## 1 Introduction
Nevertheless, existing time-frequency transfer methodologies based on commercial GEO communication satellites face technical challenges stemming from their onboard crystal oscillators [21]. For instance, in satellite two-way time and frequency transfer (TWSTFT)--a critical contribution to realizing Coordinated Universal Time (UTC)--phase jitter in the local oscillators of GEO satellite transponders induces signal phase noise during transmission. This jitter compromises the precision of high-precision carrier-phase measurements [22]. In timing and positioning applications of the Chinese Area Positioning System (CAPS), the limited accuracy and long-term stability of hybrid frequency sources onboard the GEO satellites can adversely affect the stability of downlink carrier frequencies, thereby degrading po sitioning precision [23; 24]. Regarding our prior work on the Einstein two-way frequency synchronization (SESAR) method [25], the phase drift introduced by the transponder's local oscillators disrupts the phase coherence between uplink and downlink signals, constraining further improvements to frequency comparison accuracy. Even when substituting the crystal oscillators with chip-scale atomic clocks [26], their long-term stability remains limited to the order of \(10^{-12}\), whereas the daily stability levels of TWSTFT or the SESAR method have already achieved \(10^{-15}\). This performance gap evidently inhibits emerging high-precision applications. Meanwhile, other frequency transfer technologies such as fiber-based optical frequency dissemination and free-space optical time-frequency transfer have demonstrated exceptional stability in ground-based systems. However, these methods are difficult to extend to GEO satellite scenarios due to atmospheric turbulence, limited link availability, and complex beam-tracking requirements. As such, scalable RF-based solutions--especially those capable of integrating with the existing GEO platforms--remain essential for the space-time infrastructure. To address these problems, this study proposed a novel phase-locked transponder designed for GEO communication satellites along with a frequency-synchronization scheme based on carrier-phase active compensation. This scheme eliminates the need for onboard atomic clocks but instead relies on onboard crystals and ground-based high-precision atomic frequency-scale phase locking for remote frequency comparison and distribution. Consequently, a reference clock source locked to the ground's highly stable atomic frequency scale can be recovered from the GEO communication satellites without onboard atomic clocks. The feasibility of this high-precision frequency-synchronization method has been demonstrated through a theoretical analysis and ground experiments. This paper presents a cost-effective and scalable solution for enhancing frequency synchronization in geostationary satellites. By improving the accuracy and stability of satellite frequency references, this method significantly enhances communication reliability, particularly in critical applications that require precise time synchronization. Moreover, the proposed solution supports a wide range of advanced scientific and navigational applications and potentially enables the construction of an integrated space-air-ground time-frequency synchronization network, thus advancing global positioning, navigation, and timing capabilities. Section 2 introduces a frequency recovery and delivery system using a novel phase-locked transponder. Section 3 models the satellite-ground link, analyzes the ionospheric and relativistic effects and describes the experimental setup, followed by an analysis of the results in Section 4. Section 5 discusses the findings, and Section 6 presents the concluding statements.