The study on generalized selection combining (GSC(N,L)) diversity systems that adaptively combines a subset of N paths with the highest instantaneous signal-to-noise ratios (SNRs) out of L available diversity paths has both theoretical and practical importance in the design of low-complexity receiver structures for cellular wideband CDMA, indoor millimeter-wave and ultra-wideband communications. This paper presents a novel mathematical framework to tackle the problem at hand by deriving a single integral expression for the moment generating function (mgf) of the GSC(N,L) output SNR when the L resolvable multipaths are independent with nonidentical fading statistics. The mgf is then used to unify the performance evaluation of a broad range of digital modulation/detection schemes in practical wireless channels.

The ability to capture significant amount of transmitted signal energy present in the resolvable multipaths using only a modest number of RAKE fingers (correlators) is an important receiver design consideration for ultra-wideband (UWB) and wideband CDMA communication systems. This, however, is achieved at the expense of RAKE receiver performance. Motivated by this need, several suboptimal hybrid receiver structures have been proposed in the literature. The study on generalized selection diversity combining with normalized threshold test per branch (T - GSC(/spl mu/,L)) is also important from a theoretical standpoint because this model encapsulates both the traditional selection diversity and maximal-ratio combining (coherent detection) or post-detection equal-gain combining (noncoherent detection) schemes as limiting cases. However, mathematical analysis for T - GSC(/spl mu/,L) has been limited to i.i.d. Rayleigh fading channels. This paper derives simple to evaluate formulas for the moment generating function (mgf) of T - GSC(/spl mu/,L) output SNR with L resolvable multipaths. In addition to providing new results for many cases that heretofore has resisted solution in a simple form, our approach also allows some of the previously obtained results to be simplified both analytically and computationally.

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.