## 2 Geometry and Signal Model
### Signal Model  
According to the geometric model in Figure 1a, a SAR platform travels at a speed of \(V\), and continuously transmits a chirp signal and receives echo signals within the azimuth time. When the SAR system is interfered with, its echo signal is composed of the real target echo signal, RFI signal, and noise signal [1; 2; 3; 4; 5; 6; 7; 8; 9]. Thus, as the range time is \(t_{r}\) and the azimuth time is \(t_{a}\), and \(K\) RFI sources exist in the scene, the interfered echo signal \(s(t_{r},t_{a})\) received by each channel can be written as:  
\[s(t_{r},t_{a})=\sum_{k=1}^{K}j^{k}(t_{r},t_{a})+e(t_{r},t_{a})+n(t_{r},t_{a}), \tag{1}\]  
where \(j^{k}(t_{r},t_{a})\) denotes the interference signal from the \(k\)-th RFI source, \(e(t_{r},t_{a})\) and \(n(t_{r},t_{a})\) denote the real target echo signal and noise signal, respectively. Due to the complex source of RFI, it is difficult to model it with a single signal form [2; 3; 4]. In terms of signal model, the form of sinusoidal modulation signal and linear modulation signal is simple and often used as the basic form of microwave radiation, which can be used to model RFI [2; 3; 4; 5; 6; 7; 8]. For the type of RFI, researchers usually classify RFI into narrowband interference (NBI) and wideband interference (WBI) according to the ratio of the RFI bandwidth to the echo signal bandwidth [2; 3; 4; 5; 6; 7; 8]. Furthermore, since the source of WBI is generally other radar systems, it can be modeled by the linear modulation signal whose parameters change over time [8], which is called wideband linear frequency modulated interference (WBLFMI) in this article. Meanwhile, NBI usually comes from communication equipment or television facilities with narrow bandwidth [4; 5; 6]. Compared with the bandwidth of SAR, this type of RFI signal may occupy a very narrow bandwidth in the frequency domain [8], or even occupy only one frequency bin like a sinusoidal signal [2]. Therefore, this article further divides NBI into narrowband linear frequency modulated interference (NBLFMI) and radio frequency noise interference (RFNI). This modeling method conforms to the signal characteristics of RFI in actual situations [2; 3; 4; 5; 6; 7; 8] and has achieved good results in the research on interference detection and suppression [19; 20]. In addition, the pulse width of most RFI signals is shorter than the echo window time of SAR, which results in the RFI observed in actual data being pulsed [7; 21]. Taking these factors into consideration, this article models the RFI signal as the pulsed signal, and these three types of interference are written as:  
\[\left\{ \begin{array}{l}j_{RFNI}(t_{r}^{\prime},t_{a})=A_{i}(t_{r}^{\prime},t_ {a})rect\left(\frac{t_{r}^{\prime}}{T_{i}}\right)\exp\{i[2\pi f_{c}t_{r}^{ \prime}+2\pi f_{i}{t_{r}}^{\prime}+\phi_{i}(t_{a})]\}\\ j_{NBLFMI}(t_{r}^{\prime},t_{a})=A_{\pi}(t_{r}^{\prime},t_{a})rect\left(\frac{t _{r}^{\prime}}{T_{n}}\right)\exp\{i\Big{[}2\pi f_{c}t_{r}^{\prime}+\pi k_{n}{t_ {r}}^{\prime}{}^{2}+\phi_{n}(t_{a})\Big{]}\}\\ j_{NBLFMI}(t_{r}^{\prime},t_{a})=A_{w}(t_{r}^{\prime},t_{a})rect\Big{(}\frac{t _{r}^{\prime}}{T_{w}}\Big{)}\exp\{i\Big{[}2\pi f_{c}t_{r}^{\prime}+\pi k_{w}{t_ {r}}^{\prime}{}^{2}+\phi_{w}(t_{a})\Big{]}\}\\ t_{r}^{\prime}=t_{r}-\frac{R^{k}(t_{a})}{C}\end{array} \right. \tag{2}\]  
where \(A_{i}(\cdot)\), \(A_{n}(\cdot)\), and \(A_{w}(\cdot)\) denote the amplitude of these three types of RFI signals, \(T_{i}\), \(T_{n}\), and \(T_{w}\) are their pulse width,\(f_{c}\) is the carrier frequency, \(f_{i}\) is the frequency of RFNI,\(k_{n}\) and \(k_{w}\) are the chirp-rate of NBLFMI and WBLFMI, \(\phi_{i}(t_{a})\), \(\phi_{n}(t_{a})\), and \(\phi_{w}(t_{a})\) denote the signal phase, \(R^{k}(t_{a})\) is the distance between the \(k\)-th RFI source and the SAR system at the azimuth time of \(t_{a}\). In addition, it needs to be pointed out that the bandwidth of these three types of interference is relatively narrow compared to the bandwidth of the SAR signal [2; 3; 4; 5].