Stacked intelligent metasurface (SIM) is a promising enabler for next-generation high-capacity networks that exhibit better performance compared to its single-layer counterpart by means of just wave propagation. However, the study of ergodic mutual information (EMI) and outage probability for SIM-assisted multiple-input-multiple-output (MIMO) systems is not available in the literature. To this end, we obtain the distribution of the MI by using large random matrix theory (RMT) tools. Next, we derive a tight closed-form expression for the outage probability based on statistical channel state information (CSI). Moreover, we apply the gradient descent method for the minimization of the outage probability. Simulation results verify the analytical results and provide fundamental insights such as the performance enhancements compared to conventional MIMO systems and the single-layer counterpart. Notably the proposed optimization algorithm is faster than the alternating optimization (AO) benchmark by saving significant overhead.

翻译：堆叠智能超表面（SIM）作为下一代高容量网络的关键使能技术，仅通过波传播即可展现出优于单层结构的性能。然而，现有文献尚未对SIM辅助多输入多输出（MIMO）系统的遍历互信息（EMI）与中断概率进行深入研究。为此，本文利用大维随机矩阵理论（RMT）工具推导了互信息的分布特性。进而，基于统计信道状态信息（CSI）建立了中断概率的紧致闭式表达式。此外，我们采用梯度下降法实现中断概率的最小化。仿真结果验证了理论分析的正确性，并揭示了SIM系统相较于传统MIMO系统及单层结构的性能增益。特别值得注意的是，所提出的优化算法通过显著降低开销，其收敛速度优于交替优化（AO）基准方案。