Secure and Energy-Efficient Beamforming for MIMO Two-way Untrusted Relay Systems

In this paper, we investigate energy-efficient secure communications in an untrusted two-way relay network, where two source nodes exchange messages via an untrusted relay. Considering both security threats and energy limitation, the performance metric secure energy efficiency is defined as the ratio of the secrecy sum rate to the total power consumption. Our objective is to maximize the secure energy efficiency by jointly designing the source and relay beamformers. We first derive the expression of secure energy efficiency under a general beamforming configuration. Then, an iterative algorithm based on the techniques of alternate optimization, fractional programming, barrier function method and semi-definite programming, is proposed to find the optimal solutions of the source and relay beamformers. Our analysis shows that the proposed scheme can not only solve the problem of secure energy efficiency maximization but also be applicable for solving the problem of secrecy sum rate maximization. Simulation results demonstrate that the proposed scheme achieves a good gain in terms of secure energy efficiency.