A closed form expression for the average SNR when combining an arbitrary number of diversity branches with non identical Rayleigh fading statistics

In Kong and Milstein (1998) a simple closed form expression for the average signal-to-noise-ratio (SNR) of combining the m largest (in instantaneous SNR) diversity signals, for arbitrary m, assuming that the Rayleigh fading statistics on each diversity branch were identically independently distributed (iid), was found. In this paper, a similar closed form expression, but for non-identically distributed statistics, is derived. This expression not only specializes to the known results, such as the average SNRs of maximal ratio combining (MRC) with either iid or non-iid diversity statistics and that of conventional selection combining (CSC) with iid diversity statistics (Jakes 1974), but also provides, for the first time, a simple closed form solution to the combined SNR of the conventional selection combining with non-iid diversity statistics. Further, the closed form solution for the SNR of selecting the m largest diversity signals has negligible computational complexity.