A new approach to performance evaluation of generalized selection diversity receivers in wireless channels

Motivated by potential applications to wideband cellular DS-CDMA and millimeter-wave communications, study on the generalized selection combining (GSC) receiver that adaptively combines a subset of M “strongest” paths out of L available paths has intensified over the past few years. The study of GSC(M,L) receiver is also important from a theoretical standpoint because this model encapsulates both the classical selection combining and maximal-ratio combining receiver as limiting cases. Despite its importance, published results on GSC(M,L) receiver performance in a generalized fading channel is still very limited, mainly due to the mathematical difficulty encountered while computing the first-order statistics of a linear sum of ordered random variables. This paper provides a partial solution to the problem on hand by deriving relatively simple-to-evaluate expressions for the MGF of GSC output SNR in a variety of fading environments given that the individual branch SNRs are independent and identically distributed. Moreover, our generic single integral expression for the MGF of GSC output SNR reduces to a closed-form formula if the branch amplitudes follow either Rayleigh or Nakagami-m (positive integer fading index) distribution. An easily programmable recursive solution of the MGF in Nakagami-m channels is also provided. Our expressions hold for any M and L values, and thus facilitate a comprehensive analysis of GSC systems including the average symbol error probability (ASEP) analysis of a broad class of binary and M-ary modulations, average combined SNR and the outage rate of error probability analysis. The GSC diversity scheme has received considerable attention in existing literature (i.e., scanning the literature, we find that that there are more than 17 published journal and conference papers on this subject over the past four years). This is owing to its ability to mitigate the detrimental effects of deep fades on wireless channels, while achieving a good compromise between receiver performance and implementation complexity (notably fewer electronics and lower power consumption). For instance, in wideband CDMA applications, the number of available correlators will limit the number of multipaths that can be utilized in a typical rake combiner. The G S C ( M , L ) receiver clearly merits consideration because it outperforms the M-MRC (i.e., signal combination from only the first Mrake fingers) receiver configuration, owing to the improved SNR statistic at the output of the hybrid combiner. It also reduces the complexity of implementation for antenna arrays using millimeter wave communications and improves the throughput performance of packet radio networks employing “selec