Skywave Ionosphere Communication Channel Characteristics for Hypersonic Vehicles at a Typical Frequency of 14 MHz

Abstract

This study starts from the physical perspective of electromagnetic wave propagation in ionosphere media, and the skywave OTH (over-the-horizon) ionosphere channel model is established for hypersonic vehicles based on the ray-tracing method, and this study identifies the key parameters influencing channel characteristics. Secondly, using the re-entry trajectory of the RAM C-II flight experiment as an example, dynamic multipath channel characteristic parameters—such as loss, delay, and Doppler shift—are analyzed in multiple seasons during the noon and midnight periods at a communication frequency of 14 MHz. The results indicate that the settling effect of the ionosphere at midnight makes the changes in the channel more complex, with the irregular sudden appearance and disappearance of multipath numbers. In addition, channel loss is greater in low-elevation propagation mode than in high-elevation propagation mode, indicating that the channel multipath exhibits high loss and low delay characteristics. The skywave communication channel model for hypersonic vehicles, and the dynamic multipath channel characteristic parameters presented in this study offer valuable support for the design, development, and evaluation of long-distance TT&C (Tracking, Telemetering, and Command) communication systems.

1. Introduction

Hypersonic vehicles have the ability to fly at hypersonic speeds in near space, with speeds reaching over Mach five. They can reach any corner of the Earth within two hours, greatly reducing flight time and possessing the ability to break through all current ground military defense equipment [1,2,3]. Therefore, hypersonic vehicles have broad applicational prospects in both civilian and military fields, and research on their related technologies is receiving increasing attention both domestically and internationally [4,5,6,7]. When a vehicle flies at hypersonic speed in the atmosphere, it violently impacts the air. At the front of the vehicle, the air is compressed violently, producing a very strong bow shock wave. Shock waves convert some of the kinetic energy of a hypersonic vehicle into thermal energy, which is then transmitted into the air to form high-temperature gases. Due to friction between high-temperature air and the surface of the vehicle, the gas near the surface of the vehicle further heats up, and a large number of air molecules are thermally ionized into ions, electrons, and charged particles. In addition, the surface of the vehicle will also be eroded by high-temperature gases, and the ablation products will participate in complex chemical processes. Subsequently, a layer of high-temperature charged gas is formed, covering the flight surface, known as a plasma sheath [8,9,10,11].

When high-density free electrons interact with incident electromagnetic waves, charged particles in the plasma, especially free electrons, oscillate. The plasma sheath strongly absorbs and reflects electromagnetic waves, which attenuate the energy of communication signals. At the same time, due to the instability of hypersonic flow fields, the parameters of the plasma sheath medium vary randomly in space and time, adding severe multiplicative interference to communication signals and causing waveform distortion and spectral dispersion of signals. Conventional TT&C (Tracking, Telemetering, and Command) communication signals are difficult to receive and correctly demodulate, and in severe cases, communication interruptions and “blackouts” occur [12,13,14]. At present, the mainstream means to alleviate a “blackout” mainly include the following: (1) designing a more reasonable vehicle shape to reduce gas ionization on the surface of the vehicle [15,16]; (2) releasing electrophilic liquids, neutralizing free electrons, and reducing the electron density of the plasma sheath [17,18]; (3) with an additional magnetic field, utilizing Lorentz force to displace electrons and form low-density regions [19,20,21]; and (4) changing the carrier frequency of communication signals, utilizing the characteristics of plasma media to find communication windows, and improving the energy transmittance of electromagnetic waves [22,23]. The first three physical methods can alleviate the influence of plasma sheaths on electromagnetic signals to a certain extent, but the shape design is constrained by various factors, such as the vehicle’s volume and function, and cannot unilaterally align with the rationality of an aerodynamic shape. Electronic liquids and high-grade magnets are difficult to achieve a lightweight design and require a large amount of vehicle load. Therefore, changing the carrier frequency of communication signals has become the most easily breakthrough communication method for hypersonic vehicles.

There are two main methods for changing communication frequency: the high-frequency method and the low-frequency method: (1) Plasma is a dispersive medium. When the frequency of electromagnetic waves (terahertz band) is greater than the frequency of plasma, the attenuation effect of plasma decreases, and electromagnetic waves can effectively penetrate the plasma sheath [24,25,26]. However, high-frequency electromagnetic waves will suffer from more severe path loss and atmospheric loss, requiring the use of satellites to achieve signal coverage and limiting the communication transmission distance. Secondly, due to the high maneuverability of the aircraft, it can be extremely difficult to effectively align the TT&C communication station with the vehicle antenna window. (2) Using lower frequency electromagnetic waves for communication can reduce the electromagnetic shielding effect of the plasma sheath. When the electromagnetic wave length is greater than the physical size of the plasma sheath, the electromagnetic wave frequency is much lower than the plasma frequency and collision frequency. At this point, the electromagnetic wave electric field component is severely attenuated by the plasma sheath, while the magnetic field component can penetrate the plasma sheath with minimal attenuation [27,28]. Therefore, magnetic receiving devices can be deployed inside the vehicle to sense magnetic field component signals for communication. In addition, compared to high-frequency electromagnetic waves, short waves (3 MHz–20 MHz) are less affected by path loss and atmospheric loss and can use ionospheric reflection to achieve OTH (over-the-horizon) communication. The shortwave beam has a wide coverage range, eliminating the need for the widespread deployment of ground TT&C communication stations and saving satellite communication resources. However, the ionosphere changes with time and space, making the propagation of skywaves more complex. The focus of this study is to explore the characteristics and laws of the impact of ionospheric spatiotemporal changes on the skywave ionosphere communication channel of hypersonic vehicles.

Since the 20th century, there has been growing interest in research on skywave ionospheric propagation [29,30]. In terms of skywave channel modeling, researchers have made further improvements based on the following two types of models: The first type of model is the Gaussian scattering model, proposed by Watterson et al. based on long-term measurement research on ionospheric reflection channels [31]. This model later became the standard channel model recommended by the International Telecommunication Union (ITU) for testing skywave communication performance [32]. However, in applications that are restricted to narrowband channel models, the effective bandwidth of the Watterson model cannot exceed 12 kHz [33,34,35,36]. The second type of model is a statistical model developed by the Institute of Telecommunication Sciences (ITS) in the United States. This model includes three modules, namely, a delay power spectrum, Doppler frequency shift, and Doppler spread, making it suitable for both broadband and narrowband communication [37]. However, the above research focused on the channel characteristics of the time-varying ionosphere within a fixed airspace, specifically the reflection propagation from one fixed point to another (where both the receiver and transmitter are stationary). For a hypersonic vehicle moving across a large airspace, the ionosphere can be considered a stationary, non-drifting scattering/reflection surface. In this case, the channel characteristics depend on the structure of the ionospheric reflection surface and the maneuvering characteristics of the vehicle. Due to differences in flight altitude, the significant delay caused by OTH propagation, the multipath variations induced by irregular ionospheric structures, and the Doppler effect resulting from vehicle motion, the conditions differ from those of traditional channels. The fundamental differences in the physical factors causing channel variations make it impossible to directly apply traditional skywave channel models to hypersonic vehicle skywave ionospheric channels. Furthermore, in the future, hypersonic vehicles will require high-bandwidth communication systems capable of supporting long-distance (above 1000 km) flight control operations. According to the ITU’s recommendations for selecting frequencies throughout the day based on the lowest usable frequency (LUF) and the highest usable frequency (MUF), the commonly used radio frequency bands are 7 MHz and 14 MHz. Compared to the 7 MHz band, the 14 MHz band not only offers a higher bandwidth but also benefits from its higher frequency. This allows electromagnetic waves to penetrate more low-altitude ionospheric layers and reflect off higher ionospheric points, enabling longer-distance communication [38]. As a result, it is a suitable choice for our model. To address the aforementioned issues, this study focuses on investigating skywave ionosphere communication channel characteristics at 14 MHz for hypersonic vehicles.

In Section 2, a skywave ionosphere channel for hypersonic vehicles is defined. Based on the calculation method of electromagnetic wave propagation in ionospheric media, key dynamic parameters that affect channel characteristics, such as delays, Doppler shifts, and losses, are analyzed and derived. In Section 3, using the re-entry trajectory of the RAM-C II vehicle as an example, the IRI ionospheric model and the NRLMSIS-00 atmospheric background molecular model are applied to analyze and discuss the dynamic characteristics of multipath channels and possible propagation states in multiple seasons during the noon and midnight periods. Finally, a summary of the entire paper is provided, along with a brief discussion on future research that needs to be conducted.

2. Skywave Ionosphere Channel for Hypersonic Vehicles

During the OTH propagation of hypersonic vehicles, multipath fading is caused by ionospheric reflections, as shown in Figure 1.

Based on the above propagation conditions, let the baseband signal be s(t), and the carrier modulation (transmission signal) of the baseband signal is denoted as s(t)e^j2πft, where f is the carrier frequency, and e^j2πft has an exponential complex number derivation process, derived from Euler’s formula. Therefore, the received signal be written as

$$y(t)={\displaystyle \sum _1^{N(t)}{h}_k(t)s(t-{\tau }_k(t))e^{j2\pi (f+f_{dk}(t))(t-{\tau }_k(t))}}$$

(1)

where N (t) is the number of multipaths at time t; f_dk (t) and τ_k (t) represent the k-th path’s Doppler frequency and delay, respectively; and h_k (t) represents ionospheric fading for the k-th path.

According to Equation (1), the parameters that affect a skywave ionosphere channel are f_dk (t), τ_k (t), and h_k. In fact, time-varying characteristics of the communication channel, including Doppler effects, delays, and attenuation, significantly impact system performance. Doppler effects cause frequency shifts and broadening, leading to difficulties in signal demodulation and increased error rates. Delays result in multipath interference and inter-symbol interference, reducing signal quality. Attenuation leads to a decreased signal-to-noise ratio (SNR) and signal fading, affecting communication reliability. Therefore, analyzing the dynamic changes in channels and designing and optimizing communication systems with targeted approaches is the foundation for achieving a high-quality and stable signal transmission.

The physical environment of the ionosphere in channel propagation belongs to the category of plasma. According to classical theory, plasma can be considered a special conductive dispersion loss medium. In what follows, the propagation theory of the ionosphere in skywave is used to derive the multipath fading and Doppler calculation of the skywave ionosphere channel for hypersonic vehicles.

The skywave ionosphere channel fading h_k consists of two components:

$$h_k(t)=l_{ak}(t)\cdot a_{iok}(t)$$

(2)

where l_ak (t) includes free-space attenuation, ground reflection loss, and other additional losses, which are detailed in the ITU recommendations for predicting skywave transmission loss and field strength distribution (ITU-R.P series) [39,40,41]; they are not discussed in this section. Aside from the aforementioned losses, the absorption loss of the ionosphere a_iok (t) is the focus in this section.

Before radio waves enter the ionosphere, neutral molecules and ions, along with electrons, undergo diffuse and irregular thermal motion. When radio waves enter the ionized gas, free electrons experience harmonic motion under the influence of the incident wave’s electric field. In general, moving electrons also collide with other particles, transferring the kinetic energy gained from the radio waves to neutral molecules and ions, resulting in thermal energy loss, known as an ionospheric absorption loss of radio waves. There are two types of ionospheric absorption losses: an offset absorption loss and a non-offset absorption loss. Offset absorption is generally less than 1 dB and can be ignored [42]. Therefore, this section primarily focuses on the impact of non-offset absorption on electromagnetic waves. For non-offset absorption, the attenuation coefficient of electromagnetic waves in the ionosphere is given by

$${\alpha }_{iok}=\omega \sqrt{{\displaystyle \frac{{\mu }_0{\epsilon }_0}{2}}\left[\sqrt{{\epsilon }_r^2+{(60\lambda \sigma )}^2}-{\epsilon }_r\right]}$$

(3)

where ω is the electromagnetic wave angular frequency, ω = 2πf, λ = f/c, c is speed of light, μ₀ represents the magnetic permeability in a vacuum (4π × 10⁻⁷ N·A⁻²), ε₀ is the vacuum dielectric constant (8.854 × 10¹² F/m), ε_r is the equivalent relative dielectric constant, and σ is the conductivity of the plasma [43,44]:

$$\sigma ={\displaystyle \frac{e^2{N}_e{\upsilon }_{en}}{m_e\left({\omega }^2+{\upsilon }_{en}^2\right)}}$$

(4)

$${\epsilon }_r=1-{\displaystyle \frac{e^2{N}_e}{m_e{\epsilon }_0\left({\omega }^2+{\upsilon }_{en}^2\right)}}$$

(5)

where λ is the electromagnetic wavelength, e is the electron charge (1.6 × 10⁻¹⁹ C), N_e is the electron density of the plasma (electrons/m³), m_e is the electron mass (9.1 × 10⁻³¹ kg), υ_en is the plasma collision frequency in radians (rad/s), υ_en = 2πυ_e, and υ_e is the plasma collision frequency (Hz).

The total attenuation (absorption loss) of radio waves propagating through the ionosphere is given by

$$a_{iok}(t)=e^{-{\displaystyle \int {\alpha }_{iok}(t)}dl(t)}$$

(6)

To calculate the total distance l(t) of skywave propagation through the ionosphere, it is essential to determine the position of the path as it passes through the ionosphere. The calculation of the propagation path of radio waves in ray tracing is carried out incrementally, starting from the initial values of a set of given variables in the Haselgrove equation [45]. In the spherical coordinate system, the component of the wave vector in spherical coordinates is defined as a = (k_r, k_φ, k_θ), where k_r is vertical to the upward direction of the ground, k_φ is the east direction, and k_θ is the south direction.

Due to the fact that collision effects primarily cause energy absorption and have minimal impact on the propagation path of signals, only the ray path is considered in the calculations, and collision effects are ignored [46]. Without considering the geomagnetic field, the Haselgrove differential equation, which is based on the group path P′ of skywave propagation, is solved as follows [47]:

$$\left\{\begin{array}{l}{\displaystyle \frac{dr}{d{P}^{\prime }}}={\displaystyle \frac{c}{\omega }}{k}_r\\ {\displaystyle \frac{d\theta }{d{P}^{\prime }}}={\displaystyle \frac{c}{\omega r}}{k}_{\theta }\\ {\displaystyle \frac{d\phi }{d{P}^{\prime }}}={\displaystyle \frac{c}{r\omega \sin \theta }}{k}_{\phi }\\ {\displaystyle \frac{d{k}_r}{d{P}^{\prime }}}=-{\displaystyle \frac{\omega }{2c}}{\displaystyle \frac{\partial X}{\partial r}}+k_{\theta }^2{\displaystyle \frac{c}{r\omega }}+k_{\phi }^2{\displaystyle \frac{c}{r\omega }}\\ {\displaystyle \frac{d{k}_{\theta }}{d{P}^{\prime }}}={\displaystyle \frac{1}{r}}(-{\displaystyle \frac{\omega }{2c}}{\displaystyle \frac{\partial X}{\partial \theta }}-k_r{k}_{\theta }{\displaystyle \frac{c}{\omega }}+k_{\phi }^2{\displaystyle \frac{c}{\omega }}\cot \theta )\\ {\displaystyle \frac{d{k}_{\phi }}{d{P}^{\prime }}}={\displaystyle \frac{1}{r\sin \theta }}(-{\displaystyle \frac{\omega }{2c}}{\displaystyle \frac{\partial X}{\partial \phi }}-k_r{k}_{\phi }{\displaystyle \frac{c}{\omega }}\sin \theta +{\displaystyle \frac{c}{\omega }}{k}_{\theta }{k}_{\phi }\cos \theta )\end{array}\right.$$

(7)

where (r, θ, φ) is the spherical coordinate of the skywave ray path, and c is the speed of light, where

$$X={\displaystyle \frac{{\omega }_p^2}{{\omega }^2}}={\displaystyle \frac{N_e{e}^2}{m_e{\epsilon }_0{\omega }^2}}=80.8{\displaystyle \frac{N_e(r,\theta ,\phi )}{f^2}}$$

(8)

The ∂X/∂r, ∂X/∂θ, and ∂X/∂φ values depend on specific ionospheric plasma parameters [48]:

$$\begin{array}{c}{\displaystyle \frac{\partial X}{\partial r}}\approx {\displaystyle \frac{80.8}{f^2}}{\displaystyle \frac{N_e\left(r+\Delta r,\theta ,\phi \right)-N_e\left(r,\theta ,\phi \right)}{\Delta r}}\\ {\displaystyle \frac{\partial X}{\partial \theta }}\approx {\displaystyle \frac{80.8}{f^2}}{\displaystyle \frac{N_e\left(r,\theta +\Delta \theta ,\phi \right)-N_e\left(r,\theta ,\phi \right)}{\Delta \theta }}\\ {\displaystyle \frac{\partial X}{\partial \phi }}\approx {\displaystyle \frac{80.8}{f^2}}{\displaystyle \frac{N_e\left(r,\theta ,\phi +\Delta \phi \right)-N_e\left(r,\theta ,\phi \right)}{\Delta \phi }}\end{array}$$

(9)

Based on the initial r, θ, φ, and a, the ray equation can be solved iteratively via the step size of the group path P’. This allows for the calculation of r, θ, φ, k_r, k_φ, and k_θ for each point along the ray path, and, by connecting these points, the trajectory of the skywave propagation can be obtained in a spherical coordinate system. If electromagnetic waves are emitted from the ground, the latitude and longitude of the emission point are denoted by λ₀ and φ₀, respectively. The launch angle starts from the south direction of the ground, with the positive direction pointing towards the zenith, denoted as β₀. The launch azimuth starts from the northern direction on the ground and is considered positive when measured clockwise, denoted as α₀. The initial values for the Haselgrove equation system for rays are set as follows:

$$\left\{\begin{array}{l}{r}_0=R_0\\ {\theta }_0={\displaystyle \frac{\pi }{2}}-{\lambda }_0\\ {\phi }_0={\phi }_0\\ k_{r0}=k\cos ({\displaystyle \frac{\pi }{2}}-\beta )={\displaystyle \frac{\omega }{c}}\sin {\beta }_0\\ k_{\theta 0}=-k\cos \beta \cos \alpha =-{\displaystyle \frac{\omega }{c}}\cos {\beta }_0\cos {\alpha }_0\\ k_{\phi 0}=k\cos \beta \cos ({\displaystyle \frac{\pi }{2}}-\alpha )={\displaystyle \frac{\omega }{c}}\cos {\beta }_0\sin {\alpha }_0\end{array}\right.$$

(10)

where R₀ is the radius of the Earth, typically taken as 6371 km.

As shown in Figure 2, let (r_M, θ_M, φ_M) be the k-th ray that reaches the current position of the vehicle, where M represents the total number of iterations for group path P′ at time t. In Formula (6), ${\displaystyle \int {\alpha }_{iok}(t)}dl(t)$ can be written as

$${\displaystyle \int {\alpha }_{iok}(t)}dl(t)={\displaystyle \sum _1^{i=M}\omega \cdot sqrt\left(\frac{{\mu }_0{\epsilon }_0}{2}\left(\sqrt{{\epsilon }_r^2(r_i,{\theta }_i,{\phi }_i)+{(60\lambda \sigma (r_i,{\theta }_i,{\phi }_i))}^2}-{\epsilon }_r(r_i,{\theta }_i,{\phi }_i)\right)\right)\cdot d^{\prime }(r_i,{\theta }_i,{\phi }_i)}$$

(11)

where l (t) is the ray path traveled by the electromagnetic wave from the emission point to the vehicle. The conductivity and equivalent relative dielectric constant of the ionosphere at this location are σ (r_i, θ_i, φ_i) and ε_r (r_i, θ_i, φ_i). d′ (r_i, θ_i, φ_i) is the distance between the previous ray trajectory position point (r_i−1, θ_i−1, φ_i−1) and this ray trajectory position point (r_i, θ_i, φ_i):

$$d^{\prime }(r_i,{\theta }_i,{\phi }_i)=\sqrt{r_i^2+r_{i-1}^2-2r_i{r}_{i-1}\left[\left(\sin {\theta }_i\sin {\theta }_{i-1}\cos ({\phi }_i-{\phi }_{i-1})+\cos {\theta }_i\cos {\theta }_{i-1}\right)\right]}$$

(12)

For skywave OTH channels, the Haselgrove ray equation is used for iterative propagation within the medium. If the ray path reaches the ground, the iteration terminates, and the complete ray path cannot be fully estimated. Typically, as the distance between the vehicle and the launch station increases, the ray (signal) experiences multiple reflections between the ionosphere and the ground before reaching the vehicle. Therefore, updating the elevation angle β_u of the ground-reflected ray during the iteration process is crucial, where u is the number of times the ray is reflected to the ground.

As shown in Figure 2, the distance from the bottom of the ionosphere to the center of the Earth is R_b = 60 + R₀ = 6431 km. Given that the trajectory of the ray passing through the ionosphere at point A is (r_j, θ_j, φ_j) and that the ray reaching the ground at position C (r_o, θ_o, φ_o), the elevation angle β can be determined according to the geometric relationship shown in Figure 2:

$${\beta }_u=\arcsin \left({\displaystyle \frac{R_{\mathrm{b}}\cos {\gamma }_{j,o}-R_0}{\sqrt{R_{\mathrm{b}}^2+R_0^2-2R_{\mathrm{b}}{R}_0\cos {\gamma }_{j,o}}}}\right)$$

(13)

The cosine of angle γ_j,o when the ray passes through the ionosphere and reaches the ground is

$$\cos {\gamma }_{j,o}=\sin {\theta }_j\sin {\theta }_o\cos ({\phi }_j-{\phi }_o)+\cos {\theta }_j\cos {\theta }_o$$

(14)

At this point, the complete skywave ionosphere channel fading (loss), h_k (t), can be calculated.

It is clear from Equation (1) that in addition to h_k affecting the characteristics of the skywave ionosphere channel for a hypersonic vehicle, the time delay and Doppler of each path also play a significant role in shaping the channel characteristics. From the above deduction, it can be inferred that the k-th channel Doppler frequency and delay is f_dk (t) = −f·v·cosθ_k (t)/c and τ_k (t) = MP’/c, respectively. θ_k(t) is the angle between the k-th wave vector k and the flight direction (vehicle vector velocity v), as shown in Figure 2. In the next section, we focus on analyzing parameters such as losses, delays, and Doppler effects, which influence the skywave ionosphere channel characteristics of hypersonic vehicles.

The atmospheric ionosphere is generally located above 60 km, and the reflection height of a 14 MHz skywave is below 400 km. Therefore, we set the ionospheric height range to 60 km–600 km. The ionospheric model, used as the propagation medium for subsequent skywave trajectory simulations, employs the internationally recognized and well-established IRI-2020 (International Reference Ionosphere 2020) numerical model. This semi-empirical model is based on historical measurement data and includes electron density and collision frequency data across different latitudes, longitudes, and altitudes. The ionosphere has cloud-like structures of different ionization densities, referred to as ionospheric irregularities, which are small-scale structures with random temporal and spatial distributions, lacking universal applicability or sufficient empirical support. Hence, our study utilizes the IRI-2020 ionospheric model as the background ionosphere to quantitatively describe its spatial variation.

The ray-tracing method employed in this study is based on Haselgrove’s differential equations, a well-established numerical technique widely applied in skywave channel calculations [46,47,48]. To verify the accuracy of the ray-tracing algorithm, we conducted a historical comparative validation using a study by Mitran et al. [49] and selected the ionospheric IRI data model for a region (24.15E 45.8N to 26.15E 45.8N) at 10:10:00 UTC (Coordinated Universal Time) on 10 October 2012 for ray tracing. Figure 3 shows the ray trajectory at an elevation angle of 60°–70° and a frequency of 6 MHz. Figure 3a shows the ray-tracing trajectory results from reference [23], while Figure 3b shows the ray-tracing trajectory results from our algorithm, which are consistent with previous studies and indirectly demonstrate the effectiveness of our method.

The 2D ray-tracing algorithm has been widely applied in shortwave communication studies [49,50] and has shown strong agreement with empirical, measured data [51,52]. One study [53] explicitly states the reliability of 2D ray tracing: “The 2-D numerical ray tracing was considered adequate for this work as OTHR modeling done by Cervera et al. [54] found that 2-D numerical ray tracing was sufficient to characterize the performance of an OTH radar”. Therefore, the influence of azimuth angle α was ignored in this study.

3. Results and Discussion

The time-varying skywave ionosphere channel for hypersonic vehicles primarily depends on the vehicle’s maneuvering characteristics. To describe the dynamic process of trajectory changes in hypersonic vehicles and their impact on ray-tracing results, the ray-tracing results at the first, middle, and last three moments during the re-entry period were selected for simulation. A simulation analysis was performed on the loss, delay, and Doppler effects for each channel over the entire re-entry time.

In this section, the IRI-2020 ionospheric model served as input for propagate physical environment data, and the NRLMSIS-00 atmospheric background molecular model served as input for the ionospheric electron collision frequency model proposed by Peter Banks [55]. The vehicle launched from Xi’an and flew due south, with the flight trajectory based on the RAM C II re-entry experiment [56,57,58,59,60], and the elevation angle of the ray emission ranged from 0° to 90°. Figure 4 shows that the range of the vehicle varied with altitude and speed. To ensure generality of the comparison between the ray-tracing results at midnight and noon, ionospheric model data from multiple seasons (vernal equinox, summer solstice, autumnal equinox, and winter solstice) at 00:00 a.m. and 12:00 p.m. were selected. The path with the minimum loss was defined as the main path of the channel (1st path/path 1).

3.1. 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 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 θ 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°. In other words, the cosine of the angle, cos θ, 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.

From the perspective of the dynamic propagation of rays and the overall characteristics of multipath channel parameters during re-entry, as the re-entry time progresses, the flight distance gradually increases, the flight altitude decreases, and the delay caused by OTH propagation gradually increases. For the Doppler frequency, most paths exhibit a decreasing trend, while a few paths show a dynamic process of first increasing and then decreasing. Secondly, the skywave OTH channel of hypersonic vehicles is affected by multipath propagation, where the number of multipath components may suddenly increase or disappear. Phenomena such as the merging of two paths or the splitting of one path into two can occur, and the loss, delay, and Doppler characteristics of each path may dynamically change, resulting in distinct behaviors. Furthermore, the channel exhibits the minimum loss and maximum delay at high-elevation angles, and vice versa. In particular, Figure 11 shows that the propagation trajectory of the wave fails to intersect with the vehicle’s re-entry trajectory, creating a hollow area where the vehicle cannot receive OTH signals.

3.2. Simulation Analysis of the Skywave OTH Channel Characteristics at 12:00 PM

Overall, as shown in Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19, compared with midnight, the number of skywave OTH channel paths for the hypersonic vehicle remains at four, with dynamic changes in the loss, delay, and Doppler of each path. The paths can be divided into two groups: low-elevation-angle paths, consisting of non-ground reflection path 1 and ground reflection path 3, and high-elevation-angle paths, consisting of non-ground reflection path 2 and ground reflection path 4. When the channel is at a high elevation angle, the loss is the highest, and the corresponding delay is the smallest, which is the opposite of what occurs at midnight (00:00). In particular, as shown in Figure 17c, the fourth path shows a positive Doppler value after 142.5 s, because the angle θ between the propagation direction of the ground reflection path in the high-elevation state and the vehicle’s velocity direction exceeds 90°.

From the above analysis, two differences between 00:00 AM (midnight) and 12:00 PM (noon) can be identified. On the one hand, the main path (first path) of the midnight channel, which is the path with the lowest loss, occurs at a high elevation angle rather than a low elevation angle, and its delay is the longest. However, at noon, the main path of the channel (the first path), characterized by the lowest loss, occurs at a low elevation angle rather than a high elevation angle and exhibits the shortest delay. On the other hand, the number of multipath channels at midnight is significantly higher than at noon, and the variations in the multipath channels at midnight are more unstable. In fact, the underlying reason for the two phenomena mentioned above is that the electron density in the ionosphere is significantly higher at low-elevation angles at midnight than at noon, reflecting the occurrence of the ionospheric “settling” phenomenon during midnight. Although the maximum electron density during the day is significantly higher than at midnight, in the 60–130 km range where ionospheric absorption occurs, the electron density at noon is notably lower than at midnight, and the altitude of the maximum electron density at noon is significantly lower than that at midnight. At noon, the low electron density in the 60–130 km region has minimal impact on the channel loss, and the multipath loss is largely influenced by the path length. As the low-elevation path is shorter than the high-elevation path, its loss is consequently smaller than that of the high-elevation path. In contrast, at midnight, the electron density in the 60–130 km region is high, and the channel loss is significantly influenced. Low-elevation paths are concentrated in the absorption zone with a high electron density (high loss), whereas high-elevation paths largely avoid this region (low loss). Because high-elevation paths have longer propagation distances (resulting in greater delays), their loss is ultimately smaller than that of low-elevation paths. It is precisely due to the ionosphere’s settling effect that the space available for ray tracing becomes “narrower” during the midnight period, leading to a greater number of channel paths and more complex variations than at noon.

Figure 20 shows the range of the characteristic parameter values for all path channels. It can be observed that at different times, the channel loss at midnight is greater than at noon, with the maximum attenuation (loss) reaching −134.43 dB, fluctuating mostly around −122 dB. The minimum attenuation (loss) fluctuates primarily around −119 dB. The maximum channel delay can reach 14.5 ms, with most values fluctuating around 6 ms, while the minimum delay typically fluctuates around 4 ms. The maximum Doppler for the channel fluctuates around 450 Hz, and the lowest Doppler is 0 Hz, with most values fluctuating around 150 Hz. Figure 21 shows the range of channel characteristic parameter values for the main path (1st path). It can be observed that at different times, the loss of the main path at midnight is greater than that at noon, and its delay is also higher. Due to the high elevation angle of the main path at midnight, its Doppler shift is smaller than that at noon. Figure 22 illustrates the characteristics of multipath numbers. It can be observed that compared with the stable four multipath numbers at noon, the number of multipaths varies significantly at midnight, ranging from a maximum of six to a minimum of four.

4. Conclusions

This study established a model for the skywave ionosphere communication channel in hypersonic vehicles and investigated its characteristics, filling the gaps in related fields. In analyzing the above channel parameters, it was found that the main factors affecting the channel are loss, delay, and Doppler, which undergo dynamic changes. Due to the settling effect of the ionosphere at midnight, the space available for ray tracing becomes “narrower”. The channel for hypersonic vehicles exhibits complex variations at midnight, including an increase in the number of signal paths. These paths may suddenly vanish or emerge, and phenomena such as path merging or splitting can occur. At midnight, the main path (first path), which has the minimum loss, is at a high elevation angle rather than a low elevation angle and exhibits the maximum delay, which is opposite to the noon conclusion. Importantly, most of the multipaths during re-entry involve 1–2 hop reflections at a communication frequency of 14 MHz. However, during certain periods, a cavity phenomenon may occur, and the skywave signals will not be able to reach the vehicle receiver, which could result in the failure of OTH communication. In summary, the conclusions of this study, along with the characteristic parameters of the skywave ionosphere communication channel for hypersonic vehicles, provide crucial support for the design, development, and evaluation of long-distance TT&C communication systems.

In addition to the impact of the ionosphere on the communication channels of a hypersonic vehicle, the plasma sheath wrapped around the surface of the vehicle can also cause varying degrees of attenuation of shortwave signals. Although the attenuation is smaller than that of the ionosphere, it cannot be ignored. Therefore, in subsequent research, numerical methods will be used to solve the fluid dynamic equations, analyze the three-dimensional electron density and temperature distribution around a vehicle of different shapes, and perform FDTD electromagnetic calculations of shortwave propagation in the plasma sheath. In addition, due to fluid disturbance, the shortwaves will exhibit dynamic and time-varying characteristics after penetrating the plasma sheath. How to establish such a channel model is also a direction that needs to be studied in the future.