Precoding and Beamforming Design for Intelligent Reconfigurable Surface-Aided Hybrid Secure Spatial Modulation

As an emerging technology for wireless communication, the intelligent reconfigurable surface (IRS) is made up of numerous low-cost passive elements with reconfigurable parameters, which can reflect signals with a certain phase shift and build a programmable communication environment. To reduce the high hardware cost and energy consumption in spatial modulation (SM), an IRS-aided hybrid secure SM (SSM) system with a hybrid precoder is proposed in this paper, where an optimization problem is formulated to maximize the secrecy rate (SR) by jointly optimizing the beamforming at IRS and the hybrid precoding at transmitter. For the IRS beamforming, an alternating direction method of multipliers (IRS-ADMM) scheme is first proposed. To achieve a higher SR, an IRS beamforming scheme via semidefinite relaxation (IRS-SDR) is put forward. To reduce the high complexity of IRS-SDR, we design a block coordinate ascend-based IRS beamforming scheme (IRS-BCA) with a closed-form solution. As for the hybrid precoding, two methods, called a successive convex approximation method based on the approximate secrecy rate (ASR-SCA) and a gradient ascend method based on cut-off rate (COR-GA), are presented. Simulation results show that the proposed IRS-ADMM and IRS-SDR harvest substantial SR performance gains over IRS-BCA. In comparison to the IRS-ADMM and IRS-SDR, the proposed IRS-BCA is of the lowest complexity at the cost of performance loss. Regarding hybrid precoding, the proposed ASR-SCA outperforms COR-GA in the high transmit power region. According to the complexity and SR performance of six combination methods including each IRS beamforming method and each hybrid precoding method, we selected three combinations: IRS-BCA plus ASR-SCA, IRS-ADMM plus ASR-SCA and IRS-SDR plus COR-GA. Moreover, it is showed that the SR performance achieved by the three combination methods is significantly higher than those of IRS with random beamforming and without IRS.