## 5 Results
### Verification and Analysis of S-Band Test Data  
China's QueQiao-1 lunar relay satellite, launched in May 2018, currently resides in the Halo orbit of the second Earth-Moon Lagrange point. The S-band TT&C transponder on Queqiao-1 has implemented regenerative pseudo-code ranging and includes a set of DOR beacons. The verification of this method is facilitated by the measured VLBI data from the CDSN during the in-orbit test of the Queqiao-1 lunar relay satellite in May 2019. The T4B code with a chip rate of 2 Mchips/s is adopted for regenerative pseudo-code ranging. The test data are sampled and recorded by a single channel with a bandwidth of 16 MHz. The downlink signal spectrum design is consistent with the recommendations of CCSDS-related specifications. The two DOR tones are about \(\pm 3.8\) MHz away from the main carrier. The first-order and second-order clock components of the PN code ranging signal are about 1 MHz and 2 MHz away from the carrier, respectively. The cross-spectrum and the corresponding fringe can be obtained by correlation processing, which are shown in Figure 5. It can be seen that the structure of the signal cross-spectrum is basically consistent with that in Figure 3. The red cycles and blue solid line in the lower half of Figure 5 indicate that the carrier and clock components of the PN code ranging signal, as well as the DOR beacon signals, exhibit clear fringes. The corresponding cross-spectrum phases are linearly distributed, which conforms to the principle described in reference [2]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **Spacecraft** & **Exploration** & **RSS** & **RSS or Distance** & **Remark** \\
**ID** & **Thermal Noise** & **Distance** & **Percentage** & **Remark** \\ \hline
1 & 0.2337 ns & 400 million km & 0.2514 ns & 100\% & Reference \\ \hline \multirow{2}{*}{2} & 0.2199 ns & 400 million km & 0.2386 ns & 94.91\% & \
\begin{tabular}{c} Distance \\ unchanged \\ \end{tabular} \\ \cline{2-5}  & 0.2337 ns & 425 million km & 0.2514 ns & 106.25\% & RSS unchanged \\ \hline \multirow{3}{*}{3} & 0.1655 ns & 400 million km & 0.1896 ns & 75.42\% &
\begin{tabular}{c} Distance \\ unchanged \\ \end{tabular} \\ \cline{2-5}  & 0.2337 ns & 565 million km & 0.2514 ns & 141.25\% & RSS unchanged \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Improvement by the proposed method. Figure 6 shows the cross-phase estimations of the DOR beacon signal, and the first-order and second-order clock components of the PN code ranging signal. As can be seen, the cross-phases of the three signal components are relatively stable. The accuracy of the first-order clock component cross-spectrum phase of the PN code ranging signal is the highest, being about 0.0023 rad. The cross-spectrum phase of the second-order clock component of the PN code range signal exhibits the poorest accuracy, roughly one order of magnitude lower than that of both the first-order component and the DOR beacon signal. This result is consistent with the spectrum amplitude shown in Figure 4. Considering the coupling effect between the cross-spectrum phase accuracy of the signal and the signal bandwidth, only the first-order clock component of the PN code ranging signal is used in the subsequent processing to obtain a higher coarse estimation accuracy of the time delay. Figure 5: The cross-spectrum and interference fringe of the Chang’E-4 relay satellite downlink signal. The upper figure is the cross-spectrum of the downlink signal; the lower figure is the interferometry fringes (also called cross-phase). Figure 6: The cross-phase of several components of Chang’E-4 relay satellite downlink signal. Figure 7 is the comparison of the cross-spectrum phase of two different combinations of the detector downlink signal. Carrier+DOR represents the traditional signal combination, namely utilizing the carrier and DOR beacon signal for frequency synchronization. The corresponding effective bandwidth is about 7.5 MHz.