Closed-Form Error Analysis of Variable-Gain Multihop Systems in Nakagami-m Fading Channels

In this paper, infinite integrals involving the product of Bessel functions of different arguments are solved in closed-form. The obtained solutions form a framework for the error probability analysis of wireless amplify and forward (AF) systems with an arbitrary number of variable-gain relays operating over independent but not necessarily identical Nakagami-m fading channels. Here we show that the error probability can be described by generalized hypergeometric functions, namely, Gauss's and Lauricella's multivariate hypergeometric functions. This work represents a significant improvement over previous contributions and extends previous formulas pertaining to dual-hop transmissions over identical Nakagami-m fading channels. Numerical examples show an excellent match between simulation and theoretical results.