MMSE-based passive beamforming for reconfigurable intelligent surface aided millimeter wave MIMO

Reconfigurable intelligent surfaces (RISs) have emerged as propitious solution to configure random wireless channel into suitable propagation environment by adjusting a large number of low-cost passive reflecting elements. It is considered that narrowband downlink millimeter wave (mmWave) multiple-input multiple-output (MIMO) communication is aided by deploying an RIS. Large antenna arrays are used to counter the huge propagation loss suffered by the mmWave signals. Hybrid precoding in which precoding is performed in digital and analog domains is employed to reduce the number of costly and power-consuming radio frequency (RF) chains. Passive beamforming at RIS is designed together with precoder and combiner through joint optimization problem to minimize the mean square error between the transmit signal and the estimate of signal at the receiver. The optimization problem is solved by an iterative procedure in which solution to the non-convex reflecting coefficients design problem is approximated by extracting the phases of the solution to unconstrained problem without unit amplitude constraint of the reflecting elements. It is shown that the proposed design principle also applies to the wideband channel. Simulation results show that the proposed design delivers performance better than existing state-of-the-art solutions, but at lower complexity.