On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach

Abstract

Scaled Largest Eigenvalue (SLE) detector stands out as the optimal single-primary-user detector in uncertain noisy environments. In this paper, we consider a multi-antenna cognitive radio system in which we aim at detecting the presence/absence of a Primary User (PU) using the SLE detector. By the exploitation of the distributions of the largest eigenvalue and the trace of the receiver sample covariance matrix, we show that the SLE could be modeled using the standard Gaussian function. Moreover, we derive the distribution of the SLE and deduce a simple yet accurate form of the probability of false alarm and the probability of detection. Hence, this derivation yields a very simple form of the detection threshold. Correlation coeÿcient between the largest eigenvalue and the trace is also considered as we derive a simple analytical expression. These analytical derivations are validated through extensive Monte Carlo simulations

Keywords

• Scaled largest eigenvalue detector
• Spectrum sensing
• Wishart matrix