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This study considers a virtual multiuser multiple-input multiple-outputsystem with PSK modulation realized via the reconfigurable intelligentsurface-based passive transmitter setup. Under this framework, the studyderives the formulation for the union-bound symbol-error probability, which isan upper bound on the actual symbol-error probability. Based on this, asymbol-level precoding power minimization problem under the condition that theunion-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 successivelyoptimizing transmit power while evaluating the feasibility of the union-boundsymbol-error probability requisite by solving, via the Riemannian conjugategradient algorithm, an auxiliary problem dependent only on the reflectioncoefficients of the reconfigurable intelligent surface elements. Numericalresults demonstrate the effectiveness of the proposed approach in minimizingthe transmit power for different symbol-error probability requirements.

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