# Modeling and Analysis of RFI Impacts on Imaging between Geosynchronous SAR and Low Earth Orbit SAR
## 2 Accurate Modeling of SINR in the Presence of RFI
### Verification of the SINR Expressions in the Presence of RFI  
In the aspect of GEO-to-LEO RFI, the target signal from the scene center and the RFI signal from the GEO SAR scattered by the scene center were generated and focused. Then, the power of the image pixel both in and without the presence of RFI were obtained, compared with the theoretical value from (16). As shown in Table 3, the error between the evaluated power and calculated power after BP algorithm is small, verifying the expression of the GEO-to-LEO RFI gain. In the aspect of LEO-to-GEO RFI, firstly, to illustrate the migration difference between the LEO-to-GEO RFI and the GEO-to-LEO RFI and explain the interference zone spread of the LEO-to-GEO RFI in the range direction, we generated a target echo received by the GEO SAR, a LEO-to-GEO RFI signal, a target echo received by the LEO SAR, and a GEO-to-LEO RFI signal according to Table 2. All of them were scattered by the scene center and adopted matched filter in the range direction. The results are shown in Figure 5. Obviously, Figure 5 agrees with Figure 4, and the length of interference in the range direction widened after the BP algorithm and can be expressed as (17). Then, to further demonstrate (17), the target echo and the RFI signal from the LEO SAR scattered by the point A and D were obtained and focused, respectively. Thus, the range-direction length of the interference zone generated by point A and D was obtained by simulation, which is shown in Table 4 compared with the theoretical value from (17). It is apparent that the range direction length of the interference zone is related to the slant range, and there is little change for different points in the same scene; as a result, it can be given using the slant range of the scene center. In addition, there is a drift of the interference zone in the range direction due to the large migration; however, it does nothing, with the area affecting a single resolution cell due to the same value for different points. Figure 5: Range compression result. (**a**) the RFI which is transmitted by the LEO SAR, scattered by the scene center, and received by the GEO SAR and the target echo which is transmitted and received by the GEO SAR; (**b**) the RFI which is transmitted by the GEO SAR, scattered by the scene center, and received by the LEO SAR and the target echo which is transmitted and received by the LEO SAR. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Target** & **RFI** \\ \hline Power before BP algorithm/dBw & \(-162.3863\) & \(-141.6115\) \\ Evaluated gains in BP algorithm/dB & \(123.5218\) & \(56.3548\) \\ Evaluated power after BP algorithm/dB & \(-38.8646\) & \(-85.2567\) \\ Calculated power after BP algorithm/dBw & \(-38.8606\) & \(-85.4212\) \\ Error/\% & \(0.1\) & \(3.7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: GEO-to-LEO RFI focusing results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Point** & **Evaluated Results/dBw** & **Calculated Results/dBw** & **Error/\%** \\ \hline GEO-to-LEO RFI & \(-\)42.2548 & \(-\)42.3657 & 2.4 \\ LEO-to-GEO RFI & \(-\)42.5571 & \(-\)42.3284 & 5.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Power affecting a signal resolution cell from RFI. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Integration Time 25 s** & **Integration Time 50 s** \\ \hline \(L_{2}\)/km & 6.25 & 24.4 \\ \(L_{1}\)/km & 2.04 & 2.04 \\ \(L_{2}\)/\(L_{1}\) & 3.07 & 12 \\ \(P_{2}\)/dBw & \(-\)84.75 & \(-\)87.54 \\ \(P_{1}\)/dBw & \(-\)79.63 & \(-\)76.66 \\ \(P_{1}\)/\(P_{2}\) & 3.26 & 12.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Focusing results of LEO-to-GEO RFI scattered by point A.  
Figure 6: Results of BP algorithm. (**a**) point A, B, C, D; (**b**) the whole scene.