Unified Analysis of Two-Hop Cooperative Amplify-and-Forward Multi-Relay Networks

This article develops an extremely simple and tight closed-form approximation for the momentgenerating function (MGF) of signal-to-noise ratio (SNR) for two-hop amplify-and-forward relayedpaths over generalized fading environments. The resulting expression facilitates efficient analysis of twohopcooperative amplify-and-forward (CAF) multi-relay networks over a myriad of stochastic channelmodels (including mixed-fading scenarios where fading statistics of distinct links in the relayed path maybe from different family of distributions). The efficacy of our proposed MGF expression for computingthe average symbol error rate (ASER), outage probability, and the ergodic capacity (with limitedchannel side-information among cooperating nodes) is also studied. Numerical results indicate that theproposed MGF expression tightly approximates the exact MGF formulas and outperforms the existingMGF of lower and upper bounds of the half-harmonic mean (HM) SNR, while overcoming the difficultiesassociated in deriving an accurate MGF formula for the end-to-end SNR over generalized fadingchannels. Further application of our new closed-form formula for the MGF of end-to-end SNR forevaluating the average bit and/or packet error rate with adaptive discrete-rate modulation in CAF relaynetworks is also discussed.