Analysis of hybrid selection/maximal-ratio combining of diversity branches with unequal SNR in Rayleigh fading

The performance of a hybrid selection/maximal-ratio combining (H-S/MRC) diversity system in a multipath-fading environment is analyzed. With H-S/MRC, L out of N diversity branches are selected and combined using maximal-ratio combining (MRC). This technique provides improved performance over L branch MRC when additional diversity is available, without requiring additional resources (i.e., power consumption, RF electronics). In particular, we consider independent Rayleigh fading on each diversity branch without assuming equal signal-to-noise ratio (SNR) averaged over the fading. We analyze this system using a "virtual branch" technique which results in a simple derivation and formula for the mean of the combiner output SNR for any L and N. We further obtain the symbol error probability (SEP) for coherent reception of M-ary phase-shift keying (MPSK) and quadrature amplitude modulation (MQAM).