## 2 Phase Synchronization Scheme
### System Design and Phase Model  
As shown in Figure 3, the hardware structure of the LT-1 system is mainly composed of the signal generation unit (orange rectangular block), the transmit-receive unit (blue rectangular block), and the calibration unit (red rectangular block). The hardware systems of the LT-1A and LT-1B radars are completely consistent. The signal generation unit, consisting of the GNSS disciplining module, reference frequency source, and frequency modulation signal source, is employed to generate LFM signals for imaging or synchronization. The GNSS disciplining module employs the disciplined rubidium clock USOs to provide a time-frequency signal for the reference frequency source module. Multiple working frequency signals are generated by the reference frequency source and sent to the frequency modulation signal source to generate corresponding signals. Figure 2: Quadrifilar helix antenna equipped in LT-1 [34]. The transmit-receive unit, consisting of synchronization antennas, synchronization transceiver, microwave combination, receiver, and data former, is employed to accurately control the transmitting and receiving of synchronization pulses. At time \(t\), the synchronization signal generated by LT-1A is transmitted by its transceiver and synchronization antenna. After the time delay of \(\tau_{\text{ab}}\), the synchronization antenna of LT-1B detects the signal and routes it through the transceiver and microwave combination. The receiver and the data former demodulate and record the synchronization signal, respectively. At time \(t+\tau_{\text{sys}}\) (\(\tau_{\text{sys}}\) denotes the signal exchange interval), LT-1B transmits synchronization signal through the same process as LT-1A, and LT-1A demodulates and records the received synchronization pulse after \(\tau_{\text{ba}}\). Finally, two sets of synchronization signals are sent to the ground system for post-processing. Through performing pulse compression on synchronization signals, the synchronization phases can be extracted in those peak positions and expressed as \(\varphi_{\text{ab}}(t)\) and \(\varphi_{\text{ba}}(t)\), respectively. The difference between \(\varphi_{\text{ab}}(t)\) and \(\varphi_{\text{ba}}(t)\) is used to obtain the synchronization compensation phase, i.e.,  
\[\varphi_{c}(t)=\frac{1}{2}(\varphi_{\text{ab}}(t)-\varphi_{\text{ba}}(t)). \tag{3}\]  
In order to accurately detect system faults, extract and compensate the phase error introduced by system equipment, the internal calibration is indispensable. The most complex calibration unit consists of five loops: a chirp transmitting loop CT, a chirp receiving loop CR, a reference loop RE, a synchronization transmitting loop ST, and a synchronization receiving loop SR [35]. The functions and composition of each calibration loop are as follows:  
1. Loop CT monitors the phase error caused by the radar transmission link. In this loop, a calibration signal generated by the signal generation unit is sent from the transmitting unit to the antenna calibration network. Then, the signal passes through the internal calibrator and enters the receiving unit. 2. Loop CR monitors the phase error caused by the radar receiving link. The calibration signal is sent to the internal calibrator, which then passes through the antenna calibration network and antenna receiving channel. After that, the signal enters the receiving unit and is measured. Figure 3: Structure block diagram the LT-1 system. 3. Loop RE measures the effects of redundant devices in the first two loops. The calibration signal passes through the internal calibrator and reaches the receiving unit for recording. 4. Loop ST monitors the phase error caused by the synchronization transmission link. The calibration signal enters the internal calibrator through the synchronization transceiver. After that, the signal is collected by the receiving unit. 5. Loop SR monitors the phase error caused by the synchronization receiving link.