Optimal Robust BICSI-FSCSI-adaptive Beamformer and FSCSI-adaptive Reflection Design for a RIS-aided PLS Wireless Communication System

In practical scenarios, the performance of reconfigurable intelligent surface (RIS)-aided physical layer security (PLS) wireless communication systems is significantly affected by the costs associated with channel estimation accuracy, reflection adjustment and computation, which are often overlooked in many existing literature. In this paper, we investigate a multi-antenna Alice (base station) communicating with a single-antenna Bob (legitimate user) with the help of a multi-element RIS under wire-tapping by a single-antenna Eve (eavesdropper). We present the computational efficient estimators for Bob’s channel state information (CSI) by linear minimum mean squared error (LMMSE) and consider imperfect Bob’s instantaneous CSI (BICSI) and statistics for Eve’s CSI, imperfect BICSI, and channel estimation error for imperfect BICSI, termed full statistical CSI (FSCSI). Then, based on the imperfect estimators, we provide a robust BICSI-FSCSI-adaptive beamformer and FSCSI-adaptive reflection design to reduce the reflection adjustment and computation costs while overcoming the channel estimation errors. Next, the maximization of the achievable ergodic secrecy rate with respect to (w.r.t.) the proposed robust design is formulated as a two-timescale stochastic non-convex problem, which is manipulated to reach the stationary point by an iterative algorithm. Then, we analyze the computational complexity and illustrate the implementation of the proposed robust design. Finally, numerical results demonstrate the proposed robust design’s practical value and notable gains over the baselines. As far as we know, this is the first work providing optimization-based robust BICSI-FSCSI-adaptive beamformer and FSCSI-adaptive reflection design for a RIS-assisted PLS wireless communication system, achieving promising secure performance and minimum reflection adjustment cost while being robust against the channel estimation errors for BICSI.