Selection combiner output distributions of multivariate equally-correlated generalised-Rician fading for any degrees of freedom

Obtaining tractable and compact expressions for cumulative distribution functions (cdfs) of multivariate correlated fading has long been difficult in wireless communications. Selection combiner output (SCO) single-user cdfs of multivariate correlated and identically distributed (c.i.d.) or equally-correlated Rayleigh, Rician and Nakagami-m fading for only even integer n-degree-of-freedom non-central chi-square distributed received signal envelopes have been studied in the literature. New infinite-summation and single-integral single-user single-input-multiple-output (SIMO) SCO cdfs of multivariate c.i.d. generalised-Rician fading for any integer n degrees of freedom (DoF) non-central chi-square, i.e. n can be even and odd, are obtained in this paper. The new distributions (i) generalise existing results, (ii) can be extended for c.i.d. single-user and multiuser multiple-input-multiple-output (MIMO) environments, and (iii) open up new research directions in this topic. Detailed mathematical proof, discussions and simulation results are given.