Novel Closed-Form Exact Expressions and Asymptotic Analysis for the Symbol Error Rate of Single- and Multiple-Branch MRC and EGC Receivers Over $\alpha$– $\mu$ Fading

In this paper, we present a novel framework for deriving closed-form exact expressions for the symbol error rate (SER) of α-μ fading channels, assuming single-branch and equalgain combining and maximal-ratio combining receivers and considering most of the commonly used modulation schemes. The proposed framework is based on Mellin transform, and the SER expressions are given in terms of the univariate and multivariate Fox H-functions, which have recently been extensively used in the literature. The proposed framework has the following advantages over previous frameworks: First, it is straightforward and general; therefore, it allows the derivation of the exact SER expressions for cases untreated before in the literature. Second, it enables direct derivation for the asymptotic expressions of the SER for high average signal-to-noise ratios (SNRs). To validate the obtained expressions, we compare the results of the special case of the Nakagami-m fading channel with those reported in the literature. Furthermore, Monte Carlo simulations are conducted, and their results are shown to perfectly match the analytic expressions. Finally, the obtained asymptotic expressions for all the studied modulation schemes and diversity receivers are shown to match the behavior of their corresponding exact values for a wide range of SNR values that are of practical interest.