Deep State-Space Modeling of Channel Dynamics for CSI Prediction in LEO Non-Terrestrial Networks

Non-terrestrial networks (NTNs) are emerging as a key enabler for global wireless coverage, yet high mobility, long propagation delays, and pronounced Doppler effects complicate the timely and accurate acquisition of channel state information (CSI). Predictive CSI modeling provides a practical solution by forecasting future channel conditions from historical observations, reducing dependence on feedback, and improving beamforming performance. In this work, we propose an enhanced predictive CSI framework for NTN based on the structured state-space for sequences (S4) model. We extend the standard S4 by introducing Doppler-Regularized S4 (DR-S4), which incorporates domain knowledge of satellite-induced Doppler shifts into the eigenvalues of the state matrix, ensuring physically consistent oscillatory modes and stable long-term predictions. To further improve system-level performance, we integrate a task-aware objective that directly optimizes downlink rate via differentiable beamforming loss, and an uncertainty-gated predict-or-feedback mechanism that dynamically balances prediction and CSI feedback to reduce overhead. We evaluate the proposed framework in a 3GPP-compliant NTN simulation environment with realistic mobility, fading, and Doppler conditions. Comparative experiments with traditional sequence models demonstrate that DR-S4 achieves superior prediction accuracy, faster convergence, and improved throughput performance across various antenna array sizes and uncertainty thresholds. These results highlight the potential of the proposed DR-S4 framework for enhancing beamforming reliability and spectral efficiency in practical NTN deployments.