Canonical expressions for the error probability performance of M-ary modulation with hybrid selection/maximal-ratio combining in Rayleigh fading

Hybrid selection/maximal-ratio combining (H-S/MRC) is a reduced-complexity diversity combining scheme, where L out of N diversity branches (with the largest signal-to-noise ratio (SNR) at each instant) are selected and combined using maximal-ratio combining (MRC). We derive closed-form expressions for the symbol error probability (SEP) of a H-S/MRC diversity system with arbitrary L and N. We consider coherent detection of M-ary phase-shift keying (MPSK) for the case of independent Rayleigh fading with equal SNR averaged over the fading.