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For the first time, the performance of pairwise amplify-and-forward multi-way relay networks (MWRNs) is studied. To this end, new end-to-end signal-to-noise ratio (e2e SNR) expression at an arbitrary source is first derived in closed-form, and thereby, an insightful statistical characterization is developed. In this context, tight closed-form approximations are derived for the cumulative distribution function, probability density function and moment generating function of the e2e SNR. Specifically, the conditional outage probability and the average bit error rate conditioned on error-free back-propagated successive interference cancellation are also derived in closed-form. Moreover, valuable insights into practical MWRN system-designing is obtained by deriving the fundamental diversity-multiplexing trade-off by employing the high SNR outage probability approximation.