## 6 Experimental Verification and Analysis
### Analysis of Inter-Satellite Topology Characterization  
Based on the ISL dynamic constraint model established in Section 2, and taking into account both Earth occlusion and antenna beam scanning limitations, an analysis of inter-satellite visibility was conducted. Figure 9 presents the visibility analysis results for satellite MEO\({}_{11}\) with all other satellites in the BDS-3 constellation.  
During the simulation period, satellite MEO\({}_{11}\) maintained continuous visibility with 8 satellites, permanent invisibility with 3 satellites, and intermittent visibility with 18 satellites. Figure 10 illustrates the variation in the number of visible satellites for MEO\({}_{11}\) throughout the simulation period. As shown in the figure, the maximum number of simultaneously visible satellites for MEO\({}_{11}\) was 23, the minimum was 15, and the average stood at 19.1602.  
The BDS-3 constellation features four distinct types of ISLs: MEO intra-orbit links (same orbital plane), MEO inter-orbit links (same altitude but different planes), MEO-GEO/IGSO cross-layer links, and GEO/IGSO-GEO/IGSO high-altitude crosslinks. After completing the inter-satellite visibility analysis, we further examined the inter-satellite distances and their rates of change. Figure 11 shows the inter-satellite distance characteristics for the four types of links in the BDS-3 constellation.  
Figure 8: 2D simulation scenarios of the BDS-3 constellation.  
Figure 9: Visibility analysis of satellite MEO\({}_{11}\) and other satellites in the BDS-3 constellation.  
Figure 11 presents the inter-satellite distance characteristics of the BDS-3 constellation. Subfigure (a) shows the distances between satellite MEO\({}_{11}\) and its co-orbital satellites,  
Figure 11: BDS-3 constellation inter-satellite distance characteristics.  
Figure 10: Variation in the number of visible satellites for satellite MEO\({}_{11}\).  
which remain essentially constant with a maximum distance of approximately 51,920 km and a minimum distance of about 39,342 km. Subfigure (b) displays the distances between MEO\({}_{11}\) and satellites in the second orbital plane, ranging from a minimum of 27,909 km to a maximum of 53,948 km. Subfigure (c) illustrates the distances between MEO\({}_{11}\) and high-altitude GEO/IGSO satellites, with maximum and minimum distances of about 68,609 km and 48,301 km, respectively. Finally, subfigure (d) demonstrates the distance characteristics between high-altitude GEO/IGSO satellites themselves, varying between approximately 42,164 km and 63,386 km. Figure 12 illustrates the characteristics of inter-satellite range rates for the four types of links.  
Figure 12 presents the analysis of inter-satellite range rate characteristics for the BDS-3 constellation. Subfigure (a) shows the range rate between satellite MEO\({}_{11}\) and its co-orbital satellites, demonstrating minimal variation with a maximum value of only about 0.001 km/s. Subfigure (b) displays the range rate between MEO\({}_{11}\) and satellites in the second orbital plane, reaching a maximum of approximately 3.781 km/s. Subfigure (c) illustrates the range rate between MEO\({}_{11}\) and high-altitude GEO/IGSO satellites, peaking at around 3.803 km/s. Finally, subfigure (d) depicts the range rate characteristics between high-altitude GEO/IGSO satellites themselves, with a maximum value of about 3.179 km/s.  
Figure 12: BDS-3 constellation inter-satellite range rate characteristics.  
Through the analysis of inter-satellite distances and range rates in the BDS-3 constellation, it is evident that the maximum inter-satellite distance reaches approximately 68,600 km, while the minimum is about 27,900 km--a difference exceeding 40,000 km. Additionally, the maximum range rate reaches approximately 3.8 km/s, fully demonstrating the high dynamicity and complex variability of inter-satellite motion in the BDS-3 system.