Joint design of hybrid beamforming and reflection coefficients for reconfigurable intelligent surface aided mmWave communication systems

This paper considers a reconfigurable intelligent surface (RIS) aided multi-user multiple-input single-output (MU-MISO) mmWave downlink communication system. The hybrid beamforming (HBF) and the programmable reflecting elements (PREs) are respectively applied at the base station (BS) and the RIS, where the HBF consists of the digital beamforming (DBF) and the analog beamforming (ABF). To maximize the geometric mean of the users' rates (GM-rate) for providing feasible links to all users in the aspect of the same time slot and same bandwidth, which results in the superiority of a rational rate distribution for the users without imposing a minimum quality of service (QoS) constraint. The joint PREs, ABF, and DBF optimization problems are formulated, the problem is generally non-convex due to the log-determinant as well as unit modulus constraints for both PREs and ABF. Efficient alternating descent iteration algorithms are developed to solve the intractable problem. Finally, simulation results are included to verify the efficiency of the proposed approaches, results also show that the proposed algorithms can improve the fairness among users and accommodate discrete phase shifts for both PREs and ABF.