Although reconfigurable intelligent surface (RIS) is a promising technology for shaping the propagation environment, it consists of a single-layer structure within inherent limitations regarding the number of beam steering patterns. Based on the recently revolutionary technology, denoted as stacked intelligent metasurface (SIM), we propose its implementation not only on the base station (BS) side in a massive multiple-input multiple-output (mMIMO) setup but also in the intermediate space between the base station and the users to adjust the environment further as needed. For the sake of convenience, we call the former BS SIM (BSIM), and the latter channel SIM (CSIM). Hence, we achieve wave-based combining at the BS and wave-based configuration at the intermediate space. Specifically, we propose a channel estimation method with reduced overhead, being crucial for SIMassisted communications. Next, we derive the uplink sum spectral efficiency (SE) in closed form in terms of statistical channel state information (CSI). Notably, we optimize the phase shifts of both BSIM and CSIM simultaneously by using the projected gradient ascent method (PGAM). Compared to previous works on SIMs, we study the uplink transmission, a mMIMO setup, channel estimation in a single phase, a second SIM at the intermediate space, and simultaneous optimization of the two SIMs. Simulation results show the impact of various parameters on the sum SE, and demonstrate the superiority of our optimization approach compared to the alternating optimization (AO) method.

翻译：尽管可重构智能表面（RIS）是一种极具前景的传播环境塑造技术，但其单层结构在波束调控模式数量上存在固有局限性。基于被称为堆叠智能超表面（SIM）的最新革命性技术，我们不仅将其部署于大规模多输入多输出（mMIMO）架构中的基站（BS）侧，还将其置于基站与用户之间的中间空间以按需进一步调整传播环境。为便于区分，我们将前者称为基站SIM（BSIM），后者称为信道SIM（CSIM）。由此，我们在基站侧实现波域合并，并在中间空间实现波域配置。具体而言，我们提出了一种低开销的信道估计方法，这对SIM辅助通信至关重要。接着，我们利用统计信道状态信息（CSI）推导出上行链路总频谱效率（SE）的闭式表达式。值得注意的是，我们采用投影梯度上升法（PGAM）同时对BSIM和CSIM的相位偏移进行优化。与现有SIM相关研究相比，本文研究了上行传输场景、mMIMO架构、单阶段信道估计、中间空间第二层SIM部署，以及双SIM联合优化。仿真结果揭示了各参数对总SE的影响，并证明了所提优化方法相较于交替优化（AO）方法的优越性。