In this study, we explore the performance of a reconfigurable reflecting surface (RIS)-assisted transmit spatial modulation (SM) system for downlink transmission, wherein the deployment of RIS serves the purpose of blind area coverage within the channel. At the receiving end, we present three detectors, i.e., maximum likelihood (ML) detector, two-stage ML detection, and greedy detector to recover the transmitted signal. By utilizing the ML detector, we initially derive the conditional pair error probability expression for the proposed scheme. Subsequently, we leverage the central limit theorem (CLT) to obtain the probability density function of the combined channel. Following this, the Gaussian-Chebyshev quadrature method is applied to derive a closed-form expression for the unconditional pair error probability and establish the union tight upper bound for the average bit error probability (ABEP). Furthermore, we derive a closed-form expression for the ergodic capacity of the proposed RIS-SM scheme. Monte Carlo simulations are conducted not only to assess the complexity and reliability of the three detection algorithms but also to validate the results obtained through theoretical derivation results.

翻译：本研究探讨了可重构反射面（RIS）辅助发射空间调制（SM）系统在下行链路传输中的性能，其中RIS部署旨在实现信道盲区覆盖。在接收端，我们提出了三种检测器，即最大似然（ML）检测器、两级ML检测和贪婪检测器，用于恢复发射信号。利用ML检测器，我们首先推导了所提方案的成对错误概率条件表达式。随后，我们借助中心极限定理（CLT）获得组合信道的概率密度函数。在此基础上，应用高斯-切比雪夫求积方法导出无条件成对错误概率的闭式表达式，并建立平均误比特率（ABEP）的联合紧上界。此外，我们还推导了所提RIS-SM方案遍历容量的闭式表达式。通过蒙特卡洛仿真，不仅评估了三种检测算法的复杂度和可靠性，还验证了理论推导所得结果。