Unified error probability analysis for generalized selectioncombining in Nakagami fading channels

We study generalized selection combining (GSC) schemes in independent Nakagami fading channels, where N diversity branches with the largest instantaneous signal-to-noise ratios (SNRs) are selected from the total of L (N⩽L) branches and then coherently or noncoherently combined. We propose two different techniques to derive the moment generating function (MGF) expressions for the GSC output SNR in generalized Nakagami fading channels, where there are distinct and noninteger fading severity parameters, as well as different average SNRs in different diversity branches. For arbitrary fading severity parameter m_k, k=1, ···L, the MGF expression is given in a summation of N-dimensional definite integrals with the limits independent of SNR or channel parameters, and therefore can be evaluated very efficiently with numerical methods. Furthermore, for integer m_k closed-form MGF expressions are derived. Specializations of our results to Rayleigh channels and independent identically distributed (i.i.d.) Nakagami channels are presented, which are either new or equivalent to previously published results. Using the newly derived MGF expression, we provide a unified error probability analysis for many coherent and noncoherent modulation/detection schemes