On the error analysis of fixed-gain relay networks over composite multipath/shadowing channels

In this paper, the analysis for the average bit error probability (ABEP) of a dual-hop fixed-gain relay network is conducted. To this end, we consider two different scenarios: 1) the second hop (relay-destination link) is subject to composite multipath/shadowing and the first hop (source-relay link) experiences only multipath fading; 2) the first hop is perturbed by the composite multipath/shadowing and the second hop undergoes only multipath fading. We develop new and exact closed-form expressions of the ABEP for the first scenario in terms of the Meijer-G and Lommel functions. Since the exact closed-form expressions for the second scenario are mathematically intractable, we derive a new approximation and bounds. These approximation and bounds are shown to be tight for medium to high average signal-to-noise ratio (SNR) regime. In addition, we also provide new and relatively simpler asymptotic expressions of the ABEP for both the scenarios. It is shown that some physical insights (e.g., diversity order) of the system can readily be obtained by using these asymptotic expressions. All our analytical results are corroborated by the Monte-Carlo simulations.