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To serve the growing demand of the bidirectional information exchange, the authors propose a single Relay Selection (RS) scheme for Physical-layer Network Coding (PNC) in a bidirectional cooperative network consisting of two sources and multiple relays. This RS scheme selects a single best relay by maximizing the bottleneck of the capacity region of both information flows in the bidirectional network. They show that the proposed RS rule minimizes the outage probability and that it can be used as a performance benchmark for any RS rules with PNC. They derive a closed-form exact expression of the outage probability for the proposed RS rule and show that it achieves full diversity gain. Finally, numerical results demonstrate the validity of their analysis.
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