# An Innovative Internal Calibration Strategy and Implementation for LT-1 Bistatic Spaceborne SAR
## 2 Internal Calibration System
### Echo Compensation  
Based on the design of the five non-delay calibration loops in Table 3 of the previous section, the system transfer function can be derived to obtain the echo compensation formula, and further, the phase and amplitude compensation accuracy formulas can be determined. The specific derivation process is as follows. In the LT-1 BiSAR system, the chirp reference calibration for the primary and auxiliary satellites does not involve the phased array antenna. The signal loop is transmitted from the _LFM_ (frequency modulation signal source) through the internal calibrator to the _RX_ (microwave combination and receiver), with its transfer function as follows:  
\[CE_{cal}^{i}=LFM^{i}\cdot CR_{1}^{i}\cdot RX^{i} \tag{1}\]  
The signal of chirp receiving calibration loops of the primary and auxiliary satellites goes from the _LFM_ through the internal calibrator, antenna calibration network, and antenna receiving channel, then transmitted to the _RX_, with its transfer function as follows:  
\[RX_{cal}^{i}=LFM^{i}\cdot CR_{3}^{i}\cdot CN_{A}^{i}\cdot RX_{A}^{i}\cdot RX^{i} \tag{2}\]  
The signal of synchronization transmitting calibration loop of the primary and auxiliary satellites goes from the _LFM_ through the transmitting link of the synchronization transceiver and the internal calibrator, then transmitted to the _RX_, with its transfer function as follows:  
\[ST_{cal}^{i}=LFM^{i}\cdot STX^{i}\cdot CR_{4}^{i}\cdot RX^{i} \tag{3}\]  
The signal of synchronization receiving calibration of the primary and auxiliary satellites goes from the _LFM_ through the internal calibrator and the receiving link of the synchronization transceiver, then transmitted to the _RX_, with its transfer function as follows:  
\[SR_{cal}^{i}=LFM^{i}\cdot CR_{5}^{i}\cdot SRX^{i}\cdot RX^{i} \tag{4}\]  
During the LT-1 inter-satellite alternate synchronization, the synchronization from the primary satellite to the auxiliary satellite and vice versa is completed within two consecutive Pulse Repetition Intervals (PRI). In such a short time, the inter-satellite transmission characteristics can be assumed to remain unchanged, hence the transfer functions for inter-satellite transmission are:  
\[H_{s}^{ab}=LFM^{a}\cdot STX^{a}\cdot TF\cdot SRX^{b}\cdot RX^{b} \tag{5}\]  
\[H_{s}^{ba}=LFM^{b}\cdot STX^{b}\cdot TF\cdot SRX^{a}\cdot RX^{a} \tag{6}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **Definition** & **Parameters** & **Definition** \\ \hline \(CR_{3}^{i}\) & Internal calibrator chirp receiving loop & \(RX_{cal}^{i}\) & Chirp receiving calibration loops \\ \(CR_{4}^{i}\) & Internal calibrator synchronization & \(ST_{cal}^{i}\) & Synchronization transmitting calibration loop \\  & transmitting loop & \(ST_{cal}^{i}\) & Synchronization receiving calibration loop \\ \(CR_{5}^{i}\) & Internal calibrator synchronization & \(SR_{cal}^{i}\) & Synchronization receiving calibration loop \\  & receiving loop & \(H_{s}^{ba}\) & Auxiliary satellite to primary satellite \\ \(CR_{6}^{i}\) & Internal calibrator chirp transmitting and & \(H_{s}^{ba}\) & synchronization \\  & receiving loop & \(H_{s}^{ba}\) & Primary satellite to auxiliary satellite \\ \(CN_{A}^{i}\) & Antenna calibration network (including & \(H_{s}^{ab}\) & synchronization \\  & coaxial cables) & \(TF\) & Interstellar transmission link \\ \(RX_{A}^{i}\) & Antenna receiving link & \(TF\) & Synchronization transceiver transmitting link \\ \(TX^{i}\) & Transmitting link & \(STX^{i}\) & Synchronization transceiver transmitting link \\ \(LFM^{i}\) & Frequency modulation signal source & \(SRX^{i}\) & Synchronization transceiver receiving link \\ \(RX^{i}\) & Microwave combination and Receiver & & \\ \hline \end{tabular}  
* * \(i=a\) or \(b\), and \(a\) represents primary satellite, \(b\) represents auxiliary satellite.  
\end{table} 
Table 4: _Cont._From Formulas (1) to (6), the expression for the difference between the receiving channels of the two satellites can be derived as follows:  
\[