Robust Beamforming Optimization Design for RIS-Aided MIMO Systems With Practical Phase Shift Model and Imperfect CSI

The ideal phase shift model and the acquisition of channel state information (CSI) are practically difficult to realize in reconfigurable intelligent surface (RIS) assisted communication systems. Therefore, these have greatly troubled the beamforming design of multiple-input–multiple-output (MIMO) systems via RIS. This article presents a robust beamforming design framework in the RIS-enhanced MIMO communication networks in the presence of considering practical phase shifts for the RIS and imperfect CSI of the cascade channels. More specifically, we propose an alternative optimization framework and adopt the distributed alternating direction method of multipliers (ADMMs) method to solve the sum-rate maximization problem by combining the true environment model (TEM) and the mismatch environment model (MEM) with beamforming. In particular, the proposed scheme is also used for the MEM scenario. It shows that the sum rate of the ADMM scheme with MEM under low SNR is about 3 bps/Hz more than the barrier function penalty method, approximately 6 bps/Hz more than the accelerated projected gradient method. Next, when the SNR is 5 dB, the above three schemes are greater than the semidefinite relaxation (SDR) method. But, the above methods are smaller than the SDR method in MEM. Then, the sum rate of the SDR method with the TEM is approximately 1.6 times of the MEM, while the CPU time of both is consistent with the computational complexity. Therefore, the differences between the two models affect the performance achieved by different methods. The proposed approach sheds a light to engineers working in wireless communication on enhancing the transmission robustness of existing wireless networks.