This research exploits the applications of reconfigurable intelligent surface (RIS)-assisted multiple input multiple output (MIMO) systems, specifically addressing the enhancement of communication reliability with modulated signals. Specifically, we first derive the analytical downlink symbol error rate (SER) of each user as a multivariate function of both the phase-shift and beamforming vectors. The analytical SER enables us to obtain insights into the synergistic dynamics between the RIS and MIMO communication. We then introduce a novel average SER minimization problem subject to the practical constraints of the transmitted power budget and phase shift coefficients, which is NP-hard. By incorporating the differential evolution (DE) algorithm as a pivotal tool for optimizing the intricate active and passive beamforming variables in RIS-assisted communication systems, the non-convexity of the considered SER optimization problem can be effectively handled. Furthermore, an efficient local search is incorporated into the DE algorithm to overcome the local optimum, and hence offer low SER and high communication reliability. Monte Carlo simulations validate the analytical results and the proposed optimization framework, indicating that the joint active and passive beamforming design is superior to the other benchmarks.

翻译：本研究探讨了可重构智能表面辅助多输入多输出系统的应用，重点研究调制信号通信可靠性的提升。具体而言，我们首先推导了每个用户下行链路符号错误率的解析表达式，该表达式是相位偏移向量与波束成形向量的多元函数。解析符号错误率使我们能够深入理解可重构智能表面与多输入多输出通信之间的协同动态特性。随后，我们在发射功率预算与相位偏移系数的实际约束条件下，提出了一个新颖的平均符号错误率最小化问题，该问题属于NP难问题。通过引入差分进化算法作为优化可重构智能表面辅助通信系统中复杂主动与被动波束成形变量的关键工具，所考虑的符号错误率优化问题的非凸性得以有效处理。此外，我们在差分进化算法中融合了高效的局部搜索策略以规避局部最优解，从而实现了低符号错误率与高通信可靠性。蒙特卡洛仿真验证了解析结果与所提优化框架的有效性，表明联合主动与被动波束成形设计性能优于其他基准方案。