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.

翻译：本研究考虑了一种在可重构智能表面无源发射机架构下实现的、采用PSK调制的虚拟多用户多输入多输出系统。在此框架下，推导出联合边界符号错误概率的表达式，该表达式是实际符号错误概率的上界。基于此，提出在联合边界符号错误概率低于给定要求的条件下进行符号级预编码功率最小化问题。该问题被表述为斜流形上的约束优化问题，并通过二分法求解。该方法通过逐次优化发射功率实现，同时利用黎曼共轭梯度算法求解仅依赖于可重构智能表面单元反射系数的辅助问题，以评估联合边界符号错误概率要求的可行性。数值结果展示了所提方法在不同符号错误概率要求下最小化发射功率的有效性。