## 4 Simulation Experiments and Results
### Simulation Experiments and Results
Similarly, the RMSE of the estimated location and the true location can be used to illustrate the localization accuracy:  
\[RMSE_{DOA}=\frac{1}{K}\sum\limits_{k=1}^{K}\sqrt{\frac{1}{N_{MC}\cdot N_{a}} \sum\limits_{l=1}^{N_{MC}}\sum\limits_{i=1}^{N_{a}}\Bigl{[}\left(\theta_{i}^{k }-\hat{\theta}_{i}^{k}\right)^{2}+\left(\varphi_{i}^{k}-\hat{\varphi}_{i}^{k} \right)^{2}\Bigr{]}}. \tag{49}\]3  
When the transmission power gradually increases, the RMSE of the estimated location in the three cases is shown in \[RMSE_{DOA}=\frac{1}{K}\sum\limits_{k=1}^{K}\sqrt{\frac{1}{N_{MC}\cdot N_{a}} \sum\limits_{l=1}^{N_{MC}}\sum\limits_{i=1}^{N_{a}}\Bigl{[}\left(\theta_{i}^{k }-\hat{\theta}_{i}^{k}\right)^{2}+\left(\varphi_{i}^{k}-\hat{\varphi}_{i}^{k} \right)^{2}\Bigr{]}}. \tag{49}\]4  
\[RMSE_{DOA}=\frac{1}{K}\sum\limits_{k=1}^{K}\sqrt{\frac{1}{N_{MC}\cdot N_{a}} \sum\limits_{l=1}^{N_{MC}}\sum\limits_{i=1}^{N_{a}}\Bigl{[}\left(\theta_{i}^{k }-\hat{\theta}_{i}^{k}\right)^{2}+\left(\varphi_{i}^{k}-\hat{\varphi}_{i}^{k} \right)^{2}\Bigr{]}}. \tag{49}\]5 Process of PSO algorithm: (**a**) Iterations = 1; (**b**) Iterations = 10; (**c**) Iterations = 50; (**d**) Iterations = 100; (**e**) Iterations = 120; (**f**) Iterations = 161. \[RMSE_{DOA}=\frac{1}{K}\sum\limits_{k=1}^{K}\sqrt{\frac{1}{N_{MC}\cdot N_{a}} \sum\limits_{l=1}^{N_{MC}}\sum\limits_{i=1}^{N_{a}}\Bigl{[}\left(\theta_{i}^{k }-\hat{\theta}_{i}^{k}\right)^{2}+\left(\varphi_{i}^{k}-\hat{\varphi}_{i}^{k} \right)^{2}\Bigr{]}}. \tag{49}\]6 RMSE of angle estimation for Case 2 and Case 3. In order to evaluate the validity of the location estimation result obtained using the proposed method, digital beamforming (DBF) is used to mitigate the RFI in the echo signal with this result as the input, and the imaging results of the suppressed signal get to illustrate the effectiveness. The RFI suppression method aligns the notch direction of the beamforming pattern with the direction of the RFI source to reduce the energy of the RFI in the echo signal [9; 10]. In this paper, we use the DBF algorithm described in Reference [9]. Specifically, the estimated RFI source geographic location is utilized to calculate the elevation and azimuth angles of the RFI signal reaching the channel array at each azimuth time, and the optimal problem for RFI suppression is established according to the linearly constrained minimum variance (LCMV) method in DBF on the basis of the estimated angles [9]. The beamforming pattern weight \(\mathbf{\omega}\) is acquired by solving the optimization problem and the signal after RFI suppressing \(\mathbf{\mathrm{S}}^{\prime}\) can be get by multiplying this weight with the channel signal \(\mathbf{\mathrm{S}}\), which is given as [9]:  
\[RMSE_{DOA}=\frac{1}{K}\sum\limits_{k=1}^{K}\sqrt{\frac{1}{N_{MC}\cdot N_{a}} \sum\limits_{l=1}^{N_{MC}}\sum\limits_{i=1}^{N_{a}}\Bigl{[}\left(\theta_{i}^{k }-\hat{\theta}_{i}^{k}\right)^{2}+\left(\varphi_{i}^{k}-\hat{\varphi}_{i}^{k} \right)^{2}\Bigr{]}}. \tag{49}\]7  
Combined with the results of Figures 8, 10 and 12, we respectively apply the estimated RFI source location results of Cases 1-3 to the DBF algorithm to obtain the beamforming pattern weights in the elevation and azimuth directions at each azimuth time. Figure 16 shows the beamforming pattern weights calculated by using the elevation and azimuth estimation results at half of the azimuth time for Cases 1-3. In Figure 16a,b, are the result of the RFI type being RFNI in Case 1, (c) and (d) are the result of the RFI type being NBLFMI in Case 2, and (e) and (f) are the result in Case 3.