Rayleigh Quotient Based Analysis of MIMO Linear Receivers

The statistics of indefinite quadratic forms in Gaussian vectors are of particular relevance as they often occur in signal processing, wireless communications, information theory and adaptive filter theory. Very recently their distribution has been characterized in closed form in [1]. In this work, we extend such results to the case of indefinite quadratic form with random kernel matrix. We focus on Rayleigh quotients in random matrices commonly met in MIMO communications. As an instance of practical application of our findings, the gap between the multiuser efficiency of a MIMO linear Minimum Mean-Squared Error (MMSE) receiver and the corresponding efficiency in the Zero Forcing (ZF) case, is statistically characterized in the finitesize setting for the first time.