Relay selection and beamforming for cooperative bi-directional transmissions with physical layer network coding

Application of network coding in wireless communications has enabled the development of physical layer network coding (PLNC). Applying the principle of PLNC to wireless cooperative networks for spectral efficiency improvement has recently received tremendous attention from the research community. The best relay selection is extensively investigated in the literature for PLNC cooperative networks with multiple relays. However, the authors study the problem of signal beamforming and relay selection for a cooperative bi-directional relay network using PLNC and consider signal beamforming and relay selection for (i) multiple relays each equipped with single antenna and (ii) multiple relays with multiple antennas on uncoded amplify-and-forward scheme for PLNC transmission. The authors derive the optimal design criteria and provide low-complexity sub-optimal solutions for relay selection and beamforming to minimise the symbol error probability.