## 4 Phase Denoise Experiment and Result
### Data Acquisition and Analysis  
The ground validation experiment adopts the system parameters listed in Table 1. The system simulates the exchanging of synchronization signals under different baselines by adjusting the antenna gain, and obtains the synchronization signals under different SNRs. Five groups of data including imaging signals and synchronization signals under 400 s long-time operation are collected in the ground validation experiment, and the phases are extracted after pulse compression according to the parameters in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Carrier frequency & \(f_{\mathrm{c}}\) & 1.26 GHz \\ Pulse repetition frequency & PRF & 1723.05 Hz \\ Imaging signal pulse duration & \(T_{r}\) & 80 \(\upmu\)s \\ Imaging signal bandwidth & \(B_{\mathrm{r}}\) & 150 MHz \\ Sync. frequency & \(f_{\mathrm{syn}}\) & 143.59 Hz \\ Sync. signal pulse duration & \(T_{\mathrm{syn}}\) & 10 \(\upmu\)s \\ Sync. signal bandwidth & \(B_{\mathrm{syn}}\) & 150 MHz \\ Acquisition duration & \(t_{\mathrm{dur}}\) & 400 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters of ground validation system. Figure 4: Flowchart of the proposed algorithm. The SNR of each group of imaging signals after pulse compression is basically the same and maintained at a high level (69 dB), and one set of imaging phases is shown in Figure 5. Figure 5a shows the imaging phases of LT-1A and LT-1B. Since the received imaging signal of LT-1A is transmitted by itself, the imaging phase \(\varphi_{a}\) is almost constant. While the received signal of LT-1B is sent by LT-1A, \(\varphi_{b}\) changes versus time. The imaging phase difference between LT-1A and LT-1B is shown in Figure 5b. Figure 5c shows the linear term of the imaging phase difference separated by LSM, which can be expressed as \(2\pi\Delta f_{c}t\). According to the fitting result, the frequency difference \(\Delta f_{c}\) of the two USOs is about \(-0.03\) Hz in this acquisition. Figure 5d shows the higher-order phase. Compared with linear phase, the higher-order term of the imaging phase difference contains richer structures and characteristics. Therefore, it is used as for K-SVD dictionary training to learn sufficient prior information. The synchronization phases are obtained from the synchronization signals after pulse compression, and the phases corresponding to the imaging phase above are shown in Figure 6a. Since the received synchronization signals come from the other satellite, both \(\varphi_{\text{ab}}\) and \(\varphi_{\text{ba}}\) changes versus time. The frequency difference between two USOs is relatively stable, so the synchronous phase shows an obvious linear trend. Finally, the synchronization compensation phase \(\varphi_{c}\) can be get by Equation (3). After collecting the signals of all calibration loops, the internal calibration compensation phase that represents the hardware error of the system is shown in the Figure 6b. The range of \(\varphi_{\text{cal}}\) is small, it changes less than 0.6\({}^{\circ}\) in the acquisition time of 400 s. However, the internal calibration compensation phase also contains linear component and phase characteristics, which can not be ignored in the process of phase synchronization. The satellites remain relatively stationary during ground verification, so the Doppler error phase was not considered in the experiment. After preliminary compensation by Equation (9), the STD of residual phase error versus SNR is shown in Figure 7, where the SNRs are evaluated from synchronization signals after pulse compression. The synchronization accuracy increases with the rise of SNR. The theoretical value represented by the blue line is obtained from Equation (17). It can be seen that the experimental results are in good agreement with the theoretical analysis within a bounded error. The measured residual phase error is slightly higher than the theoretical value, which may be introduced by other tiny errors in the link.