Joint RIS and Beamforming Design for Secure and Energy-Efficient Two-Way Relay Communications

This paper examines the enhancement of secrecy energy efficiency (SEE) in a reconfigurable intelligent surface (RIS)-assisted two-way relay (TWR) system. We first establish a theoretical model for the system's secrecy rate, energy consumption, and SEE, and formulate the SEE maximization problem through the joint design of the RIS phase shifts and beamforming matrix. Using techniques such as weighted minimum mean square error (WMMSE), alternating optimization, and the augmented Lagrange method, we then develop a theoretical framework that identifies locally optimal solutions for the RIS and beamforming settings under unit-modulus and power constraints. The proposed framework is also shown to be applicable to solving the system's secrecy rate maximization problem. To address the computational complexity involved in optimizing the RIS phase shifts, we further propose a suboptimal scheme leveraging the Newton's method, which significantly reduces the computational burden while achieving performance close to the optimal SEE. Extensive numerical results validate the effectiveness of the proposed schemes, showing significant SEE improvements compared to traditional channel-capacity-based secure transmission scheme.