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This paper investigates the use of a reconfigurable intelligent surface (RIS)to aid point-to-point multi-data-stream multiple-input multiple-output (MIMO)wireless communications. With practical finite alphabet input, the reflectingelements at the RIS and the precoder at the transmitter are alternativelyoptimized to minimize the symbol error rate (MSER). In the reflectingoptimization with a fixed precoder, two reflecting design methods aredeveloped, referred as eMSER-Reflecting and vMSER-Reflecting. In theoptimization of the precoding matrix with a fixed reflecting pattern, thematrix optimization is transformed to be a vector optimization problem and twomethods are proposed to solve it, which are referred as MSER-Precoding andMMED-Precoding. The superiority of the proposed designs is investigated bysimulations. Simulation results demonstrate that the proposed reflecting andprecoding designs can offer a lower SER than existing designs with theassumption of complex Gaussian input. Moreover, we compare RIS with afull-duplex Amplify-and-Forward (AF) relay system in terms of SER to show theadvantage of RIS.

Joint Reflecting and Precoding Designs for SER Minimization in Reconfigurable Intelligent Surfaces Assisted MIMO Systems