Exact error probability expressions for H-S/MRC in Rayleigh fading: a virtual branch technique

We use a virtual branch technique to derive exact expressions for the symbol error probability (SEP) of hybrid selection/maximal-ratio combining (H-S/MRC) in a multipath fading environment. We consider coherent detection of M-ary phase-shift keying and quadrature amplitude modulation for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading on each diversity branch. We further obtain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEPs, which are the SEPs for MRC of independent and identically distributed branches, whose closed-form expressions are well-known