RIS-Assisted Physical-Layer Key Generation for D2D Communications With Correlated and Imperfect Channels

Physical-layer key generation (PKG) technology offers a lightweight encryption solution for device-to-device (D2D) communications. However, it faces significant challenges due to the high correlation between the eavesdropping and legitimate channels, as well as the imperfect estimated channel, which cause substantial degradation of secret key capacity. To address the challenges, we propose a novel PKG framework that leverages the reflective beamforming of reconfigurable intelligent surface (RIS) for D2D communications. Specifically, we first derive closed-form expression for the secret key capacity under correlated and imperfect estimated channels. Then, we propose to maximize the minimum secret key capacity by optimizing the reflection coefficient matrix (O-RCM) of RIS, which is a non-convex optimization problem. Next, a semi-definite relaxation and successive convex approximation-based method for O-RCM (SSO-RCM) is proposed to tackle the non-convex max-min-min problem. To further reduce the computational complexity, we propose a low-complexity method based on the path-following algorithm for O-RCM (PFO-RCM). Simulation results show that under correlated and imperfect channels, both proposed methods significantly improve the minimum secret key capacity compared to the existing RIS-assisted methods. Moreover, the PFO-RCM method, while exhibiting lower computational complexity than the SSO-RCM method, incurs a small performance loss.