Optimal Analogue Relaying with Multi-Antennas for Physical Layer Network coding

This paper considers a wireless relay network where two nodes S1 and S2 exchange their information through a relay node RL. It is assumed that both S1 and S2 are equipped with single antenna and RL is equipped with multi-antennas. Based on the principle of physical layer network coding (PNC), we study the optimal design for the analogue relaying, also known as amplify-and-forward (AF), at RL so as to maximize the sum- rate of bi-directional information exchange between S1 and S2. Optimal solution for the multi-antenna linear processing at RL is presented and low-complexity suboptimal schemes are proposed. Simulation results show that the proposed methods perform better than the conventional zero-forcing (ZF) and minimum- mean-squared-error (MMSE) -based linear relaying, and the performance gain is very significant when the two channels from S1 and S2 to RL are highly correlated.