Analysis on the Empirical Spectral Distribution of Large Sample Covariance Matrix and Applications for Large Antenna Array Processing

Abstract

This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row numbers of the matrices are large and of the same order, while signals have diverged and the time delays of the channel are fixed. We prove that the empirical spectral distribution of the large dimension sample covariance matrix and a well-studied spiked central Wishart matrix converge to the same distribution. As an application, an asymptotic power function is presented for the generalized likelihood ratio statistics for testing the presence of the signal in large array signal processing.