Joint Transceiver and Reconfigurable Intelligent Surface Design for Multiuser mmWave MIMO Systems Relying on Non-Diagonal Phase Shift Matrices

The downlink (DL) of a reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter wave (mmWave) multiple-input multiple-output (MIMO) system relying on a non-diagonal RIS (NDRIS) phase shift matrix is considered. A max-min fairness (MMF) problem is formulated under the total transmit power constraint while employing joint active hybrid beamforming (HBF) both at the base station (BS) as well as at each user equipment (UE), and passive beamforming at the NDRIS. To solve this non-convex problem, a sequential optimization method is conceived, wherein the UE having the poorest channel is identified first, which is termed as the worst-case UE. Then the phase shifter coefficients of the NDRIS are optimized using the alternating direction method of multipliers (ADMM) followed by the hybrid transmit precoder (TPC) and receiver combiner (RC) design using the Karcher mean, the least squares and the regularized zero forcing (RZF) principles. Finally, the optimal power allocation is computed using the path-following algorithm. Simulation results show that the proposed NDRIS-HBF system yields an improved worst-case UE rate in comparison to its conventional diagonal RIS (DRIS)-HBF counterpart, while approaching the half-duplex relay (HDR)-HBF benchmark for large values of the number of reflecting elements (REs). Furthermore, the energy efficiency (EE) of the NDRIS structure is significantly higher than that of the DRIS, HDR systems, while being higher than that achieved by the full-duplex relay (FDR) system at high SNR.