Exact Performance Analysis of Amplify-and-Forward Bidirectional Relaying over Nakagami-m Fading Channels with Arbitrary Parameters

Abstract

The exact performance of amplify-and-forward (AF) bidirectional relay systems is studied in generalized and versatile Nakagami-m fading channels, where the parameter m is an arbitrary positive number. We consider three relaying modes: two, three, and four time slot bidirectional relaying. Closed form expressions of the moment generating function (MGF), higher order moments of signal-to-noise ratio (SNR), ergodic capacity, and average signal error probability (SEP) are derived, which are different from previous works. The obtained expressions are very concise, easy to calculate, and evaluated instantaneously without a complex summation operation, in contrast to the nested multifold numerical integrals and truncated infinite series expansions used in previous work, which lead to computational inefficiency, especially when the fading parameter m increases. Simulation results corroborate the correctness and tightness of the theoretical analysis.