## 2 Interfering Mechanism and Major RFI Sources
### General Signal Model for Typical RFI Sources  
For a SAR system, each echo received during a pulse repetition time can be considered as a 1-D time series. Then, an RFI contaminated, complex-valued radar pulse \(X(n)\) can be modelled as a mixture of target echoes, noise, and interference [12]:  
\[X(n)=S(n)+W(n)+I(n),\quad 1\leq n\leq N\enspace, \tag{1}\]  
where \(X(n)\) denotes the complex-valued received signal, \(S(n)\) denotes the useful target echoes, \(W(n)\) is the additive noise and \(I(n)\) is the RFI. \(n\) denotes the sampling index for range fast-time samples with \(N\) denoting the number of total samples. An obvious property of the RFI signals in SAR system is its relatively large power. Owing to the 2-D matched filtering processing, SAR possess large signal processing gain along range and azimuth. Therefore, low power incoherent RFI could be mitigated during the SAR image formation process. However, large-power RFI will still remain in the focused image as visible artifacts or noise [30]. However, if there are a multitude of low-power RFI sources, then the injected noise will be crucial for phase related applications such as SAR interferometry. The RFI signal can be pulsed or continuous wave. Typically, the type of RFI sources can be categorized into four major classes [1]. (1) Narrow-Band RFI  
Narrow-band interference often possess relatively narrow bandwidth than that of the SAR system, while continuous in time relative to the integration time. Typical examples are commercial land-mobile radio and amateur radio. This kind of interfering signal model is well studied in early studies for RFI [31]. In mathematical representation, it can be modeled as a sum of the complex sinusoidal tones, i.e.,:  
\[I_{NBI}(n)=\sum_{l=1}^{L}A_{l}(n)\cdot\exp(j(2\pi f_{l}n+\theta_{l})), \tag{2}\]  
where \(A_{l}\), \(f_{l}\), and \(\theta_{l}\) denotes the amplitude, carrier frequency, and phase for the \(l\)-th interference component, respectively. \(L\) is the number of RFI sources. Figure 8 illustrates the range spectra of radar echoes contaminated with narrow band RFI and in range-frequency azimuth-time representation. The data is recorded by a Chinese L-band airborne SAR system transmitting a linear frequency modulated pulse with a bandwidth of 300 MHz. The energy of interferences is concentrated into a few frequency bins, and appear as prominent peaks in the frequency domain and bright lines in the range-frequency azimuth-time representation, respectively. This feature makes it easier to be identified and detected. Generally, the frequencies of the narrow-band RFI are rather stationary. (2) Pulsed Wide Band RFI  
Pulsed wide band RFI are pulsed in time with various pulse repetition time, and the bandwidth is wider than the continuous narrow-band. A common case of such RFI comes from the ground-based radiolocation radar. According to the modulation type, it can be further modeled as two major forms of wide-band interference (WBI), i.e., chirp modulated (CM) WBI and sinusoidal modulated (SM) WBI [8]. In a practical situation, the WBI may not match these two special models perfectly. However, the CM WBI and SM WBI can be considered as two special end examples of a larger family of WBI signatures whose properties are a combination of them. Mathematically, the CM WBI is modeled as:  
\[I_{CM}(n)=\sum_{l=1}^{L}A_{l}(n)\exp\{j\big{(}2\pi f_{l}n+\pi\gamma_{l}n^{2} \big{)}\}, \tag{3}\]  
where \(A_{l}\), \(f_{l}\), and \(\gamma_{l}\) is the amplitude, frequency, and chirp rate of the \(l\)-th component, respectively. Moreover, the SM WBI can be expressed as:  
\[I_{SM}(n)=\sum_{l=1}^{L}A_{l}(n)\exp\{j\beta_{l}\sin(2\pi f_{l}n+\phi_{l})\}, \tag{4}\]  
Figure 8: Illustration of narrow-band interference in (**a**) range spectrum and (**b**) range spectrum-azimuth–time representation. where \(A_{l}\), \(\beta_{l}\), \(f_{l}\) and \(\phi_{l}\) are the amplitude, modulation factor, frequency and initial phase of the \(l\)-th component, respectively.