Unified performance bounds for generalized selection diversity combining in independent generalized fading channels Limites unifiées de performance pour la diversité par combinaison avec sélection généralisée dans les canaux indépendants généralisés d’évanouissements

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, , 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 -ary digital modulations in a variety of fading channel models that heretofore had resisted simple solutions.