Bivariate Fisher–Snedecor F Distribution and its Applications in Wireless Communication Systems

Recently, a Fisher-Snedecor .T composite fading model has gained great attention due to its mathematical tractability and modeling accuracy. However, its bivariate statistical characteristics have not been considered yet in the previous technical literature. In this paper, we present a bivariate Fisher-Snedecor .T distribution with identical shaping parameters and study its applications in the wireless communication systems. We first derive novel theoretical formulations of the statistical characteristics for the bivariate Fisher-Snedecor .T distribution model, which include the joint probability density function (PDF), the joint cumulative distribution function (CDF), the joint moment generating function (MGF) and the joint moments. Then, capitalizing on the above statistical expressions, some exact and asymptotic expressions of performance criteria, such as the outage probability, the average bit/symbol error probability (ABEP/ASEP), and the average channel capacity, for dual-branch selection combing and maximal ratio combing diversity systems are derived, respectively. Especially, the exact expressions of the ABEP/ASEP for several classical modulation schemes are obtained in terms of the multivariate Fox's H-function by applying the Mellin-Barnes type contour integral. Furthermore, we investigate the second-order statistics of a sampled Fisher-Snedecor .T composited fading envelope by utilizing the joint CDF, and obtain the mathematical expressions of the level crossing rate (LCR) and the average fade duration (AFD). Finally, we employ numerical and simulation results to demonstrate the validity of the theoretical analysis under various correlated fading and shadowing scenarios.