Robust Secure Beamforming for Intelligent Reflecting Surface Assisted Full-Duplex MISO Systems

This paper investigates a full-duplex (FD) secure communication system with the assistance of an intelligent reflecting surface (IRS). Compared with the traditional FD system, the IRS-assisted FD communication not only greatly improves the spectrum efficiency but also provides a new way to enhance physical layer security due to the overlapping of multiple signals at the eavesdropper. Furthermore, we consider a more practical scenario without perfect channel state information (CSI) because it is very difficult to obtain the perfect CSI especially for cascaded channels via IRS. In addition, the eavesdropper is usually passive and hidden which will not actively exchange CSI with the user, which leads to an obstacle for obtaining the perfect CSI of eavesdropping channels. To this end, a worst-case achievable security rate (ASR) optimization problem is formulated under the bounded CSI error model. Due to the existence of non-convexity and highly coupled variables, this problem is extremely challenging. To directly tackle the nonconvexity of the considered optimization problem, similar to successive convex approximation (SCA), we first transform the original problem into its equivalent convex optimization problem directly, and finally obtain the optimal solution of the original non-convex problem by iteratively calculating the convex optimization problem. On this basis, we iteratively solve the transmission beamforming and IRS phase shift through Alternate Optimization (AO). In particular, when optimizing the phase shift coefficient, a penalty convex-concave procedure solution is proposed. Simulation results demonstrate that our proposed robust secure beamforming scheme can effectively improve ASR, and also outperforms the nonrobust one.