On the Performance of Eigenvalue-Based Cooperative Spectrum Sensing for Cognitive Radio

Abstract

Abstract-In this paper, the distribution of the ratio of extreme eigenvalues of a complex Wishart matrix is studied in order to calculate the exact decision threshold as a function of the desired probability of false alarm for the maximum-minimum eigenvalue (MME) detector. In contrast to the asymptotic analysis reported in the literature, we consider a finite number of cooperative receivers and a finite number of samples and derive the exact decision threshold for the probability of false alarm. The proposed exact formulation is further reduced to the case of two receiver-based cooperative spectrum sensing. In addition, an approximate closed-form formula of the exact threshold is derived in terms of a desired probability of false alarm for a special case having equal number of receive antennas and signal samples. Finally, the derived analytical exact decision thresholds are verified with Monte-Carlo simulations. We show that the probability of detection performance using the proposed exact decision thresholds achieves significant performance gains compared to the performance of the asymptotic decision threshold.Index Terms-Complex Wishart matrix, cooperative spectrum sensing, eigenvalue-based detection.

Maximum Eigenvalue detection for spectrum sensing under correlated noise

“…In this context, several SS techniques such as Energy Detection (ED), matched filter based detection, cyclostationary feature based detection, covariance based detection, eigenvalue based detection have been proposed in the literature for sensing the presence of a Primary User (PU) [3]. Furthermore, in order to enhance the SS efficiency in wireless fading channels, a multidimensional CR receiver has been studied considering multiple receive dimensions at the CR receiver in the form of multiple antennas, oversampled branches and cooperative nodes [6,7,8,10]. These methods are mostly based on the statistics of the eigenvalues of the received signal's covariance matrix and use recent results from Random Matrix Theory (RMT).…”

“…The contributions related to the eigenvalue based sensing exploiting RMT methods include [6,7,8,10,11,12,13,14,15]. The existing techniques can be categorized into Maximum Eigenvalue (ME) based [14], Signal Condition Number (SCN) based [6,7,10,12] and Scaled Largest Eigenvalue (SLE) based [15,16].…”

The effect of noise correlation on fractional sampling based spectrum sensing

“…Different diversity enhancing techniques such as multi-antenna, cooperative and oversampled techniques have been introduced in the literature to enhance the SS efficiency in wireless fading channels [8][9][10]. In most of these methods, the properties of the eigenvalues of the received signal's covariance matrix have been considered using the recent results from advances in Random Matrix Theory (RMT) [11,12].…”

“…Several eigenvalue based SS methods utilizing the properties of the eigenvalues of Wishart random matrices have been proposed in [8,10,13]. Wishart random matrices appear in the analysis under noise only cases and in white noise scenarios.…”

Cognitive Radios: Discriminant Analysis for Automatic Signal Detection in Measured Power Spectra

“…To overcome these shortcomings, test-statistic based methods: the Covariance (CV) method [6], [7] and the Maximum-Minimum Eigenvalue (MME) detection [12] are blind algorithms insensitive to noise. MME assumes an infinite number of samples and requires knowledge the number of primary users [9], [10]. A latest method [11] is based on Random Vandermonde Matrices (RVM), which presents a better performance than the previous methods even for a finite number of measurement samples.…”