Beamforming Design for Cooperative Double-RIS Aided mmWave MU-MIMO Communications

This research delves into the design of collaborative beamforming for millimeter-wave (mmWave) multi-user multiple-input multiple-output (MU-MIMO) communications, which takes advantage of double reconfigurable intelligent surfaces (RISs) for enhanced signal transmission. The core objective is to jointly optimize the transmit beamforming at the base station and the phase shifts of the RISs to achieve the highest possible sum rate. To derive an efficient solution, the original problem is recast using the weighted minimum mean square error (WMMSE) approach, paving the way for an equivalent problem formulation. An effective alternating optimization strategy is introduced to tackle this problem, sequentially adjusting the transmit beamforming matrix and the RIS phase shifts for near-optimal results. In particular, a specialized WMMSE-based algorithm is devised for designing the transmit beamforming, while the passive beamforming of the RIS is optimized through semi-definite relaxation and majorization-minimization techniques. This balance ensures both high system performance and manageable computational load. Further analysis delves into the convergence properties and computational demands of the proposed methods. Simulation results are presented to validate the efficacy of the proposed algorithm and demonstrate the enhanced spectral efficiency achieved through the utilization of the double-RIS.