Hybrid Time-Frequency Domain Frequency Offset Compensation Under GHz Doppler Shift for LEO Satellite-to-Ground Coherent Free-Space Optical Communication

Coherent free-space optical (FSO) communication is a promising solution for low Earth orbit (LEO) satellite downlink transmission. However, high orbital velocity introduces multi-GHz Doppler shifts that appear as a rapidly time-varying carrier frequency offset (CFO), which is a major challenge for conventional coherent optical receivers. Narrow-range digital loops cannot acquire the initial offset, while wide-range feedforward or optical domain solutions either leave large residual errors or impose substantial implementation cost. In this paper, a Doppler-aware hybrid time-frequency frequency offset compensation (HTF-FOC) receiver architecture is proposed for coherent LEO satellite-to-ground FSO links using a cumulative time-varying random process model for the dynamic Doppler-induced phase shift. The proposed receiver implements a hybrid acquisition and tracking procedure to acquire and compensate for multi-GHz Doppler variations, including 4th-power FFT-based coarse CFO acquisition, residual CFO handover verification, and low-complexity decision-directed (DD) frequency-locked loop (FLL) tracking. The phase-averaged pairwise error probability (PEP) and union-bound symbol error rate (SER) expressions are derived and verified using Monte Carlo simulations. The results demonstrate that the proposed HTF-FOC method tracks Doppler shifts beyond $\pm5$ GHz while keeping the residual CFO below $80$ MHz with a success rate of $100\%$ for typical LEO altitudes of $400{\!-\!}800$ km and orbital speeds of $7.3{\!-\!}7.9$ km/s.