Near optimal power allocation in two-way relay systems with physical layer network coding

In this study, the authors examine the power allocation (PA) in a two-way relay system, where the relay adopts physical layer network coding based on decode-and-forward protocol. In the PA, the optimisation objective is to minimise the end-to-end symbol error probability (SEP) under a total power constraint. Since the optimal power allocation (OPA) scheme requires numerical methods (for exhaustive search) to find the solution, which might be infeasible for practical systems, the authors propose a near optimal power allocation (NOPA) scheme that has a closed-form solution by studying the properties of the OPA scheme. The asymptotic SEP expression of the proposed NOPA scheme is also derived. Simulation results show that the performance of proposed NOPA scheme is quite close to that of the OPA scheme. Furthermore, it is shown that the NOPA scheme can provide asymptotic SNR gains of 1.76 dB and 2.22 dB over two well-known schemes.