Exact analysis of equal-gain diversity systems over fading channels

Performance evaluation of equal-gain (EG) diversity systems is notoriously difficult - a classical problem dating back to Lord Rayleigh himself almost a century ago. A number of references to this problem and to its difficulty can be found in the research literature and textbooks. In this paper, we derive exact analytical expressions for the EG receiver performance in Rayleigh, Rician, Nakagami-m and Nakagami-q fading channels in terms of the Appell hypergeometric function. Our methodology and analytical framework can readily handle any order of diversity as well as arbitrary fading statistics (including mixed-fading). The method also applies to a broad class of coherent, differentially coherent and noncoherent modulation formats. For coherent BPSK and BFSK, the solution is particularly simple because a desirable exponential integral representation for the Gaussian probability integral is available.