Beamforming for secure two-way relay networks with physical layer network coding

We investigate the secrecy beamforming in two-way relay channels (TWRC) with physical layer network coding (PNC). The multi-antenna relay broadcasts the superimposed signal of two user messages with secrecy beamforming after receiving the signals transmitted by the two legitimate users. We first propose a lower bound of the secrecy sum rate to quantify the secrecy performance of the TWRC with PNC. Because the maximization of the lower bound is non-convex under total power constraint, we propose a joint beamforming and power allocation scheme, in which the problem is successively approximated by several convex semidefinite programs. In order to reduce the complexity, we further propose an suboptimal scheme with closed-form solution. Numerical results indicate that the proposed schemes with PNC achieve much better secrecy sum-rate performance than the traditional AF schemes.