Asymptotic Outage Probability Analysis for General Fixed-Gain Amplify-and-Forward Multihop Relay Systems

In this paper, we present an analysis of the outage probability for fixed-gain amplify-and-forward (AF) multihop relay links operating in the high SNR regime. Our analysis exploits properties of Mellin transforms to derive an asymptotic approximation that is accurate even when the per-hop channel gains adhere to completely different fading models. The main result contained in the paper is a general expression for the outage probability, which is a functional of the Mellin transforms of the per-hop channel gains. Furthermore, we explicitly calculate the asymptotic outage probability for four different systems, whereby in each system the per-hop channels adhere to either a Nakagami-m, Weibull, Rician, or Hoyt fading profile, but where the distributional parameters may differ from hop to hop. This analysis leads to our second main result, which is a semi-general closed-form formula for the outage probability of general fixed-gain AF multihop systems. We exploit this formula to analyze an example scenario for a four-hop system where the per-hop channels follow the four aforementioned fading models, i.e., the first channel is Nakagami-m fading, the second is Weibull fading, and so on. Finally, we provide simulation results to corroborate our analysis.