Eigenvalue-based spectrum ‘hole’ detection for Nakagami-m fading channels with Gaussian and impulse noise

Abstract

The detection of spectrum ‘holes’ is one of the primary tasks of a cognitive radio (CR). Blind detection techniques using eigenvalues have attracted a great amount of interest because of the fact that no a-priori knowledge is needed. The majority of the literature only considers the effect of thermal noise in detector performance; however in practice, man-made noise also exists and degrades detector performance. This motivated one to consider the performance of blind eigenvalue-based spectrum sensing for the dual condition of thermal (Gaussian) and man-made (impulse) noise. In the literature, most of the sensing schemes perform very well for large sample length. This can be achieved either by increasing the sensing duration or by oversampling the signal. The former increases the frequency of missed opportunities, whereas the latter causes samples to become highly correlated thus degrading the detector performance. Hence, the authors are motivated to investigate algorithms that perform well for smaller sample length. Three new eigenvalue-based sensing algorithms are proposed, viz. maximum-eigenvalue-harmonic-mean (ME-HM), maximum-eigenvalue-contra-harmonic-mean-p (ME-CHM-p) and contra-harmonic-mean-minimum-eigenvalue (CH-ME). ME-HM outperforms all existing eigenvalue-based sensing schemes including the maximum-eigenvalue-geometric-mean (ME-GM) algorithm previously presented by the authors of this paper, for smaller sample length, low signal-to-noise ratio (SNR) and increased number of cooperative secondary users. The ME-CHM-p algorithm, which only allows negative values of p, the filter order, performs identically to ME-HM when p=−1. However, for smaller values of p the probability of detection (PD) improves significantly more until p=−5. The CH-ME algorithm also exhibits an improvement in PD but does not outperform ME-GM. In addition, the proposed schemes and ME-GM exhibit a significant degree of immunity to impulse noise compared to existing schemes. The analytical and simulation results are presented for the proposed schemes and ME-GM for the Gaussian and impulse noise scenario in the Nakagami-m fading channel. In addition, the algorithms are evaluated for wireless microphone (WM) signals and show improved performance. The ME-CHM-p algorithm performed the best compared with other algorithms, for small and large sample lengths, low SNR, correlated signals and for increased number of cooperating secondary radios, with and without impulse noise.