## 4 Numerical Results and Discussion
### Signal Quality  
In this section, we show and discuss the results of signal quality. Firstly, we show the simulation result of the proposed scheme for the equivalent antenna aperture, antenna gain, half-power beamwidth, and elevation angle of the center beam in Figure 4. The results show that the optimal equivalent antenna aperture increases while the elevation angle decreases. The increasing equivalent antenna aperture provides a higher antenna gain \begin{table}
\begin{tabular}{c c} \hline \hline
**Assumption** & **Value** \\ \hline Satellite height & 600 km \\ Satellite beam pattern & 19 spot beams with wrap-around \\ Max antenna gain for 3 GPP setting and FRF3 & 30 dBi \\ Carrier frequency & 2 GHz \\ UE-type & Handheld \\ UE antenna configuration & Omni-directional, \(-5.5\) dBi antenna gain [19] \\ UE transmit power & 23 dBm \\ UE attachment & RSRP \\ Scheduled bandwidth & 180 kHz (1 resource block) \\ Noise power & \(-147\) dBW \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation assumptions. and narrower beamwidth. Figure 5 shows the CDF of SINR for different settings in the NTN rural scenario. With the significant interference mitigation, the FRF3 performs best on SINR at \(t=0\), as shown in Figure 5a. Compared to the 3 GPP setting, the proposed scheme improves the SINR by 8.15 dB and 7.4 dB at the 50-percentile point and 5-percentile point at \(t=60\) and by 12.25 dB and 12.23 dB at the 50-percentile point and 5-percentile point at \(t=100\). Compared to the FRF3, the proposed scheme improves the SINR by 2.29 dB and 1.63 dB at the 50-percentile point and 5-percentile point at \(t=60\) and by 7.68 dB and 8.53 dB at the 50-percentile point and 5-percentile point at \(t=100\). The SINR results for the NTN urban scenario are shown in Figure 6. The figure also shows that the proposed scheme significantly improves the SINR at low elevation angles. Figure 7 shows the CDF of interference power for different settings in the NTN rural scenario. As shown in Figure 7, the interference power increases while time increases (elevation angle decreases) for both the 3 GPP setting, FRF3, and the proposed scheme. In Figure 7a, compared to the 3 GPP setting, the proposed scheme and the FRF3 decrease interference power by 1.3 dB and 11.6 dBW at the 95-percentile point. In Figure 7b, compared to the 3 GPP setting, the proposed scheme decreases interference power by 1.8 dBW and 5.2 dBW at the 95-percentile point and the 50-percentile point, and the FRF3 decreases interference power by 6.6 and 8.7 dB at the 95-percentile point and the  
Figure 4: Elevation angle of the center beam \(\epsilon_{0}(t)\) and optimal solutions of equivalent antenna aperture, max receive antenna gain, and half-power beamwidth with target SINR \(-5.6\) dB in NTN rural scenario. Figure 5: The SINR results for 3 GPP setting, FRF3, and the proposed scheme (target SINR \(-5.6\) dB) in NTN Rural scenario at (**a**) t = 0, (**b**) t = 60, (**c**) t = 100. 50-percentile point. In Figure 7c, compared to the 3 GPP setting, the proposed scheme decreases interference power by 1.2 dBW and 5.5 dBW at the 95-percentile point and the 50-percentile point, and the FRF3 decreases interference power by 4.9 dBW and 5.2 dB at the 95-percentile point and the 50-percentile point. The results presented in Figure 7 highlight a notable increase in interference over time. This trend primarily arises due to the significant overlap of beam footprints. Figure 8 visually represents the beam topology and footprints at \(t=0\) and \(t=100\) for the 3 GPP setting and FRF3. It illustrates how the beam footprints expand, particularly at low elevation angles, thereby reducing the angular difference between the serving beam and interfering UE, consequently leading to increased interference. Furthermore, Figure 9 shows the angular difference and antenna gain from interfering UEs to the center beam. The interfering UEs in the figure are at the center of their serving beams.