# A Novel Channel Calibration Method for Bistatic ISAR Imaging System
## 3 The Channel Calibration Method for Bistatic ISAR System
### Accumulation Method of Multi-Period Echoes  
SNR of the calibration satellite echoes are low due to the small RCS and the long distance from the radar system. Hence, coherent accumulation of multiple-period echoes should be conducted to improve SNR. The coherent accumulation of multi-period echoes in the time domain is significant to estimate accurate channel transfer function. In addition, the calibration satellite is not a stationary target, and the impact of the high-speed motion needs to be compensated for. In a previous study [28], intra-pulse velocity compensation methods have been studied for the high-speed moving targets of bistatic ISAR. The velocity compensation method is used to compensate for the high-speed motion of the calibration satellite to make sure the echo signals satisfy the \"stop and go\" model for coherent accumulation.  
Figure 1: The comparison of HRRP: (**a**) HRRP with an ideal channel; (**b**) HRRP with a non-ideal channel.  
Figure 2: The comparison of two-dimensional image: (**a**) Two-dimensional image with an ideal channel; (**b**) two-dimensional image with a non-ideal channel.  
The down-conversion of the calibration satellite echo is completed by the coherent local oscillator, and the baseband signal is obtained. The method proposed in [28] is used to compensate the intra-pulse velocity. Considering the non-ideal channel characteristics, the \(i\)-th echo signal in Equation (4) can be rewritten as:  
\[s_{i\_ball}\left(\hat{t},t_{m}\right)=\left[\sigma\cdot s_{b}\left(\hat{t}- \tau_{i},t_{m}\right)\exp(-j2\pi f_{c}\tau_{i})\right]\otimes h_{TR}(t) \tag{9}\]  
where \(\sigma\) is the RCS of the calibration satellite, and \(\tau_{i}\) is time delay, \(\otimes\) represents convolution operation, and \(h_{TR}(t)\) is the transmitting and receiving channels' impulse response in time domain.  
After pulse compression using the matched filter, the signal can be expressed as:  
\[s_{i\_compression}\left(\hat{t},t_{m}\right)=\left[A\sin c\left(\hat{t}-\tau_{i} \right)\exp(-j2\pi f_{c}\tau_{i})\right]\otimes h_{TR}(t) \tag{10}\]  
where \(A\) is the amplitude of the pulse compression result. In order to realize the coherent accumulation of the calibration satellite echo in the time domain, both the initial phase and zero frequency positions of the baseband echo signal in each period should be the same. The initial phase and zero frequency positions can be obtained through pulse compression. Comparing Equation (9) with Equation (10), the'zero frequency position is equal to the peak position of the pulse compression result \(P_{i}\), and the initial phase is equal to the corresponding phase \(\varphi_{i}\)[18]. The phase compensation factors are calculated in accordance with the difference of initial phase compared with the first period \(\Delta\varphi=\varphi_{i}-\varphi_{1}\), and original echoes of each period \(s_{i\_ball}\left(\hat{t},t_{m}\right)\) are compensated respectively. The central translation of echoes is achieved by circularly shifting according to the difference of peak position compared with the first period \(\Delta P=P_{i}-P_{1}\). Then, the coherent accumulation of echoes can be achieved by accumulating the adjusted echoes in the time domain. The process of coherent accumulation and the waveforms of accumulated signal at different stages are shown in Figure 3.