Unified performance bounds for generalized selection diversity combining in independent generalized fading channels

The cumulative distribution function (cdf) and the moment generating function (mgf) of a linear sum of ordered random variables (RVs) are needed for characterizing the performance of a generalized selection combining (GSC) receiver. Unfortunately, in all but a few cases, the mgf and the cdf either are not in closed form or exist only as multidimensional integrals. Consequently, analyzing the GSC performance in a generalized fading environment is difficult and time-consuming, especially when the number of diversity branches, L, is large. This paper therefore derives new upper and lower bounds for the cdf of the GSC output signal-to-noise ratio (SNR) in generalized fading channels. These bounds are either closed-form or single finite integral expressions. New bounds are also derived for the average symbol error rates (SERs) for a multitude of binary and M-ary digital modulations in a variety of fading channel models that heretofore had resisted simple solutions.