Secrecy Energy Efficiency Optimization for RIS-Aided Multi-User Multi-Eavesdropper Wireless Networks

This correspondence investigates the secrecy energy efficiency (SEE) issue with the assistance of a reconfigurable intelligent surface (RIS). More particularly, we consider the downlink communications of multiple-input-multiple-output wireless networks, where multiple active colluding and non-colluding eavesdroppers (Es) attempt to wiretap the legitimate transmissions. To evaluate the SEE performance of the system, we introduce two distinct schemes: the SEE maximization based colluding eavesdropping (SEEM-CE) scheme and the SEE maximization based non-colluding eavesdropping (SEEM-NCE) scheme. Then, the proposed optimization problem is decomposed into two sub-problems, namely the base station (BS) precoding vectors optimization sub-problem and the RIS's phase shifters adjustment sub-problem. To be specific, for the first sub-problem, the BS precoding vectors are derived through the Dinkelbach's method and successive convex approximation (SCA) strategy. For the second sub-problem, an SCA-based approach is developed to optimize the RIS phase shifts. Building on these solutions, a block coordinate descent algorithm is proposed to alternately optimize the BS precoding vectors and RIS phase shifts, thereby addressing the original problem. Finally, numerical simulations demonstrate that the proposed SEEM-NCE algorithm achieves superior performance compared to the SEEM-CE scheme and other benchmark methods.