Optimal and near optimal power allocation schemes in two-way relay systems with physical layer network coding

In this paper, we investigate the power allocation (PA) schemes in a two-way relay system, where the relay adopts physical layer network coding (PNC) based on decode-and-forward (DF) protocol. The objective is to determine the optimal power allocation (OPA) scheme at both the source nodes and at the relay that minimizes the end-to-end symbol error probability (SEP) performance under a total power constraint. The perfect channel state information (CSI) is assumed to be available at both the source nodes and at the relay. Since numerical methods (e.g., exhaustive search) are required to find the solution of the OPA scheme, which might be infeasible for practical systems, based on upper and lower bounds on the optimal solution, we propose a near optimal power allocation (NOPA) scheme. The asymptotic SEP expression of the proposed NOPA scheme is also derived. By both the analytical and simulated results, it is shown that the proposed NOPA scheme provides the asymptotic SNR gains of about 1.76dB and 2.22dB over two well-known schemes in high SNR. Furthermore, simulation results show that the performance of proposed NOPA scheme is quite close to that of the OPA scheme.