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：堆叠智能超表面（SIM）是一种革命性技术，其通过利用波传播实现高级信号处理，性能可超越单层超表面。本文利用SIM在全息多输入多输出（HMIMO）通信中实现发射预编码与接收合并，通过联合优化收发两端SIM的相移以及发射信号的协方差矩阵，研究系统的可达速率。值得注意的是，我们提出了一种基于投影梯度法的迭代优化算法来求解该问题，该算法能够同时考虑所有优化参数，并确定了保证算法收敛的步长。仿真结果提供了基础性见解，例如相较于单RIS方案和传统MIMO系统的性能提升。尤为突出的是，所提算法在实现与交替优化（AO）基准相同可达速率的同时，所需的迭代次数更少。