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. Index Terms Amplify-and-forward relaying, semi-blind relaying, fading, outage, Mellin transforms. The authors are with Toshiba Research Europe Ltd., Telecommunications Research Laboratory, 32 Queen Square, Bristol, BS1 4ND; tel: +44 (0)117 906 0700, fax: +44 (0)117 906 0701, email: {justin,yue.wang,gillian.huang}@toshiba-trel.com. May 1, 2014 DRAFT 2