Performance of Joint Symbol Level Precoding and RIS Phase Shift Design in the Finite Block Length Regime with Constellation Rotation

In this paper, we tackle the problem of joint symbol level precoding (SLP) and reconfigurable intelligent surface (RIS) phase shift design with constellation rotation in the finite block length regime. We aim to increase energy efficiency by minimizing the total transmit power while satisfying the quality of service constraints. The total power consumption can be significantly minimized through the exploitation of multiuser interference by symbol level precoding and by the intelligent manipulation of the propagation environment using reconfigurable intelligent surfaces. In addition, the constellation rotation per user contributes to energy efficiency by aligning the symbol phases of the users, thus improving the utilization of constructive interference. The formulated power minimization problem is non-convex and correspondingly difficult to solve directly. Hence, we employ an alternating optimization algorithm to tackle the joint optimization of SLP and RIS phase shift design. The optimal phase of each user's constellation rotation is obtained via an exhaustive search algorithm. Through Monte-Carlo simulation results, we demonstrate that the proposed solution yields substantial power minimization as compared to conventional SLP, zero forcing precoding with RIS as well as the benchmark schemes without RIS.