Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading

In this paper, we derive analytical expressions for the symbol error probab ility (SEP) for a hybrid selection/maximal-ratio combining (H-S/MRC) divers ity system in multipath-fading wireless environments. With H-S/MRC, L out o f N diversity branches are selected and combined using maximal-ratio combin ing (MRC). We consider coherent detection of M-ary phase-shift keying (MPSK ) and quadrature amplitude modulation (MQAM) using H-S/MRC for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading. The proposed problem is made analytically tractable by transfor ming the ordered physical diversity branches, which are correlated, into in dependent and identically distributed (i.i.d.) "virtual branches," which re sults in a simple derivation of the SEP for arbitrary L and N. We further o btain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEP's, which are the SEP's using MRC with i.i.d. diversity bran ches in Rayleigh fading, or equivalently the SEP's of the nondiversity (sin gle-branch) system in Nakagami fading, whose closed-form expressions are we ll-known. We present numerical examples illustrating that H-S/MRC, even wit h L much less than N, can achieve performance close to that of N-branch MRC .