This article develops an extremely simple and tight closed-form approximation for the moment generating function (MGF) of signal-to-noise ratio (SNR) for two-hop amplify-and-forward relayed paths over generalized fading environments. The resulting expression facilitates efficient analysis of twohop cooperative amplify-and-forward (CAF) multi-relay networks over a myriad of stochastic channel models (including mixed-fading scenarios where fading statistics of distinct links in the relayed path may be from different family of distributions). The efficacy of our proposed MGF expression for computing the average symbol error rate (ASER), outage probability, and the ergodic capacity (with limited channel side-information among cooperating nodes) is also studied. Numerical results indicate that the proposed MGF expression tightly approximates the exact MGF formulas and outperforms the existing MGF of lower and upper bounds of the half-harmonic mean (HM) SNR, while overcoming the difficulties associated in deriving an accurate MGF formula for the end-to-end SNR over generalized fading channels. Further application of our new closed-form formula for the MGF of end-to-end SNR for evaluating the average bit and/or packet error rate with adaptive discrete-rate modulation in CAF relay networks is also discussed.
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