New Performance Approximations for Multi-Hop Fixed-Gain AF Relay Networks

A novel approximation for the end-to-end signal-to-noise ratio (e2e SNR) of multi-hop (N≥2) fixed-gain amplify-and-forward (FG-AF) relay networks over independent and non-identically distributed Nakagami-m fading channels is proposed. Two types of FG-AF relays; (i) blind-AF, and (ii) semi-blind-AF are treated. The cumulative distribution and the moment generating function of the proposed e2e SNR approximation are derived in closed-form and used to derive the outage probability, the average symbol error rate, and the generalized SNR moments. The resulting performance metrics for the blind-AF relay case are asymptotically exact and thus, the asymptotic outage probability, the asymptotic average SER, the diversity order, and the coding gain are derived. Numerical and simulation results are presented to verify the comparative performance against the exact performance metrics and existing bounds. Our results reveal that the proposed performance approximations outperform the existing bounds in most of the cases.