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

Motivated by potential applications to wide-band 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.