On the Sum of Squared Correlated Rayleigh Variates and Applications to Maximal-Ratio Diversity

An infinite series representation for the moment generating function of the sum of squared arbitrarily correlated Rayleigh random variables is presented. Based on the derived formula, corresponding analytical expressions for the probability density and cumulative distribution functions are extracted. As an application for the aforementioned sum, exact analytical expressions for the outage and the average error probability, as well as, the channel average spectral efficiency of multibranch maximal-ratio 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.