Relay Selection with Physical-Layer Network Coding

We study relay selection with the physical-layer network coding (PNC), which is a major decode-and-forward (DF)-based bidirectional protocol. We consider a network consists of two different end-sources and multiple relays, where each relay adopts XOR-encoding to combine two received symbols from the two end-sources. For this network, we propose a relay selection scheme by modifying the well-known selection cooperation (SC) to use in the PNC protocol, and it is referred to as SC-PNC. The SC-PNC consists of two phases: a multiple access channel (MAC) phase and a broadcast channel (BC) phase. In the MAC phase, a set of relays that correctly decode two received symbols from the two end-sources is determined; in the BC phase, among the relays in the determined set, a single best relay is selected such that the minimum mutual information of the two links from each relay to the two end-sources is maximized. Finally, we derive the exact outage probability of the SC-PNC in closed-form.