Symbol-Error Probability Constrained Power Minimization for Reconfigurable Intelligent Surfaces-based Passive Transmitter

This study considers a virtual multiuser multiple-input multiple-output system with PSK modulation realized via the reconfigurable intelligent surface-based passive transmitter setup. Under this framework, the study derives the formulation for the union-bound symbol-error probability, which is an upper bound on the actual symbol-error probability. Based on this, a symbol-level precoding power minimization problem under the condition that the union-bound symbol-error probability is below a given requirement is proposed. The problem is formulated as a constrained optimization on an oblique manifold, and solved via a bisection method. The method consists of successively optimizing transmit power while evaluating the feasibility of the union-bound symbol-error probability requisite by solving, via the Riemannian conjugate gradient algorithm, an auxiliary problem dependent only on the reflection coefficients of the reconfigurable intelligent surface elements. Numerical results demonstrate the effectiveness of the proposed approach in minimizing the transmit power for different symbol-error probability requirements.