Reward-Maximization-Based Passive Beamforming for Multi-RIS-Aided Multi-User MISO Systems

Recently, reconfigurable intelligent surfaces (RISs) have emerged as a potential technique for future 6G communications. Considering the practical hardware constraints of RISs, e.g., the availability of only quantized phase shifts for reflecting elements, we investigate codebook-based passive beamforming, and then develop a two-phase precoding algorithm for multi-RIS-aided multi-user multiple-input single-output (MU-MISO) systems, where the required pilot overhead is much less than that for training the perfect channel state information (CSI). Compared with the maximum ratio transmission (MRT), we propose a more efficient codebook-based passive beamforming scheme based on the sum reward maximization. To verify the feasibility of the proposed reward-maximization-based passive beamforming, we compare the average sum rates achieved by the proposed method, the MRT method, as well as the exhaustive method. Further, we design a feasible set with a few codewords to reduce the computational complexity of the exhaustive method. Moreover, the obtained results based on different codebooks are given to illustrate the generality of the proposed scheme.