## 2 Geometry and Signal Model
### Signal Model
Besides, in related research on RFI, the following assumptions are often mentioned generally:  
1. The real target echo signal, the RFI signal, and the noise signal are statistically independent [4; 5]. 2. The RFI signal possesses dominant energy in the interfered echo signal, and the real target echo signal has a noise-like spectrum compared with the RFI signal, which means we can define the sum of the real target echo signal and noise signal as the equivalent additive noise [4; 5; 6]: \[g(t_{r},t_{a})=e(t_{r},t_{a})+n(t_{r},t_{a}).\] (3)
3. RFI signals from different interference sources are uncorrelated [9; 10; 11; 12; 13]. 4. The antennas of each channel of the SAR system are isotropic and not coupled to each other [9; 10; 11; 12; 13]. 5. The distance between RFI source and the spaceborne SAR system usually meets the far field condition [9; 10; 11]. According to Equations (1) and (3), the contaminated echo signal \(s_{zm}\) received by the m-th channel on the Z-axis of the channel array of the SAR system can be expressed as:  
\[s_{zm}(t_{r},t_{a})=\sum_{k=1}^{K}z_{zm}^{k}(t_{r},t_{a})+g_{zm}(t_{r},t_{a}), \tag{4}\]  
where \(\hat{z}_{zm}(t_{r},t_{a})\) denotes the signal from the \(k\)-th RFI source received by this channel, \(g_{zm}(t_{r},t_{a})\) denotes the equivalent additive noise composed of the sum of the real target echo signal and the noise signal. At the same azimuth time, the interference signal from the \(k\)-th RFI source is received by channel \(z_{1}\), and its received signal can be expressed as \(\hat{j}_{1}^{k}(t_{r},t_{a})\). The relationship between \(\hat{j}_{1}^{k}(t_{r},t_{a})\) and \(\hat{j}_{zm}^{k}(t_{r},t_{a})\) can be written as:  
\[\hat{j}_{zm}^{k}(t_{r},t_{a})=\hat{j}_{1}^{k}(t_{r}-\tau_{zm}^{k},t_{a}), \tag{5}\]where \(\tau_{zm}^{k}\) denotes the time difference between the interference signal of the \(k\)-th RFI source reaching channel \(z_{1}\) and channel \(z_{m}\). Since the RFI signal can be regarded as a narrowband signal compared with the echo signal, Equation (5) can be written as:  
\[j_{1}^{k}(t_{r}-\tau_{zm}^{k},t_{a})\approx j_{1}^{k}(t_{r},t_{a})e^{-i2\pi f_{r }\tau_{zm}^{k}}. \tag{6}\]  
Figure 2 shows a schematic diagram of the signal from the \(k\)-th RFI source being received by channel \(z_{1}\) and channel \(z_{m}\). Based on assumption E, the RFI signal received by these channels can be approximately regarded as a plane wave, which means that the two red lines representing the direction of the RFI signal in Figure 2 can be considered parallel. According to the geometric relationship in Figure 2 and the definition of elevation angle in Figure 1b, the time difference \(\tau_{zm}^{k}\) of the \(k\)-th RFI signal reaching the two channels can be obtained:  
\[\tau_{zm}^{k}=\frac{(m-1)d\cos\theta^{k}}{C}, \tag{7}\]  
where \(C\) is the light speed, \(\theta^{k}\) is the elevation angle between the interference signal of the \(k\)-th RFI source and the array. Thus, combined with Equations (4) and (6), we can obtain:  
\[s_{zm}(t_{r},t_{a})=\sum_{k=1}^{K}j_{1}^{k}(t_{r},t_{a})e^{-i2\pi f_{r}\tau_{zm }^{k}}+g_{zm}(t_{r},t_{a}). \tag{8}\]  
The signal received by the M channels on the \(Z\)-axis can be expressed as a vector \(\mathbf{S}_{Z}\):  
\[\mathbf{S}_{Z}=\left[ \begin{array}{c}s_{z1}(t_{r},t_{a})\\ s_{z2}(t_{r},t_{a})\\ \vdots\\ s_{zM}(t_{r},t_{a})\end{array} \right]=\left[ \begin{array}{cccc}e^{-i2\pi f_{r }\tau_{z1}^{k}}&e^{-i2\pi f_{r}\tau_{z1}^{2}}&\ldots&e^{-i2\pi f_{r}\tau_{z1}^{ k}}\\ e^{-i2\pi f_{r}\tau_{z2}^{k}}&e^{-i2\pi f_{r}\tau_{z2}^{k}}&\ldots&e^{-i2\pi f_{r} \tau_{z2}^{k}}\\ \vdots&\vdots&\ddots&\vdots\\ e^{-i2\pi f_{r}\tau_{zM}^{k}}&e^{-i2\pi f_{r}\tau_{zM}^{k}}&\ldots&e^{-i2\pi f _{r}\tau_{zM}^{k}}\end{array} \right]\left[ \begin{array}{c}j_{1}^{1}(t_{r},t_ {a})\\ j_{1}^{2}(t_{r},t_{a})\\ \vdots\\ j_{1}^{K}(t_{r},t_{a})\end{array} \right]+\left[ \begin{array}{c}g_{z1}(t_{r},t_{a})\\ g_{z2}(t_{r},t_{a})\\ \vdots\\ g_{zM}(t_{r},t_{a})\end{array}