Beyond Diagonal RIS for Physical-Layer Security: Low-Complexity Solution in the Low-SNR Regime

This letter investigates beyond diagonal reconfigurable intelligent surfaces (BD-RIS) for physical-layer security (PLS) in correlated wiretap channels. A multi-antenna transmitter is considered, and transmit antenna selection (TAS) is used to exploit transmit-side diversity with a single active radio-frequency (RF) chain. Using the first-order secrecy rate approximation, we develop a two-stage scheme to maximize the secrecy rate in the low signal-to-noise ratio (SNR) regime. In the first stage, two TAS schemes are developed based on the effective channel upper-bound. In the second stage, an eigenvector-based BD-RIS scattering matrix is designed for single-connected, group-connected, and fully-connected architectures. Unlike legitimate-user-centric or eavesdropping-nulling designs, the proposed approach balances legitimate-user signal enhancement and information-leakage suppression without forcing zero leakage. Simulation results show improved secrecy performance, particularly under a strong correlation between legitimate and eavesdropping channels.