One-Shot Beam Tracking for Stacked Intelligent Metasurfaces-Assisted LEO Broadcasting

Abstract

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.