Electromagnetic pulse propagation simulation method and system based on scattering matrix

Abstract

The application provides a simulation method and system for electromagnetic pulse propagation through ionosphere based on a scattering matrix, the method comprising the following steps: constructing a source area waveform signal, performing Fourier transform on the source area waveform signal to obtain the amplitude and phase of different frequency components of the source area signal; evenly layering the ionosphere to obtain the electron density, electron collision frequency and total electron content along the path of the layered ionosphere, and writing the scattering matrix according to the boundary conditions; combining the scattering matrices between all adjacent layers after the ionosphere is evenly layered to construct a global matrix and calculate the total transmission coefficient; calculating the amplitude attenuation and phase change of a single-frequency signal during propagation through the ionosphere according to the total transmission coefficient; performing inverse Fourier transform according to the amplitude attenuation and phase change to obtain a time-domain signal after the ionosphere, and updating the source area waveform signal, and the final simulation result can comprehensively and accurately describe the scattering characteristics of electromagnetic waves in a complex environment.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic pulse waveform simulation technology, and specifically relates to a simulation method and system for electromagnetic pulse propagation through the ionosphere based on a scattering matrix. Background Technology

[0002] The research background of electromagnetic pulse waveform simulation through the ionosphere stems from the complex characteristics of the interaction between electromagnetic pulses generated by natural and man-made phenomena such as lightning and the ionosphere, as well as the practical needs in fields such as communication security and disaster monitoring. Since the 1970s, the interaction between strong electromagnetic pulses and the ionosphere has gradually attracted attention, and with the development of computer technology, related simulation research has been deepened.

[0003] Traditional simulations of electromagnetic pulses passing through the ionosphere primarily employ ray tracing algorithms. However, ray tracing algorithms are computationally intensive, and they struggle to accurately simulate the scattering effects of electromagnetic waves in complex media or with multiple scatterers. Summary of the Invention

[0004] Based on this, the present invention provides a simulation method and system for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, which aims to comprehensively and accurately describe the scattering characteristics of electromagnetic waves in complex environments, and to comprehensively consider the scattering characteristics of electromagnetic waves from multiple paths and directions, thereby performing waveform simulation more efficiently.

[0005] A first aspect of this invention provides a simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, the method comprising:

[0006] Construct a source region waveform signal, perform a Fourier transform on the source region waveform signal to obtain the field strength amplitude and phase of different frequency components of the source region signal;

[0007] The electron density, electron collision frequency, and total electron content of the ionosphere are obtained, and the ionosphere is uniformly layered. The scattering matrix is ​​written out from the boundary conditions. The propagation constant in the scattering matrix is ​​calculated using the electron density and electron collision frequency. The time delay result is fitted using the total electron content along the path, and compared and analyzed with the time delay result derived from the scattering matrix.

[0008] The scattering matrices of all adjacent layers after the ionosphere is uniformly stratified are combined to construct a global matrix, and the total transmission coefficient is calculated.

[0009] Based on the total transmission coefficient, calculate the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere;

[0010] Based on the amplitude attenuation and the phase change, an inverse Fourier transform is performed to obtain the time-domain signal after passing through the ionosphere, and the source region waveform signal is updated.

[0011] Furthermore, in the steps of obtaining the electron density, electron collision frequency, and total electron content of the ionosphere, uniformly dividing the ionosphere into layers, and writing the scattering matrix from the boundary conditions, the critical frequency of the ionosphere is calculated, and frequency components greater than the critical frequency are selected. Subsequently, the propagation attenuation of the frequency components greater than the critical frequency in free space is calculated.

[0012] Furthermore, when radio waves are emitted vertically upwards and enter the ionosphere from the air, the first critical frequency of the ionosphere is expressed as:

[0013] ;

[0014] When radio waves are incident at an angle θ0 from the air into the ionosphere, the second critical frequency of the ionosphere is expressed as:

[0015] ;

[0016] Where, N max This represents the maximum electron density of the ionosphere.

[0017] Furthermore, the step of performing an inverse Fourier transform based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere, and updating the source region waveform signal, includes:

[0018] Based on the dispersion relation of the ionosphere, the group velocity expressions for electromagnetic waves of different frequencies are derived, and the group velocity for each frequency component is calculated based on the group velocity expressions.

[0019] Based on the path length of electromagnetic waves propagating in the ionosphere and the group velocity, the group delay corresponding to each frequency component is calculated, and the group delay difference of each frequency component is calculated based on the group delay of the center frequency.

[0020] Based on the group delay difference, the phase of each frequency component is corrected and an inverse Fourier transform is performed to obtain a time-domain signal considering the group delay difference.

[0021] The phase correction corresponding to the group delay difference is incorporated into the total transmission coefficient to obtain the corrected total transmission coefficient. The corrected total transmission coefficient is then subjected to an inverse Fourier transform to obtain the system impulse response containing the dispersion effect.

[0022] The source region waveform signal is convolved with the system impulse response to obtain the time-domain signal after passing through the ionosphere, and the error between the time-domain signal after passing through the ionosphere and the time-domain signal considering the group delay difference is calculated.

[0023] Determine whether the error is less than a preset value;

[0024] If so, output the time-domain signal after passing through the ionosphere.

[0025] Furthermore, in the steps of obtaining the electron density, electron collision frequency, and total electron content of the ionosphere, uniformly dividing the ionosphere into layers, and writing the scattering matrix from the boundary conditions, the boundary conditions for the m-th layer are:

[0026] ;

[0027] b m Let b be the transmission coefficient of the m-th sublayer. m-1 Let c be the transmission coefficient of the (m-1)th sublayer. m Let c be the reflection coefficient of the m-th sublayer. m-1 S is the reflection coefficient of the (m-1)th sublayer. m Let m be the propagation matrix of the m-th sublayer in the plasma region, expressed as:

[0028] ;

[0029] Where j is the imaginary unit, k m Let k be the propagation constant of the m-th sublayer. m-1 Let θ be the propagation constant of the (m-1)th sublayer. m Let θ represent the incident angle of the m-th sublayer. m-1 d is the incident angle of the (m-1)th sublayer; m Let d be the lower boundary of the m-th sub-layer. m-1 This is the lower boundary of the (m-1)th sublayer;

[0030] The transmission region is represented as:

[0031] ;

[0032] ;

[0033] S p The scattering matrix of the transmission region is expressed as:

[0034] ;

[0035] Among them, b n Let k be the transmission coefficient of the nth sublayer. n Let d be the propagation constant of the nth sublayer. n Let θ be the lower boundary of the nth sublayer. n c represents the incident angle of the nth sublayer. n Let T be the reflection coefficient of the nth sublayer, and k be the total transmission coefficient. p Let θ be the propagation constant of the p-th sublayer. p For the final transmission angle, d pThe thickness of the entire ionosphere.

[0036] Furthermore, in the step of simulating the scattering matrices of all adjacent layers after the ionosphere is uniformly stratified to construct a global matrix and calculating the total transmission coefficient, the global matrix is ​​represented as:

[0037] ;

[0038] Among them, S g S is the global matrix. g1 For the global matrix S g The first column vector, i.e. S g2 For the global matrix S g The second column vector, i.e. ;

[0039] The total transmittance is expressed as:

[0040] ;

[0041] Where r is the total reflection coefficient, T is the total transmission coefficient, and S p is the scattering matrix of the transmission region.

[0042] Furthermore, in the step of calculating the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere based on the total transmission coefficient, the amplitude is expressed as:

[0043] ;

[0044] Phase is represented as:

[0045] ;

[0046] Where T is the total transmittance coefficient, A0 is the initial amplitude, and A_end is the amplitude after passing through the ionosphere. For phase change, arg{•} is the argument function.

[0047] A second aspect of this invention provides a simulation system for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, used to implement the simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix provided in the first aspect. The system includes:

[0048] A construction module is used to construct a source region waveform signal, and to perform a Fourier transform on the source region waveform signal to obtain the amplitude and phase of different frequency components of the source region signal;

[0049] The layering module is used to uniformly layer the ionosphere, obtain the electron density, electron collision frequency, and total electron content along the path of the layered ionosphere, and write the scattering matrix from the boundary conditions. The propagation constant in the scattering matrix is ​​calculated using the electron density and the electron collision frequency. The time delay result is fitted using the total electron content along the path and compared with the time delay result derived from the scattering matrix.

[0050] The first calculation module is used to combine the scattering matrices of all adjacent layers after the ionosphere is uniformly stratified, construct a global matrix, and calculate the total transmission coefficient.

[0051] The second calculation module is used to calculate the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere based on the total transmission coefficient.

[0052] The inverse Fourier transform module is used to perform an inverse Fourier transform based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere, and to update the source region waveform signal.

[0053] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix provided in the first aspect.

[0054] A fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix provided in the first aspect.

[0055] This invention provides a simulation method and system for electromagnetic pulse propagation through the ionosphere based on a scattering matrix. The method constructs a source region waveform signal, performs a Fourier transform on the source region waveform signal to obtain the amplitude and phase of different frequency components of the source region signal; it uniformly divides the ionosphere into layers, obtains the electron density, electron collision frequency, and total electron content along the path of each layer, and writes the scattering matrix based on boundary conditions; it combines the scattering matrices of all adjacent layers after uniform ionosphere division to construct a global matrix and calculates the total transmission coefficient; based on the total transmission coefficient, it calculates the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere; based on the amplitude attenuation and phase change, it performs an inverse Fourier transform to obtain the time-domain signal after passing through the ionosphere and updates the source region waveform signal. The final simulation results can comprehensively and accurately describe the scattering characteristics of electromagnetic waves in complex environments. Attached Figure Description

[0056] Figure 1The flowchart illustrates the implementation of a simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, as provided in Embodiment 1 of the present invention.

[0057] Figure 2 For electromagnetic waves at the angle of incidence A schematic diagram of propagation in the ionosphere;

[0058] Figure 3 Standard time-domain waveform;

[0059] Figure 4 Standard frequency domain waveform;

[0060] Figure 5 To simulate time-domain waveforms;

[0061] Figure 6 For simulation time-frequency diagrams;

[0062] Figure 7 This is a structural block diagram of a simulation system for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, provided in Embodiment 4 of the present invention.

[0063] Figure 8 This is a structural block diagram of an electronic device provided in Embodiment 5 of the present invention. Detailed Implementation

[0064] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Several embodiments of the invention are illustrated in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0065] It should be noted that when a component is said to be "fixed to" another component, it can be directly on the other component or there may be an intervening component. When a component is said to be "connected to" another component, it can be directly connected to the other component or there may be an intervening component. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0066] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0067] Example 1

[0068] According to an embodiment of the present invention, a simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix is ​​provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0069] This first embodiment provides a simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, which can be used in electronic devices, such as computers. Please refer to... Figure 1 , Figure 1 The flowchart of the implementation of a simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix provided in Embodiment 1 of the present invention is shown, specifically including steps S01 to S05.

[0070] Step S01: Construct the source region waveform signal, perform Fourier transform on the source region waveform signal to obtain the amplitude and phase of different frequency components of the source region signal.

[0071] The source region waveform signal, i.e., the source region electromagnetic pulse waveform signal, is a double exponential function, and its electric field strength can be expressed as:

[0072] ;

[0073] E0 represents the peak field strength, K is the correction coefficient, β is the parameter at the pulse leading edge, α is the parameter at the pulse trailing edge, and u is the time. Subsequently, a Fast Fourier Transform (FFT) is performed on this time-domain waveform to obtain its amplitude and phase spectra at the source point, further yielding the field strength amplitude and phase of different frequency components at the source point.

[0074] Step S02: The ionosphere is uniformly divided into layers, and the electron density, electron collision frequency, and total electron content along the path of the layered ionosphere are obtained. The scattering matrix is ​​written out from the boundary conditions.

[0075] Specifically, the propagation constant in the scattering matrix is ​​calculated using the electron density and the electron collision frequency. The time delay result is fitted using the total electron content along the path, and then compared and analyzed with the time delay result derived from the scattering matrix.

[0076] In this embodiment of the invention, the International Reference Ionospheric (IRI) model is selected as the primary ionospheric model. The IRI model, based on an empirical standard model of the ionosphere generated from all available data sources, can provide reference parameters such as electron density, temperature, and particle temperature within the ionospheric height range (the IRI-2016 model supports a range of 60km to 2000km) based on given latitude and longitude coordinates, date, and time information. Electron density data in the ionosphere is obtained using the IRI-2016 model. The density of each neutral particle is obtained using the International Reference Atmospheric Model (MSIS). Ionospheric absorption loss is closely related to the electron collision frequency within the ionosphere. The collision frequencies between electrons and neutral particles, and between electrons and ions, satisfy the following relationships:

[0077] The expression for the collision frequency between electrons and neutral particles is:

[0078]

[0079] The expression for the electron-ion collision frequency is:

[0080]

[0081] The expression for the total electron collision frequency is:

[0082]

[0083] in, The frequency of collisions between electrons and nitrogen molecules. The frequency of collisions between electrons and oxygen molecules. The frequency of collisions between electrons and oxygen atoms. The frequency of collisions between electrons and helium molecules. Let be the collision frequency between electrons and i types of ions, where i types of ions include , as well as , For electrons and The collision frequency, For electrons and The collision frequency, For electrons and The collision frequency, This refers to the concentration of nitrogen molecules. The concentration of oxygen molecules. Oxygen atom concentration, Helium molecule concentration, for Seed ion concentration, It represents the electron temperature.

[0084] The total electron content is expressed as:

[0085] ;

[0086] Where TEC is the total electron content, H is the height of the propagation path, and n e Electron density number (number / m) 3 TEC is usually measured in TECUs (1 TECU = 10 TECUs). 16 pcs / m 3 ).

[0087] Furthermore, the critical frequency of the ionosphere is calculated, and frequency components higher than the critical frequency are selected. Then, the free-space propagation attenuation of these frequency components is calculated. Specifically, when a radio wave with frequency f enters the ionosphere from the air at a certain incident angle θ0, the wave refracts once as it passes through each thin layer. As the number of thin layers increases infinitely, the trajectory of the wave becomes a smooth curve. According to the law of refraction, we can obtain:

[0088] ;

[0089] n n Let θ be the refractive index of the nth ionospheric sub-region. n Let n be the angle of incidence in the nth ionospheric sub-region, n0 be the refractive index of air, and θ0 be the angle of incidence of the radio wave entering the ionosphere from the air at an angle of incidence θ0. Since the refractive index gradually decreases with increasing altitude, the radio wave will continuously propagate along a trajectory where the angle of refraction is greater than the angle of incidence. When the radio wave penetrates to a certain height in the ionosphere, the angle of refraction is exactly 90°, meaning that after refraction, the propagation direction of the radio wave becomes horizontal, and its equiphase surface becomes vertical. At this point, the radio wave trajectory reaches its highest point. The phase velocity is higher at the height of the equiphase surface and lower at the height, which creates a downward-curving propagation trajectory. Continuing to apply the law of refraction, the ray gradually bends back from the depths of the ionosphere along a trajectory where the angle of refraction gradually decreases. Since the electron density changes continuously with altitude, the trajectory of the propagating radio wave is a smooth curve. Setting n0=1, θ n Substituting 90° into the above equation, we obtain the condition for electromagnetic waves to be reflected from the ionosphere:

[0090] ;

[0091] N is a related quantity to the square root of the complex permittivity of the ionosphere. n Let f be the electron density and f be the radio wave frequency. When radio waves are emitted vertically upwards and enter the ionosphere from the air, the first critical frequency of the ionosphere is expressed as:

[0092] ;

[0093] Critical frequency fc It is used to determine which frequency components can propagate through the ionosphere, and which frequencies are less than f. c The light will be reflected and cannot propagate through the ionosphere;

[0094] When radio waves are incident at an angle θ0 from the air into the ionosphere, the second critical frequency of the ionosphere is expressed as:

[0095] ;

[0096] Where, N max At the maximum electron density of the ionosphere, all radio waves with frequencies below the critical frequency can be reflected back from the ionosphere.

[0097] It should be noted that the propagation of electromagnetic waves in free space leads to an exponential decay in amplitude. This is because the wave energy is dispersed over an increasingly larger spatial region during propagation. Free space path loss (FSPL) can be expressed by the following formula:

[0098] ;

[0099] Where f is the frequency component greater than the critical frequency, L is the basic free-space propagation loss, and D is the propagation distance. It can be understood that when an electromagnetic pulse propagates through the ionosphere, the amplitude loss mainly consists of two parts: ionospheric absorption loss and free-space propagation loss. The above formula is used to calculate the free-space propagation loss.

[0100] To calculate the field strength attenuation and phase change of a single-frequency signal propagating in the ionosphere, the ionosphere is first divided into n sub-regions, each with equal thickness. When n is sufficiently large, the particle concentration within each sub-region can be considered to follow a uniform distribution. First, the electromagnetic field values ​​between each sub-layer are obtained using Maxwell's equations. Second, the reflection and transmission coefficients of each sub-layer are obtained by continuously matching the scattering matrix to each boundary condition. Finally, the total reflection and transmission coefficients can be obtained by iterating through a cascaded approach using the scattering equations of each layer.

[0101] Please see Figure 2 , is an electromagnetic wave with an incident angle The schematic diagram of propagation in the ionosphere specifically illustrates that electromagnetic waves are obliquely incident into the plasma at any angle. From region (0) to region (n), only the reflected and transmitted components of the electromagnetic waves exist. The reflected component considered here refers to the wave component reflected back at the interface. The wave component that has undergone multiple reflections and refractions in the plasma region is very small and will not have a significant impact on the actual analysis, so it is ignored. Only the transmitted component of the electromagnetic waves exists in region (p).

[0102] The total electric field in the vacuum region includes the reflected component and the incident component:

[0103] ;

[0104] This represents the total electric field value in the vacuum region. Let be the electric field amplitude of the incident wave. Let k be the phase factor of the incident wave, and k0 be the vacuum wavenumber. Let be the wave propagation phase term, and r be the reflection coefficient. The phase factor of the reflected wave;

[0105] Depend on Figure 2 It can be seen that electromagnetic waves refract at the interface between adjacent sublayers, causing an angular shift in the signal incident on the next sublayer. The refraction angle of electromagnetic waves at the interface between different media can be calculated using Snell's law:

[0106] ;

[0107] θ n Let be the incident angle of the nth sublayer within the plasma region. Let be the square root of the complex permittivity of the nth sublayer in the plasma region. By integrating the two formulas above, the total electric field of the mth sublayer in the plasma region can be expressed as:

[0108] ;

[0109] Let k be the total electric field of the m-th sublayer within the plasma region. m This represents the propagation constant of the m-th sublayer, obtained by calculating the dielectric constant, b. m Let c be the transmission coefficient of the m-th sublayer. m Let be the reflection coefficient of the m-th sublayer.

[0110] The total electric field in the transmission region can be expressed as:

[0111] ;

[0112] Let θ be the total electric field in the transmission region. p For the final transmission angle, k p is the propagation constant of the transmission region, and T is the total transmission coefficient.

[0113] When electromagnetic waves propagate in different media, changes in the propagation medium cause changes in the electromagnetic wave field. Therefore, when propagating at different interfaces, the field vectors will satisfy certain boundary conditions. The boundaries of various interfaces during the propagation of electromagnetic waves in plasma are shown below:

[0114] ;

[0115] Let E be the z-direction component of the electric field intensity in the 0th region at the interface where x=0. z , Let E be the z-direction component of the electric field intensity in the first region at the interface where x=0. z , Let H be the component of the electric field intensity in the y-direction of the 0th region at the interface where x=0. y , Let H be the component of the electric field intensity in the y-direction of the first region at the interface where x=0. y , For x=d m At the interface, the component of the electric field intensity in the z-direction of the (m-1)th region is E z , For x=d m At the interface, the component of the electric field intensity in the z-direction of the m-th region is E z , For x=d m At the interface, the electric field intensity in the (m-1)th region has a component H in the y-direction. y , For x=d m At the interface, the electric field intensity in the m-th region has a component H in the y-direction. y , For x=d p At the interface, the component of the electric field intensity in the z-direction of the nth region is E z , For x=d p At the interface, the component of the electric field intensity in the z-direction of the p-th region is E z , For x=d p At the interface, the component H of the electric field intensity in the z-direction of the nth region z , For x=d p At the interface, the component H of the electric field intensity in the z-direction of the p-th region z .

[0116] By combining the field vectors and boundary conditions of each sublayer, the boundary equations for each sublayer can be derived. The following are the boundary equations and their corresponding matrix forms for the incident region (0) and the plasma region (1):

[0117] ;

[0118] A is the reflection coefficient of electromagnetic waves incident on the surface of the first plasma layer, B1 is the transmission coefficient of electromagnetic waves incident from free space into plasma region (1), and C1 is the reflection coefficient of electromagnetic waves reflected from plasma region (2) back to plasma region (1).

[0119] S1 is defined as the propagation matrix on this interface, and its expression can be derived as follows:

[0120] ;

[0121] Similarly, the expression for the m-th layer according to the boundary equation is as follows:

[0122] ;

[0123] b m Let b be the transmission coefficient of the m-th sublayer. m-1 Let c be the transmission coefficient of the (m-1)th sublayer. m Let c be the reflection coefficient of the m-th sublayer. m-1 S is the reflection coefficient of the (m-1)th sublayer. m Let m be the propagation matrix of the m-th sublayer in the plasma region, expressed as:

[0124] ;

[0125] Where j is the imaginary unit, k m Let k be the propagation constant of the m-th sublayer. m-1 Let θ be the propagation constant of the (m-1)th sublayer. m Let θ represent the incident angle of the m-th sublayer. m-1 d is the incident angle of the (m-1)th sublayer; m Let d be the lower boundary of the m-th sub-layer. m-1 This is the lower boundary of the (m-1)th sublayer, with a thickness of d. m -d m-1 ;

[0126] The formula for the transmission region, based on the boundary equation, is as follows:

[0127] ;

[0128] ;

[0129] S pThe scattering matrix of the transmission region is expressed as:

[0130] ;

[0131] Among them, b n Let k be the transmission coefficient of the nth sublayer. n Let d be the propagation constant of the nth sublayer. n Let θ be the lower boundary of the nth sublayer. n c represents the incident angle of the nth sublayer. n Let T be the reflection coefficient of the nth sublayer, and k be the total transmission coefficient. p Let θ be the propagation constant of the p-th sublayer. p For the final transmission angle, d p The thickness of the entire ionosphere.

[0132] Step S03: Combine the scattering matrices of all adjacent layers after the ionosphere is uniformly stratified to construct a global matrix and calculate the total transmission coefficient.

[0133] It should be noted that by simultaneously solving the previous equations, the relationship between the total transmittance and reflectance can be obtained:

[0134] ;

[0135] S g The global matrix, also known as the global transfer matrix, is obtained by multiplying the first n transfer matrices:

[0136] ;

[0137] S g It can be written in the following form:

[0138] ;

[0139] Among them, S g1 For the global matrix S g The first column vector, i.e. S g2 For the global matrix S g The second column vector, i.e. .

[0140] The total transmittance is expressed as:

[0141] ;

[0142] Where r is the total reflection coefficient, T is the total transmission coefficient, and S p is the scattering matrix of the transmission region.

[0143] Step S04: Calculate the amplitude attenuation and phase change of the single-frequency signal as it propagates in the ionosphere based on the total transmission coefficient.

[0144] The amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere can be calculated using the total transmission coefficient:

[0145] The amplitude is expressed as:

[0146] ;

[0147] Phase is represented as:

[0148] ;

[0149] Where T is the total transmittance coefficient, A0 is the initial amplitude, and A_end is the amplitude after passing through the ionosphere. For phase change, arg{•} is the argument function.

[0150] Step S05: Perform an inverse Fourier transform based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere, and update the source region waveform signal.

[0151] During electromagnetic wave propagation, for frequency components above the critical frequency, a scattering matrix is ​​used to calculate their amplitude attenuation and phase change. Subsequently, these frequency components are converted back to time-domain signals using an inverse Fourier transform, thus obtaining the time-domain signal after passing through the ionosphere. Finally, the electromagnetic pulse waveform expression at the exit point is:

[0152] ;

[0153] Where N represents N distinct frequency components, and T m A represents the total transmission coefficient corresponding to the m-th frequency component. 0m ω represents the initial amplitude of the m-th component. m Let be the angular frequency of the m-th component, and t be the time variable. Let m be the initial phase of the m-th component. Let m be the phase change of the m-th component.

[0154] In summary, the electromagnetic pulse propagation simulation method based on scattering matrix in the above embodiments of the present invention involves constructing a source region waveform signal, performing a Fourier transform on the source region waveform signal to obtain the field strength amplitude and phase of different frequency components of the source region signal; obtaining the electron density, electron collision frequency, and total electron content of the ionosphere; uniformly dividing the ionosphere into layers and writing the scattering matrix based on the boundary conditions; combining the scattering matrices of all adjacent layers after uniform ionosphere division to construct a global matrix and calculating the total transmission coefficient; calculating the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere based on the total transmission coefficient; and performing an inverse Fourier transform based on the amplitude attenuation and phase change to obtain the time-domain signal after passing through the ionosphere and updating the source region waveform signal.

[0155] Example 2

[0156] To verify the electromagnetic pulse propagation simulation method based on the scattering matrix in Embodiment 1 of this invention, Embodiment 2 of this invention provides a specific experimental example. Specifically, the source region waveform signal is as follows:

[0157] ;

[0158] Where E0 = 5000 V / m, =4×10 7 s -1 , =6×10 8 s -1 K=1.3, E0 represents the peak field strength in volts per meter, and u represents time in seconds. Please refer to [link / reference]. Figure 3 and Figure 4 , Figure 3 For standard time-domain waveforms, Figure 4 This is a standard frequency domain waveform.

[0159] Using the latitude and longitude of the launch point, the date (year, month, day), the altitude range (60km~800km), and the altitude step size (10km) as input parameters, in this embodiment of the invention, ionospheric data at noon in a certain region (latitude 30°N, longitude 120°E) on January 1, 2021 are selected, and the electron density along the propagation path is calculated using the IRI model. Ion density ), n( n( ), electronic temperature The density of each neutral particle was calculated using the MSIS model. The density is then calculated, and the total electron collision frequency is calculated using the electron collision frequency calculation formula. At the same time, the total electron content is calculated using the formula.

[0160] The maximum electron density value is determined from the calculated electron density distribution, and then the critical frequency of the ionosphere is derived using relevant formulas. The propagation distance D between the receiving point and the transmitting point is 800 km. The propagation attenuation of each frequency component is calculated using the free-space propagation attenuation formula.

[0161] Furthermore, disregarding the influence of the Earth's magnetic field, according to Maxwell's equations, in the absence of an external magnetic field, the current density of unmagnetized plasma satisfies:

[0162] ;

[0163] For current intensity, For electric field strength, The dielectric constant in vacuum. Let be the angular frequency. Substituting the above equation into Maxwell's equations and using... By converting the phase factor to the frequency domain, the dielectric constant of the plasma can be derived as follows:

[0164] ;

[0165] Then the relative permittivity for:

[0166] ;

[0167] ω is the angular frequency, and v is the electron collision frequency. N is the plasma angular frequency. e For electron density, The amount of electron charge. For electronic quality, Let be the vacuum permittivity. The electron density and electron collision frequency of each layer of the ionosphere are calculated using the IRI model. Based on these parameters, the relative permittivity of each layer is further calculated. According to the boundary conditions, the scattering matrix of each layer of the ionosphere is calculated. The scattering matrices of each layer are then multiplied together to obtain the global scattering matrix. Based on this global scattering matrix, the total transmission coefficient of each frequency component is calculated using formulas. Finally, using these total transmission coefficients, the amplitude and phase changes of the signal are accurately calculated using relevant formulas.

[0168] Finally, the amplitude and phase changes of each frequency component above the critical frequency after propagation in the ionosphere are calculated using the scattering matrix, and then the final time-domain waveform is synthesized using inverse Fourier transform. (See also...) Figure 5 and Figure 6 , Figure 5 To simulate time-domain waveforms, Figure 6 For the simulation of the time-frequency diagram, where, Figure 6The curve in the figure is the data fitting line. It can be seen that the time delay calculated using the scattering matrix is ​​consistent with the time delay fitted using TEC.

[0169] Example 3

[0170] Embodiment 3 of the present invention also proposes a simulation method for electromagnetic pulse propagation through the ionosphere based on the scattering matrix. The difference from Embodiment 1 of the present invention is that the step of performing an inverse Fourier transform based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere and updating the source region waveform signal takes into account the influence of the ionosphere's dispersion characteristics on waveform distortion and nonlinear effects.

[0171] Specifically, firstly, based on the dispersion relation of the ionosphere, the group velocity expressions corresponding to electromagnetic waves of different frequencies are derived. Then, based on the group velocity expressions, the group velocity corresponding to each frequency component is calculated. In this embodiment of the invention, the group velocity expression is:

[0172] ;

[0173] ;

[0174] c is the speed of light. Let be the real part of the dielectric constant. The plasma angular frequency, ω is the electron collision frequency, and ω is the angular frequency;

[0175] Based on the path length of the electromagnetic wave propagating in the ionosphere and the group velocity, the group delay corresponding to each frequency component is calculated. Then, based on the group delay of the center frequency, the group delay difference of each frequency component is calculated, where the group delay is expressed as:

[0176] ;

[0177] ;

[0178] L is the path length of the electromagnetic wave propagating in the ionosphere, and θ is the angle between the path and the direction perpendicular to the ionosphere. Correcting the actual propagation distance caused by path tilt. For group velocity, f n Effective frequency components are those whose amplitude is greater than 10% of the peak value in the frequency domain signal obtained after Fourier transform of the source waveform signal.

[0179] The group delay difference is expressed as:

[0180] ;

[0181] The group delay is the center frequency, which is the frequency corresponding to the maximum amplitude of the signal in the frequency domain.

[0182] Based on the group delay difference, the phase of each frequency component is corrected, and an inverse Fourier transform is performed to obtain the time-domain signal considering the group delay difference. It should be noted that the original frequency domain phase... After considering the group delay difference, the phase is corrected. , For frequency domain signals, maintain the amplitude at each frequency. No change, use the revised version Reconstructing frequency domain signal Then perform an inverse Fourier transform to obtain the time-domain signal considering the group delay difference. , among which, calculation The pulse width difference between the source region waveform signal s(t) and the pulse width of the source region waveform signal is used to verify whether the broadening caused by dispersion is in line with theoretical expectations.

[0183] The phase correction corresponding to the group delay difference is incorporated into the total transmission coefficient to obtain the corrected total transmission coefficient. T(f) is the total transmission coefficient at frequency f. The corrected total transmission coefficient at frequency f is... It is a continuous function of frequency, by Interpolation is performed, and an inverse Fourier transform is applied to the corrected total transmission coefficient to obtain the system impulse response with dispersion effects. ;

[0184] Convolve the source region waveform signal with the system impulse response to obtain the time-domain signal after passing through the ionosphere. And calculate the time-domain signal after passing through the ionosphere. Compared with the time-domain signal considering group delay difference The error is calculated using the root mean square error (RMSE).

[0185] Determine whether the error is less than a preset value;

[0186] If so, output the time-domain signal after passing through the ionosphere.

[0187] More specifically, based on the Townsend ionization coefficient, the threshold electric field E for electron collisional ionization in the ionosphere is determined. th Then, based on the time-domain signal after passing through the ionosphere Given vacuum impedance, calculate the instantaneous electric field strength. When the instantaneous electric field strength is greater than the threshold electric field E... th At that time, based on Townsend's ionization theory, the increase in electron density in each layer of the ionosphere caused by the strong electromagnetic pulse was calculated. ;

[0188] Increase in electron density Superimposed on the original electron density of each layer The updated electron density is obtained. ;

[0189] Based on the updated electron density, the electron collision frequency of each layer, and the total electron content along the path, the scattering matrix and total transmission coefficient are recalculated. Using the new total transmission coefficient, the inverse Fourier transform described in Embodiment 3 of this invention is performed again based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere, and the source region waveform signal is updated to obtain a new time-domain signal after passing through the ionosphere considering the strong field nonlinear effect.

[0190] Using the new time-domain signal as the new source region waveform signal, repeat the above process of "judging the electric field strength threshold → dynamically updating the ionospheric parameters → recalculating the scattering matrix and transmission coefficient → calculating the new time-domain signal" until the signal change obtained from the two iterations is within the allowable error range, thus achieving closed-loop simulation.

[0191] Example 4

[0192] Please see Figure 7 , Figure 7 This is a structural block diagram of an electromagnetic pulse propagation simulation system based on a scattering matrix, provided in Embodiment 4 of the present invention. This electromagnetic pulse propagation simulation system 200 based on a scattering matrix is ​​used to implement the above embodiments and preferred embodiments; details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0193] Specifically, the electromagnetic pulse propagation simulation system 200 based on the scattering matrix includes: a construction module 21, a layering module 22, a first calculation module 23, a second calculation module 24, and an inverse Fourier transform module 25, wherein:

[0194] Construction module 21 is used to construct the source region waveform signal, perform Fourier transform on the source region waveform signal, and obtain the amplitude and phase of different frequency components of the source region signal;

[0195] Layering module 22 is used to uniformly layer the ionosphere, obtain the electron density, electron collision frequency, and total electron content along the path of the layered ionosphere, and write the scattering matrix based on boundary conditions. The propagation constant in the scattering matrix is ​​calculated using the electron density and electron collision frequency. The time delay result is fitted using the total electron content along the path and compared with the time delay result derived from the scattering matrix. Specifically, the critical frequency of the ionosphere is calculated, and frequency components greater than the critical frequency are selected. Then, the free-space propagation attenuation of frequency components greater than the critical frequency is calculated. When radio waves are emitted vertically upwards and enter the ionosphere from the air, the first critical frequency of the ionosphere is expressed as:

[0196] ;

[0197] When radio waves are incident at an angle θ0 from the air into the ionosphere, the second critical frequency of the ionosphere is expressed as:

[0198] ;

[0199] Where, N max This represents the maximum electron density of the ionosphere.

[0200] Free space propagation attenuation is expressed as:

[0201] ;

[0202] Where f is the frequency component greater than the critical frequency, L is the free space basic transmission loss, and D is the propagation distance;

[0203] The boundary conditions for the m-th layer are:

[0204] ;

[0205] b m Let b be the transmission coefficient of the m-th sublayer. m-1 Let c be the transmission coefficient of the (m-1)th sublayer. m Let c be the reflection coefficient of the m-th sublayer. m-1 S is the reflection coefficient of the (m-1)th sublayer. m Let m be the propagation matrix of the m-th sublayer in the plasma region, expressed as:

[0206] ;

[0207] Where j is the imaginary unit, k m Let k be the propagation constant of the m-th sublayer. m-1 Let θ be the propagation constant of the (m-1)th sublayer. m Let θ represent the incident angle of the m-th sublayer. m-1d is the incident angle of the (m-1)th sublayer; m Let d be the lower boundary of the m-th sub-layer. m-1 This is the lower boundary of the (m-1)th sublayer;

[0208] The transmission region is represented as:

[0209] ;

[0210] ;

[0211] S p The scattering matrix of the transmission region is expressed as:

[0212] ;

[0213] Among them, b n Let k be the transmission coefficient of the nth sublayer. n Let d be the propagation constant of the nth sublayer. n Let θ be the lower boundary of the nth sublayer. n c represents the incident angle of the nth sublayer. n Let T be the reflection coefficient of the nth sublayer, and k be the total transmission coefficient. p Let θ be the propagation constant of the p-th sublayer. p For the final transmission angle, d p The thickness of the entire ionosphere;

[0214] The first calculation module 23 is used to combine the scattering matrices of all adjacent layers after the ionosphere is uniformly stratified, construct a global matrix, and calculate the total transmission coefficient. The global matrix is ​​represented as follows:

[0215] ;

[0216] Among them, S g S is the global matrix. g1 For the global matrix S g The first column vector, i.e. S g2 For the global matrix S g The second column vector, i.e. ;

[0217] The total transmittance is expressed as:

[0218] ;

[0219] Where r is the total reflection coefficient, T is the total transmission coefficient, and S p is the scattering matrix of the transmission region.

[0220] The second calculation module 24 is used to calculate the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere based on the total transmission coefficient. The amplitude is expressed as:

[0221] ;

[0222] Phase is represented as:

[0223] ;

[0224] Where T is the total transmittance coefficient, A0 is the initial amplitude, and A_end is the amplitude after passing through the ionosphere. For phase change, arg{•} is the argument function;

[0225] The inverse Fourier transform module 25 is used to perform an inverse Fourier transform based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere, and to update the source region waveform signal.

[0226] Furthermore, in some other embodiments of the present invention, the inverse Fourier transform module 25 includes:

[0227] The derivation unit is used to derive the group velocity expressions for electromagnetic waves of different frequencies based on the dispersion relation of the ionosphere, and to calculate the group velocity for each frequency component based on the group velocity expressions.

[0228] The first calculation unit is used to calculate the group delay corresponding to each frequency component based on the path length of the electromagnetic wave propagating in the ionosphere and the group velocity, and to calculate the group delay difference of each frequency component based on the group delay of the center frequency.

[0229] The correction unit is used to correct the phase of each frequency component according to the group delay difference and perform an inverse Fourier transform to obtain a time-domain signal considering the group delay difference.

[0230] The inverse Fourier transform unit is used to incorporate the phase correction corresponding to the group delay difference into the total transmission coefficient to obtain the corrected total transmission coefficient, and to perform an inverse Fourier transform on the corrected total transmission coefficient to obtain the system impulse response containing the dispersion effect.

[0231] A convolution unit is used to convolve the source region waveform signal with the system impulse response to obtain the time-domain signal after passing through the ionosphere, and to calculate the error between the time-domain signal after passing through the ionosphere and the time-domain signal considering the group delay difference.

[0232] The judgment unit is used to determine whether the error is less than a preset value;

[0233] The output unit is used to output the time-domain signal after passing through the ionosphere when it is determined that the error is less than a preset value.

[0234] Example 5

[0235] In another aspect, the present invention also proposes an electronic device, please refer to [link to relevant documentation]. Figure 8 The image shows an electronic device according to Embodiment 5 of the present invention, including a memory 20, a processor 10, and a computer program 30 stored in the memory and executable on the processor. When the processor 10 executes the computer program 30, it implements the above-described simulation method for electromagnetic pulse propagation through the ionosphere based on the scattering matrix.

[0236] In some embodiments, the processor 10 may be a central processing unit (CPU), controller, microcontroller, microprocessor or other data processing chip, used to run program code stored in memory 20 or process data, such as executing access restriction programs.

[0237] The memory 20 includes at least one type of readable storage medium, such as flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 20 can be an internal storage unit of an electronic device, such as the hard disk of the electronic device. In other embodiments, the memory 20 can also be an external storage device of the electronic device, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. Furthermore, the memory 20 can include both internal and external storage units of the electronic device. The memory 20 can be used not only to store application software and various types of data of the electronic device, but also to temporarily store data that has been output or will be output.

[0238] It should be pointed out that, Figure 8 The structure shown does not constitute a limitation on the electronic device. In other embodiments, the electronic device may include fewer or more components than shown, or combine certain components, or have different component arrangements.

[0239] This invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix.

[0240] Those skilled in the art will understand that the logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can mean any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0241] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0242] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0243] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0244] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A simulation method for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, characterized in that, The method includes: Construct a source region waveform signal, and perform a Fourier transform on the source region waveform signal to obtain the amplitude and phase of different frequency components of the source region signal; The ionosphere is uniformly layered, and the electron density, electron collision frequency, and total electron content along the path of the layered ionosphere are obtained. The scattering matrix is ​​written out from the boundary conditions. The propagation constant in the scattering matrix is ​​calculated using the electron density and the electron collision frequency. The time delay result is fitted using the total electron content along the path and compared with the time delay result derived from the scattering matrix. The scattering matrices of all adjacent layers after the ionosphere is uniformly stratified are combined to construct a global matrix, and the total transmission coefficient is calculated. Based on the total transmission coefficient, calculate the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere; Based on the amplitude attenuation and the phase change, an inverse Fourier transform is performed to obtain the time-domain signal after passing through the ionosphere, and the source region waveform signal is updated. In the steps of uniformly dividing the ionosphere into layers, obtaining the electron density, electron collision frequency, and total electron content along the path of the layered ionosphere, and writing the scattering matrix from the boundary conditions, the boundary conditions for the m-th layer are: ； b m Let b be the transmission coefficient of the m-th sublayer. m-1 Let c be the transmission coefficient of the (m-1)th sublayer. m Let c be the reflection coefficient of the m-th sublayer. m-1 S is the reflection coefficient of the (m-1)th sublayer. m Let m be the propagation matrix of the m-th sublayer in the plasma region, expressed as: ； Where j is the imaginary unit, k m Let k be the propagation constant of the m-th sublayer. m-1 Let θ be the propagation constant of the (m-1)th sublayer. m Let θ represent the incident angle of the m-th sublayer. m-1 d is the incident angle of the (m-1)th sublayer; m Let d be the lower boundary of the m-th sub-layer. m-1 This is the lower boundary of the (m-1)th sublayer; The transmission region is represented as: ； ； S p The scattering matrix of the transmission region is expressed as: ； Among them, b n Let k be the transmission coefficient of the nth sublayer. n Let d be the propagation constant of the nth sublayer. n Let θ be the lower boundary of the nth sublayer. n c represents the incident angle of the nth sublayer. n Let T be the reflection coefficient of the nth sublayer, and k be the total transmission coefficient. p Let θ be the propagation constant of the p-th sublayer. p For the final transmission angle, d p The thickness of the entire ionosphere; In the step of simulating the scattering matrices of all adjacent layers after the ionosphere is uniformly stratified to construct a global matrix and calculating the total transmission coefficient, the global matrix is ​​represented as follows: ； Among them, S g S is the global matrix. g1 For the global matrix S g The first column vector, i.e. S g2 For the global matrix S g The second column vector, i.e. ; The total transmittance is expressed as: ； Where r is the total reflection coefficient, T is the total transmission coefficient, and S p The scattering matrix of the transmission region; In the step of calculating the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere based on the total transmission coefficient, the amplitude is expressed as: ； Phase is represented as: ； Where T is the total transmittance coefficient, A0 is the initial amplitude, and A_end is the amplitude after passing through the ionosphere. For phase change, arg{•} is the argument function.

2. The simulation method for electromagnetic pulse propagation through the ionosphere based on the scattering matrix according to claim 1, characterized in that, In the steps of uniformly dividing the ionosphere into layers, obtaining the electron density, electron collision frequency, and total electron content along the path of the layered ionosphere, and writing the scattering matrix from the boundary conditions, the critical frequency of the ionosphere is calculated, and frequency components greater than the critical frequency are selected. Then, the propagation attenuation of the frequency components greater than the critical frequency in free space is calculated.

3. The simulation method for electromagnetic pulse propagation through the ionosphere based on the scattering matrix according to claim 2, characterized in that, When radio waves are emitted vertically upwards and enter the ionosphere from the air, the first critical frequency of the ionosphere is expressed as: ； When radio waves are incident at an angle θ0 from the air into the ionosphere, the second critical frequency of the ionosphere is expressed as: ； Where, N max This represents the maximum electron density of the ionosphere.

4. The simulation method for electromagnetic pulse propagation through the ionosphere based on the scattering matrix according to claim 3, characterized in that, The step of performing an inverse Fourier transform based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere, and updating the source region waveform signal, includes: Based on the dispersion relation of the ionosphere, the group velocity expressions for electromagnetic waves of different frequencies are derived, and the group velocity for each frequency component is calculated based on the group velocity expressions. Based on the path length of electromagnetic waves propagating in the ionosphere and the group velocity, the group delay corresponding to each frequency component is calculated, and the group delay difference of each frequency component is calculated based on the group delay of the center frequency. Based on the group delay difference, the phase of each frequency component is corrected and an inverse Fourier transform is performed to obtain a time-domain signal considering the group delay difference. The phase correction corresponding to the group delay difference is incorporated into the total transmission coefficient to obtain the corrected total transmission coefficient. The corrected total transmission coefficient is then subjected to an inverse Fourier transform to obtain the system impulse response containing the dispersion effect. The source region waveform signal is convolved with the system impulse response to obtain the time-domain signal after passing through the ionosphere, and the error between the time-domain signal after passing through the ionosphere and the time-domain signal considering the group delay difference is calculated. Determine whether the error is less than a preset value; If so, output the time-domain signal after passing through the ionosphere.

5. A simulation system for electromagnetic pulse propagation through the ionosphere based on a scattering matrix, characterized in that, For implementing the electromagnetic pulse propagation simulation method based on the scattering matrix as described in any one of claims 1-4, the system comprises: A construction module is used to construct a source region waveform signal, and to perform a Fourier transform on the source region waveform signal to obtain the amplitude and phase of different frequency components of the source region signal; The layering module is used to uniformly layer the ionosphere, obtain the electron density, electron collision frequency, and total electron content along the path of the layered ionosphere, and write the scattering matrix from the boundary conditions; The first calculation module is used to combine the scattering matrices of all adjacent layers after the ionosphere is uniformly stratified, construct a global matrix, and calculate the total transmission coefficient. The second calculation module is used to calculate the amplitude attenuation and phase change of a single-frequency signal propagating in the ionosphere based on the total transmission coefficient. The inverse Fourier transform module is used to perform an inverse Fourier transform based on the amplitude attenuation and the phase change to obtain the time-domain signal after passing through the ionosphere, and to update the source region waveform signal.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the simulation method for electromagnetic pulse propagation through the ionosphere based on the scattering matrix as described in any one of claims 1-4.

7. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the simulation method for electromagnetic pulse propagation through the ionosphere based on the scattering matrix as described in any one of claims 1-4.

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