Sub-nanosecond quasi-dual-frequency distributed time synchronization for scenarios with varying propagation delays

Time synchronization is a fundamental requirement in contemporary optical communication systems and serves as a critical enabler for the effective operation of diverse applications. When the frontier of optical communication networks extends from ground to space, research on non-terrestrial networks (NTN) gained increasing attention, and new challenges for synchronization arose. The introduction of moving nodes makes it infeasible to construct a stable hierarchical architecture for synchronization, and the relative motion between nodes significantly increases the complexity and difficulty of synchronization. In addition to external factors, intrinsic sync system errors persist, such as time reading errors caused by limited clock resolution, which are inherently difficult to eliminate. Several efforts have been made to mitigate time reading errors, yet these approaches exhibit inherent limitations, and their applicability to non-terrestrial networks remains uncertain. To solve this problem, we developed a unified theoretical framework for time synchronization that encompasses both static and dynamic scenarios. A cost-effective sync method called quasi-dual-frequency distributed time synchronization (QDF-DTS) is proposed in uniform motion scenarios. This method exploits linearly varying propagation delays between moving nodes to achieve temporal modulation of sync pulses, and employs a statistical method for demodulation, thereby reducing time reading errors induced by limited clock resolution. The theoretical sync accuracy is analyzed through mathematical derivation, and the influence of special relativity is taken into consideration, with special relativistic corrections derived by applying the Lorentz transformation. Furthermore, we designed two sync strategies tailored for non-uniform motion scenarios. Simulation results present their effectiveness under different conditions. Finally, we developed a propagation delay emulation system with 20-ps resolution for both point-to-point and three-node QDF-DTS network time sync experiments. The experimental results provide preliminary validation of the effectiveness of QDF-DTS in scenarios with linearly varying propagation delays.