Householder-Matrices based Analysis of SC Receivers over Rayleigh Fading Channels with Arbitrary Correlation

In this paper, new results for the multivariate Rayleigh distribution with an arbitrary correlation matrix are presented. By using an efficient tridiagonalization method based on Householder matrices, closed-form union upper bounds for its joint probability density and cumulative density functions are derived. Based on the proposed mathematical analysis, a tight union upper bound and an analytical approximation for the outage probability of multibranch selection diversity receivers operating over identically distributed and arbitrarily correlated Rayleigh fading channels are obtained. Our analysis is verified by comparing numerically evaluated results with extensive computer simulation ones.