## 4 Simulation Experiments and Results
### Simulation Experiments and Results  
According to the parameters in Tables 1 and 2, the contaminated echo signals are simulated. At each azimuth time, the interference signal of all RFI sources, the real target echo signal, and the noise signal constitute the echo signal of the SAR system according to Equation (1). Figure 7 shows the time-domain and frequency-domain forms of the demodulated SAR echo signals interfered by the three types of RFI signals. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of RFI** & **Parameters** & **Range** & **Distribution** \\ \hline \multirow{4}{*}{RFNI} & Frequency (KHz) & \([0.5,500]\) & Uniform \\  & Pulse Width (\(\upmu\)s) & \([1,9]\) & Uniform \\  & Amplitude(dB) & \([-10,50]\) & Uniform \\  & Phase & \([0,2\pi)\) & Uniform \\ \hline \multirow{4}{*}{NBLFMI} & Bandwidth (MHz) & \([0.09,0.9]\) & Uniform \\  & Pulse Width (\(\upmu\)s) & \([1,9]\) & Uniform \\  & Amplitude (dB) & \([-10,50]\) & Uniform \\  & Phase & \([0,2\pi)\) & Uniform \\ \hline \multirow{4}{*}{WBLFMI} & Bandwidth (MHz) & \([0.9,4.5]\) & Uniform \\  & Pulse Width (\(\upmu\)s) & \([1,9]\) & Uniform \\ \cline{1-1}  & Amplitude (dB) & \([-10,50]\) & Uniform \\ \cline{1-1}  & Phase & \([0,2\pi)\) & Uniform \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The range and approach of randomly generating RFI signal parameters. The performance of the two-dimensional DOA algorithm is proved via the simulation experiments. Based on the obtained echo signal, we adopt the Monte Carlo simulation method for the DOA estimation method proposed in Section 3.3, and for each case, the number of Monte Carlo trials \(N_{MC}\) is 1000. Generally, the root mean square error (RMSE) of the angle estimation result is defined as an index to evaluate the performance of the two-dimensional DOA algorithm:  
\[RMSE_{DOA}=\frac{1}{K}\sum\limits_{k=1}^{K}\sqrt{\frac{1}{N_{MC}\cdot N_{a}} \sum\limits_{l=1}^{N_{MC}}\sum\limits_{i=1}^{N_{a}}\Bigl{[}\left(\theta_{i}^{k }-\hat{\theta}_{i}^{k}\right)^{2}+\left(\varphi_{i}^{k}-\hat{\varphi}_{i}^{k} \right)^{2}\Bigr{]}}. \tag{49}\]  
In Case 1, the RFI source is located at \(P_{j}^{1}=\left(0,0,973\right)_{\text{ENU}}\), and it is expressed in meters. In each experiment, we set the transmit power of the RFI source and set it to transmit one of the three interference signals, and then use the two-dimensional DOA method to process the echo signal and estimate the arrival angle. Figure 8 shows the DOA estimation error when the RFI source transmits three kinds of interference signals separately. Each point in Figure 8 represents the error between the estimated DOA and the true DOA in azimuth \(\varphi\) and elevation \(\theta\). Figure 7: Time-domain and frequency-domain form of the contaminated SAR signal: (**a**) time-domain form of echo signal contaminated by radio frequency noise interference (RFNI); (**b**) frequency-domain form of (**a**); (**c**) time-domain form of echo signal contaminated by narrowband linear frequency modulated interference (NBLFMI); (**d**) frequency-domain form of (**c**); (**e**) time-domain form of echo signal contaminated by wideband linear frequency modulated interference (WBLFMI); (**f**) frequency-domain form of (**e**). For each type of RFI, we gradually increase the transmit power of the RFI source, which will make the ISR of the echo signal increase accordingly. Then, the RMSE of the DOA estimation under each ISR is calculated and recorded. The RMSE of the angle estimation for this case can be calculated by substituting the DOA estimation result into Equation (49).