Unified error probability analysis for generalized selection combining in Nakagami fading channels

We study generalized selection combining (GSC) schemes in independent Nakag ami fading channels, where N diversity branches with the largest instantane ous signal-to-noise ratios (SNR's) are selected from the total of L (N less than or equal to L) branches and then coherently or noncoherently combined . We propose two different techniques to derive the moment generating funct ion (MGF) expressions for the GSC output SNR in generalized Nakagami fading channels, where there are distinct and noninteger fading severity paramete rs, as well as different average SNR's in different diversity branches. For arbitrary fading severity parameter m(k), k = 1, ..., L, the MGF expressio n is given in a summation of N-dimensional definite integrals with the limi ts independent of SNR or channel parameters, and therefore can be evaluated very efficiently with numerical methods. Furthermore, for integer mi, clos ed-form MGF expressions are derived. Specializations of our results to Rayl eigh channels and independent identically distributed (i,i,d,) Nakagami cha nnels are presented, which are either new or equivalent to previously publi shed results, Using the newly derived MGF expression, we provide a unified error probability analyzes for many coherent and noncoherent modulation/det ection schemes.