Distributions of multivariate equally-correlated fading employing selection combining

Abstract

Selection combiner output distributions of multivariate correlated fading have been very scarce in the literature. Distributions of multivariate for popular correlated fading environments employing selection combining such as Rayleigh, Rician and Nakagami-m have been obtained and thoroughly studied. However, selection combiner output distributions of multivariate correlated generalised-Rayleigh, central chi-square, non-central chi-square fading and performance of popular modulation schemes under correlated generalised-Rician and correlated generalised-Rayleigh fading have not been rigorously studied. In this paper, single-integral and infinite-summation selection combiner output distributions of multivariate correlated fading environments including generalised-Rayleigh, central chi-square, generalised-Rician and non-central chi-square are examined. Using the newly-derived distributions, average bit error rates of Binary Phase-Shift Keying, Differential Binary Phase-Shift Keying, π4-Shift Differential Quadrature Phase Shift Keying, Minimum-Shift Keying and M-ary Frequency-Shift Keying under correlated and identically distributed (c.i.d.) generalised-Rician and c.i.d. generalised-Rayleigh are derived and plotted against common branch normalised SNR, diversity order, fading parameter, number of degrees of freedom and correlation coefficient. Simulation results exactly match the proposed findings which validate the new findings. Detailed discussions are given. Mathematical proofs are given in Appendices A–D.