# A Framework for Assessing the Interference from NGSO Satellite Systems to a Radio Astronomy System
## 4 Simulation Results
### Aggregate EPFD  
Since there are different satellite operators around the globe, the interference to the RAS telescope is the aggregate interference of multiple NGSO systems. Assuming that the interference to the RAS telescope from different NGSO satellites was independent of each other, we obtained the distribution of the aggregate interference to the RAS telescope by the method in Section 3. To analyse the interference of multiple NGSO satellite constellations, we added a constellation of 1296 satellites to the analysis. The constellation configuration is shown in Table 3, the other radiofrequency parameters remained the same as in the previous satellite constellation, and the beam activation probability for both constellations was one at any latitude. Figure 11: The EPFD of the RAS telescope with the beam activation of method 3: (a) the latitude of the RAS telescope is 0 degrees; (b) the latitude of the RAS telescope is 30 degrees; (c) the latitude of the RAS telescope is 60 degrees; (d) the latitude of the RAS telescope is 90 degrees. Figure 10: The EPFD of the RAS telescope with the beam activation of method 2: (a) the latitude of the RAS telescope is 0 degrees; (b) the latitude of the RAS telescope is 30 degrees; (c) the latitude of the RAS telescope is 60 degrees; (d) the latitude of the RAS telescope is 90 degrees. For the whole field of view of the RAS telescope, we selected three directions for the analysis, whose detailed parameters are shown in Table 4. The latitude and longitude of the RAS telescope were 30 degrees and 0 degrees, respectively. In the previous EPFD simulation of the RAS telescope, the EPFD was calculated only once for all directions of it. In order to obtain the EPFD distribution of the observation directions, several trails were required. The number of trails for the EPFD calculation was 2000 in order to obtain an accurate EPFD distribution. In the following figures, we give the CDF curves of the EPFD of the two satellite constellations, respectively, as well as their aggregate EPFD. The specific results are shown in Figure 12.  
Based on the simulation results presented above, we calculated the values of the EPFD at which the percentage of exceeding these values was at most 2%. The results of this analysis are shown in Table 5.  
From the above simulations, the minimum EPFDs of \(-131.22\), \(-122.15\), and \(-120.80\) were larger than the EPFD threshold of \(-160\) for the three constellation configurations, so the NGSO constellations in the Ku band would cause harmful interference to the RAS telescope without any interference protection measures. In order to avoid interference effectively, it was necessary to ensure that the interference at the RAS was further attenuated by approximately 39.2 dB. The following methods of interference avoidance could be adopted:  
* Increase the guard band between the RAS band and the band of the NGSO satellite beams. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Directions of RAS** & **Direction 1** & **Direction 2** & **Direction 3** \\ \hline
**Elevation angle (deg)** & 1.5 & 31.5 & 61.5 \\
**Azimuth angle (deg)** & 1.5 & 1.73 & 2.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters. Figure 12: The CDF of the EPFD at the RAS telescope with the beam activation of method 1: (a) direction 1; (b) direction 2; (c) direction 3. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Configuration** & **Constellation of 720** & **Constellation of 1296** &
\begin{tabular}{l} **Constellation of 720 +** \\ **1296** \\ \end{tabular} \\ \hline EPFD of direction 1 (dBW/100 MHz/m\({}^{2}\)) & \(-132.15\) & \(-128.62\) & \(-127.10\) \\ EPFD of direction 2 (dBW/100 MHz/m\({}^{2}\)) & \(-131.73\) & \(-124.22\) & \(-123.26\) \\ EPFD of direction 3 (dBW/100 MHz/m\({}^{2}\)) & \(-131.22\) & \(-122.15\) & \(-120.80\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: EPFD values corresponding to 2%.