum-Minimum Eigenvalue Detection for Cognitive Radio

paper_content:

Sensing (signal detection) is a fundamental problem in cognitive radio. In this paper, a new method is proposed based on the eigenvalues of the covariance matrix of the received signal. It is shown that the ratio of the maximum eigenvalue to the minimum eigenvalue can be used to detect the signal existence. Based on some latest random matrix theories (RMT), we can quantize the ratio and find the threshold. The probability of false alarm is also found by using the RMT. The proposed method overcomes the noise uncertainty difficulty while keeps the advantages of the energy detection. The method can be used for various sensing applications without knowledge of the signal, the channel and noise power. Simulations based on randomly generated signals and captured ATSC DTV signals are presented to verify the methods.
---
paper_title: Covariance Based Signal Detections for Cognitive Radio

paper_content:

Sensing (signal detection) is a fundamental problem in cognitive radio. The statistical covariances of signal and noise are usually different. In this paper, this property is used to differentiate signal from noise. The sample covariance matrix of the received signal is computed and transformed based on the receiving filter. Then two detection methods are proposed based on the transformed sample covariance matrix. One is the covariance absolute value (CAV) detection and the other is the covariance Frobenius norm (CFN) detection. Theoretical analysis and threshold setting for the algorithms are discussed. Both methods do not need any information of the signal, the channel and noise power as a priori. Simulations based on captured ATSC DTV signals are presented to verify the methods.
---
paper_title: Radiometric detection of spreadspectrum signals in noise of uncertain power

paper_content:

The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval. >
---
paper_title: Fundamental limits on detection in low SNR under noise uncertainty

paper_content:

In this paper we consider the problem of detecting whether a frequency band is being used by a known primary user. We derive fundamental bounds on detection performance in low SNR in the presence of noise uncertainty - the noise is assumed to be white, but we know its distribution only to within a particular set. For clarity of analysis, we focus on primary transmissions that are BPSK-modulated random data without any pilot tones or training sequences. The results should all generalize to more general primary transmissions as long as no deterministic component is present. Specifically, we show that for every 'moment detector' there exists an SNR below which detection becomes impossible in the presence of noise uncertainty. In the neighborhood of that SNR wall, we show how the sample complexity of detection approaches infinity. We also show that if our radio has a finite dynamic range (upper and lower limits to the voltages we can quantize), then at low enough SNR, any detector can be rendered useless even under moderate noise uncertainty.
---
paper_title: Eigenvalue-based spectrum sensing algorithms for cognitive radio

paper_content:

Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.
---
paper_title: On the marginal distribution of the eigenvalues of wishart matrices

paper_content:

Random matrices play a crucial role in the design and analysis of multiple-input multiple-output (MIMO) systems. In particular, performance of MIMO systems depends on the statistical properties of a subclass of random matrices known as Wishart when the propagation environment is characterized by Rayleigh or Rician fading. This paper focuses on the stochastic analysis of this class of matrices and proposes a general methodology to evaluate some multiple nested integrals of interest. With this methodology we obtain a closed-form expression for the joint probability density function of k consecutive ordered eigenvalues and, as a special case, the PDF of the lscrth ordered eigenvalue of Wishart matrices. The distribution of the largest eigenvalue can be used to analyze the performance of MIMO maximal ratio combining systems. The PDF of the smallest eigenvalue can be used for MIMO antenna selection techniques. Finally, the PDF the kth largest eigenvalue finds applications in the performance analysis of MIMO singular value decomposition systems.
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paper_title: Maximum-Minimum Eigenvalue Detection for Cognitive Radio

paper_content:

Sensing (signal detection) is a fundamental problem in cognitive radio. In this paper, a new method is proposed based on the eigenvalues of the covariance matrix of the received signal. It is shown that the ratio of the maximum eigenvalue to the minimum eigenvalue can be used to detect the signal existence. Based on some latest random matrix theories (RMT), we can quantize the ratio and find the threshold. The probability of false alarm is also found by using the RMT. The proposed method overcomes the noise uncertainty difficulty while keeps the advantages of the energy detection. The method can be used for various sensing applications without knowledge of the signal, the channel and noise power. Simulations based on randomly generated signals and captured ATSC DTV signals are presented to verify the methods.
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paper_title: Shape fluctuations and random matrices

paper_content:

We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.
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paper_title: METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES, A REVIEW

paper_content:

In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electrical and Electronic Engineering. Thus, we convert almost all results to the complex case, whenever possible. Only the latest results, including some new ones, are stated as theorems here. The main purpose of the paper is to show how important methodologies, or mathematical tools, have helped to develop the theory. Some unsolved problems are also stated.
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paper_title: The distribution of the largest eigenvalue in the Gaussian ensembles: β

paper_content:

The focus of this survey is on the distribution function F Nβ (t) for the largest eigenvalue in the finite N Gaussian Orthogonal Ensemble (GOE, β = 1), the Gaussian Unitary Ensemble (GUE, β = 2), and the Gaussian Symplectic Ensemble (GSE, β = 4) in the edge scaling limit of N → ∝. These limiting distribution functions are expressible in terms of a particular Painleve II function. Comparisons are made with finite N simulations and of the universality of these distribution functions is discussed.
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paper_title: Eigenvalue-based spectrum sensing algorithms for cognitive radio

paper_content:

Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.
---
paper_title: Robust Estimation of a Location Parameter

paper_content:

This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)
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paper_title: Signal detection under noise interference in a game situation

paper_content:

With application to radar and data transmission, a game situation is studied where one player selects a suitable receiving filter, and the other a function describing the noise power density under restriction of a fixed total amount of power. The payoff function is a signal to noise ratio. The information the players have about each others' choice defines two extreme situations of practical interest. The fundamental relation of game theory holds for pure strategies.
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paper_title: Robust techniques for signal processing: A survey

paper_content:

In recent years there has been much interest in robustness issues in general and in robust signal processing schemes in particular. Robust schemes are useful in situations where imprecise a priori knowledge of input characteristics makes the sensitivity of performance to deviations from assumed conditions an important factor in the design of good signal processing schemes. In this survey we discuss the minimax approach for the design of robust methods for signal processing. This has proven to be a very useful approach because it leads to constructive procedures for designing robust schemes. Our emphasis is on the contributions which have been made in robust signal processing, although key results of other robust statistical procedures are also considered. Most of the results we survey have been obtained in the past fifteen years, although some interesting earlier ideas for minimax signal processing are also mentioned. This survey is organized into five main parts, which deal separately with robust linear filters for signal estimation, robust linear filters for signal detection and related applications, nonlinear methods for robust signal detection, nonlinear methods for robust estimation, and robust data quantization. The interrelationships among many of these results are also discussed in the survey.
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paper_title: Robust matched filters

paper_content:

The problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered. Two general aspects of this problem are treated. First, maximin robust designs are characterized for a general Hilbert-space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty. These results are seen to generalize earlier results for specific matched filtering problems. The second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion. Channel distortion is modeled by considering an unknown received signal which may differ in L_{2} -norm from the transmitted or nominal signal by no more than a fixed amount. The effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion. General expressions are developed for the determination of the robust filter and its performance, and numerical results are presented for the case of baseband detection in Gauss-Markov noise.
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paper_title: Robust techniques for signal processing: A survey

paper_content:

In recent years there has been much interest in robustness issues in general and in robust signal processing schemes in particular. Robust schemes are useful in situations where imprecise a priori knowledge of input characteristics makes the sensitivity of performance to deviations from assumed conditions an important factor in the design of good signal processing schemes. In this survey we discuss the minimax approach for the design of robust methods for signal processing. This has proven to be a very useful approach because it leads to constructive procedures for designing robust schemes. Our emphasis is on the contributions which have been made in robust signal processing, although key results of other robust statistical procedures are also considered. Most of the results we survey have been obtained in the past fifteen years, although some interesting earlier ideas for minimax signal processing are also mentioned. This survey is organized into five main parts, which deal separately with robust linear filters for signal estimation, robust linear filters for signal detection and related applications, nonlinear methods for robust signal detection, nonlinear methods for robust estimation, and robust data quantization. The interrelationships among many of these results are also discussed in the survey.
---
paper_title: Signal detection under noise interference in a game situation

paper_content:

With application to radar and data transmission, a game situation is studied where one player selects a suitable receiving filter, and the other a function describing the noise power density under restriction of a fixed total amount of power. The payoff function is a signal to noise ratio. The information the players have about each others' choice defines two extreme situations of practical interest. The fundamental relation of game theory holds for pure strategies.
---
paper_title: Robust techniques for signal processing: A survey

paper_content:

In recent years there has been much interest in robustness issues in general and in robust signal processing schemes in particular. Robust schemes are useful in situations where imprecise a priori knowledge of input characteristics makes the sensitivity of performance to deviations from assumed conditions an important factor in the design of good signal processing schemes. In this survey we discuss the minimax approach for the design of robust methods for signal processing. This has proven to be a very useful approach because it leads to constructive procedures for designing robust schemes. Our emphasis is on the contributions which have been made in robust signal processing, although key results of other robust statistical procedures are also considered. Most of the results we survey have been obtained in the past fifteen years, although some interesting earlier ideas for minimax signal processing are also mentioned. This survey is organized into five main parts, which deal separately with robust linear filters for signal estimation, robust linear filters for signal detection and related applications, nonlinear methods for robust signal detection, nonlinear methods for robust estimation, and robust data quantization. The interrelationships among many of these results are also discussed in the survey.
---
paper_title: Robust matched filters

paper_content:

The problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered. Two general aspects of this problem are treated. First, maximin robust designs are characterized for a general Hilbert-space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty. These results are seen to generalize earlier results for specific matched filtering problems. The second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion. Channel distortion is modeled by considering an unknown received signal which may differ in L_{2} -norm from the transmitted or nominal signal by no more than a fixed amount. The effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion. General expressions are developed for the determination of the robust filter and its performance, and numerical results are presented for the case of baseband detection in Gauss-Markov noise.
---
paper_title: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

paper_content:

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as follows. Suppose that f is a superposition of |T| spikes f(t)=/spl sigma//sub /spl tau//spl isin/T/f(/spl tau/)/spl delta/(t-/spl tau/) obeying |T|/spl les/C/sub M//spl middot/(log N)/sup -1/ /spl middot/ |/spl Omega/| for some constant C/sub M/>0. We do not know the locations of the spikes nor their amplitudes. Then with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the /spl lscr//sub 1/ minimization problem. In short, exact recovery may be obtained by solving a convex optimization problem. We give numerical values for C/sub M/ which depend on the desired probability of success. Our result may be interpreted as a novel kind of nonlinear sampling theorem. In effect, it says that any signal made out of |T| spikes may be recovered by convex programming from almost every set of frequencies of size O(|T|/spl middot/logN). Moreover, this is nearly optimal in the sense that any method succeeding with probability 1-O(N/sup -M/) would in general require a number of frequency samples at least proportional to |T|/spl middot/logN. The methodology extends to a variety of other situations and higher dimensions. For example, we show how one can reconstruct a piecewise constant (one- or two-dimensional) object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.
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paper_title: White-Space Sensing Device for Detecting Vacant Channels in TV Bands

paper_content:

Measurements performed at several locations clearly show that frequency spectrum is under-utilized. Cognitive radio is a strong candidate to ensure better spectrum utilization by providing access in an opportunistic manner. Simulations performed on the algorithm that we proposed show promising results in sensing vacant channels in TV bands. Here we present the work, which implements the algorithm on a real-time prototype, and measure its sensing performance in actual environments. Results show that our algorithm is robust under realistic conditions. This confirmation will give much needed confidence in the capability of cognitive radio systems to detect the operation of primary users and protect their use of spectrum.
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paper_title: TV white-space sensing prototype

paper_content:

Measurements performed at several locations clearly show that frequency spectrum is under-utilized. Cognitive radio (CR) is a strong candidate to ensure better spectrum utilization by providing access in an opportunistic manner, i.e., when the spectrum is temporary or spatially unutilized (a.k.a. white-space). The key enabling technology for realizing better frequency spectrum utilization in CR system is spectrum sensing. In particular, spectrum sensing in television (TV) bands is of great interest due to the potential availability of spectrum as a result of the planned migration of analog TV broadcasting to digital TV broadcasting. In this paper, we present the TV white-space prototype that we developed to detect vacant spectrum in TV bands. The prototype is implemented on a real-time platform and tested in practical environments. Results show that our prototype is able to detect vacant channels up to sensitivities from -116 to -120 dBm under realistic conditions. This confirmation will give the much needed confidence in the capability of CR systems to detect the operation of primary users and protect their use of spectrum. Copyright © 2008 John Wiley & Sons, Ltd.
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paper_title: Proactive Detection of Spectrum Holes in Cognitive Radio

paper_content:

Most of existing works on spectrum sensing detect primary transmitters while the purpose of spectrum sensing is to avoid interfering with primary receivers (PRs). Therefore, it is more important to detect PRs. In this paper, we propose a proactive spectrum sensing method that detects whether a PR is within the coverage or the interference range of a CR transmitter by exploiting the close-loop power control policy in primary systems. With the proposed scheme, the CR user may still access the spectrum band even though a primary signal is present as long as its transmission does not interfere with the PR. Simulation results show the advantages of the proposed method.
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paper_title: An Introduction To Compressive Sampling

paper_content:

Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.
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paper_title: Exploiting Hidden Power-Feedback Loops for Cognitive Radio

paper_content:

Prior study on the cognitive radio (CR) has mostly adopted the passive sensing protocol, where the CR keeps monitoring the spectrum of interest, and decides to transmit when the sensing result indicates that the primary radio (PR) is inactive. In this paper, we propose an alternative active sensing protocol where, prior to the sensing, the CR generates a temporary jamming signal to deliberately interfere with the PR. The jamming signal is aimed to trigger an interesting interaction between the CR and PR, named as the hidden power-feedback loop: If the PR is indeed active and reacts upon receiving the jamming signal by increasing its transmit power, the CR will receive a power-boosted PR signal that is more easily detectable. Moreover, this paper demonstrates the usefulness of exploiting the power-feedback loop for the CR to effectively estimate the channel from the CR to the PR. This is well-known as a crucial task to implement for the CR operating under the so-called interference temperature constraint, where the CR is allowed to transmit regardless of the PR's on/off status, provided that the resultant interference power level at the PR is kept below some predefined threshold.
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paper_title: Cooperative Covariance and Eigenvalue Based Detections for Robust Sensing

paper_content:

Spectrum sensing is a fundamental problem in cognitive radio. As a result, it has been reborn as a very active research area in recent years despite its long history. Although various sensing methods have been proposed, their robustness at very low signal-to-noise ratio (SNR) and uncertain noise/interference environment is generally not satisfactory. In this paper, the concept of robust sensing is discussed first. Subsequently the cooperative covariance and eigenvalue based detections are proposed for robust spectrum sensing. It is proved mathematically that under some conditions the proposed methods are robust to uncertain and unpredictable noise and interference. The performances of the methods are also verified by simulations.
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paper_title: Mitigation of digital array nonlinearities

paper_content:

In a digital array, each receiver performs analog-to-digital-conversion (ADC), with the resulting digital data later combined via digital beamforming techniques. Since ADC is performed prior to beamforming, it is thus possible to enhance the dynamic range of each digital receiver through post-ADC array integration gain. Unfortunately, receiver correlation nonlinearities, such as spurious signals (spurs) or intermodulation distortion (intermods), across receivers can severely limit the achievable dynamic range enhancement. This paper proposes a methodology for mitigating the impact of receiver nonlinearities. In our approach the receiver input signals are carefully modified in a way that varies from channel to channel. The resulting signals are then processed by each digital receiver, introducing nonlinearities. Finally, the digital signals are corrected to restore the desired linear signal components. Examples are given of how this methodology can be applied to ADC, direct digital synthesizers (DDS), digital-to-analog converters (DAC), amplifiers, and mixers. In some cases, distortion is effectively reduced by a factor of N to N/sup 2/, where N is the number of receivers.
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paper_title: Compressed sensing

paper_content:

Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear procedure defined here, the number of measurements n can be dramatically smaller than the size m. Thus, certain natural classes of images with m pixels need only n=O(m1/4log5/2(m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. More specifically, suppose x has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)-so the coefficients belong to an lscrp ball for 0<ples1. The N most important coefficients in that expansion allow reconstruction with lscr2 error O(N1/2-1p/). It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients. Moreover, a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing. The nonadaptive measurements have the character of "random" linear combinations of basis/frame elements. Our results use the notions of optimal recovery, of n-widths, and information-based complexity. We estimate the Gel'fand n-widths of lscrp balls in high-dimensional Euclidean space in the case 0<ples1, and give a criterion identifying near- optimal subspaces for Gel'fand n-widths. We show that "most" subspaces are near-optimal, and show that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces
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paper_title: Subcarrier Sensing for Distributed OFDMA in Powerline Communication

paper_content:

Powerline communication (PLC) is a preferred choice for smart home network. In this paper, a new system structure is proposed for PLC, which is based on distributed orthogonal frequency division multiple access (DOFDMA). Sub-carrier sensing, i.e., sensing every OFDM subcarrier to see if it is occupied or not, is proposed to replace the conventional carrier sensing multiple access (CSMA) for multi-user contention of a channel. This structure, borrowed from cognitive radio, allows multiple users to opportunistically share the same channel on different subcarriers and therefore increases the channel capacity. Two subcarrier sensing methods are proposed: one is based on information theory and the other is based on successive energy comparison. Simulations are provided to verify the methods.
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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: How much time is needed for wideband spectrum sensing?

paper_content:

In this paper, we consider a wideband cognitive radio network (CRN) which can simultaneously sense multiple narrowband channels and thus aggregate the perceived available channels for transmission. We study the problem of designing the optimal spectrum sensing time and power allocation schemes so as to maximize the average achievable throughput of the CRN subject to the constraints of probability of detection and the total transmit power. The optimal sensing time and power allocation strategies are developed under two different total power constraints, namely, instantaneous power constraint and average power constraint. Finally, numerical results show that, under both cases, for a CRN with three 6 MHz channels, if the frame duration is 100 ms and the target probability of detection is 90% for the worst case signal-to-noise ratio of primary users being -12 dB, -15 dB and -20 dB, respectively, the optimal sensing time is around 6 ms and it is almost insensitive to the total transmit power.
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paper_title: Eigenvalue-based spectrum sensing algorithms for cognitive radio

paper_content:

Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.
---

Title: A Review on Spectrum Sensing for Cognitive Radio: Challenges and Solutions

Section 1: Introduction
Description 1: Provide an overview of the spectrum usage issues addressed by cognitive radio, the role of spectrum sensing, and the challenges it faces.

Section 2: System Model
Description 2: Describe the general setup for spectrum sensing using multiple receivers/antennas, including the assumptions and objectives of the model.

Section 3: Neyman-Pearson Theorem
Description 3: Discuss the optimal likelihood ratio test (LRT) based on the Neyman-Pearson theorem and its practical challenges.

Section 4: Bayesian Method and the Generalized Likelihood Ratio Test
Description 4: Explain the Bayesian method and the generalized likelihood ratio test for spectrum sensing in the presence of uncertain parameters.

Section 5: Exploiting Spatial Correlation of Multiple Received Signals
Description 5: Review detection methods that utilize the spatial correlation of signals received by multiple antennas to improve sensing performance.

Section 6: Combining Space and Time Correlation
Description 6: Discuss methods that leverage both spatial and temporal correlations of received signals for more effective spectrum sensing.

Section 7: Cyclostationary Detection
Description 7: Outline the principles of cyclostationary detection and its advantages and disadvantages in spectrum sensing.

Section 8: Cooperative Sensing
Description 8: Provide an overview of cooperative sensing methods, including data fusion and decision fusion strategies, and their benefits and challenges.

Section 9: Noise Power Uncertainty and Estimation
Description 9: Analyze the impact of noise power uncertainty on detection performance and discuss methods for real-time noise power estimation.

Section 10: Detection Threshold and Test Statistic Distribution
Description 10: Examine methods to set detection thresholds based on test statistic distributions under the null hypothesis to achieve desired performance metrics.

Section 11: Robust Spectrum Sensing
Description 11: Review robust spectrum sensing techniques designed to handle uncertainties in signal and noise characteristics.

Section 12: Practical Considerations and Future Developments
Description 12: Identify practical challenges in implementing spectrum sensing methods and discuss possible future research directions.

Section 13: Conclusion
Description 13: Summarize the reviewed spectrum sensing techniques and highlight the key findings and future directions.