ASER Analysis of Cooperative Non-Regenerative Relay Systems over Generalized Fading Channels

In this article, we present a novel moment generating function (MGF) approach for performance evaluation of twohops cooperative non-regenerative multi-relay networks over a myriad of stochastic channel models. First, we develop very tight exponential approximations for the erfc(.) and erfc²(.) functions which will facilitate the development of a unified closed-form expression for the average symbol error rate (ASER) of a wide range of digital modulation schemes over generalized fading channels (with and without cooperative diversity). Next, we derive a new "asymptotic" approximation for the MGF of signalto noise ratio (SNR) of a two-hops relayed path in cooperative amplify-and-forward (CAF) diversity systems, which closely approximates its "exact" MGF. Combining these two techniques allows us to dramatically reduce the computational complexity for ASER of CAF multi-relay networks that have been treated in the literature for specific fading environments, besides providing accurate ASER estimates for CAF relay networks in many fading environments that heretofore had resisted a simple solution. Moreover, our final expression for the MGF of end-to-end SNR is expressed in closed-form, which is a desirable attribute for system-level performance analysis and optimization such as optimal power assignment among cooperative relay nodes, ergodic capacity analysis with adaptive transmission policies, outage probability, joint PHY/MAC layer design, and so on. The accuracies of our approximations have been validated with "exact" closed-form formulas that are available for specific wireless fading environments (e.g., Rayleigh and Nakagami-m channels) and via Monte Carlo computer simulations.