In the context of emerging stacked intelligent metasurface (SIM)-based holographic MIMO (HMIMO) systems, a fundamental problem is to study the mutual information (MI) between transmitted and received signals to establish their capacity. However, direct optimization or analytical evaluation of the MI, particularly for discrete signaling, is often intractable. To address this challenge, we adopt the channel cutoff rate (CR) as an alternative optimization metric for the MI maximization. In this regard, we propose an alternating projected gradient method (APGM), which optimizes the CR of a SIM-based HMIMO system by adjusting signal precoding and the phase shifts across the transmit and receive SIMs in a layer-by-layer basis. Simulation results indicate that the proposed algorithm significantly enhances the CR, achieving substantial gains proportional to those observed for the corresponding MI. This justifies the effectiveness of using the channel CR for the MI optimization. Moreover, we demonstrate that the integration of digital precoding, even on a modest scale, has a significant impact on the ultimate performance of SIM-aided systems.

翻译：在基于新兴堆叠智能超表面（SIM）的全息MIMO（HMIMO）系统中，一个基础性问题是研究发射与接收信号之间的互信息（MI）以确定其信道容量。然而，直接优化或解析计算互信息（特别是针对离散信令）通常是棘手的。为应对这一挑战，我们采用信道截止率（CR）作为互信息最大化的替代优化指标。据此，我们提出一种交替投影梯度法（APGM），该方法通过逐层调整信号预编码以及发射和接收SIM的相位偏移，来优化基于SIM的HMIMO系统的信道截止率。仿真结果表明，所提算法能显著提升截止率，其性能增益与对应互信息的提升幅度成比例。这验证了采用信道截止率进行互信息优化的有效性。此外，我们证明，即使采用中等规模的数字预编码，也会对SIM辅助系统的最终性能产生重要影响。