High-frequency ionosphere channel simulation method and system, medium and product

Abstract

The invention provides a high-frequency ionized layer channel simulation method and system, a medium and a product, and relates to the technical field of wireless communication, and the method comprises the steps: generating an initial Doppler frequency spectrum according to a preset frequency spectrum mode and a Doppler frequency spectrum generation function; a frequency domain filtering method is adopted, the complex Gaussian white noise is filtered through the initial Doppler spectrum, and a Rayleigh fading process related to a time domain is generated; generating multipath time delay based on exponential distribution, and applying a time domain-related Rayleigh fading process to each time delay path to obtain a channel impulse response; performing statistical analysis on the channel impulse response to obtain a channel statistical characteristic parameter; and comparing the channel statistical characteristic parameter with a preset standard limit value, and outputting a compliance verification result. By implementing the method, the possible problem that a model is too simplified and is disjointed with actual channel characteristics in a traditional simulation method can be solved, and the dependence on a complex and changeable real channel environment is reduced.

Description

Technical Field

[0001] This application relates to the field of wireless communication technology, and in particular to a high-frequency ionospheric channel simulation method, system, medium, and product. Background Technology

[0002] High-frequency (HF) communication, a classic communication method capable of beyond-line-of-sight transmission utilizing ionospheric reflection, plays an indispensable role in critical fields such as ocean navigation, aviation communication, emergency rescue, and national defense. The reliable propagation of HF signals is highly dependent on the state of the ionosphere, a dynamic and dispersive medium influenced by various factors including solar activity, geographical location, and day-night cycles. Signals propagating within the ionosphere experience complex fading, multipath propagation, and the Doppler effect, all of which pose significant challenges to the performance of communication systems. Therefore, accurately reproducing the characteristics of HF channels in a laboratory environment using channel simulation technology is crucial for the design, verification, and optimization of communication equipment.

[0003] In related technologies, to simulate the time-selective fading characteristics of ionospheric channels, a common channel simulation method is based on a simplified physical assumption: that the scattering process within the channel is homogeneous and can be described by a unified statistical model. In practice, this method typically pre-defines a Doppler power spectrum with a single symmetric spectral type, such as the classic Gaussian spectrum. This single spectrum is fully defined by a center frequency and a Doppler spread factor, representing a macroscopic, averaged statistical abstraction of the entire complex scattering environment. Subsequently, this single, symmetric Doppler spectrum is used as a filter to filter a Gaussian white noise process, thereby generating a time-domain fading sequence that statistically conforms to the pre-defined spectral type, used to simulate the overall fading behavior of the channel.

[0004] However, the real ionospheric environment is far more complex than the homogenization assumptions described above. For example, when high-frequency signals pass through the ionosphere, the Earth's magnetic field causes Faraday rotation and magnetostrictive birefringence, splitting the original signal into two different propagation modes: ordinary waves (O-waves) and extraordinary waves (X-waves). These two modes experience different propagation paths, refractive indices, and absorption attenuation within the ionosphere, exhibiting independent and differentiated Doppler shifts and Doppler spread characteristics upon reaching the receiver. When these two or more signal components coexist and are received by the receiver, the overall fading characteristics of the channel are a composite result of the superposition of these independent fading processes. Because current technologies use a single, symmetrical spectral model to characterize the fading of the entire channel, this model is structurally unable to simultaneously accommodate and express two or more independent scattering components with different center shifts and broadening characteristics. As a result, when faced with real-world multi-mode propagation scenarios, this method can only generate an "averaged" fading process. This forces the complex, multi-mode coexistence-induced fading characteristics to be simplified and distorted into a single, homogeneous fading process, leading to a significant mismatch between simulation results and actual physical channel characteristics. Summary of the Invention

[0005] This application provides a high-frequency ionospheric channel simulation method, system, medium, and product to address the problem that related technologies use a single, homogeneous scattering assumption for channel modeling, which makes it difficult to accurately reflect the complex fading characteristics when multiple modes of scattering effects coexist in the ionosphere.

[0006] In a first aspect, this application provides a high-frequency ionospheric channel simulation method, applied to a high-frequency ionospheric channel simulation system, the method comprising: An initial Doppler spectrum is generated based on a preset spectrum mode and a Doppler spectrum generation function. The spectrum mode includes a single Gaussian mode and a double Gaussian mode. A time-domain correlated Rayleigh fading process is generated by filtering the complex Gaussian white noise using the initial Doppler spectrum through a frequency domain filtering method. Multipath delays are generated based on exponential distribution, and the time-domain correlated Rayleigh fading process is applied to each delay path to obtain the channel impulse response; Statistical analysis of the channel impulse response yields channel statistical characteristic parameters; The channel statistical characteristic parameters are compared with preset standard limits, and the compliance verification result is output.

[0007] Through the above embodiments, the system integrates Doppler spectrum generation, time-domain fading process construction, multipath effect simulation, and final statistical verification to create a structurally complete and quantifiable channel simulation framework. This method not only simulates the core fading characteristics of the channel but also introduces a comparison step with preset standards, thereby verifying the compliance and realism of the simulation results. This solves the problems of overly simplified models and disconnect from actual channel characteristics that may exist in traditional simulation methods. It provides a reliable and standardized technical means for performance testing and verification of high-frequency communication equipment in a laboratory environment, effectively reducing dependence on the complex and ever-changing real channel environment.

[0008] In some embodiments, the step of generating an initial Doppler spectrum based on a preset spectral mode and a Doppler spectrum generation function specifically includes: When the spectrum mode is a single Gaussian mode, the initial Doppler spectrum is directly generated based on the preset Doppler broadening factor and single Gaussian function; When the spectrum mode is a dual Gaussian mode, a first Gaussian spectrum component and a second Gaussian spectrum component are generated according to preset weights and broadening factors, respectively. The first Gaussian spectrum component and the second Gaussian spectrum component have different weights and broadening factors. The first Gaussian spectral component and the second Gaussian spectral component are weighted and summed to obtain the initial Doppler spectrum.

[0009] Through the above embodiments, the system specifically defines two generation modes of the initial Doppler spectrum, improving the flexibility of the channel model and the simulation fidelity for complex ionospheric scattering environments. The single Gaussian mode is suitable for simulating relatively simple scattering conditions, while the double Gaussian mode, by weighted summing two spectral components with different broadening and weights, can accurately simulate the complex and asymmetric Doppler spectrum morphology generated when multiple propagation modes exist in the ionosphere (such as O-wave and X-wave separation, reflections from different layers, etc.). This refined spectrum modeling capability allows the simulated channel to more realistically reflect actual physical effects, thereby improving the accuracy and reliability of the entire simulation system. In some embodiments, the step of using a frequency domain filtering method to filter complex Gaussian white noise through the initial Doppler spectrum to generate a time-domain correlated Rayleigh fading process specifically includes: Perform a Fast Fourier Transform on a randomly generated complex Gaussian white noise sequence to obtain the noise spectrum; The noise spectrum is multiplied point by point with the initial Doppler spectrum to obtain the shaped fading spectrum; Perform an inverse fast Fourier transform on the shaped fading spectrum to generate the time-domain correlated Rayleigh fading process.

[0010] Through the above embodiments, the system accurately assigns the desired channel time correlation (determined by the Doppler spectrum) to the stochastic process by "shaping" Gaussian white noise in the frequency domain—that is, multiplying its spectrum by a preset Doppler spectrum. Utilizing the Fast Fourier Transform (FFT) and its inverse IFFT, this method is computationally far more efficient than methods such as time-domain convolution, making it particularly suitable for generating long sequences of fading data. This ensures that the simulation system can complete a large number of simulation tasks within a reasonable timeframe, while guaranteeing that the generated fading process strictly conforms to the theoretical model in terms of statistical characteristics.

[0011] In some embodiments, the step of performing statistical analysis on the channel impulse response to obtain channel statistical characteristic parameters specifically includes: The power delay distribution is obtained by averaging the channel impulse response along the time dimension. Calculate the root mean square delay spread value based on the power delay distribution; The power spectral density and the measured Doppler power spectrum are obtained by performing a Fourier transform on the channel impulse response along the time dimension. A center frequency shift value was calculated based on the measured Doppler power spectrum. By combining the root mean square delay spread value and the center frequency shift value, the channel statistical characteristic parameters are obtained.

[0012] Through the above embodiments, the system calculates key parameters such as power delay distribution, root mean square delay spread, measured Doppler power spectrum, and center frequency shift. This method transforms the complex channel impulse response function into a set of intuitive and physically meaningful indicators. These indicators can not only be directly compared with theoretical models and international standards (such as ITU recommendations) to verify the accuracy of the simulation, but also provide communication system designers with key basis for analyzing channel quality and evaluating multipath and Doppler resistance performance, giving the simulation results greater engineering application value.

[0013] In some embodiments, prior to the step of generating an initial Doppler spectrum according to a preset spectral mode and a Doppler spectrum generation function, the method further includes: Obtain external physical variables, which are real-time or predicted data characterizing the physical environment of the current ionosphere; The macroscopic physical state is calculated based on the external physical variables and the preset physical model. The macroscopic physical state is a quantitative description of the physical properties of the main propagation modes of the ionosphere. Based on the macroscopic physical state, a set of instantaneous channel parameters that evolve over time are determined. These instantaneous channel parameters include multipath delay, Doppler shift, Doppler spread, and path gain.

[0014] Through the above embodiments, the system transforms a static, general channel model into a dynamic, non-stationary channel model tightly coupled with the real physical environment. By introducing real-time or predicted external physical data such as sunspot number and geomagnetic index, and combining them with an ionospheric physical model, the simulation system can generate instantaneous channel parameters that evolve over time. This allows the simulation to move beyond simply simulating a certain "average" or "typical" channel, and instead reproduce the real ionospheric state at a specific time and location, significantly improving the simulation's relevance and predictive capabilities.

[0015] In some embodiments, the steps of employing a frequency domain filtering method to filter complex Gaussian white noise using the initial Doppler spectrum to generate a time-domain correlated Rayleigh fading process; generating multipath delays based on an exponential distribution; and applying the time-domain correlated Rayleigh fading process to each delay path to obtain the channel impulse response specifically include: The target Doppler spectrum is generated based on the Doppler spread information in the instantaneous channel parameters; Based on the target Doppler spectrum, a frequency domain fading filter is constructed to weight the signal spectrum in the frequency domain; The frequency domain fading filter is used to process the spectrum of complex Gaussian white noise to obtain the filtered fading spectrum. The time-domain fading process is obtained by performing an inverse Fourier transform on the filtered fading spectrum. Based on the time-domain fading process and the multipath delay and Doppler frequency shift information in the instantaneous channel parameters, a non-stationary channel impulse response is generated.

[0016] Through the above embodiments, the system utilizes dynamically evolving instantaneous Doppler spread, multipath delay, and other information to construct and apply fading filters in real time, ultimately generating a non-stationary channel impulse response. This means that the statistical characteristics of the channel change during the simulation process, which more closely reflects the actual performance of real ionospheric channels under conditions such as sunrise and sunset, and ionospheric disturbances.

[0017] In some embodiments, the preset standard limits are determined according to International Telecommunication Union (ITU) standards. This ensures that the channel generated by the simulation system is not only logically self-consistent but also conforms to standards widely accepted and used in the global communications industry. This not only enhances the credibility and universality of the simulation results but also makes the performance evaluation results of communication equipment developed based on this simulation system more convincing and ensures interoperability when undergoing certification or participating in international cooperation.

[0018] Secondly, this application provides a high-frequency ionospheric channel simulation system, which includes one or more processors and a memory; The memory is coupled to the one or more processors. The memory is used to store computer program code, which includes computer instructions. The one or more processors call the computer instructions so that the high-frequency ionospheric channel simulation system can implement the high-frequency ionospheric channel simulation method provided in the above embodiments, which will not be described in detail here.

[0019] Thirdly, this application provides a computer-readable storage medium including instructions that, when executed on a high-frequency ionospheric channel simulation system, enable the high-frequency ionospheric channel simulation system to implement a high-frequency ionospheric channel simulation method provided in the above embodiments, which will not be elaborated here.

[0020] Fourthly, this application provides a computer program product that, when run on a high-frequency ionospheric channel simulation system, enables the high-frequency ionospheric channel simulation system to implement a high-frequency ionospheric channel simulation method provided in the above embodiments, which will not be elaborated here.

[0021] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: 1. By acquiring and utilizing real-time or predicted data characterizing the current ionospheric physical environment (such as solar activity, geomagnetic index, etc.), the system can calculate and generate a set of instantaneous channel parameters that evolve over time. This allows the simulation to completely break free from the constraints of traditional static, general models, enabling it to simulate non-stationary channel characteristics under specific time and conditions. This greatly enhances the realism and predictive ability of the simulation, transforming it from a simple "scene reproduction" into a "channel forecasting" tool with environmental awareness.

[0022] 2. By creating a "dual Gaussian mode" and using weighted summation of spectral components with different weights and broadening factors, this method can accurately simulate the asymmetric, complex Doppler spectrum generated when complex physical phenomena such as O-wave and X-wave separation and multi-layer reflection coexist. This in-depth characterization of spectral morphology far surpasses traditional single, idealized assumptions, significantly improving the simulation fidelity of channel fading characteristics and enabling the simulation results to more realistically reflect the complexity of the physical world.

[0023] 3. Not only does it define in detail how to generate the spectrum and construct the channel impulse response, but more importantly, it mandates the introduction of statistical analysis and compliance verification of the simulation results. By calculating key parameters such as root mean square delay spread and Doppler shift, and comparing them with authoritative standards such as the International Telecommunication Union (ITU), a complete closed loop from generation to verification is formed. This mechanism ensures that the simulation system's output is not only internally logically consistent but also has credibility in terms of external standards, guaranteeing the objectivity and accuracy of the simulation results. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a high-frequency ionospheric channel simulation method according to an embodiment of this application; Figure 2 This is another flowchart illustrating a high-frequency ionospheric channel simulation method in this application embodiment; Figure 3 This is a schematic diagram of the physical device structure of a high-frequency ionospheric channel simulation system in the embodiments of this application. Detailed Implementation

[0025] The terminology used in the following embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. As used in the specification and appended claims of this application, the singular expressions “a,” “an,” “the,” “the,” “the,” and “this” are intended to include the plural expressions as well, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this application refers to any or all possible combinations including one or more of the listed items.

[0026] Hereinafter, the terms "first" and "second" are used for descriptive purposes only and should not be construed as implying or suggesting relative importance or implicitly indicating the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature, and in the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more.

[0027] For ease of understanding, the method provided in this implementation is described in process below. Please refer to [link / reference]. Figure 1 This is a flowchart illustrating a high-frequency ionospheric channel simulation method in an embodiment of this application.

[0028] S101. Obtain the spectrum mode set by the user.

[0029] Among them, "spectral mode" refers to the classification of types used to describe the Doppler spectrum morphology in high-frequency ionospheric channels. In this simulation system, it specifically includes single Gaussian mode and double Gaussian mode, with different modes corresponding to different ionospheric scattering environment simulation scenarios.

[0030] Specifically, to generate an initial Doppler spectrum that accurately reflects the actual ionospheric scattering characteristics, a high-frequency ionospheric channel simulation system first needs to define the spectrum's morphology, as different spectral morphologies correspond to different ionospheric physical scenarios. A single Gaussian mode is suitable for simulating scenarios where the scatterers in the ionosphere are relatively uniformly distributed and only a single propagation mode exists, such as a single ionospheric reflector channel during a stable period. A double Gaussian mode, on the other hand, is suitable for simulating complex scattering scenarios where multiple propagation modes exist in the ionosphere (such as O-wave and X-wave separation, or the simultaneous action of different ionospheric reflectors). Therefore, before proceeding with subsequent spectrum generation, the system must first obtain the spectrum mode set by the user according to the specific simulation objective.

[0031] S102, the preset weights and broadening factors generate the first Gaussian spectral component and the second Gaussian spectral component, respectively.

[0032] In this context, "preset weights" refers to the values ​​pre-set in the dual-Gaussian mode to characterize the relative importance of the first and second Gaussian spectral components when synthesizing the initial Doppler spectrum; "preset broadening factors" refers to the parameters pre-set to describe the frequency distribution width of the Gaussian spectral components. The larger the broadening factor, the wider the distribution of the spectral components on the frequency axis, and vice versa; "first Gaussian spectral component" refers to the first Gaussian spectral portion generated in the dual-Gaussian mode using a pre-set set of weights and broadening factors; and "second Gaussian spectral component" refers to the second Gaussian spectral portion generated in the dual-Gaussian mode using another set of pre-set weights and broadening factors, with different weights and broadening factors than the first Gaussian spectral component.

[0033] Specifically, when the high-frequency ionospheric channel simulation system determines that the user-defined spectrum mode is a dual-Gaussian mode, since this mode corresponds to a complex ionospheric scattering scenario, a single Gaussian spectral component cannot accurately reflect the spectral characteristics of multiple propagation modes. Therefore, it is necessary to generate two Gaussian spectral components with different characteristics. The preset weights determine the contribution ratio of each spectral component in the final synthesized initial Doppler spectrum. For example, if the first Gaussian spectral component corresponds to the scattering characteristics of the main propagation mode in the ionosphere, its weight can be preset to 0.7, and the second Gaussian spectral component corresponds to the scattering characteristics of the secondary propagation mode, with a preset weight of 0.3. The preset broadening factor determines the frequency distribution range of each spectral component. If the first Gaussian spectral component corresponds to a propagation mode with a slower scattering velocity, its broadening factor can be preset to a smaller value (e.g., 1.5 × Doppler spread), and the second Gaussian spectral component corresponds to a propagation mode with a faster scattering velocity, with a preset broadening factor (e.g., 0.5 × Doppler spread). The system calculates two Gaussian spectral components with different shapes and amplitudes by substituting them into the Gaussian function formula according to two preset sets of different weights and broadening factors. These two components correspond to different propagation mode characteristics in complex ionospheric environments.

[0034] S103. The first Gaussian spectral component and the second Gaussian spectral component are weighted and summed to obtain the initial Doppler spectrum.

[0035] Specifically, in the dual-Gaussian mode, the first and second Gaussian spectral components correspond to the Doppler spectral characteristics of different propagation modes in a complex ionospheric environment. Neither component alone can fully reflect the Doppler spectrum of the entire channel; therefore, a weighted summation is needed to fuse them into a complete initial Doppler spectrum. During the weighted summation, the system first determines the preset weight w_1 corresponding to the first Gaussian spectral component and the preset weight w_2 corresponding to the second Gaussian spectral component (and w_1 + w_2 = 1). Then, for each frequency point on the frequency axis, it calculates the product of the amplitude of the first Gaussian spectral component and w_1, and the product of the amplitude of the second Gaussian spectral component and w_2 at that frequency point. The two products are then added together to obtain the amplitude of that frequency point in the initial Doppler spectrum. By performing the above operation on all frequency points, a complete initial Doppler spectrum is finally formed. This initial Doppler spectrum integrates the spectral characteristics of two propagation modes, enabling a more realistic simulation of Doppler frequency shift distributions in complex scattering scenarios such as the simultaneous presence of O-waves and X-waves in the ionosphere and the combined effects of different reflective layers.

[0036] S104. Generate the initial Doppler spectrum directly based on the preset Doppler broadening factor and single Gaussian function.

[0037] The "preset Doppler broadening factor" refers to a key parameter that is pre-set in single Gaussian mode to describe the width of the single Gaussian Doppler spectrum on the frequency axis. It is related to the velocity of the scatterer in the ionosphere. The faster the scatterer moves, the larger the Doppler broadening factor and the wider the spectrum distribution.

[0038] Specifically, when the high-frequency ionospheric channel simulation system determines that the user-defined spectrum mode is a single Gaussian mode, since this mode corresponds to a scenario where scatterers in the ionosphere are uniformly distributed and have a single propagation mode, its Doppler spectrum characteristics can be accurately simulated using only a single Gaussian function. The preset Doppler broadening factor is the core parameter that determines the width of the single Gaussian spectrum. It is determined by the motion characteristics of the ionospheric scatterers corresponding to the simulation target. For example, when simulating a channel with low-velocity scatterers, the Doppler broadening factor is preset to a smaller value (e.g., 0.5Hz), and when simulating a channel with high-velocity scatterers, it is preset to a larger value (e.g., 2Hz). The sigma parameter in the single Gaussian function is usually fixedly related to the preset Doppler broadening factor. f_0 is the preset center frequency of the spectrum (usually set according to the carrier frequency of the high-frequency communication signal and the motion characteristics of the ionosphere, such as a fixed value within 0Hz or ±5Hz), and A is the amplitude coefficient (usually set to 1 to ensure spectrum normalization and facilitate subsequent signal processing). The system first generates frequency axis data covering the target frequency range (e.g., a frequency range of -10Hz to 10Hz, with 1024 sampling points to ensure the frequency resolution meets simulation requirements). Then, it converts a preset Doppler broadening factor into the sigma parameter of a single Gaussian function. Combining this with a preset center frequency f_0 and amplitude coefficient A, the frequency value of each frequency point is substituted into the single Gaussian function formula to calculate the corresponding spectral amplitude. By performing the above calculations on all frequency points, a complete initial Doppler spectrum conforming to the ionospheric characteristics under a single propagation mode is finally formed. This spectrum will serve as the core template for subsequent frequency domain filtering methods, used to filter complex Gaussian white noise to generate a Rayleigh fading process with time-domain correlation.

[0039] S105. Perform a Fast Fourier Transform on the randomly generated complex Gaussian white noise sequence to obtain the noise spectrum.

[0040] Specifically, Rayleigh fading in high-frequency ionospheric channels exhibits specific time-domain correlation, which is determined by the channel's Doppler spectrum. Since complex Gaussian white noise sequences are uncorrelated in the time domain, they cannot directly simulate the time-domain characteristics of Rayleigh fading. Therefore, frequency-domain filtering is needed to impart a correlation matching the Doppler spectrum. First, the system needs to generate a complex Gaussian white noise sequence: two independent Gaussian distributed random sequences with a mean of 0 and a variance of sigma^2 (usually set to 1 / 2 to ensure the total power of the complex noise sequence is 1) are generated by a random number generation module. These sequences serve as the real and imaginary parts of the complex noise, respectively, and are combined to form the complex Gaussian white noise sequence. The sequence length needs to be determined based on the simulation duration and sampling rate (e.g., a simulation duration of 10 seconds and a sampling rate of 100 Hz result in a sequence length of 1000 points). Next, to achieve filtering in the frequency domain, a fast Fourier transform is needed to convert the time-domain complex Gaussian white noise sequence into a frequency-domain noise spectrum. The Fast Fourier Transform (FFT) can convert a time-domain discrete signal x(n) into a frequency-domain discrete signal X(k), where each element of X(k) corresponds to the amplitude and phase information of different frequency components. Through this transformation, the system can intuitively adjust the noise spectrum in the frequency domain. The resulting noise spectrum is in complex form, containing the amplitude and phase information of each frequency component. It will then be multiplied point-by-point with the initial Doppler spectrum (also in frequency-domain complex form) to "shape" the noise spectrum, making it conform to the Doppler spectral characteristics of high-frequency ionospheric channels, thereby providing a frequency-domain basis for generating time-correlated Rayleigh fading processes.

[0041] S106. Multiply the noise spectrum by the initial Doppler spectrum point by point to obtain the shaped fading spectrum.

[0042] Specifically, the fading characteristics of a high-frequency ionospheric channel are determined by its Doppler spectrum, which is the mathematical description of this characteristic. The noise spectrum, on the other hand, is the frequency domain representation of uncorrelated white noise. The point-by-point multiplication of these two spectra essentially filters the noise in the frequency domain, "attributing" the characteristics of the initial Doppler spectrum to the noise spectrum. In the frequency domain, the signal at each frequency point can be represented as a complex number A + θ (A is the amplitude, θ is the phase). During point-by-point multiplication, the amplitudes at corresponding frequency points are multiplied (A_{noise} × A_{Doppler}) and the phases are added (θ_{noise} + θ_{Doppler}). That is, for frequency points with a large initial Doppler spectrum amplitude, the noise spectrum amplitude at that frequency point is amplified, resulting in stronger energy for that frequency component in the time domain; conversely, for frequency points with a small initial Doppler spectrum amplitude, the noise spectrum amplitude at that frequency point is suppressed, resulting in weaker energy for that frequency component in the time domain. This ensures that the final fading spectrum amplitude distribution perfectly matches the initial Doppler spectrum, exhibiting the frequency selectivity of a true channel. Meanwhile, the superposition of phases preserves the random phase characteristics of the noise, ensuring that the subsequent time-domain fading process has random fluctuations, which is consistent with the random characteristics of Rayleigh fading.

[0043] It is important to note that the noise spectrum and the initial Doppler spectrum must have a one-to-one correspondence at frequency points (i.e., their lengths and frequency resolutions are completely identical), for example, both must have N points and a frequency range of -f_s / 2 to f_s / 2 (where f_s is the sampling rate), to ensure the correctness of point-by-point multiplication. The shaped fading spectrum obtained through point-by-point multiplication retains both the random characteristics of complex Gaussian white noise and the Doppler spectral distribution of a high-frequency ionospheric channel, providing an accurate frequency domain signal basis for subsequent conversion to a time-domain correlated Rayleigh fading process.

[0044] S107. Perform an inverse fast Fourier transform on the shaped fading spectrum to generate a time-domain correlated Rayleigh fading process.

[0045] Specifically, the shaped fading spectrum is a frequency domain signal. Although its characteristics conform to the channel's Doppler spectrum, the fading effect of the high-frequency ionospheric channel ultimately manifests in the time domain. Therefore, it is necessary to use the inverse fast Fourier transform (IFT) to convert the frequency domain fading spectrum back to the time domain fading process. The IFT can restore the frequency domain discrete signal X(k) to the time domain discrete signal x(n). Its mathematical essence is to reconstruct the time domain signal by weighted superposition of the frequency components. In this step, the input of the IFT is the shaped fading spectrum (a complex signal in the frequency domain), and the output is a sequence of complex signals in the time domain. Since the fading spectrum after shaping has the same amplitude distribution as the initial Doppler spectrum, the time-domain signal obtained by the inverse fast Fourier transform will have time-domain correlation determined by this Doppler spectrum. For example, if the Doppler spectrum broadening is small (corresponding to a slow scatterer speed), the time-domain fading process will change relatively smoothly; if the Doppler spectrum broadening is large (corresponding to a fast scatterer speed), the time-domain fading process will fluctuate more violently. Meanwhile, since the fading spectrum after shaping originates from the frequency domain filtering of complex Gaussian white noise, according to stochastic process theory, the amplitude of the time-domain signal obtained by its inverse Fourier transform follows a Rayleigh distribution. Therefore, this time-domain signal is a "time-domain correlated Rayleigh fading process." This process simulates the single-path fading characteristics of a high-frequency ionospheric channel. Subsequently, multipath delay will be incorporated to assign an independent (or correlated) Rayleigh fading process to each delay path, thereby simulating the independent fading characteristics of each path signal in a multipath channel. Finally, a channel impulse response that reflects the combined effects of multipath and fading will be constructed. It is important to note that when performing the inverse fast Fourier transform, the number of IFFT points must be consistent with the length of the fading spectrum after shaping. Furthermore, the transform result usually needs to be normalized (e.g., divided by the square root of the number of IFFT points) to ensure that the power of the time-domain signal is consistent with the power of the frequency-domain signal, thus avoiding signal amplitude distortion.

[0046] S108. Generate multipath delays based on exponential distribution, and apply a time-domain correlated Rayleigh fading process to each delay path to obtain the channel impulse response.

[0047] Specifically, the multipath effect in high-frequency ionospheric channels originates from signals passing through different ionospheric reflection paths during propagation. The difference in propagation distance along these paths leads to different arrival times at the receiver, resulting in multipath delay. Based on the characteristics of ionospheric channels, the distribution of multipath delay follows an exponential distribution. Therefore, the system first generates multipath delays based on this exponential distribution. During generation, the rate parameter λ needs to be set according to the actual ionospheric scenario (for example, for F-layer reflection channels with significant multipath effects, λ is smaller, resulting in a wider delay distribution range; for E-layer reflection channels with weaker multipath effects, λ is larger, resulting in a narrower delay distribution range). The system generates a set of delay values ​​conforming to this exponential distribution through a random number generation module (e.g., generating delay values ​​for 5 paths: 0ms, 0.5ms, 1.2ms, 2.1ms, and 3.5ms), which typically includes a primary path delay (set to 0ms, corresponding to the shortest propagation path) and multiple secondary path delays (greater than 0ms). After generating the multipath delay, the system needs to apply a time-dependent Rayleigh fading process to each delay path. Since the scattering environments of different multipath paths may differ, two methods can be used to apply the fading process: one is to assign an independently generated Rayleigh fading process to each path (more realistic, as the fading of each path is independent); the other is to generate the fading processes for each secondary path by delaying or scaling the primary path fading process (simplifies calculations and is suitable for scenarios with high simulation efficiency requirements). During application, the fading process of each path must correspond to the delay of that path; that is, the fading process of the secondary path has a delay in the time domain equal to the delay of the primary path. Simultaneously, a path gain needs to be set for each path (usually the primary path gain is the largest, and the secondary path gain decreases as the delay increases, consistent with signal propagation loss characteristics). The path gain is multiplied by the corresponding Rayleigh fading process to obtain the time-domain response component of each path. Finally, the time-domain response components of all paths are superimposed in the time domain to obtain the channel impulse response. Each sampling point of the channel impulse response corresponds to the channel response value at a specific time. The peak position corresponds to the time delay of each multipath path, and the peak amplitude corresponds to the product of the gain and fading amplitude of each path. This impulse response fully describes the impact of high-frequency ionospheric multipath fading channels on signals. When a signal passes through this channel, its output signal can be obtained by convolving the input signal with the channel impulse response. Therefore, the channel impulse response is the core basis for subsequent channel statistical analysis (such as calculating power delay distribution and root mean square delay spread) and communication system performance testing.

[0048] S109. Perform power averaging on the channel impulse response along the time dimension to obtain the power delay distribution.

[0049] Specifically, the channel impulse response is a time-domain random signal whose amplitude fluctuates randomly over time (simulation time) due to Rayleigh fading. Directly using the channel impulse response amplitude at a specific moment to calculate power cannot accurately reflect the true power distribution of each multipath path (random fluctuations mask stable path power characteristics). Therefore, it is necessary to perform power averaging along the time dimension of the channel impulse response to eliminate the influence of fading random fluctuations and obtain a stable power delay distribution.

[0050] Here, the time dimension refers to the "delay dimension" of the channel impulse response itself (i.e., the horizontal axis, corresponding to the delay of the multipath path, in milliseconds); it is also the "simulation time dimension" (i.e., the time series of multiple samples, in seconds). Power averaging is performed on the "simulation time dimension." For each fixed delay point on the "delay dimension," the average power over multiple simulation moments is calculated. For example, if the simulation time is 10 seconds and the sampling rate is 100 Hz, then 1000 channel impulse response samples are obtained (each sample contains response values ​​at multiple delay points); for the "0.5 ms" delay point on the delay dimension, the response value at that delay point needs to be extracted from the 1000 samples, and its average power is calculated.

[0051] Furthermore, for each channel impulse response sample at each simulation moment, the squared value of its amplitude (i.e., the instantaneous power at that moment and at that delay point) is calculated; for each fixed delay, the average instantaneous power of all samples at that delay point is calculated; and by combining all delay points and their corresponding power values, a complete power delay distribution curve is obtained.

[0052] S110. Calculate the root mean square delay spread value based on the power delay distribution.

[0053] Specifically, while power delay distribution can show the power and delay distribution of multipath paths, it cannot directly quantify the degree of dispersion of multipath delays. The root mean square delay spread (RMS) is a mathematical quantification of this dispersion. In actual simulations, the power delay distribution exists in a discrete form. It is necessary to first determine the discrete delay points and their corresponding power values, and then normalize the power values ​​to ensure that the sum of all power values ​​is 1, thus avoiding the influence of total power differences on the calculation results.

[0054] The calculation first involves calculating the average delay, which is the weighted average of the delays of all multipath paths. The weights here are the normalized power of each path. The average delay reflects the average arrival time of the signal in the multipath channel. The greater the power of the main path, the closer the average delay is to the main path delay. Next, the squared average of the delays is calculated, which is the sum of the squares of the delays at each delay point multiplied by the corresponding normalized power. Finally, the variance is obtained by subtracting the square of the average delay from the squared average of the delays. Taking the square root of this variance yields the root mean square delay spread.

[0055] For example, if the power delay distribution contains three main paths with delays of 0ms, 0.8ms, and 1.5ms, corresponding to normalized powers of 0.6, 0.3, and 0.1, the average delay is first calculated as 0 × 0.6 + 0.8 × 0.3 + 1.5 × 0.1 = 0.39ms, and then the squared average delay is calculated as 0. 2 ×0.6 + 0.8 2 ×0.3 + 1.5 2 ×0.1 = 0.411ms 2 The variance is 0.411 - 0.39. 2 ≈ 0.281ms 2 The root mean square delay spread is the square root of the variance, approximately 0.53 ms. If this value is within the range of 0.1-5 ms, it complies with the requirements of the ITU-R F.1487 protocol.

[0056] S111. Perform a Fourier transform on the channel impulse response along the time dimension to obtain the power spectral density and the measured Doppler power spectrum.

[0057] Specifically, the time-domain characteristics of the channel impulse response (such as multipath delay and Rayleigh fading) have been analyzed through previous steps. However, another core characteristic of high-frequency ionospheric channels—the Doppler effect—needs to be obtained through frequency-domain analysis. The Doppler effect, caused by ionospheric motion and scattering body motion, causes frequency shifts and spreads in the signal. Performing a Fourier transform on the channel impulse response along the time dimension converts the change in signal amplitude with simulation time in the time domain into the distribution of signal power with frequency in the frequency domain, thereby extracting the Doppler characteristics.

[0058] The "time dimension" here refers to the simulation time dimension, not the time delay dimension. The channel impulse response is represented as a series of discrete samples in the simulation time dimension, with each sample corresponding to the channel response at a specific simulation moment. During the calculation, firstly, the time-domain response sequences corresponding to fixed delay points of the main multipath paths in the power delay distribution are extracted from the channel impulse response samples at all simulation times. This sequence reflects the change of signal amplitude of a specific multipath path with simulation time, and its fluctuation frequency is determined by the Doppler effect. Next, a Discrete Fourier Transform is performed on the extracted time-domain sequence to convert the time-domain signal into a frequency-domain response. The Fourier Transform converts slowly fluctuating signals (corresponding to small Doppler broadening) in the time domain into narrowband spectra in the frequency domain, and rapidly fluctuating signals (corresponding to large Doppler broadening) into wideband spectra, directly reflecting the Doppler extension characteristics. Finally, the power spectral density and the measured Doppler power spectrum are calculated. The power spectral density is the square of the amplitude of the frequency domain response divided by the simulation time length, used to normalize the total power to a unit frequency. The measured Doppler power spectrum is obtained by smoothing the power spectral density (such as Hanning window smoothing) to eliminate spectral noise, and then normalizing it to a maximum power of 1, making it comparable to the initial Doppler spectrum theoretical model.

[0059] For example, if the initial Doppler spectrum is set to a double Gaussian mode (weights 0.7:0.3, broadening factor 1.5Hz:0.5Hz), the measured Doppler power spectrum should exhibit a double Gaussian shape with a "main lobe + side lobe". The main lobe corresponds to the spectral component with a weight of 0.7, and the side lobe corresponds to the spectral component with a weight of 0.3. The broadening width is consistent with the preset broadening factor. The degree of agreement between this spectrum shape and the initial theoretical model directly reflects the accuracy of the Doppler characteristic simulation.

[0060] S112. A center frequency shift value is calculated based on the measured Doppler power spectrum.

[0061] Specifically, the shape of the measured Doppler power spectrum not only reflects the Doppler extension characteristics (spectral width), but may also have an overall frequency shift, that is, the "power centroid" of the spectrum deviates from the theoretical center frequency (usually preset to 0Hz, corresponding to an ideal scenario without additional frequency shift). This shift is caused by ionospheric motion (such as overall ionospheric drift) or directional motion of scatterers, and needs to be quantified by the center frequency shift value.

[0062] During the calculation, firstly, the discrete frequency points of the measured Doppler power spectrum and their corresponding normalized power values ​​are determined, ensuring that the sum of the normalized power values ​​is 1. Next, the power-weighted average frequency (i.e., the "power centroid") of the spectrum is calculated by multiplying the frequency value of each discrete frequency point by the corresponding normalized power value and then summing all the results. Finally, the center frequency shift value is calculated, which is the difference between the power-weighted average frequency and the theoretical center frequency. Since the theoretical center frequency is usually preset to 0Hz, the center frequency shift value is equal to the power-weighted average frequency.

[0063] If the center frequency shift is positive, it indicates that the measured Doppler power spectrum has shifted towards the positive frequency direction (signal frequency increases); if it is negative, it indicates a shift towards the negative frequency direction (signal frequency decreases). The smaller the absolute value, the slighter the spectral shift, and the closer it is to the ideal scenario. For example, if the discrete frequency points of a measured Doppler power spectrum are [-5, -4, ..., 0, ..., 4, 5] Hz, corresponding to an approximately symmetrical distribution of normalized power, the calculated power-weighted average frequency is 0.3 Hz, and the center frequency shift is also 0.3 Hz, which meets the requirement of "±5 Hz" in the ITU-R F.1487 protocol. If the calculated center frequency shift is 6 Hz, it exceeds the protocol range, and it is necessary to return to the Doppler spectrum generation step, adjust the center frequency parameters of the initial Doppler spectrum, and regenerate the channel impulse response until the shift meets the requirements.

[0064] S113. Combine the root mean square delay spread and center frequency shift to obtain the channel statistical characteristic parameters.

[0065] Specifically, the root mean square delay spread and center frequency shift describe the statistical characteristics of the channel from the two dimensions of multipath characteristics and Doppler characteristics, respectively. However, individual parameters cannot fully reflect the overall performance of the channel. They need to be "combined" to form a complete set of channel statistical characteristic parameters to achieve a comprehensive quantification of channel characteristics.

[0066] Three core principles must be followed when combining parameters: First, cover key characteristics to ensure that the parameter set includes the two core characteristics of "multipath-Doppler" without omitting any key indicators; second, adhere to the requirements of the associated protocol, ensuring that the naming and units of the parameters are consistent with the ITU-RF.1487 protocol to facilitate subsequent compliance verification; and third, add scenario information to supplement auxiliary parameters related to the simulation scenario and improve the traceability of the parameters.

[0067] A typical set of channel statistical characteristic parameters includes three categories: multipath characteristic parameters, Doppler characteristic parameters, and scenario auxiliary parameters. Multipath characteristic parameters, in addition to the root mean square delay spread, include average delay (reflecting the average arrival time of multipath signals, in milliseconds) and path number (indicating the complexity of the multipath effect, unitless). Doppler characteristic parameters, in addition to the center frequency shift, include Doppler broadening (calculated using the measured Doppler power spectrum's "-3dB bandwidth," quantifying the degree of spectral broadening, in Hertz) and spectral mode (recording the initially set spectral mode, such as single Gaussian or double Gaussian, unitless). Scenario auxiliary parameters include simulation time length (indicating the time range of parameter calculation, in seconds) and sampling rate (used to verify the frequency resolution of parameter calculation, in Hertz).

[0068] For example, the set of channel statistical characteristic parameters for a certain simulation scenario is as follows: {Root mean square delay spread = 0.58ms, average delay = 0.42ms, number of paths = 3; center frequency shift = 0.45Hz, Doppler broadening = 1.8Hz, spectral mode = double Gaussian; simulation duration = 10s, sampling rate = 200Hz}. This set comprehensively covers multipath, Doppler characteristics, and scenario information, facilitating subsequent comparison with protocol limits and allowing for tracing the scenario conditions under which the parameters were generated, thus supporting the reproduction of simulation results.

[0069] S114. Compare the channel statistical characteristic parameters with the preset standard limits and output the compliance verification results.

[0070] Specifically, the ultimate goal of high-frequency ionospheric channel simulation is to generate a channel model that conforms to actual channel characteristics and meets industry standards. Compliance verification is the core basis for judging whether the model is usable. By comparing parameters with limits, the compliance of simulation results is quantitatively evaluated to avoid the use of non-standard channel models in subsequent communication system testing, which would lead to distorted test results.

[0071] The entire process consists of four steps: First, determine the core parameters to be verified and their corresponding preset standard limits. Based on the ITU-R F.1487 protocol, select the core parameters that have the greatest impact on channel performance and clarify their limit ranges, such as RMS delay spread (0.1-5ms), center frequency shift (±5Hz), Doppler broadening (0.1-1Hz), and single-path multipath delay (0.1-5ms). If the user has specific scenario requirements, the preset standard limits can be adjusted based on the protocol limits, but the reason for the adjustment must be noted in the verification results. Second, compare each core parameter with the preset standard limits. For each core parameter, determine whether its value is within the corresponding limit range and record the "compliant" or "non-compliant" result. For example, RMS delay spread = 0.58ms (compliant), center frequency shift = 0.45Hz (compliant), Doppler broadening = ... 1.2Hz (non-compliant); The third step is to comprehensively judge the compliance result type. Based on the comparison results of all core parameters, it is divided into three types: "compliant" (all core parameters are compliant), "partially compliant" (some core parameters are compliant, some are non-compliant), and "non-compliant" (most core parameters are non-compliant); The fourth step is to generate a compliance verification report. The report includes a core parameter comparison table (parameter name, measured value, preset limit, compliance status), compliance result type and conclusion, improvement suggestions (for non-compliant parameters), and scenario information notes (such as the reason for limit adjustment).

[0072] For example, the core content of a compliance verification report for a certain simulation scenario is as follows: In the core parameter comparison, the root mean square delay spread is 0.58ms (0.1-5ms, compliant), the center frequency shift is 0.45Hz (±5Hz, compliant), and the Doppler broadening is 1.2Hz (0.1-1Hz, non-compliant); the result type is partially compliant; the improvement suggestion is "the Doppler broadening value is out of range, it is recommended to reduce the broadening factor of the initial Doppler spectrum"; the report clearly points out the problems in the simulation and the direction of improvement, and users can quickly optimize the simulation parameters according to the suggestions.

[0073] The following provides a more detailed description of the process of the method provided in this implementation. Please refer to [link / reference]. Figure 2 This is another flowchart illustrating a high-frequency ionospheric channel simulation method in this application.

[0074] S201. The macroscopic physical state is calculated based on external physical variables and a preset physical model.

[0075] Specifically, the channel characteristics of the high-frequency ionosphere are essentially determined by its physical environment. For example, an increase in the number of sunspots leads to an increase in the electron density of the ionosphere, thereby increasing the maximum usable frequency (MUF); geomagnetic storms disrupt the ionospheric structure and increase the randomness of multipath propagation. Therefore, to generate a realistic non-stationary channel, it is necessary to first capture the real-time state of the ionosphere through external physical variables, and then transform these macroscopic physical data into macroscopic physical states that can be used for channel modeling through a pre-defined physical model.

[0076] First, the system acquires multi-source external physical variables: real-time data can be obtained through satellite observation data (such as ionospheric detection data from the COSMIC satellite), ground observation stations (such as ionospheric plumb bobs), or forecast data for the next few hours to days can be obtained through prediction models from meteorological departments and space weather agencies. For example, it can acquire data such as sunspot number (SSN=120), Kp index (level 2, calm geomagnetism), and solar zenith angle (30°) at a certain time (e.g., 12:00 on June 15, 2024) and a certain location (30°N, 120°E).

[0077] Next, the system calls a preset physical model for calculation: taking the International Reference Ionospheric Model (IRI) as an example, the system inputs external physical variables into the model and calculates key parameters through the model's built-in formulas, such as the height of the E layer (approximately 110 km), the peak height of the F2 layer (approximately 350 km), and the critical frequency of the F2 layer (foF2=12 MHz); then, it combines the transmission model (such as PIM) to calculate the characteristics of the propagation mode, such as the incident angle of the E layer reflection (25°), the mode type of the F2 layer reflection (O wave / X wave separation), and the transmission loss of each mode.

[0078] The final output macroscopic physical state must meet the requirement of "directly supporting channel parameter generation", for example: List of propagation modes: E-layer single reflection, F2-layer single reflection, F2-layer double reflection; Physical properties of each mode: Electron collision frequency reflected by the E-shell (1×10⁻⁶) 6 Hz), the phase constant of the reflection from the F2 layer; Mode priority: F2 layer reflection is the primary mode (accounting for 70%), and E layer reflection is the secondary mode (accounting for 30%).

[0079] This information provides a physical basis for subsequent determination of instantaneous channel parameters (such as multipath delay and Doppler spread), ensuring that channel simulation does not deviate from the actual ionospheric mechanism.

[0080] S202. Determine a set of instantaneous channel parameters that evolve over time based on the macroscopic physical state.

[0081] Specifically, the macroscopic physical state describes the physical properties of the ionosphere, but it needs to be further transformed into instantaneous parameters that are "directly usable by the channel"—for example, an increase in the height of the F2 layer reflector leads to an increase in signal propagation distance, which in turn increases multipath delay; random fluctuations in the electron density of the ionosphere lead to a larger Doppler spread. The core of this step is to establish a mapping relationship between "macroscopic physical state parameters → instantaneous channel parameters," and this mapping is dynamically updated over time.

[0082] First, determine the mapping rules: the system has a built-in mapping algorithm based on physical mechanisms, for example: Multipath delay calculation: The propagation time of each path (i.e., multipath delay) is obtained by the ratio of the path length of the propagation mode (calculated from the height of the reflector and the distance between the transmitter and receiver) to the speed of light, while considering the correction for the ionospheric refraction effect (such as the propagation speed of radio waves in the ionosphere being less than the speed of light). Doppler frequency shift calculation: Based on the velocity of the reflector (derived from the geomagnetic index and solar activity) and the incident angle of the radio wave, the frequency shift is calculated using the Doppler effect formula. For example, when the reflector moves away from the receiver, the Doppler frequency shift is negative. Doppler spread calculation: positively correlated with the intensity of fluctuations in ionospheric electron density (the stronger the fluctuation, the greater the spread), and can be quantified by the geomagnetic index Kp (the higher the Kp index, the greater the spread). Path gain calculation: based on the transmission loss of the propagation mode (determined by the reflection coefficient and path length), combined with the logarithmic attenuation model (e.g., the gain decreases by 3dB for every 100km increase in path length).

[0083] Next, the instantaneous parameters are dynamically updated: if the macroscopic physical state changes over time (e.g., the reflector height increases by 20 km per hour), the system will recalculate the instantaneous channel parameters according to a set time step (e.g., 1 minute), for example: Initial time (t=0): F2 layer height 350km → multipath delay 1.2ms, Doppler spread 0.5Hz; t=30 minutes: F2 layer height 370km → multipath delay 1.3ms, Doppler spread 0.6Hz (due to increased solar activity, electron density fluctuations increase); At t=60 minutes: the geomagnetic index Kp increases from 2 to 4 → the Doppler spread abruptly changes to 0.9 Hz, and the multipath delay fluctuates by ±0.1 ms.

[0084] Finally, output structured instantaneous parameters: the parameters must include timestamps (to ensure time correlation) and independent parameters for each path (such as the different Doppler frequency shifts of the main path and the secondary path).

[0085] S203. Generate the target Doppler spectrum based on the Doppler spread information in the instantaneous channel parameters.

[0086] Specifically, the Doppler spectrum is the core carrier describing the Doppler effect of a channel. Its width is determined by the Doppler spread, and its shape is determined by the ionospheric propagation mode (e.g., a single propagation mode corresponds to a single Gaussian, and multiple modes correspond to a double Gaussian). In non-stationary channel simulations, since the Doppler spread information in the instantaneous channel parameters changes over time, the target Doppler spectrum also needs to be updated in real time to match the fading characteristics of the current channel.

[0087] First, determine the spectrum shape and parameters: The system selects the spectrum shape based on the propagation mode information in the instantaneous channel parameters (derived from the macroscopic physical state), for example: Single Gaussian morphology: When only one main propagation mode exists (such as F2 layer reflection), the spectrum is a single Gaussian curve, the width of which is determined by the current Doppler spread value - for example, when the Doppler spread is 0.5Hz, the "-3dB bandwidth" of the Gaussian curve is 0.5Hz; Dual Gaussian morphology: When there are two propagation modes (such as F2 layer + E layer reflection), the spectrum is a weighted superposition of two Gaussian components. The width of each component corresponds to the Doppler spread value of each mode, and the weight corresponds to the power ratio of each mode (such as F2 layer component weight 0.7, E layer component weight 0.3).

[0088] At the same time, the spectral center needs to be adjusted in conjunction with the instantaneous Doppler frequency shift information. For example, when the current Doppler frequency shift is -1.5Hz, the center of the single Gaussian spectrum will shift to -1.5Hz instead of the ideal 0Hz.

[0089] Next, the spectrum is generated and updated in real time: the system synchronously updates the target Doppler spectrum according to the time step (e.g., 1 second) of the instantaneous channel parameters, for example: t=0 seconds: Doppler spread 0.5Hz, single propagation mode (F2 layer) → single Gaussian spectrum, center 0Hz, -3dB bandwidth 0.5Hz; t=30 seconds: Solar activity intensifies, Doppler spread increases to 0.8 Hz, propagation mode remains single → single Gaussian spectrum, center 0 Hz, -3dB bandwidth 0.8 Hz; At t=60 seconds: A geomagnetic storm occurs, and the propagation mode changes to F2 layer + E layer. The F2 layer Doppler extension is 1.0 Hz, and the E layer is 0.4 Hz. The weights are 0.7:0.3 → a double Gaussian spectrum, with centers at -1.2 Hz (F2 layer) and 0.5 Hz (E layer), respectively, and the bandwidths correspond to their respective extension values.

[0090] Finally, structured spectral data is output: the target Doppler spectrum for each time step must include a frequency axis and the corresponding amplitude (complex form, including amplitude and phase), for example, the frequency axis range is -10Hz to 10Hz, the number of sampling points is 1024, and the amplitude of each frequency point is calculated by a Gaussian function. This data will be directly used to construct a frequency domain fading filter (step S204) to ensure that the filter characteristics match the real-time channel.

[0091] S204. Based on the target Doppler spectrum, construct a frequency domain fading filter that weights the signal spectrum in the frequency domain.

[0092] Specifically, the essence of a frequency-domain fading filter is to "encode the characteristics of the target Doppler spectrum into the filter's frequency response"—when a signal passes through the filter, its frequency spectrum is "shaped" by the filter's frequency response, thus producing fading in the time domain that conforms to the channel characteristics. In non-stationary channel simulations, since the target Doppler spectrum evolves over time, the filter's frequency response also needs to be updated in real time to ensure that the filtering effect is synchronized with the current ionospheric state.

[0093] First, determine the frequency response of the filter: the frequency response of the filter (complex form) is directly related to the target Doppler spectrum, for example: Amplitude response: equal to the amplitude of the target Doppler spectrum, ensuring that the attenuation of the signal components at different frequencies matches the Doppler spectrum—for frequencies with larger spectral amplitudes, the filter attenuates less, and more of that signal component is retained; Phase response: It is usually set to random phase (or noise-based random phase) to simulate the randomness of channel fading and avoid distortion caused by fixed phase. For example, the phase value (0 to 2π) of each frequency point is randomly generated from a uniform distribution.

[0094] If the target Doppler spectrum is of a double Gaussian shape, the amplitude response of the filter is also a double Gaussian curve, ensuring that the fading characteristics of both propagation modes are captured.

[0095] Next, the filter structure is constructed: the system adopts a "frequency domain tapped filter" structure to adapt to the dynamically updated frequency response, specifically including: Frequency axis alignment: Ensure that the frequency axis of the filter is completely consistent with the target Doppler spectrum and the input signal spectrum (e.g., frequency range -10Hz to 10Hz, number of sampling points 1024) to avoid filtering errors caused by frequency mismatch; Tap weighting: The frequency response of the filter is used as the tap weight. Each frequency point corresponds to a tap, and the weight is the complex response (amplitude + phase) at that frequency point. Real-time update mechanism: The tap weights of the filter are updated synchronously according to the time step of the target Doppler spectrum (e.g., 1 second). For example, the spectrum at t=0 is used as the weight at t=0 seconds, and the spectrum at t=1 is switched to the weight at t=1 seconds, so as to realize the dynamic adjustment of the filter characteristics.

[0096] Finally, verify the filter performance: verify the filter effect by test signal (such as complex Gaussian white noise). For example, after passing white noise through the filter, calculate the power spectral density of the output signal and check whether it is consistent with the target Doppler spectrum. If the deviation exceeds 1% (RMSE), readjust the phase or amplitude response of the filter to ensure that the filtering accuracy meets the requirements.

[0097] S205. Use a frequency domain fading filter to process the spectrum of complex Gaussian white noise to obtain the filtered fading spectrum.

[0098] Specifically, the system first generates a complex Gaussian white noise sequence with a length consistent with the number of frequency points of the frequency-domain fading filter to avoid spectral aliasing. Then, a Fast Fourier Transform (FFT) is used to convert the time-domain noise into a frequency-domain noise spectrum, where the amplitudes of each frequency component are approximately equal and the phases are random. Next, the noise spectrum is multiplied point-by-point with the frequency response of the frequency-domain fading filter, multiplying the amplitudes and adding the phases at corresponding frequency points to match the amplitude distribution of the fading spectrum to the target Doppler spectrum, thus preserving the channel's frequency-selective fading characteristics. In non-stationary channel simulations, the noise spectrum needs to be regenerated according to the time step and weighted using the updated filter to ensure that the fading spectrum matches the current channel state.

[0099] S206. Perform an inverse Fourier transform on the filtered fading spectrum to obtain the time-domain fading process.

[0100] Specifically, the system first confirms that the number of inverse Fourier transform points matches the fading spectrum length, ensuring matching of sampling rates and sequence lengths in the time and frequency domains. Next, it performs the inverse Fourier transform and normalizes the result by dividing by the square root of the number of transform points, ensuring consistent signal power in the time and frequency domains and avoiding amplitude distortion. Then, it verifies the statistical characteristics of the time-domain fading process by plotting an amplitude histogram and comparing it with the theoretical Rayleigh distribution; a good fit exceeding 0.95 is considered valid. Simultaneously, it calculates the autocorrelation function to confirm its correlation matches the target Doppler spectrum. In non-stationary simulations, the above process is repeated at time steps to generate a "time-time domain fading" sequence, simulating the non-stationary characteristics of the channel.

[0101] S207. Based on the multipath delay and Doppler frequency shift information in the time-domain fading process and instantaneous channel parameters, generate a non-stationary channel impulse response.

[0102] Specifically, the system first determines the number of paths, the delay of each path, the Doppler shift, and the gain based on instantaneous channel parameters. A time-domain fading process is assigned to each path (the main path uses the current process, while secondary paths can be generated independently or based on the main path delay), and the magnitude is adjusted according to the gain. Next, the corresponding Doppler shift modulation is applied to the time-domain fading process of each path, and then the secondary path signal is time-delayed according to the multipath delay. Finally, the time-domain signals of all paths are superimposed to obtain the channel impulse response at the current time step. In non-stationary simulations, the above process is repeated at each time step to generate an impulse response sequence that evolves over time, simulating the non-stationary characteristics of the channel, while ensuring that the parameters conform to the ITU-R F.1487 protocol.

[0103] The high-frequency ionospheric channel simulation system of this invention is applied to electronic devices. Figure 3 A schematic diagram of the architecture of an electronic device suitable for implementing embodiments of the present invention is shown.

[0104] It should be noted that, Figure 3 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0105] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by instructions (computer programs), or by instructions (computer programs) controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor. The electronic device of this embodiment includes a storage medium and a processor, wherein the storage medium stores multiple instructions that can be loaded by the processor to execute any step of the method provided in the embodiments of the present invention.

[0106] Specifically, the storage medium and the processor are electrically connected directly or indirectly to enable data transmission or interaction. For example, these components can be electrically connected to each other via one or more signal lines. The storage medium stores computer-executable instructions that implement data access control methods, including at least one software functional module that can be stored in the storage medium in the form of software or firmware. The processor executes various functional applications and data processing by running the software program and module stored in the storage medium. The storage medium can be, but is not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc. The storage medium stores the program, and the processor executes the program after receiving the execution instructions.

[0107] Furthermore, the software programs and modules within the aforementioned storage medium may also include an operating system, which may include various software components and / or drivers for managing system tasks (e.g., memory management, storage device control, power management, etc.) and can communicate with various hardware or software components to provide an operating environment for other software components. The processor may be an integrated circuit chip with signal processing capabilities. The aforementioned processor may be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc., which can implement or execute the methods, steps, and logic flowcharts disclosed in this embodiment. The general-purpose processor may be a microprocessor or any conventional processor.

[0108] Since the instructions stored in the storage medium can execute the steps in any of the methods provided in the embodiments of the present invention, the beneficial effects of any of the methods provided in the embodiments of the present invention can be achieved, as detailed in the preceding embodiments, and will not be repeated here.

[0109] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A high-frequency ionospheric channel simulation method, applied to a high-frequency ionospheric channel simulation system, characterized in that, The method includes: An initial Doppler spectrum is generated based on a preset spectrum mode and a Doppler spectrum generation function. The spectrum mode includes a single Gaussian mode and a double Gaussian mode. A time-domain correlated Rayleigh fading process is generated by filtering the complex Gaussian white noise using the initial Doppler spectrum through a frequency domain filtering method. Multipath delays are generated based on exponential distribution, and the time-domain correlated Rayleigh fading process is applied to each delay path to obtain the channel impulse response; Statistical analysis of the channel impulse response yields channel statistical characteristic parameters; The channel statistical characteristic parameters are compared with preset standard limits, and the compliance verification result is output.

2. The method according to claim 1, characterized in that, The step of generating an initial Doppler spectrum based on a preset spectral mode and a Doppler spectrum generation function specifically includes: When the spectrum mode is a single Gaussian mode, the initial Doppler spectrum is directly generated based on the preset Doppler broadening factor and single Gaussian function; When the spectrum mode is a dual Gaussian mode, a first Gaussian spectrum component and a second Gaussian spectrum component are generated according to preset weights and broadening factors, respectively. The first Gaussian spectrum component and the second Gaussian spectrum component have different weights and broadening factors. The first Gaussian spectral component and the second Gaussian spectral component are weighted and summed to obtain the initial Doppler spectrum.

3. The method according to claim 1, characterized in that, The step of using frequency domain filtering to filter complex Gaussian white noise through the initial Doppler spectrum to generate a time-domain correlated Rayleigh fading process specifically includes: Perform a Fast Fourier Transform on a randomly generated complex Gaussian white noise sequence to obtain the noise spectrum; The noise spectrum is multiplied point by point with the initial Doppler spectrum to obtain the shaped fading spectrum; Perform an inverse fast Fourier transform on the shaped fading spectrum to generate the time-domain correlated Rayleigh fading process.

4. The method according to claim 1, characterized in that, The step of performing statistical analysis on the channel impulse response to obtain channel statistical characteristic parameters specifically includes: The power delay distribution is obtained by averaging the channel impulse response along the time dimension. Calculate the root mean square delay spread value based on the power delay distribution; The power spectral density and the measured Doppler power spectrum are obtained by performing a Fourier transform on the channel impulse response along the time dimension. A center frequency shift value was calculated based on the measured Doppler power spectrum. By combining the root mean square delay spread value and the center frequency shift value, the channel statistical characteristic parameters are obtained.

5. The method according to claim 1, characterized in that, Before the step of generating an initial Doppler spectrum based on a preset spectral mode and a Doppler spectrum generation function, the method further includes: Obtain external physical variables, which are real-time or predicted data characterizing the physical environment of the current ionosphere; The macroscopic physical state is calculated based on the external physical variables and the preset physical model. The macroscopic physical state is a quantitative description of the physical properties of the main propagation modes of the ionosphere. Based on the macroscopic physical state, a set of instantaneous channel parameters that evolve over time are determined. These instantaneous channel parameters include multipath delay, Doppler shift, Doppler spread, and path gain.

6. The method according to claim 5, characterized in that, The frequency domain filtering method is used to filter the complex Gaussian white noise through the initial Doppler spectrum to generate a time-domain correlated Rayleigh fading process; The steps of generating multipath delays based on exponential distribution and applying the time-domain correlated Rayleigh fading process to each delay path to obtain the channel impulse response specifically include: The target Doppler spectrum is generated based on the Doppler spread information in the instantaneous channel parameters; Based on the target Doppler spectrum, a frequency domain fading filter is constructed to weight the signal spectrum in the frequency domain; The frequency domain fading filter is used to process the spectrum of complex Gaussian white noise to obtain the filtered fading spectrum. Perform an inverse Fourier transform on the filtered fading spectrum to obtain the time-domain fading process; Based on the time-domain fading process and the multipath delay and Doppler shift information in the instantaneous channel parameters, a non-stationary channel impulse response is generated.

7. The method according to claim 1, characterized in that, The preset standard limits are determined in accordance with the standards of the International Telecommunication Union.

8. A high-frequency ionospheric channel simulation system, characterized in that, The high-frequency ionospheric channel simulation system includes: one or more processors and a memory; The memory is coupled to the one or more processors, the memory being used to store computer program code, the computer program code including computer instructions, the one or more processors calling the computer instructions to cause the high-frequency ionospheric channel simulation system to perform the method as described in any one of claims 1-7.

9. A computer-readable storage medium comprising instructions, characterized in that, When the instruction is run on the high-frequency ionospheric channel simulation system, the high-frequency ionospheric channel simulation system performs the method as described in any one of claims 1-7.

10. A computer program product, characterized in that, When the computer program product is run on the high-frequency ionospheric channel simulation system, the high-frequency ionospheric channel simulation system performs the method as described in any one of claims 1-7.

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