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This paper provides a complete study on the end-to-end performance of multi-hop wireless communication systems equipped with re-generative (decode-and-forward) relays over Rayleigh fading channels assuming single-antenna terminals. More specifically, the probability density function (pdf) of the tightly approximated end-to-end SNR of the systems is derived. Using this approximation allows us to avoid considering all possible combinations of correct and erroneous decisions at the relays and the destination for which the end-to-end transmission is error-free, thus reducing computation burden in evaluating important multi-hop system's performance metrics. Simulations are performed to verify the accuracy and to show the tightness of the theoretical analysis.