Low-complexity Joint Beamforming for RIS-Aided Multi-User Downlink over Correlated Channels

This paper considers the reconfigurable intelligent surface (RIS)-assisted communication scenario, where an RIS is used to assist the base station (BS) for serving multiple users. The RIS consisting of passive reflecting elements can manipulate the reflected direction of the incoming electromagnetic waves and thus it offers a new design dimension to the system designer. To maximize the sum rate, the active beamforming at the BS and the passive phase shifts at the RIS need to be jointly optimized, which is an NP-hard problem. In this work, we consider the joint active and passive (JAPB) beamforming problem over correlated fading channels. To facilitate practical implementation, we propose two low-complexity schemes along with user grouping to solve JAPB. Besides, we theoretically analyze the mean correlation coefficient between two cascade RIS channels and obtain a closed-form expression for arbitrary phase-shift values. Asymptotic analysis is also conducted to get insights into the channel correlation of cascade RIS channels when the numbers of BS antennas and RIS elements are large. Simulation results are presented to validate the analysis accuracy of the derived mean correlation coefficient. Also, the sum rate performance of the proposed methods under different system settings is evaluated and compared with the benchmark that optimizes the RIS phase shifts using element-wise successive refinement.