This paper investigates a reconfigurable intelligent surface (RIS) aided communication scenario in which the RIS and the transmitter jointly send information to the receiver. While most studies of the RIS focus on its ability to beamform and boost the received signal-to-noise ratio (SNR), it is known that if the information data stream is also available at the RIS and can be modulated through the adjustable phases at the RIS, significant improvement in the multiplexing gain of the overall channel is possible. To achieve the theoretic multiplexing gain, this paper provides a symbol-level precoding (SLP) approach for modulating data through the phases of the RIS. The SLP strategy is to set the received signal to be as close to the desired points in a constellation as possible. The idea is to directly make the received signal to be the symbols corresponding to the information to be transmitted and to design the transmitter and the reflective coefficients of the RIS so that the desired symbols are synthesized at the receiver. This strategy is formulated as an optimization problem and an augmented Lagrangian approach with the Riemannian conjugate gradient descent method is proposed to solve the optimization problem efficiently. Numerical simulation results show that the proposed method can achieve the theoretical multiplexing gain.
 

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