EMD-THNet: An Energy-Guided Hierarchical Temporal Network for Doppler Signal Restoration and Frequency Tracking

Accurate restoration and frequency tracking of non-stationary Doppler signals remain difficult under mixed and distribution-shifted noise. This study proposes EMD-THNet, a supervised one-dimensional framework that preserves the full 4096-sample resolution after offline empirical mode decomposition (EMD), combines a raw-waveform branch with a shared IMF encoder and energy-guided masked attention, and uses a hierarchical temporal encoder-decoder with waveform-restoration and instantaneous-frequency heads. The model was trained, validated, and tested using 96, 32, and 32 independently generated AM/FM windows sampled at 500 MHz. Robustness was further assessed through 1080 paired evaluations covering six input-SNR levels and six noise types. On the held-out synthetic set, EMD-THNet achieved an output SNR of 14.470 dB, an SNR gain of 12.296 dB (95% CI: 10.849–13.742 dB), and an SSIM of 0.8176. Six baselines were organized as classical filtering, Bayesian state estimation, and deep-learning temporal models. Relative to the strongest SNR-gain baseline in each group, EMD-THNet showed paired output-SNR advantages of 9.499, 4.676, and 2.389 dB, respectively (Holm-adjusted Wilcoxon p ≤ 7.68 × 10−8 for these three group-leading comparisons). On TSMS-Drone real I/Q waveforms with controlled added noise, zero-shot transfer yielded an SNR gain of 0.556 dB (95% CI: −0.316–1.416 dB), whereas adaptation using disjoint training distances yielded 10.241 dB (95% CI: 10.015–10.449 dB). These results demonstrate the effectiveness of EMD-THNet across the evaluated synthetic and semi-synthetic protocols and indicate its potential for robust Doppler-signal restoration and frequency tracking in future real-flight sensing applications.