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In this paper, we investigate the two-way relaying (TWR) system in multi-source multi-relay scenarios and use the proposed tight upper bounds of instantaneous end-to-end signal-to-noise ratio (SNR) of the considered system to deduce a source-relay pair selection scheme, which can be performed in a distributed manner without requiring global channel state information (CSI). Specifically, we derive the closed-form lower bound of outage probability over independent but not identically distributed Nakagami-m fading channels. In addition, based on the asymptotic analysis in the high SNR regime, the diversity-multiplexing tradeoff (DMT) of the considered system is obtained. The effectiveness of our proposed source-relay pair selection scheme and analytical results is verified by simulations.