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

Abstract

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.