## 3 Results and Discussion
### Simulation Analysis of the Skywave OTH Channel Characteristics at 00:00 AM  
The simulation show the variations in the ray-tracing results and channel characteristic parameters at specific moments for the hypersonic vehicle (annotated with a white triangle), and the white line represents the re-entry trajectory. For example, Figure 5 presents the ray-tracing simulation results for different trajectory positions of the hypersonic vehicle. Figure 5a shows the ray-tracing trajectory at a re-entry distance of 1081.239 km and a time of 393.4 s for the RAM C II vehicle. Figure 5b corresponds to a re-entry distance of 1130.692 km and a time of 400.4 s. Figure 5c represents the ray-tracing trajectory at a re-entry distance of 1253.401 km and a time of 418.4 s. The ray trajectories (in red) presented in Figure 5 exhibit dynamic variations, which distinguishes them from traditional point-to-point shortwave channel ray-tracing scenarios where both the transmitter and receiver antennas remain stationary. Figure 6 shows the calculation results of channel characteristic parameters under ray tracing corresponding to Figure 5, such as corresponding loss, delay, and Doppler parameters. Specifically, in Figure 5, the ray can be categorized into high- and low-angle states. At the initial stage (393.4 s), there are two high-elevation-angle paths: a non-ground reflection path (path 1) and ground reflection paths (paths 3 and 4). As the flight trajectory changes, the high-elevation reflection paths 3 and 4 gradually split into two distinct ground reflection paths. During the final stage of re-entry, these evolve into a high-elevation ground reflection path (path 3) and a low-elevation ground reflection path (path 4). In the corresponding loss parameters in Figure 6a, due to the ground reflection loss of paths 3 and 4, the loss is approximately 2 dB higher than that of paths 1 and 2. In the corresponding delay parameters in Figure 6b, it can be observed that the delay gradually evolves from three initial values to four values. The delays of paths 3 and 4 progressively approach the delays  
Figure 4: The range of the vehicle varies with altitude and speed. Figure 5: Ray-tracing results of vehicle in spring at 00:  
of paths 1 and 2, respectively. In Figure 6c, the Doppler dynamic process of path 4 initially increases and then decreases after 415 s. This is because the change in the angle \(\theta\) between path 4 and the flight trajectory follows a process of first increasing, then decreasing, and finally increasing again, with a dynamic range of variation not exceeding 90\({}^{\circ}\). In other words, the cosine of the angle, \(\cos\theta\), first increases and then decreases. In Figure 7, during the dynamic changes in the high-elevation paths (1 and 2) and the low-elevation paths (5 and 6) at the beginning, ground reflection paths (3 and 4) are suddenly generated at 413.6 s. Subsequently, the ground reflection paths (3 and 4) gradually split, with their elevation angles approaching those of paths 1 and 2, respectively, forming paths 3 and 4. According to the channel delay parameters in Figure 8b, this is consistent with the above evolution process, where the delays of paths 3 and 4 gradually approach the delays of paths 1 and 2, respectively. In Figure 9, the initial number of multipaths in the channel is six. As the re-entry trajectory dynamically changes, the low-elevation paths (5 and 6) gradually converge. At 406.1 s, the two paths merge into one path, path 5, which disappears at 410.8 s, reducing the number of multipaths to four (1, 2, 3, and 4). In Figure 10b, the delay parameters of paths 5 and 6 also show a dynamic process of gradual merging and disappearance. For the Doppler frequency of path 4 in Figure 10c, similar to the situation in Figure 6c, it follows a dynamic process of first increasing and then decreasing. Figure 6: Characteristic parameters of the multipath channel during re-entry in spring at 00:00 AM: (**a**) loss; (**b**) delay; (**c**) Doppler.