Product manifold optimization-based joint beamforming for RIS-aided MIMO systems: A fairness based approach

Reconfigurable intelligent Surface (RIS) can effectively improve the communication quality and extend the signal coverage range by reconfiguring the wireless communication transmission environment, which is very suitable for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. In this paper, a product manifold optimization-based beamforming design (PMO-BD) algorithm for a RIS-assisted multi-user MIMO system is proposed to enhance fairness among users. We establish a lower bound for the minimum signal-to-interference-plus-noise ratio (SINR) among users as the optimization objective, which is subjected to multiple constraints. By maximizing the lower bound to ensure the quality of service (QoS) for each user, fairness among users get improved. The PMO-BD algorithm exploits the internal structure of the product manifold to deal with the high dimension and nonlinear characteristics of the problem effectively, thereby reducing algorithm complexity and enhancing convergence rates. Simulation results verify the advantages of the proposed PMO-BD algorithm in comparison to other algorithms.