Energy efficient MIMO two-way relay system with physical layer network coding

We investigate error performance and an optimum power allocation scheme for multiple-input multiple-output (MIMO) channel physical layer network coding (PNC) based two-way relay system. Zero forcing precoding technique is used at source nodes to facilitate PNC operations at the relay node. First, system error performance is investigated by introducing upper and lower bounds for BPSK modulation system. They are validated with numerical results and bounds provide accurate results at high SNR regime. Then, we consider sum rate maximization under a total power constraint to obtain the optimum power allocation scheme. Analytical solutions are derived and compared with other possible schemes, which are suboptimal. Numerical results confirm that the power allocation scheme provides the optimal solution for the achievable sum rate with the total available power and the relay position.