Asymptotic Error Rate Analysis of Multi-Hop Multi-Relay Cooperative Non-Regenerative Networks over Generalized Fading Channels

In this article, we present three moment generating function (MGF) based methods for performance evaluation of multi-hop, multi-relay cooperative amplify-and-forward (CAF) networks over a myriad of stochastic fading channel models. Method I is based on a recursive expansion of the MGF of effective SNR for a 2-hop CAF relay network developed in [10]. The second method is also similar to Method I except that it now requires the exact MGF of the end-to-end SNR for a 2-hop relay network. Method III involves the split of a multi-hop route path into two sections, evaluating the MGF of the "weakest link" in each section, and then finding the MGF of end-to-end SNR using the result in [10] for a 2-hop CAF network. We show that all the above mentioned methods closely approximate the 'exact' MGF of end-to-end SNR and the average symbol error rate (ASER) of CAF relay networks. Unlike the existing bounds (which are restrictive to specific fading channels), our proposed solutions is quite general and can be applied to a wide range of fading environments while dramatically reducing the computational complexity of ASER for multi-hop multi-branch CAF relay networks. Moreover, our final solutions for the ASER are expressed in closed-form for first two methods, and in terms of a single integral for Method III. The accuracies of our approximations have been validated with "exact" formulas that are available for specific wireless fading environments and via Monte Carlo computer simulations.