A Useful Integral for Wireless Communication Theory and Its Application in Amplify-And-Forward Multihop Relaying

In this paper, infinite integrals involving the product of Bessel functions of different arguments are solved in closed-form. These solutions provide novel expressions in the error rate analysis for wireless amplify and forward (AF) systems with an arbitrary number of variable-gain relays. Here we show that the error probability can be described by generalized hypergeometric functions, namely Lauricella functions. This work represents a significant improvement on 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.