Eigenvalue-Based Spectrum SensingWith Two Receive Antennas

National audience"Le concept de la radio intelligente définit deux types d’utilisateurs: les utilisateurs primaires (UP) qui ont accès aux ressources spectrales d’une façon prioritaire et les utilisateurs secondaires (US) qui exploitent les opportunités de communication laissées vacantes parles UPs. Dans ce papier on s’int´eresse au probl`eme de d´etection des ressources spectrales libres en utilisant les distributions du nombre deconditionnement (NDC) de la matrice de covariance des signaux reus par l’US. Une nouvelle formule math´ematique est propos´ee pour ladistribution du NDC dans le cas d’absence des UPs permettant ainsi de d´evelopper un nouveau algorithme de d´etection. Les r´esultats dessimulations nous permettent de valider la formulation th´eorique et les hypoth`eses de bases.

Eigenvalue Based Detector in Finite and Asymptotic Multi-antenna Cognitive Radio Systems

In Cognitive Radio, Spectrum Sensing (SS) is the task of obtaining awareness about the spectrum usage. Mainly it concerns two scenarios of detection: (i) detecting the absence of the Primary User (PU) in a licensed spectrum in order to use it and (ii) detecting the presence of the PU to avoid interference. Several SS techniques were proposed in the literature. Among these, Eigenvalue Based Detector (EBD) has been proposed as a precious totally-blind detector that exploits the spacial diversity, overcome noise uncertainty challenges and performs adequately even in low SNR conditions. The first part of this study concerns the Standard Condition Number (SCN) detector and the Scaled Largest Eigenvalue (SLE) detector. We derived exact expressions for the Probability Density Function (PDF) and the Cumulative Distribution Function (CDF) of the SCN using results from finite Random Matrix Theory; In addition, we derived exact expressions for the moments of the SCN and we proposed a new approximation based on the Generalized Extreme Value (GEV) distribution. Moreover, using results from the asymptotic RMT we further provided a simple forms for the central moments of the SCN and we end up with a simple and accurate expression for the CDF, PDF, Probability of False-Alarm, Probability of Detection, of Miss-Detection and the decision threshold that could be computed and hence provide a dynamic SCN detector that could dynamically change the threshold value depending on target performance and environmental conditions. The second part of this study concerns the massive MIMO technology and how to exploit the large number of antennas for SS and CRs. Two antenna exploitation scenarios are studied: (i) Full antenna exploitation and (ii) Partial antenna exploitation in which we have two options: (i) Fixed use or (ii) Dynamic use of the antennas. We considered the Largest Eigenvalue (LE) detector if noise power is perfectly known and the SCN and SLE detectors when noise uncertainty exists.La thèse aborde le problème de la détection d’un signal dans une bande de fréquences donnée sans aucune connaissance à priori sur la source (détection aveugle) dans le contexte de la radio intelligente. Le détecteur proposé dans la thèse est basé sur l’estimation des valeurs propres de la matrice de corrélation du signal reçu. A partir de ces valeurs propres, plusieurs critères ont été développés théoriquement (Standard Condition Number, Scaled Largest Eigenvalue, Largest Eigenvalue) en prenant pour hypothèse majeure un nombre fini d’éléments, contrairement aux hypothèses courantes de la théorie des matrices aléatoires qui considère un comportement asymptotique de ces critères. Les paramètres clés des détecteurs ont été formulés mathématiquement (probabilité de fausse alarme, densité de probabilité) et une correspondance avec la densité GEV a été explicitée. Enfin, ce travail a été étendu au cas multi-antennes (MIMO) pour les détecteurs SLE et SCN

Collaboration et Coordination de réseaux de communications intelligents dans un environnement incertain

During the last decades, wireless communications have visualized an exponential growth due to rapidly expanding market of wireless broadband and multimedia users and applications. Indeed, the demand for more radio spectrum increased in order to support this growth which highlighted on the scarcity and under-utilization problems of the radio spectrum resources. To this end, Cognitive Radio (CR) technology has received an enormous attention as an emerging solution to the spectrum shortage problem for the next generation wireless communication systems. For the CR to operate efficiently and to provide the required improvement in spectrum efficiency, it must be able to effectively identify the spectrum holes. Thus, Spectrum Sensing (SS) is the key element and critical component of the CR technology. In CR networks, Spectrum Sensing (SS) is the task of obtaining awareness about the spectrum usage. Mainly it concerns two scenarios of detection: (i) detecting the absence of the Primary User (PU) in a licensed spectrum in order to use it and (ii) detecting the presence of the PU to avoid interference. Several SS techniques were proposed in the literature. Among these, Eigenvalue Based Detector (EBD) has been proposed as a precious totally-blind detector that exploits the spacial diversity, overcome noise uncertainty challenges andperforms adequately even in low SNR conditions. However, the complexity of the distributions of decision metrics of the EBD is one of the important challenges. Moreover, the use massive MIMO technology in SS is still not explored. The first part of this study concerns the Standard Condition Number (SCN) detector and the Scaled Largest Eigenvalue (SLE) detector. The focus is on the complexity of the statistical distributions of the SCN and the SLE decision metrics since this will imply a complicated expressions for the performance probabilities as well as the decision threshold if it could be derived. We derive exact expressions for the Probability Density Function (PDF) andthe Cumulative Distribution Function (CDF) of the SCN using results from finite Random Matrix Theory (RMT). In addition, we derived exact expressions for the moments of the SCN and we proposed a new approximation based on the Generalized Extreme Value (GEV) distribution. Moreover, using results from the asymptotic RMT we further provide a simple forms for the central moments of the SCN and we end up with a simple and accurate expression for the CDF, PDF, Probability of False-Alarm (Pfa), Probability of Detection (Pd), Probability of Miss-Detection (Pmd) and the decision threshold that could be computed on the y and hence provide a dynamic SCN detector that could dynamically change the threshold value depending on target performance and environmental conditions. On the other hand, we proved that the SLE decision metric could be modelled using Gaussian function and hence we derived its PDF, CDF, Pfa, Pd and decision threshold. In addition, we also considered the correlation between the largest eigenvalue and the trace in the SLE study. The second part of this study concerns the massive MIMO technology and how to exploit the large number of antennas for SS and CRs. Two antenna exploitation scenarios are studied: (i) Full antenna exploitation and (ii) Partial antenna exploitation in which we have two options: (i) Fixed use or (ii) Dynamic use of the antennas. We considered the Largest Eigenvalue (LE) detector if noise power is perfectly known and the SCN and SLE detectors when noise uncertainty exists. For fixed approach, we derived the optimal threshold which minimizes the error probabilities. For the dynamic approach, we derived the equation from which one can compute the minimum requirements of the system. For full exploitation, asymptotic approximation of the threshold is considered using the GEV distribution. Finally, a comparisons between these scenarios and different detectors are provided in terms of system performance and minimum requirements. This work presents a novel study in the field of SS applications in CR with massive MIMO technology.Dans cette thèse,nousanalysons l'impact de l'utilisation d'un nombrefini d'échantillons sur lesperformances de difféerents détecteurs utilisant desvaleurs propres de la matrice de covariance

Détecteurs de bandes libres utilisant les valeurs propres pour la radio intelligente multi-antennes : comportement asymptotique et non-asymptotique

La thèse aborde le problème de la détection d’un signal dans une bande de fréquences donnée sans aucune connaissance à priori sur la source (détection aveugle) dans le contexte de la radio intelligente. Le détecteur proposé dans la thèse est basé sur l’estimation des valeurs propres de la matrice de corrélation du signal reçu. A partir de ces valeurs propres, plusieurs critères ont été développés théoriquement (Standard Condition Number, Scaled Largest Eigenvalue, Largest Eigenvalue) en prenant pour hypothèse majeure un nombre fini d’éléments, contrairement aux hypothèses courantes de la théorie des matrices aléatoires qui considère un comportement asymptotique de ces critères. Les paramètres clés des détecteurs ont été formulés mathématiquement (probabilité de fausse alarme, densité de probabilité) et une correspondance avec la densité GEV a été explicitée. Enfin, ce travail a été étendu au cas multi-antennes (MIMO) pour les détecteurs SLE et SCN.In Cognitive Radio, Spectrum Sensing (SS) is the task of obtaining awareness about the spectrum usage. Mainly it concerns two scenarios of detection: (i) detecting the absence of the Primary User (PU) in a licensed spectrum in order to use it and (ii) detecting the presence of the PU to avoid interference. Several SS techniques were proposed in the literature. Among these, Eigenvalue Based Detector (EBD) has been proposed as a precious totally-blind detector that exploits the spacial diversity, overcome noise uncertainty challenges and performs adequately even in low SNR conditions. The first part of this study concerns the Standard Condition Number (SCN) detector and the Scaled Largest Eigenvalue (SLE) detector. We derived exact expressions for the Probability Density Function (PDF) and the Cumulative Distribution Function (CDF) of the SCN using results from finite Random Matrix Theory; In addition, we derived exact expressions for the moments of the SCN and we proposed a new approximation based on the Generalized Extreme Value (GEV) distribution. Moreover, using results from the asymptotic RMT we further provided a simple forms for the central moments of the SCN and we end up with a simple and accurate expression for the CDF, PDF, Probability of False-Alarm, Probability of Detection, of Miss-Detection and the decision threshold that could be computed and hence provide a dynamic SCN detector that could dynamically change the threshold value depending on target performance and environmental conditions. The second part of this study concerns the massive MIMO technology and how to exploit the large number of antennas for SS and CRs. Two antenna exploitation scenarios are studied: (i) Full antenna exploitation and (ii) Partial antenna exploitation in which we have two options: (i) Fixed use or (ii) Dynamic use of the antennas. We considered the Largest Eigenvalue (LE) detector if noise power is perfectly known and the SCN and SLE detectors when noise uncertainty exists

Approximating the standard condition number for cognitive radio spectrum sensing with finite number of sensors

International audienc

On the Performance Evaluation of Eigenvalue-Based Spectrum Sensing Detector for MIMO Systems

International audienceThe agility of any cognitive radio system largely depends on the performance of the spectrum sensing technique used. While the Energy Detector (ED) is considered to be a very simple technique in practice, it suffers from noise and measurement uncertainty. To overcome this uncertainty, the Eigenvalue Based Detector (EBD) is currently proposed as a promising technique for spectrum sensing. In this paper, we propose to analyze the performance of such a detector in a finite context. More specifically, we derive the analytical form of the cumulative density function (CDF) and the probability density function (PDF) of the 3xN MIMO like signal based on Wishart matrix. Then, we evaluate the performance of the EBD detector with 2 and 3 antennas in terms of CDF, probability of false alarm, and probability of detection

A Simple formulation for the Distribution of the Scaled Largest Eigenvalue and application to Spectrum Sensing

12 pagesInternational audience"Scaled largest eigenvalue (SLE) detector stands out as thebest single-primary-user detector in uncertain noisy environments. Inthis paper, we consider a multi-antenna cognitive radio system in whichwe aim at detecting the presence/absence of a primary user (PU) usingthe SLE detector. We study the distribution of the SLE as a large num-ber of samples are used in detection without constraint on the numberof antennas. By the exploitation of the distributions of the largest eigen-value and the trace of the receiver sample covariance matrix, we showthat the SLE could be modeled as a normal random variable. Moreover,we derive the distribution of the SLE and deduce a simple yet accurate form of the probability of false alarm. Hence, this derivation yields avery simple form of the detection threshold. The analytical derivations are validated through extensive Monte Carlo simulations.

On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach

International audienc

On the detection probability of the standard condition number detector in finite-dimensional cognitive radio context

International audienceStandard condition number (SCN) detector is an efficient detector in multi-dimensional cognitive radio systems since no a priori knowledge is needed. The earlier studies usually assume a large number of dimensions and a large number of samples per dimension and use random matrix theory (RMT) to derive asymptotic distributions of the SCN metric. In practice, the number of dimensions may not be large enough for the SCN distribution to be well approximated by the asymptotic ones. In this context, the false alarm probability is considered in literature and formulas for 2D, 3D, and infinite-dimensional systems have been derived. However, the detection probability, which is of great importance in cognitive radio, has not been well discussed in literature. In this paper, we discuss, analytically, the detection probability of the SCN detector. Since the probability of detection is totally related to the SCN distribution, we derive new results on the joint ordered eigenvalues and SCN distributions for central semi-correlated Wishart matrices. These results are used to approximate the detection probability by the non-central/central approximation. We consider systems with three or more dimensions, and we give an approximated form of the detection probability. The analytical results of this paper on probability of detection along with those on probability of false alarm present a complete performance analysis and are validated through simulations. We show that the proposed analytical expressions provide high accuracy and that the SCN detector outperforms the well-known energy detector and the largest eigenvalue detector even with a small number of dimensions and low noise uncertainty environments

Asymptotic Approximation of the Standard Condition Number Detector for Large Multi-Antenna Cognitive Radio Systems

Standard condition number (SCN) detector is a promising detector that can work eÿciently in uncertain environments. In this paper, we consider a Cognitive Radio (CR) system with large number of antennas (eg. Massive MIMO) and we provide an accurate and simple closed form approximation for the SCN distribution using the generalized extreme value (GEV) distribution. The approximation framework is based on the moment-matching method where the expressions of the moments are approximated using bi-variate Taylor expansion and results from random matrix theory. In addition, the performance probabilities and the decision threshold are considered. Since the number of antennas and/or the number of samples used in the sensing process may frequently change, this paper provides simple form decision threshold and performance probabilities offering dynamic and real-time computations. Simulation results show that the provided approximations are tightly matched to relative empirical ones