Spectrum Sensing Based on Asymptotic Behavior of Random Vandermonde Matrices

Abstract

Free probability theory as a main branch of random matrix theory is a valuable tool for describing the asymptotic behavior of multiple systems, especially for those with large random matrices. But classical freeness results mainly focus on random matrices with independent and identically distributed (i.i.d.) entries. In this paper, by using the latest research results of random Vandermonde matrix (a class of matrix that does not satisfy the i.i.d. condition) in free probability theory, a new spectrum sensing scheme is proposed, which shows how the asymptotic behavior of random Vandermonde matrices can be used to assist spectrum sensing for cognitive radio. Simulation results show that the proposed scheme has a better detection performance than the energy detection technique and the maximum-minimum eigenvalue scheme even for the case of a small sample of observations.