# Performance and Requirements of GEO SAR Systems in the Presence of Radio Frequency Interferences
## 4 Performance Evaluation and Discussion: Example of GEO SAR Design
### Impact of Ground RFI  
In the simulation of the ground RFI case, the location of the beam centre of the GEO SAR is set in Beijing (40\({}^{\circ}\)N, 116\({}^{\circ}\)E), when the GEO SAR is at the orbit position of 162\({}^{\circ}\) true anomaly with a 2.6\({}^{\circ}\) look angle. Moreover, we assume the one-way signal loss of GEO SAR is 3 dB. According to the analysis of the real RFI data obtained by the spaceborne systems in the appendix, as the RFI brightness temperature is general thousands of Kelvin, the scope of the RFI brightness temperature in the analysis is from 0 to 10,000 K.  
According to the SINR requirement in Table 3, the average transmitted power requirement of the GEO SAR system with the variation of RFI intensity and the distance from the position of the  
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Carrier central frequency (GHz) & 1.25/5.4/9.6 & Inclination (\({}^{\circ}\)) & 10–60 \\ Look angle (\({}^{\circ}\)) & 2–7 & Argument of perigee (\({}^{\circ}\)) & 270 \\ Eccentricity & 0.07 & Antenna area (m\({}^{2}\)) & 531 \\ Duty cycle (\%) & 15 & Incidence angle (\({}^{\circ}\)) & 10–60 \\ Bandwidth (MHz) & 18 & Integration time (s) & 30–250 \\ Polarization & HH & Equivalent thermal noise (K) & 879 \\ \hline \end{tabular}
\end{table}
Table 2: Classical parameters of the inclined orbit GEO SAR system.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Number of beams & 1 (L band) & & \\
16 (C band) & SINR (dB) & 10 \\
64 (X band) & & & \\ \hline Resolution (m) & \textless{}20 \(\times\) \textless{}20 (Single look) & Coverage (km) & 400 \(\times\) 400 \\ \hline \end{tabular}
\end{table}
Table 3: Performance of GEO SAR system.  
point-like RFI source to the beam centre of GEO SAR is shown in Figure 7. The average transmitted power requirements in all three working frequencies will increase with the increasing of the brightness temperature. In the meantime, the average transmitted power requirements are also very sensitive to the relative distance between the beam centre of GEO SAR and the position of the point-like RFI. When the distance increases, the average transmitted power requirement will decrease, because the power of the RFI after weighting by the antenna pattern of GEO SAR becomes small. Taking the L band system and the brightness temperature of 5000 K as an example, when the distance changes from 0 to 60 km, the average transmitted power requirements varies from more than 2.4 kW to less than 2.3 kW. At last, because of the shorter wavelength, the smaller beam width and the higher backscatter coefficient, comparing the three sub-figures in Figure 7, a higher frequency is helpful to reduce the required average transmitted power. Under the case of a 5000 K brightness temperature RFI and locating at 60 km away from the centre of the GEO SAR beam, the average transmitted power requirement changes from about 2.3 kW to only 0.2 W from L band to X band. Thus, an L band GEO SAR system needs a higher transmit power to compensate the RFI impact.  
Likewise, shown in Figure 8, in the case of distributed RFI, the average transmitted power requirement will increase when the RFI brightness temperature turns higher. In the meantime, similarly, the GEO SAR system with a higher working frequency also has a much lower average transmitted power requirement in the distributed RFI case, which suggests the system will be easier to be implemented. Nevertheless, as the interference is uniform, the impact does not depend on the positions of the RFI and the beam centre of GEO SAR.