Beamforming and relay selection schemes for multi-antenna two-way relaying systems with physical network coding

In this paper, we consider a beamforming technique and relay selection method in two-way relaying systems employing physical network coding where the relays are equipped with multiple antennas. In order to exploit the benefits of multiple antennas, we design an efficient closed-form beamforming vector. Furthermore, to achieve diversity gain from multiple relays, we suggest the minimum distance based relay selection criterion. Since the minimum distance based approach generally requires a huge search size, we also propose a method to calculate the minimum distance with the reduced search size. Simulation results confirm that the proposed schemes are able to attain the full diversity order which results from both beamforming and relay selection.