An efficient physical layer security algorithm for two-way relay systems

In this paper, we study the physical layer security in a two-way relay system consisting of two transceivers, one eavesdropper, and multiple relays. We study the system in case of the channel state information (CSI) of the eavesdropper is unknown, and hence artificial noise is used to degrade the signal to noise ratio at the eavesdropper. In order to reserve the maximum possible power for artificial noise, we consider the problem of minimizing the total power of the information signal transmitted by the relays, under quality of service constraints at the legitimate transceivers. This problem has been solved using semidefinite programming (SDP) and second order cone programming (SOCP) methods. Here, aiming to significantly decrease the complexity, we propose a novel approach to find the optimal solution using the generalized eigenvalue. We show that in most cases, we can provide a closed-form expression of the optimal solution. In addition, our proposed solution can be used for all quadratically constrained quadratic programs (QCQPs) with positive definite objective function and two constraints. Simulation results demonstrate the effectiveness of our algorithm in terms of optimality and low complexity compared to SDP.