Robust beamforming design for the STAR-RIS-assisted secure SWIPT system

This paper investigates the secure simultaneous wireless information and power transfer (SWIPT) assisted by the simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs). Specifically, a base station (BS) configured multi-antennas has secure communication demand to an information receiver (IR) and performs wireless power transmission to an energy receiver (ER). We consider the fact that non-linear energy harvesting model is applied at the ER. Moreover, there is no direct link between the BS and the IR/ER, only the STAR-RIS-assisted cascade channel exists, and cascade channel state information (CSI) is imperfect. In particular, two CSI error models, i.e., the bounded CSI error model and the statistical CSI error model, are taken into account. Considering the potential eavesdropping risk of the ER under these two models, we study the quality of service (QoS) based robust design problems by jointly optimizing transmit beamforming and artificial noise (AN) at the BS as well as amplitude and phase shift at the STAR-RIS. To handle the formed non-convex optimization problems, we adopt S-Procedure to transform the bounded CSI error signal-to-interference-plus-noise-ratio (SINR) constraints into linear matrix inequalities (LMIs), and we utilize the Bernstein-Type Inequality (BTI) to convert the outage probability constraints with statistical CSI errors into second-order cone (SOC) constraints and linear inequalities. Accordingly, we propose two effective algorithms based on alternating optimization (AO), in which the semi-definite programming (SDP), penalty method, successive convex approximation (SCA) and semi-define relaxation (SDR) are used to solve the decomposed non-convex subproblems. We also analyze the complexity for the proposed algorithms. Finally, extensive simulation results are presented to verify the effectiveness of the proposed algorithms, and the impacts of the CSI uncertainty and the STAR-RIS parameters on the system performance are analyzed.