## 2 Phase Synchronization Scheme
### Synchronization Scheme of LT-1  
In BiSAR system, the primary satellite transmits pulses to the targets, and both the slave satellite and primary satellite receive the echoes scattered from the ground simultaneously. The azimuth signal received by the slave satellite can be expressed as  
\[s(\eta)=\exp\{-j2\pi\tau_{c}\tau_{0}(\eta)\}\exp\{j\Delta\varphi(\eta)\} \tag{1}\]  
where \(\eta\) denotes azimuth slow time, \(f_{c}\) denotes carrier frequency, \(\tau_{0}(\eta)\) denotes the delay time of the target. The first exponential term represents the azimuth modulation, which is used for BiSAR imaging. \(\Delta\varphi(\eta)\) indicates the random phase error caused by frequency deviation between USOs, which is often treated as a second-order stationary stochastic process and conforms to the power-law spectrum model. In this model, the one-sided power spectral density of the random phase noise \(\Delta\varphi(\eta)\) is expressed as [41]  
\[S_{\Delta\varphi}(f)=\left\{ \begin{array}{cc}2\big{(}af^{-4}+bf^{-3}+cf^{-2}+ df^{-1}+e\big{)}&,f>0\\ 0&,f\leqslant 0\end{array} \right. \tag{2}\]  
where the coefficients \(a\) to \(e\), respectively, represent five independent noises: random walk frequency noise, frequency flicker noise, white frequency noise, flicker phase noise, and white phase noise. The objective of phase synchronization is to measure and eliminate the above random phase noise. According to Equation (1), if a calibration target with a known slant distance history is obtained, the phase error can be estimated after compensating the imaging phase of this target. Therefore, a pair of point targets can be specifically constructed to measure the phase error. The primary satellite sends a point target signal to the slave one to extract the synchronization phase, then the slave satellite replies with a point target signal to offset the slant distance history of the target. In the process of signal transmission, assuming that the distance is constant, half of the phase difference of the pair of signals after pulse compression is the required phase error. The alternate pulse synchronization scheme employed by TanDEM-X is based on the above principle. However, unlike the scheme of TanDEM-X, the LT-1 mission adopts the time-division transmission mode, which avoids the interruption of normal BiSAR data acquisition and the interference of radar signals to synchronization signals [34]. The timing diagram of synchronization pulse exchange is shown in Figure 1. In the current PRT, LT-1A first transmits the radar signal and then enters the first free duration. After that, both LT-1A and LT-1B complete SAR data acquisition in the echo receiving window. Finally, in the second free duration, LT-1A transmits the synchronization pulse and LT-1B receives it. In the next PRT, after normal BiSAR data acquisition, LT-1B replies with a synchronization pulse to LT-1A. Thus, the alternate transmission of phase synchronization pulses can be realized in 2 PRTs. Therefore, the maximum synchronization frequency can reach to PRF/2 theoretically. Several key technologies are implemented to ensure the successful operation of the non-interrupted phase synchronization scheme in the LT-1 mission [9; 34]:  
1. Timing control: the LT-1 system employs GNSS-disciplined rubidium clock USOs to calibrate time, which combines the excellent short-term stability of high-quality  
Figure 1: Timing diagram of synchronization pulse exchange. USO and the long-term advantages of GNSS signal. The frequency stability of the rubidium clock can be up to \(10^{-11}\), and such a stable clock source contributes to the high accuracy of timing control. 2. Spatial coverage: compared with the six horn antennas of TanDEM-X, only four quadrifilar helix antennas as shown in Figure 2 are equipped in LT-1, which are smaller and lighter.