Stacked intelligent metasurfaces (SIM) is a revolutionary technology, which can outperform its single-layer counterparts by performing advanced signal processing relying on wave propagation. In this work, we exploit SIM to enable transmit precoding and receiver combining in holographic multiple-input multiple-output (HMIMO) communications, and we study the achievable rate by formulating a joint optimization problem of the SIM phase shifts at both sides of the transceiver and the covariance matrix of the transmitted signal. Notably, we propose its solution by means of an iterative optimization algorithm that relies on the projected gradient method, and accounts for all optimization parameters simultaneously. We also obtain the step size guaranteeing the convergence of the proposed algorithm. Simulation results provide fundamental insights such the performance improvements compared to the single-RIS counterpart and conventional MIMO system. Remarkably, the proposed algorithm results in the same achievable rate as the alternating optimization (AO) benchmark but with a less number of iterations.

翻译：堆叠式智能超表面（SIM）是一种革命性技术，通过依赖波传播的先进信号处理，其性能可超越单层超表面。本文利用SIM实现全息多输入多输出（HMIMO）通信中的发射预编码与接收合并，并通过联合优化收发两端SIM相移与发射信号协方差矩阵，研究系统可达速率。我们提出一种基于投影梯度法的迭代优化算法，同步优化所有参数，并推导保证算法收敛性的步长。仿真结果揭示了关键机理，例如与单RIS系统及传统MIMO系统相比的性能提升。值得注意的是，所提算法在实现与交替优化（AO）基准相同可达速率的同时，减少了迭代次数。