The Beamforming Design for Optimal Outage Probability of Analog Network Coding with Multi-Antenna Relay Channel

This paper considers the analog network coding (ANC), which is an amplify-and-forward (AF) protocol for two-way relay channel (TWRC). In the ANC protocol, two end-sources exchange information through the help of the relay in two stages. In some recent studies, the outage probability of single-antenna relay in TWRC is presented and strategies for selecting the optimal relay are proposed. This paper studies the bidirectional network where each end-source has a single antenna and the relay has multiple antennas. We analyze the outage probability for the bidirectional network. The beamforming structure to reach the optimal outage performance is proposed. Then we compare the performance with the system of single-antenna relay network. Simulations demonstrate that multi-antenna relay system achieves the diversity gain as compared to single-antenna system.