Unified error probability analysis for generalized selection diversity in Rician fading channels

Motivated by practical considerations in the design of low-complexity receiver structures for wideband cellular CDMA, millimeter-wave and ultra-wideband communications, the study on the generalized selection combining receiver that adaptively combines a subset of M "strongest" paths out of L available paths has intensified over the past few years. The study on GSC(M, L) receiver is also important from a theoretical standpoint because this model encapsulates both the classical selection diversity and maximal-ratio combining (coherent detection) or post-detection equal-gain combining (noncoherent detection) receiver structures as limiting cases. We first derive a concise analytical expression for the moment generating function (MGF) of the GSC(M, L) output signal-to-noise ratio with independent and identically distributed diversity paths over Rician fading channels (in terms of only a single finite range integral whose integrand is composed of tabulated functions). Previous studies have only treated either Rayleigh or Nakagami-m (1960) channel models using numerous ad-hoc approaches to simplify an M-dimensional nested integral that arise in the computation of the MGF. The novelty of our mathematical framework for computing the MGF relies on the fact that it allows us to treat all common multipath fading channel models (Rayleigh, Rician, Nakagami-m and Nakagami-q) in a unified sense, it leads to a much More elegant and computationally efficient expression than those available in the literature, and it holds for any combinations of M and L values. Using this newly derived MGFs, we provide a unified error probability analysis for many coherent and noncoherent digital modulation/detection schemes in a myriad of fading environments.