Two-Stage Coded-Sliding Beam Training and QoS-Constrained Sum-Rate Maximization for SIM-Assisted Wireless Communications

TL;DR

This work tackles CSI acquisition and phase-shift optimization in SIM-assisted wireless systems by proposing a unified, low-complexity framework. It introduces TSCC to decouple 2-D angular design into two 1-D problems and solves them with relaxed Gerchberg–Saxton and PDMM-based updates, enabling efficient codebook construction. Building on TSCC, TSCSBT embeds error-correcting codes and sliding beam refinement to achieve high training accuracy with low overhead, extended to multi-path scenarios via MP-TSBT. For SRM under QoS constraints, the VD-BSUM algorithm delivers closed-form iterative updates with substantially reduced complexity compared to SCA/SDR while ensuring QoS; simulations show precise beam patterns, improved angular resolution, higher user rates, and better fairness. Overall, the framework offers a scalable, practical pathway to high-performance SIM-based communications and can extend to very large near-field architectures.

Abstract

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.

Figures (18)

• Figure 1: Traditional beam training frameworks. (a) Exhaustive beam training; (b) Hierarchical beam training.
• Figure 2: Example of the beam pattern corresponding to the second layer of codewords in the hierarchical codebook.
• Figure 3: An illustration of two-dimensional angle decoupling and the equivalence between linear arrays and planar arrays.
• Figure 4: Different beam training strategies. (a) Traditional 2-D grid search; (b) Proposed 1-D linear search.
• Figure 5: Angle coverage range corresponding to the ideal beam pattern.