发表机构
Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg（卢森堡大学安全、可靠与信任跨学科中心（SnT））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于物理信息的单次波束跟踪方法，利用轨道运动预测和解析雅可比矩阵，通过单次正则化高斯-牛顿校正实现堆叠智能超表面辅助LEO广播的快速高精度跟踪。
AI 中文摘要
本文提出了一种基于物理信息的单次波束跟踪方法，用于堆叠智能超表面（SIM）辅助的低地球轨道（LEO）链路，其中包含$K$个用户和每层具有$N$个超原子的$L$层SIM。通过视距（LoS）几何传播可预测的轨道运动，以预测用户信噪比（SNR）剖面的有限区间变化，并利用解析多层雅可比矩阵将该变化与$LN$个SIM相位系数相关联。波束跟踪被表述为归一化SNR剖面保持问题，并通过单次正则化高斯-牛顿校正求解，该校正仅需一次雅可比矩阵评估和一次$K\ imes K$线性求解，从而避免了迭代重新优化。跟踪误差界将正则化残差与非线性泰勒余项分离，并在雅可比矩阵满行秩条件下建立了二阶局部误差。数值结果表明，所提方法在$L=2$和$L=4$时分别保留了迭代重新优化速率的约$94\%$和$92\%$，同时在$N=225$时运行速度分别快约$350\ imes$和$260\ imes$，并证实了预测的二阶残差误差行为。
英文摘要
This letter develops a physics-informed one-shot beam tracking method for stacked intelligent metasurface (SIM)-enabled low-Earth-orbit (LEO) links with $K$ users and an $L$-layer SIM with $N$ meta-atoms per layer. The predictable orbital motion is propagated through the line-of-sight (LoS) geometry to forecast the finite-interval variation of the user signal-to-noise ratio (SNR) profile, and an analytical multilayer Jacobian relates this variation to the $LN$ SIM phase coefficients. Beam tracking is formulated as normalized SNR-profile preservation and solved through a single regularized Gauss--Newton correction that requires one Jacobian evaluation and a $K\times K$ linear solve, thereby avoiding iterative reoptimization. A tracking-error bound separates the regularization residual from the nonlinear Taylor remainder and establishes a second-order local error under a full-row-rank Jacobian. Numerical results show that the proposed method retains approximately $94\%$ and $92\%$ of the iterative-reoptimization rate for $L=2$ and $L=4$, respectively, while running about $350\times$ and $260\times$ faster at $N=225$, and confirm the predicted second-order residual error behavior.
