AG Kommunikationstheorie

Thema:

Quickest Eigenvalue-Based Spectrum Sensing using Random Matrix Theory

Abstract:

In this work we investigate the potential for using quickest detection based on the eigenvalues of the sample covariance matrix for spectrum sensing applications. A simple phase shift keying (PSK) model with additive white Gaussian noise (AWGN), with 1 primary user (PU) and K secondary users (SUs) is utilised in this work. We identify the Wishart distributions of the eigenvalues of the sample covariance matrix under both detection hypotheses, i.e., noise only and signal with additive noise. After deriving analytical formulations of the probability density functions (PDFs) of the maximum-minimum eigenvalue (MME) test statistic under both hypotheses for the case of K = 2 SUs, we apply these results to two detection schemes. First, we calculate the ROC for the well known MME block detector directly without the need of expensive simulations. Second, we introduce two eigenvalue-based quickest detection algorithms. When the SNR of the PU signal is known a CUSUM algorithm is applicable. To cope with the situation when the SNR is unknown a GLR algorithm was deduced. Bounds on the mean time to false-alarm and the mean time to detection are given for the CUSUM algorithm. Numerical simulations illustrate the potential advantages of the quickest detection approach compared to the block detection scheme for spectrum sensing applications. Finally, some future research directions are given.

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