## 4 Coexistence Simulations  
For simplicity, both GEO and LEO users are placed in the same location of the GEO central beam, and the simulation time is set to the duration that the LEO satellite passes over the users. The simulation parameters are presented in Table 3. First, the CCI between GEO and LEO systems is analyzed. Figure 7a,b shows the signal quality of the GEO and LEO users during the simulation, respectively, where the blue curve represents the original signal without interference, and the red curve represents the signal with interference. The original signal quality of the GEO user is almost unchanged because of the static characteristics of GEO satellites, whereas the original signal quality of the LEO user periodically varies as the beams pass through one by one. When the LEO and GEO systems share the frequency, the signal quality in the red curve declines because of the CCI, and it  
Figure 6: The clustering idea based on a 7-cell frequency reuse pattern.  
varies with the motion of the LEO satellite. When the satellites and users are in alignment, the signal quality deteriorates severely, which may make systems paralyzed.  
Next, we analyze the performance of the proposed dynamic frequency allocation algorithm. \(l\)th is set to 600 km according to the relationship between the SINR and the distance in Figure 4. During the passage of the LEO satellite, the amount of frequency allocations on clusters is 9, and the total switch of beams is 50, which is much less than frequency allocation without clusters. In addition, the SINR of the proposed algorithm is compared with APC in Figure 8. If the APC is adopted, the SINR of the LEO user declines again because of the protection mechanism for the primary user, as depicted in the green curve. The red curve shows that the SINR of both users for the proposed algorithm performs better than the APC. It should be noted that the SINR of the secondary user is always higher than the threshold, which indicates that the interference can be effectively avoided:  
\[\Re=B\text{log}_{2}\left(1+\gamma_{\text{L}}\right)+B\text{log}_{2}\left(1+ \gamma_{\text{G}}\right). \tag{28}\]  
Finally, the total throughput under ideal conditions calculated by (28) is shown in Figure 9, where the blue dashed curve denotes the coexistent systems with interference, and the green solid and red dotted curves denote the networks which employ the APC technique and the proposed algorithm, respectively. We can see that, during the passage of the LEO satellite, when none of the LEO beams enter the keep-out region of the co-channel GEO beams, the two satellite systems can coexist  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Notations** & **Value** \\ \hline Analysis start time & \(t_{\text{st}}\) & 24 August 2018 06:50:51 \\ Analysis stop time & \(t_{\text{sp}}\) & 24 August 2018 06:53:45 \\ Time step & \(\Delta t\) & 1 s \\ Latitude of users & \(P_{\text{lat}}\) & \(1^{\circ}\) \\ Longitude of users & \(P_{\text{lon}}\) & \(25^{\circ}\) \\ Number of LEO clusters & \(N_{0}\) & 7 \\ Frequency reuse factor of GEO satellite & \(K\) & 7 \\ Number of LEO beams & \(N\) & 37 \\ Threshold value of SINR & \(\gamma_{\text{th}}\) & 14 dB \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters.  
Figure 7: Comparison of signal quality with and without interference. (**a**) GEO user; (**b**) LEO user.  
peacefully without protective measures, as shown in the coincidence of curves. When there is an LEO beam entering the keep-out region, the throughput in the blue dashed curve declines because of the in-line interference. The throughput with the APC technique is improved compared to the scenario with interference. However, the improvement is limited because the APC technique guarantees the primary system at the sacrifice of the secondary system. Furthermore, the proposed dynamic frequency algorithm achieves the best performance, twice as large as the others when the in-line interference occurs because the interference can be almost avoided rather than mitigated.