Unified performance bounds for generalized selection diversity combining in fading channels

A generalized selection combiner (GSC) ranks the L available diversity paths and then combines a subset of M paths with the highest signal-to-noise ratios (SNRs). The cumulative distribution function (cdf) and moment generating function (mgf) of a linear sum of ordered random variables are therefore needed for computing the outage probability and error rates needed for computing the outage probability and error rates of a GSC receiver. Unfortunately, except for simple cases, these functions are either not known in closed form or exist only as multidimensional integrals. Consequently, an exact performance analysis is extremely difficult and time-consuming for many fading environments specifically when L is large. This paper therefore derives new upper and lower bounds for the cdf of GSC output SNR over generalized fading channels. These bounds are then used to derive new bounds for the average symbol error rates for a multitude of binary and M-ary digital modulation schemes in a variety of fading channel models that heretofore had resisted simple solutions.