SNR of generalized diversity selection combining with nonidentical Rayleigh fading statistics

A closed-form expression for the average signal-to-noise-ratio (SNR) of generalized diversity selection combining, using the m largest (in instantaneous SNR) diversity signals, for arbitrary m, assuming that the Rayleigh fading statistics on each diversity branch are identically, independently distributed (i.i.d.), already exists in the literature. In this paper, a similar closed-form expression, but for nonidentically distributed statistics, is derived. This expression specializes to known results, such as the average SNR's of maximal-ratio combining with either i.i.d. or non-i.i.d. diversity statistics and that of conventional selection combining (CSC) with i.i.d. diversity statistics. In addition, it provides, for the first time, a simple closed-form solution to the combined SNR of CSC with non-i.i.d. diversity statistics. Further, the closed-form solution for the SNR of selecting the m largest diversity signals has negligible computational complexity.