Quickest Eigenvalue-Based Spectrum Sensing using Random Matrix Theory

We investigate the potential of 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 considered. Under both detection hypotheses H0 (noise only) and H1 (signal + noise) the eigenvalues of the sample covariance matrix follow Wishart distributions. For the case of K = 2 SUs, we derive an analytical formulation of the probability density function (PDF) of the maximum-minimum eigenvalue (MME) detector under H1. Utilizing results from the literature under H0, we investigate two detection schemes. First, we calculate the receiver operator characteristic (ROC) for MME block detector based on analytical results. Second, we introduce two eigenvaluebased quickest detection algorithms: a cumulative sum (CUSUM) algorithm, when the signal-to-noise ratio (SNR) of the PU signal is known and an algorithm using the generalized likelihood ratio, in case the SNR is unknown. Bounds on the mean time to falsealarm τfa and the mean time to detection τd are given for the CUSUM algorithm. Numerical simulations illustrate the potential advantages of the quickest detection approach over the block detection scheme.