Stacked intelligent metasurfaces (SIM) provide a cost-effective and scalable solution for large-scale antenna communications.However, efficient channel state information acquisition and phase shift optimization remain critical challenges. In this paper, we develop a unified framework of low-complexity algorithms for SIM-assisted communication systems to address these issues. Specifically, we propose a generalized two-step codebook construction (TSCC) method that leverages two-dimensional angular-domain decoupling to transform planar array beamformer design into two independent one-dimensional linear array beamformer design problems, efficiently solved via the Gerchberg-Saxton algorithm and our proposed majorization-minimization-based proximal distance (PDMM) algorithm. We further develop a two-stage coded-sliding beam training (TSCSBT) method for low-overhead and high-accuracy beam training, where error-correcting codes are embedded in the first-stage training to enhance robustness against noise, and sliding sampling is subsequently performed around the matched angular samples to improve angular resolution. The proposed framework is further extended to multi-path user channels. Finally, a variable decoupling-based block successive upper bound minimization (VD-BSUM) algorithm is proposed to directly solve the QoS-constrained sum-rate maximization problem through closed-form iterative updates with substantially reduced computational complexity. Simulation results demonstrate the effectiveness of the proposed methods in achieving precise beam pattern realization, improved beam training accuracy and angular resolution, and enhanced sum-rate performance.

翻译：堆叠智能超表面（SIM）为大规模天线通信提供了一种经济高效且可扩展的解决方案。然而，高效的信道状态信息获取和相移优化仍然是关键挑战。本文针对SIM辅助通信系统，开发了一个统一的低复杂度算法框架以解决这些问题。具体而言，我们提出了一种广义的两步码本构建（TSCC）方法，该方法利用二维角度域解耦，将平面阵列波束成形器设计转化为两个独立的一维线性阵列波束成形器设计问题，并通过Gerchberg-Saxton算法和我们提出的基于Majorization-Minimization的近端距离（PDMM）算法高效求解。我们进一步开发了一种两阶段编码滑动波束训练（TSCSBT）方法，用于实现低开销、高精度的波束训练。该方法在第一阶段训练中嵌入纠错码以增强对噪声的鲁棒性，随后在匹配的角度样本周围进行滑动采样以提高角度分辨率。所提出的框架进一步扩展到多径用户信道。最后，提出了一种基于变量解耦的块连续上界最小化（VD-BSUM）算法，通过闭式迭代更新直接求解QoS约束的和速率最大化问题，并显著降低了计算复杂度。仿真结果证明了所提方法在实现精确波束方向图、提高波束训练精度和角度分辨率以及增强和速率性能方面的有效性。