## 6 Conclusions  
This study proposed a novel communication satellite phase-locked transponder design based on the satellite-based Einstein synchronization theory and the carrier-phase real-time compensation method. The transponder could replicate the precision of a terrestrial atomic frequency standard in space by modifying the existing transponder's RF structure. Accordingly, this study modeled a satellite-terrestrial link and calculated and analyzed the ionospheric and relativistic effects, demonstrating that the ionospheric error introduced by this method would be at the picosecond level when conducting actual satellite-ground station experiments using the Ka-band. Ground experiments were conducted to evaluate the system's accuracy level and dynamic characteristics. The standard deviation of the recovered clock phase synchronization error was 6.33 ps, with a 10,000 s stability of 3.36 \(\times\) 10\({}^{-16}\) under dynamic conditions. These results demonstrate the potential of the frequency-synchronization method based on a phase-locked transponder. It offers a foundation for developing a synchronous-orbit satellite time-frequency synchronization method.  
Moreover, this technology holds strong potential for integration into future large-scale satellite navigation and timing frameworks. By enabling the high-precision frequency synchronization without the need for onboard atomic clocks, it opens new possibilities for space-air-ground integrated timing networks, GNSS augmentation systems, and high-stability time transfer in GNSS-denied environments. Such a system could serve as a complementary time-frequency distribution architecture for existing satellite navigation constellations, contributing to enhanced global synchronization capability and resilience. The proposed approach is not only technically feasible but may also hold significant practical value for next-generation, timing-critical applications in communications, navigation, and scientific observations.  
Conceptualization, X.T., L.W. and S.W.; methodology, X.T. and C.Y.; software, X.T. and C.Y.; validation, X.T., H.S. and L.M.; formal analysis, X.T.; investigation, X.T. and C.Y.; resources, L.W. and S.W.; data curation, X.T., Y.H. and R.L.; writing--original draft preparation, X.T.; writing--review and editing, S.W.; visualization, X.T.; supervision, L.W. and S.W.; project administration, L.W. and S.W.; funding acquisition, L.W. and S.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China, grant number 2021 YFA1402100.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors are grateful to the Xi'an Institute of Space Radio Technology for their help in conducting this study.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} BPF & Bandpass filter \\ CFS & Cesium frequency standard \\ FPGA & Field-programmable gate array \\ GEO & Geostationary Earth orbit \\ GPS & Global Positioning System \\ \end{tabular}