Closed form and infinite series solutions for the MGF of a dual-diversity selection combiner output in bivariate Nakagami fading

Using a circular contour integral representation for the generalized Marcum-Q function, Q_m(a,b), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagami-m fading with positive integer fading severity index. This result involves only elementary functions and holds for any value of the ratio a/b in Q_m(a,b). As an aside, we show that previous integral representations for Q_m(a,b) can be obtained from a contour integral and also derive a new, single finite-range integral representation for Q_m(a,b). A new infinite series expression for the MGF with arbitrary m is also derived. These MGFs can be readily used to unify the evaluation of average error performance of the dual-branch SC for coherent, differentially coherent, and noncoherent communications systems.