High-Frequency Channel Modeling Based on the Multi-Source Ionospheric Assimilation Model

Abstract

In this paper, we explored how to more accurately predict the quality of high-frequency links and how to better research and improve the capabilities of high-frequency communication, reconnaissance, and positioning systems. Based on the background electron density generated by the ionospheric assimilation model and 3D ray-tracing technology, more realistic and accurate high-frequency channel parameters with physical meanings were obtained. On this basis, a complete high-frequency channel model that can be used for simulation and prediction was constructed. First, the ionospheric assimilation model, the high-frequency channel model, and the method used for calculating the parameters of the high-frequency channel model based on the background electron density generated by the multi-source ionospheric assimilation model are introduced. Then, the HF oblique sounding experiment and experimental data processing are introduced. Finally, the modeling and simulation of the high-frequency channel are compared with the HF oblique sounding experimental results. The simulation results showed that the modeling results of the high-frequency channel based on the multi-source ionospheric assimilation model proposed in this paper were similar to the HF oblique sounding experimental results. The average deviation of the difference between the simulation results and the experimental ones of the group path, the group path broadening, and the Doppler frequency shift are 29.2200 km, 17.3456 km, and 0.2121 Hz, respectively. The group delay, Doppler frequency shift, and delay broadening results calculated by the high-frequency channel model simulation were relatively accurate and could be used in high-frequency channel quality reporting and prediction, high-frequency reconnaissance and geolocation, and high-frequency radar frequency selection and positioning, etc.

1. Introduction

The ionosphere [1] is part of the Earth’s space environment. The ionosphere starts at about 60 km above the ground, with an upper boundary generally between 1000 and 1500 km. It is formed by the partial or complete ionization of the neutral components of the atmosphere by the sun’s electromagnetic radiation and particle deposition. The ionosphere not only has a layered structure in height, but its electron density also varies with day and night, seasons, latitude, and solar activity. At the same time, the ionosphere is also a random stratified medium. The spatiotemporal changes of the ionosphere directly affect the characteristics of the ionospheric channel and the propagation of radio waves, resulting in energy absorption, phase variation, propagation delay, path refraction, frequency dispersion, polarization rotation, the multipath effect, and other effects on electromagnetic signals. Among them, HF (high-frequency, 3–30 MHz) propagation is the electromagnetic wave band most closely related to the ionosphere. The formation and morphology of the ionosphere are controlled or influenced by the sun [2,3], geomagnetic field [4], and mesosphere activities. The regular variation of the ionosphere is the basic condition that determines the propagation of HF radio waves. The ionosphere’s medium properties determine that HF radio wave propagation differs from other propagation modes. Under the action of the geomagnetic field, the ionosphere becomes an anisotropic medium. The plasma in the ionosphere is immersed in the geomagnetic field and becomes magnetized plasma. The propagation of ionospheric radio waves can be dealt with by Magneto ionic theory [5,6], and the propagation law can be summarized by the famous Appleton–Hartree formula [7].

Due to the characteristic frequency of the ionosphere, the impact of the ionosphere on HF systems is significant. On the one hand, the ionosphere provides a good propagation medium for the over-the-horizon and ultra-long-range propagation of HF radio waves. On the other hand, the ionosphere has effects on the propagation of HF radio waves, such as amplitude fading, phase fluctuation, and the multipath effect, which greatly affect the HF system performance. The ionospheric coherent bandwidth also limits the available frequency band of HF radio waves. It can be said that the performance of the HF system with the ionosphere as a channel is a reflection of ionosphere changes, so the HF channel is part of the HF system. In practical engineering applications, whether the aim is to study the efficiency of HF communication systems or conduct HF reconnaissance and positioning, or even undertake HF radar frequency selection, etc., further research on the HF channel is inevitable.

Because the ionosphere is a layered, inhomogeneous, anisotropic, dispersed, random, spatiotemporal medium [8,9], the HF channel belongs to the random variable-parameter channel; that is, the transmission parameters are time-varying and irregular. For a long time, HF channel modeling [10,11,12] has been regarded as an effective means to predict the quality of the HF channel, and HF wideband channel modeling and simulation have been of great significance to the performance evaluation of HF wideband systems [13,14]. The classic HF channel models include the Watterson model [15], Milson model [16], sub-band parallel model, Vogler model, etc. Among them, the Vogler model is an HF channel model that was proposed by Vogler and Hoffmeyer of the American ITS organization [17]. Because the model was proposed based on measured data, it has become the most widely used HF wideband channel model so far. However, most of the HF channel models mentioned above are mathematical models, and no one has studied the relationship between mathematical parameters and actual physical mechanisms and the ionospheric background. In many studies, the mathematical parameters in the HF channel models are formulated by themselves or are fitted according to experimental results [18,19]. However, such an HF channel model is not a computer simulation in the true sense, and the validity of the simulation channel cannot be verified [20]. In this paper, we used ionospheric assimilation [21] to generate the background electron density and 3D ray-tracing techniques [22,23] to calculate the high-frequency channel parameters with a more realistic and accurate physical meaning. On this basis, we were able to build a complete HF channel model for simulation and effective verification.

In this paper, the background electron density was generated based on the multi-source ionospheric assimilation model, and a high-frequency channel model was established. In Section 2, we briefly introduce the ionospheric assimilation model, the HF channel model, and the method of obtaining the parameters of the HF channel model based on the background electron density calculation generated by the multi-source ionospheric assimilation model. In Section 3, we introduce the experimental content and data processing of the HF oblique sounding experiment. In Section 4, we bring in the relevant parameters of the oblique detection experiment to obtain the HF channel scattering function based on the multi-source ionospheric assimilation model and compare them with the experimental results of the oblique sounding experiment. A summary is given at the end of the article.

2. Ionospheric Assimilation Model and High-Frequency Channel Parameter Calculation Method

2.1. Ionospheric Assimilation Model

The first step of the HF channel modeling described in this paper is to obtain the real-time (or simulated prediction) ionospheric background electron density; only then can HF channel model parameter estimation be performed on this basis. In recent years, many ionospheric simulations and prediction models have been developed worldwide. According to the simulation method, they can be divided into theoretical models, empirical models, and semi-empirical models. The International Ionospheric Reference Model (IRI Model) [24] and NeQuick model [25] are commonly used empirical models in the ionospheric field. Compared with other models, the biggest advantage of empirical models is that the calculation speed is very fast. However, the average value of some of the related quantities is generally used in the modeling process. Therefore, such a model can only provide an average of the ionospheric parameters over time, making it difficult to accurately predict the actual state of the ionosphere. In contrast, using an effective data assimilation algorithm based on observed data and selecting an appropriate ionospheric model to construct the ionospheric assimilation model is more consistent with the ionospheric characteristics of each region, and is closer to the actual ionospheric conditions. Therefore, this paper used the Kalman filter data assimilation algorithm to assimilate the ionospheric electron density distribution in China and its surrounding areas, based on the VTEC data observed by GNSS [26,27] and the IRI model [28]. Then, a complete ionospheric current report (or prediction) background electron density model is constructed.

2.2. HF Channel Modeling

Attenuation, delay, delay broadening, Doppler shift, and Doppler broadening occur in HF signals transmitted through the ionosphere. For HF signal propagation, the main factors affecting channel quality are the signal-to-noise ratio (SNR), multipath broadening (delay broadening), and Doppler broadening, among which SNR is also related to the transceiver and environmental noise. Therefore, the most important ionospheric parameters affecting the HF channel quality are multipath broadening and Doppler broadening. The Doppler effect of the ionosphere causes channel frequency dispersion, which results in time-selective fading. The multipath effect of HF signal propagation causes channel time dispersion, which results in frequency-selective fading. Therefore, the HF channel can be represented as a two-dimensional time-frequency selective fading channel or a two-dimensional frequency-time dispersion channel; that is, it can be represented by a scattering function, $\sigma \left(\tau ,f\right)$, which can be obtained by the Fourier transform of the autocorrelation function of the impulse response in the HF channel. This can be written as:

$$\sigma \left(\tau ,\mathsf{\Delta }f\right)={\displaystyle {\int }_{-\infty }^{+\infty }{\displaystyle {\int }_{-\infty }^{+\infty }{h}^{\ast }\left(\tau ,t\right)h\left(\tau ,t+\mathsf{\Delta }t\right)}\exp \left(i2\pi \mathsf{\Delta }f\mathsf{\Delta }t\right)}dtd\mathsf{\Delta }t,$$

(1)

where $h\left(\tau ,t\right)$ represents the high-frequency channel impulse response, $h^{\ast }\left(\tau ,t\right)$ represents the conjugate of $h\left(\tau ,t\right)$, $\mathsf{\Delta }f=f-f_c$, $f$ is the signal frequency, $f_c$ is the carrier frequency, $\tau$ represents the delay variable, and $\mathsf{\Delta }t$ represents the time interval of the correlation function. The scattering function, $\sigma \left(\tau ,\Delta f\right)$, represents the spread of the received signal energy along the frequency and time axis.

Based on the shape of Doppler broadening, HF channel scattering function models can be divided into two types: Gaussian and Lorentzian. The mathematical model of the HF channel scattering function based on the Vogler channel model can be expressed as follows:

$$S_G\left(\tau ,f_D\right)=\sqrt{T\left(\tau \right)}\exp \left\{-\pi {\left[\left(f_D-f_B\right)/{\sigma }_f\right]}^2+i2\pi {\varphi }_0\right\}\left(\mathrm{Gaussian}\right),$$

(2)

$$S_L\left(\tau ,f_D\right)=\sqrt{T\left(\tau \right)}\exp \left(i2\pi {\varphi }_0\right){\sigma }_f{\left\{i2\pi \left(f_D-f_B\right)+{\sigma }_f\right\}}^{-1}\left(\mathrm{Lorentzian}\right).$$

(3)

In Equations (2) and (3), there are ${\sigma }_f=2\pi {\sigma }_D{\left\{s_v/\left(1-s_v\right)\right\}}^{1/2}$ (Gaussian) and ${\sigma }_f={\sigma }_D{\left\{2\pi /\left(-\ln s_v\right)\right\}}^{1/2}$ (Lorentzian), where ${\sigma }_D$ is the unilateral Doppler broadening; $s_v=A_{fl}/A$, $A$ and $A_{fl}$, respectively, represent the maximum amplitude value and the amplitude threshold (receiver threshold) of the received signal; $T\left(\tau \right)$ represents the shape factor of the received signal pulse delay broadening, $T\left(\tau \right)=A\frac{{\alpha }^{\alpha +1}}{\mathsf{\Delta }\tau \Gamma \left(\alpha +1\right)}{z}^{\alpha }{e}^{-\alpha z}$; $\alpha$ is the shape factor, which controls the symmetry of the distribution function, $z=\left(\tau -{\tau }_c\right)/\mathsf{\Delta }\tau +1$; $\tau$ is the delay variable, $\mathsf{\Delta }\tau ={\tau }_c-{\tau }_l={\tau }_c-{\tau }_u$; $\mathsf{\Gamma }(\cdot )$ is the gamma function; ${\tau }_c$ is the average delay at the center frequency, which determines the delay offset; ${\tau }_l$ and ${\tau }_u$, respectively, correspond to the minimum and maximum delays when the delay amplitude factor, $T\left(\tau \right)$, decays to $A_{fl}$; that is: $T\left({\tau }_l\right)=T\left({\tau }_u\right)=A_{fl}$; $f_D$ represents the Doppler shift variable, $f_B=f_s+\left(\tau -{\tau }_c\right)\frac{\left(f_s-f_{sl}\right)}{\left({\tau }_c-{\tau }_l\right)}$; $f_s$ is the Doppler shift at the point of delay ${\tau }_c$; and $f_{sl}$ is the Doppler shift at the point of delay ${\tau }_l$.

Comparing the HF channel scattering function model with the measured data, it was found that the Gaussian channel model was closer to the measured data. Therefore, the following elaboration is based on the Gaussian HF channel scattering function model. In this paper, the shape of the pulse delay broadening of the signal was considered as symmetric; that is: ${\tau }_c-{\tau }_l={\tau }_u-{\tau }_c$, and similarly, the shape of the pulse-Doppler broadening of the signal was also considered to be symmetrical. Therefore, after obtaining the ionospheric background electron density using the ionospheric assimilation model, it was only necessary to calculate the following five parameters to establish the HF channel scattering function model based on the Vogler model: (1) Average delay at central frequency, ${\tau }_c$, (2) unilateral delay broadening, ${\tau }_D$, ${\tau }_D={\tau }_c-{\tau }_l={\tau }_u-{\tau }_c$, (3) average Doppler shift at central frequency, $f_s$, (4) unilateral Doppler broadening, ${\sigma }_D$, and (5) the maximum amplitude of the received signal, $A$. Other required parameters, such as the receiver threshold, $A_{fl}$, refers to the actual receiver parameters, and the shape factor, $\alpha$, was uniformly set to 1. In terms of noise and interference, it was assumed that there was no interference, and the noise was gaussian white noise. In the next section, we will introduce the algorithm for estimating these four parameters (unilateral Doppler broadening cannot be calculated temporarily, so it was set to a random number).

2.3. Parameter Estimation Algorithm

2.3.1. Average Delay at the Center Frequency (Group Delay at the Center Frequency), ${\tau }_c$

When the transmitting point and the receiving point are known, and the ionospheric background electron density is obtained by the ionospheric assimilation model, the group path, $P_g$, of the radio wave propagation can be obtained by traversing the elevation angle using 3D ray-tracing. The average delay at the center frequency, ${\tau }_c$, can then be obtained by the following formula:

$${\tau }_c=\frac{P_g{\mu }_g}{c}=\frac{P_g}{c}\frac{\partial \mu \omega }{\partial \omega },$$

(4)

where $c$ is the speed of light in a vacuum, ${\mu }_g$ is the group refractive index of rays on the path, $\mu$ is the phase refractive index of rays on the path, and $\omega$ is the angular frequency of the radio waves. The relation between $\omega$ and the signal frequency, $f$, is: $\omega =2\pi f$. The phase refractive index, $\mu$, is related to the electron density along the ray path, the electron collision frequency, and the external magnetic field (the geomagnetic field), which is the famous A–H formula mentioned above. In order to simplify the calculation, ignoring the influence of external magnetic fields and collision, the group refraction index is about: ${\mu }_g\approx 1+40.3Ne/f^2$(only ordinary waves were considered this paper), where $Ne$ is the electron concentration on the ray path and $f$ is the frequency of the radio wave.

2.3.2. Unilateral Delay Broadening, ${\tau }_D$

The essence of signal delay broadening is that the signal has a certain bandwidth; that is, the propagation path of two radio waves of different frequencies within the signal bandwidth is not the same, resulting in the delay difference. Based on this idea, our method for estimating unilateral delay broadening can be attributed to the following formula:

$${\tau }_D={\tau }_c-{\tau }_l={\tau }_u-{\tau }_c,$$

(5)

where ${\tau }_c$ is the average delay at the center frequency, ${\tau }_l$ is the average delay at the lowest of the signal bandwidth frequencies, and ${\tau }_u$ is the average delay at the uppermost of the signal bandwidth frequency. The estimation method of these parameters can refer to the estimation method of ${\tau }_c$.

2.3.3. Average Doppler Shift at the Center Frequency, $f_s$

Due to the overall movement of the ionosphere, the frequency of the radio waves received by the receiving station will be offset to a certain extent from the frequency of the transmitted radio waves. The average Doppler shift, $f_s$, between the radio frequency received by the receiving station and the radio frequency transmitted is given by the following formula:

$$f_s=-\frac{1}{\lambda }\frac{dP}{dt},$$

(6)

where $\lambda$ is the wavelength of the transmitted radio wave and $P$ is the phase path during the propagation process of the radio wave. After the ionospheric assimilation model was use to obtain the ionospheric background electron density, the following formula, derived by Boldovskaya [29], can be used to estimate $f_s$:

$$f_s=-\frac{f}{c}\left(\frac{\partial P}{\partial f_m}\frac{d{f}_m}{dt}+\frac{\partial P}{\partial y_m}\frac{d{y}_m}{dt}+\frac{\partial P}{\partial h_m}\frac{d{h}_m}{dt}\right),$$

(7)

where

$$\frac{\partial P}{\partial f_m}=\frac{y_m}{f_m}\left[1-\frac{1}{2x}\left(1+x^2\right)\ln \left(\frac{1+x}{1-x}\right)\right],$$

(8)

$$\frac{\partial P}{\partial y_m}=-\left[1+\frac{1}{2x}\left(1-x^2\right)\ln \left(\frac{1+x}{1-x}\right)\right],$$

(9)

$$\frac{\partial P}{\partial h_m}=2,$$

(10)

where $x=\frac{f}{f_m}$; $f$ is the radio frequency; $f_m$ is the critical frequency of the D, E, F1, or F2 layer (resembling a parabolic layer) of the ionosphere at the intermediate reflection point (choose the layer that the ray can reach), and its relationship between the maximum value of the electron density, $N_m$, can be approximated as: $f_m\approx \sqrt{80.6N_m}$; $h_m$ is the height of the parabolic layer peak at the intermediate reflection point; $y_m$ refers to the half-thickness of the parabolic layer at the intermediate reflection point, and we refer to Titheridge’s definition [30]: $y_m=\frac{1.5\ast TE{C}_m}{N_m}$, where $TE{C}_m$ is the total electron content from the ground to the parabolic layer peak.

2.3.4. The Amplitude Peak of the Received Signal, $A$

For each ray, the formula for calculating the sky-wave electric field strength, defined in P.533-14 of the ITU report, was used, and the median electric field strength of the receiving point was estimated as follows:

$$A=136.6+P_t+G_t+20\log f-L_b\hspace{1em}dB\left(1\mu V/m\right),$$

(11)

where $f$ is the radio frequency (MHz); $P_t$ is the transmitter power (dB (1 kW)); $G_t$ is the transmitting antenna power (dB) at the desired azimuth and elevation Angle ($\mathsf{\Delta }$) relative to the isotropic antenna; and $L_b$ is the basic transmission loss of the ray path for the mode under consideration, which can be calculated by the following formula:

$$L_b=32.5+20\log f+20\log P_g+L_i+L_m+L_g+L_h+L_z,$$

(12)

where $P_g$ is the group path of radio wave propagation; $L_i$ is the absorption loss (dB) of n-hop mode; $L_m$ is the “above-the-MUF” loss; $L_g$ is the summed ground-reflection loss at the intermediate reflection point; $L_h$ is the factor to allow auroral and other signal losses; and $L_z$ is other loss.

3. HF Oblique Sounding Experiment Content and Experimental Data Processing

The distribution of stations in the experimental scheme is shown in Figure 1. The three observation stations are as follows: Wuhan (30.5°N, 114.37°E), Leshan (29.6°N, 103.75°E), and Daofu (31.0°N, 101.12°E), among which the ground distance between Wuhan and Leshan is 1031 km, and the ground distance between Wuhan and Daofu is 1273 km. The working mode is Wuhan launch; Leshan and Daofu receive synchronously. Thus, with Wuhan–Daofu and Wuhan–Leshan, two oblique sounding paths are obtained.

According to the equipment and site conditions, the transceiver antennas used by each station are as follows: Wuhan: Inverted V transmitting antenna, 8 m high; Leshan: three-wire receiving antenna, 6 m high; Daufu: Inverted V receiving antenna, 8 m high.

Experiment time: From 20 October 2020 to 28 October 2020, the fixed frequency points were selected as 4 MHz and 10.8 MHz, and the operation was unattended for 24 h.

Wuhan, Leshan, and Daofu stations used the same ionospheric sounding system of Wuhan University for observation, and specific relevant technical indicators are shown in

Table 1. Technical parameters of the ionospheric sounding system.

Indicators Category	Typical Value
Detection system	Pulse compression pseudo-random code phase modulation system
Detection methods	Fixed-frequency sounding
Peak power	200 W
Detection frequency	4 MHz/10.8 MHz
Frequency stability	≤5 × 10−8/d
Doppler range of observation	±30.5 Hz
Doppler resolution	0.06 Hz
Range resolution	7.68 km
Single observation time	300 s
Reception sensitivity	Better than –108 dBm
Receiving dynamic range	>70 dB
Signal bandwidth	40 KHz

.

For this fixed-frequency sounding experiment, it was difficult to receive low-frequency signals at any time due to the limited power and antenna form, as well as the long-distance between the transmitting and receiving stations in the experiment. During the day, the signal with a frequency of 10.8 MHz had a better reception effect, while the signals with a frequency of 4 MHz and 10.8 MHz were unable to obtain a good oblique measurement reception effect at night, and the signal with a frequency of 4 MHz could only receive the vertical measurement echo. Therefore, the analysis in this paper mainly focuses on the 10.8 MHz signal in the daytime. After pulse compression and FFT transformation of the original data, the HF channel scattering function diagram for the oblique sounding experiment was obtained. Because the antenna and receiver were not calibrated in the fixed-frequency experiment, the amplitude of the signal sampling was a relative value, so the energy of the signal on the HF channel scattering function diagram was also a relative value rather than an absolute value. Due to the large amount of data, in order not to be complicated and not to lose generality, we only selected some of the data in this paper, including the data at 00:00 LT, 10:00 LT, 12:00 LT, 14:00 LT, 16:00 LT, and 20:00 LT from 21 October 2020 to 23 October 2020.

Figure 2, Figure 3 and Figure 4 show the HF channel scattering function diagram of the received signal at Leshan station after processing. To be more intuitive, the ordinate of the scattering diagram used the group path instead of group delay, and the relationship between the group path and group delay is given by Equation (4).

Figure 5, Figure 6 and Figure 7 show the HF channel scattering function diagram of the received signal at Daofu station after processing.

Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7 show the processing results of data received from Leshan station and Daofu station. In the process of the oblique sounding experiment, the state of the ionosphere was changing with time, so the HF channels of the two links of Leshan–Wuhan and Daofu–Wuhan was also changing with time. As a result, the processing results of data were changing over time, as shown in Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7. Therefore, it is necessary to analyze the state of the ionosphere over the region of the oblique sounding experiment. Among the parameters of the HF channel scattering function, Doppler shift is the best parameter to characterize the state of the ionosphere. When the Doppler shift is a positive number, it means that the hmD, hmE, hmF1, and hmf2 (the height of the maximum electron density of the ionospheric D, E, F1, and F2 layer) descend, and it also represents an increased electron density in the ionosphere, which usually occurs in the morning and noon. From the afternoon to the evening, the Doppler shift is generally a negative number, and the change of the ionosphere is exactly the opposite. Therefore, the oblique sounding experimental data were processed to obtain the relationship between the Doppler shift of the two HF links with time, as shown in Figure 8:

After analyzing Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8, the following experimental conclusions were reached:

1.

If elliptic-like bright spots appear in the figure, it means that the receiver can receive signals reflected from the ionosphere. Because there is a stone’s throw between the two receiving sites, the HF channel variation of the Wuhan–Leshan and Wuhan–Daofu links was almost the same. For either Leshan station or Daofu station, the signal transmitted from Wuhan can be received from 10:00 to 16:00 during the day, but no signal can be received at 00:00, during the night. At 20:00, the signal could only be received at Leshan station and Daofu station on 22 October 2020.

2.

Both Leshan station and Daofu station can receive signals of two modes from 12:00 to 16:00 in the daytime, which are shown as two separate elliptic-like bright spots in the figure. The group path of the rays propagating from the E layer was smaller than that of the F layer. The delay, delay broadening, Doppler shift, and Doppler shift broadening of the rays propagating from layer E were all smaller than the corresponding parameters of the rays propagating from layer F, which is also in line with our general cognition.

3.

Because the ground distance of Daofu–Wuhan is larger than that of Leshan–Wuhan, the scattering function diagram of Daofu station was more blurred and noisy. It is worth noting that the ionospheric regions traversed by the rays of the two paths were very close to each other. It can be seen from Figure 3 and Figure 6 that the ionospheric disturbance changes on the two paths were very similar. In Figure 6, the Doppler broadening and time delay broadening of the signal received by the Daofu station during the daytime on 22 October 2020 shows that the ionosphere of the link has a strong disturbance, which can also be seen in Figure 3. Figure 2 and Figure 5 show a similar pattern.

4.

Because the signals with a frequency of 10.8 MHz were unable to obtain a good oblique measurement reception effect at night, only the state of the ionosphere during the day was analyzed. The average Doppler shifts of the Leshan–Wuhan link and the Daofu–Wuhan link are 0.0733 Hz and 0.0714 Hz, which shows that the channels of the two links are very similar. It is worth noting that the value of the Doppler shift is gradually approaching zero during this time, indicating that the ionosphere was tending to be quiet. By comparison, during the period of 14:00–19:00 LT, the change of the ionosphere is exactly the opposite. This is also very consistent with our theoretical understanding of the diurnal variation of the ionosphere and the Chapman theory. Of course, there are some exceptions. In Figure 8, there are many such cases in the Daofu–Wuhan link on 22 October and the Leshan–Wuhan link on 22 and 23 October. These circumstances may result from the rapid changes in the ionosphere. There are many physical mechanisms that lead to this, such as the irregularities in the E or F layers in the ionosphere, traveling ionosphere disturbances (TID), Magnetic storms, Magnetospheric substorms, and so on.

4. HF Channel Modeling and Simulation

In this section, the ionospheric electron density background obtained by ionospheric assimilation, combined with relevant parameters of the oblique sounding experiment (such as time, geolocation, radio frequency, antenna form, and so on), were brought into the estimation and simulation of the HF channel scattering function and compared with the oblique sounding experimental results. It is worth noting that, in Equation (11), $G_t$ is the transmitting antenna power (dB) at the required azimuth and elevation Angle ($\mathsf{\Delta }$) relative to the isotropic antenna. To obtain the parameter $G_t$, the directive gain of the transmitting and receiving antennas was simulated, and the values were assigned according to the theoretical elevation angle obtained by 3D ray-tracing. Figure 9 shows the 3D directive gain diagram by simulation of the three-wire antenna and the inverted V antenna obtained in the experiment.

The specific process of HF channel modeling and simulation was as follows:

1.

The background electron density was generated based on the multi-source ionospheric assimilation model according to the time, geolocation, and other parameters of the oblique sounding experiment.

2.

According to the radio frequency of the oblique sounding experiment, 3D ray-tracing of the traversing elevation angle was carried out. The group path (group delay), launching elevation, propagation mode, and other parameters in the process of HF radio wave propagation were determined according to the ground distance between the transceiver stations.

3.

Parameters such as propagation loss, received electric field strength, time delay broadening, and Doppler frequency shift were estimated based on the 3D ray-tracing results and the background electron density generated by the multi-source ionospheric assimilation model.

4.

In this paper, the Doppler broadening was set to be random numbers in the range of 0–0.2 Hz (E layer mode) and 0–0.25 Hz (F layer mode), and finally the HF channel was modeled according to Formula (2).

The HF channel modeling and simulation results are shown in Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15.

Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15 show the modeling and simulation results of the HF channel for Wuhan–Leshan and Wuhan–Daofu from 21 to 23 October 2020. By comparing the simulation results with the experimental results, the deviation of the difference between the simulation results and the experimental ones was obtained, as shown in

Table 2. The deviation of the difference between the simulation results and the experimental ones.

Parameter	The Deviation Value of Leshan–Wuhan Link	The Deviation Value of Daofu–Wuhan Link
Group path (km)	33.2043	25.2357
Group path broadening (km)	15.1544	19.5368
Doppler frequency shift (Hz)	0.2498	0.1744

:

By comparing Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7 with Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15, combined with Table 2, it can be found that:

1.

The HF channel modeling was more accurate in the estimation of the group path (group delay) of the HF radio wave, but there were some deviations in the calculation of Doppler and delay broadening. However, it could still be used in practical follow-up projects.

2.

The received signal electric field strength was in the range of 35–45 $dB(1\mu V/m)$.

3.

During the ionospheric quiet period, the modeling and simulation accuracy of the HF channel was more accurate, similar to the measured data. During the ionospheric disturbance period (afternoon of 22 October 2020), the HF channel modeling was quite different from the experimental results.

4.

The HF channel modeling and simulation accuracy of the Wuhan–Daofu link were slightly higher than those of the Wuhan–Leshan link, which may be because the GNSS observation station is closer to the Wuhan–Daofu link, so the ionospheric background of assimilation was closer to reality.

5. Conclusions

This stud y aimed to predict the HF link quality more accurately and to better study and improve the capabilities of HF communication, reconnaissance, and positioning systems. A complete HF channel model was constructed using ionospheric assimilation to generate the background electron density and 3D ray-tracing technology, and this was compared with the experimental data. The simulation results showed that the proposed HF channel model for simulation prediction was close to the HF oblique sounding experimental results. The average deviation of the difference between the simulation results and the experimental ones of the group path, the group path broadening, and the Doppler frequency shift are 29.2200 km, 17.3456 km, and 0.2121 Hz. The results of group delay, Doppler frequency shift, and delay broadening calculated by the HF channel model were relatively accurate and can be applied to HF channel quality reporting and prediction, HF reconnaissance and positioning, and HF radar frequency selection and positioning.

However, there are still two problems in this paper: (1) We could not simulate the unilateral Doppler broadening of the channel scattering function. (2) The phenomenon of ionospheric clutter and ray group distance, Doppler, and other parameter dispersion caused by ionospheric disturbance could not be simulated (the middle right, bottom left, and bottom right pictures in Figure 6). These two questions will be the focus of our future research.