Moments generating function of the harmonic mean of two non-identical gamma random variables and its applications in wireless communications

In this paper, a closed-form expression for the moments generating function of the half-harmonic mean of two independent, not necessarily identically distributed gamma random variables with arbitrary parameters is presented. This statistical result is useful to the performance analysis of dual-hop wireless communication systems with amplify-and-forward relays in a Nakagami-m fading environment. The proposed mathematical analysis is substantiated by various numerically evaluated and computer simulation results.