The revolutionary technology of \emph{Stacked Intelligent Metasurfaces (SIM)} has been recently shown to be capable of carrying out advanced signal processing directly in the native electromagnetic (EM) wave domain. An SIM is fabricated by a sophisticated amalgam of multiple stacked metasurface layers, which may outperform its single-layer metasurface counterparts, such as reconfigurable intelligent surfaces (RISd) and metasurface lenses. We harness this new SIM concept for implementing efficient holographic multiple-input multiple-output (HMIMO) communications that dot require excessive radio-frequency (RF) chains, which constitutes a substantial benefit compared to existing implementations. We first present an HMIMO communication system based on a pair of SIMs at the transmitter (TX) and receiver (RX), respectively. In sharp contrast to the conventional MIMO designs, the considered SIMs are capable of automatically accomplishing transmit precoding and receiver combining, as the EM waves propagate through them. As such, each information data stream can be directly radiated and recovered from the corresponding transmit and receive ports. Secondly, we formulate the problem of minimizing the error between the actual end-to-end SIMs'parametrized channel matrix and the target diagonal one, with the latter representing a flawless interference-free system of parallel subchannels. This is achieved by jointly optimizing the phase shifts associated with all the metasurface layers of both the TX-SIM and RX-SIM. We then design a gradient descent algorithm to solve the resultant non-convex problem. Furthermore, we theoretically analyze the HMIMO channel capacity bound and provide some useful fundamental insights. Extensive simulation results are provided for characterizing our SIM-based HMIMO system, quantifying its substantial performance benefits.

翻译：堆叠智能超表面（SIM）作为一项革命性技术，近期被证实能够直接在原生电磁波域执行高级信号处理。SIM由多个超表面层精密堆叠而成，其性能可能超越单层超表面方案（如可重构智能表面RIS和超表面透镜）。我们利用这一新型SIM概念实现高效的全息多输入多输出（HMIMO）通信，无需大量射频链路，相较于现有方案具有显著优势。首先提出基于发射端（TX）和接收端（RX）一对SIM的HMIMO通信系统。与传统MIMO设计截然不同，电磁波在穿透SIM时，所考虑的SIM能自动完成发射预编码和接收合并处理。因此，每个信息数据流可直接通过对应发射/接收端口辐射并恢复。其次，将实际端到端SIM参数化信道矩阵与目标对角矩阵（代表理想无干扰并行子信道系统）之间的误差最小化问题建模，通过联合优化TX-SIM和RX-SIM所有超表面层的相移参数实现。随后设计梯度下降算法求解此非凸问题。进一步，从理论上分析HMIMO信道容量界，提供若干基础性洞见。大量仿真结果验证了基于SIM的HMIMO系统特性，量化其显著的性能优势。