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Reconfigurable Intelligent Surface Aided Secure Transmission Exploiting Statistical CSI of Eavesdropper

We investigate the reconfigurable intelligent surface (RIS) aided downlink secure transmission where only the statistical channel of eavesdropper is available. To handle the stochastic ergodic secrecy rate (ESR) maximization problem, a deterministic lower bound of ESR (LESR) is derived. We aim to maximize the LESR by jointly designing the transmit beamforming at the access point (AP) and reflect beamforming by the phase shifts at the RIS. Based on penalty dual decomposition (PDD) framework and block successive convex approximation (BSCA) algorithm, a penalty dual convex approximation (PDCA) algorithm with low computational complexity is proposed and a Karush-Kuhn-Tucker (KKT) solution of this non-convex LESR maximization problem is guaranteed. Simulation results show that the proposed PDCA scheme is better than the commonly used alternating optimization (AO) scheme with the knowledge of statistical channel of eavesdropper.