  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 reflecting
elements at the RIS and the precoder at the transmitter are alternatively
optimized to minimize the symbol error rate (MSER). In the reflecting
optimization with a fixed precoder, two reflecting design methods are
developed, referred as eMSER-Reflecting and vMSER-Reflecting. In the
optimization of the precoding matrix with a fixed reflecting pattern, the
matrix optimization is transformed to be a vector optimization problem and two
methods are proposed to solve it, which are referred as MSER-Precoding and
MMED-Precoding. The superiority of the proposed designs is investigated by
simulations. Simulation results demonstrate that the proposed reflecting and
precoding designs can offer a lower SER than existing designs with the
assumption of complex Gaussian input. Moreover, we compare RIS with a
full-duplex Amplify-and-Forward (AF) relay system in terms of SER to show the
advantage of RIS.
