This paper explores the performance of reconfigurable intelligent surface (RIS) assisted spatial modulation (SM) downlink communication systems, focusing on the average bit error probability (ABEP). Notably, in scenarios with a large number of reflecting units, the composite channel can be approximated by a Gaussian distribution using the central limit theorem. The receiver utilizes a maximum likelihood detector to recover information in both spatial and symbol domains. In the proposed RIS-SM system, we analytically derive a closed-form expression for the union tight upper bound of ABEP, employing the Gaussian-Chebyshev quadrature method. The validity of these results is rigorously confirmed through exhaustive Monte Carlo simulations.

翻译：本文探讨了可重构智能表面（RIS）辅助空间调制（SM）下行链路通信系统的性能，重点分析了平均误比特概率（ABEP）。特别地，在反射单元数量较大的场景下，利用中心极限定理可将复合信道近似为高斯分布。接收端采用最大似然检测器恢复空间域和符号域的信息。在所提出的RIS-SM系统中，我们利用高斯-切比雪夫求积方法，解析推导了ABEP联合紧致上界的闭式表达式。通过详尽的蒙特卡洛仿真严格验证了这些结果的有效性。