## 4 Simulation Experiments and Results  
### System Establishment and Parameter Setting  
In Section 3, the multiple RFI sources geolocation method based on the 2D-ESPRIT and PSO algorithm has been discussed. In this section, the simulation results obtained by processing on the simulated data using the proposed method are presented. First, we establish a spaceborne multi-channel SAR system that may be affected by single or multiple RFI source. Next, on the basis of this system, the RFI transmitted from multiple different spatial locations and existing at the same time is simulated, and the contaminated echo signals received by the SAR under these conditions are obtained. The key parameters of SAR system in the simulation works are shown in Table 1.  
For the echo signal, we take the pixel value of a real SAR image as the backscattering coefficient of the scene, in accordance with the radar and antenna parameters set in Table 1, and the relative position of SAR and the scene set as Figure 1a, the scene echo signal is  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Pulse Width (\(\mathrm{\SIUnitSymbolMicro s}\)) & 5 \\ Bandwidth (MHz) & 90 \\ Sampling Frequency (MHz) & 100 \\ Pulse Repetition Frequency (Hz) & 1000 \\ Receive Window Width (\(\mathrm{\SIUnitSymbolMicro s}\)) & 20 \\ Average Orbit Height (km) & 500 \\ Average Speed (km/s) & 7.61 \\ Wavelength (m) & 0.30 \\ Distance between adjacent channel (m) & 0.15 \\ Number of channels & 19 \\ Signal-to-Noise Ratio (dB) & \(-15\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Synthetic aperture radar (SAR) system parameters.  
Figure 6: Flowchart of the particle swarm optimization (PSO) algorithm.  
calculated pulse by pulse. We have successfully applied this method in previous studies to generate echo signals [17; 19; 20].  
For RFI sources, we define that RFI sources are independent of each other, and each RFI source is located at a place not lower than the surface of the earth, the form of interference signals emitted by them is in accordance with Equation (2). In order to fully verify the effectiveness of the proposed method, various simulation experiments are conducted. In each simulation experiment, the emission signal of the interference source is randomly generated according to Equation (2). The specific method is to first randomly generate the characteristic parameters of the signal within a certain range and then substitute these parameters into the equation to obtain the signal. In this way, the interference signal of each simulation can conform to the RFI signal characteristics and independent characteristics. The range and approach of randomly generating RFI signal parameters are shown in Table 2. Based on the above system parameters and interference parameters, a spaceborne SAR simulation system interfered with by RFI sources can be established.  
Further, pursuant to the number of RFI sources and the type of interference signal, we design three situations when the SAR system is jammed:  
* Case 1. A single RFI source.
* Case 2. Multiple RFI sources of the same interference type.
* Case 3. Multiple RFI sources of mixed types.  
With the established SAR system, we simulate the SAR echo signals with different interference -to-signal ratios in these three conditions and use them as experimental data.