Parabolic equation time-domain simulation modeling method for anisotropic ionospheric shortwave propagation

Abstract

The application relates to the field of communication technology, and particularly discloses a parabolic equation time domain simulation modeling method for anisotropic ionosphere shortwave propagation; based on a sub-step Fourier transform algorithm, an atmospheric refraction index model is introduced to distinguish and model ordinary wave and non-ordinary wave propagation modes; through in-band sampling and multi-frequency point scanning calculation, a channel transfer function between a transmitting point and a receiving point is obtained; in combination with a Fourier synthesis method and a correlation function method, frequency domain and time domain characteristic parameters of electromagnetic wave propagation are obtained. The application can improve the electromagnetic simulation precision of skywave propagation and effectively improve the multi-domain electromagnetic simulation capability of skywave propagation.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and more specifically, to a time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionospheric regions. Background Technology

[0002] Shortwave skywave communication (operating frequency band 2MHz-30MHz) relies on single or multiple reflections from the ionosphere to achieve long-distance signal transmission, with communication distances reaching thousands of kilometers. The wireless link quality of shortwave skywave communication largely depends on the ionospheric characteristics when the communication equipment is operating; see the principle section for details. Figure 1 The electron density distribution and electron collision frequency in the ionosphere typically exhibit significant differences across different regions (latitude and longitude), atmospheric altitudes, seasons, and times of day. Furthermore, they are influenced by solar eclipse cycles. Therefore, in engineering, it is necessary to rationally select or design operating frequencies, operating periods, and transmission elevation angles based on the inherent characteristics and real-time variations of the ionosphere. However, acquiring extensive field measurements or long-term monitoring of the ionospheric shortwave propagation characteristics to optimize communication parameters would be extremely costly in terms of manpower, resources, and time. In contrast, electromagnetic simulation technology based on electromagnetic theory and high-precision numerical calculations offers a practical, lower-cost, and more efficient solution.

[0003] Currently, electromagnetic simulation models for skywave propagation mainly include semi-empirical models based on measured data (such as ITU-REC-533), ray tracing, and parabolic equation methods. Semi-empirical models are simple and fast, but suffer from low computational accuracy and unclear physical processes. Ray tracing is well-suited for tropospheric and ionospheric propagation problems, often used to calculate electromagnetic wave trajectories. Furthermore, the parabolic equation method, derived from splitting the wave equation, has been proven equally applicable to ionospheric electromagnetic numerical simulation. This method, given initial conditions and boundaries, iterates spatially to obtain electromagnetic field information across the entire propagation domain. For linearly polarized electromagnetic waves, influenced by the Earth's magnetic field, they split into ordinary and extraordinary waves during ionospheric propagation. Due to the different refractive indices of these two waves in the ionosphere, birefringence occurs, with the refraction angle influenced by the Earth's magnetic field strength within the propagation region. Traditional parabolic equation simulation models neglect the influence of the Earth's magnetic field, treating the ionosphere as an isotropic medium, thus failing to characterize the birefringence phenomenon and reducing the accuracy of the electromagnetic model. Furthermore, traditional simulation modeling methods are based on single-frequency processing and are mainly used to simulate the attenuation characteristics of electromagnetic waves. They cannot reflect the multipath delay of propagation modes such as single-hop / multi-hop skywaves, high elevation angle / low elevation angle, and time-domain characteristic information such as the envelope of the received pulse. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionosphere. This invention improves the accuracy of electromagnetic simulation of skywave propagation and effectively enhances the multi-domain electromagnetic simulation capability of skywave propagation, enabling effective characterization of phenomena such as attenuation, dispersion, birefringence, waveform distortion, and time delay generated by the ionosphere.

[0005] The solution adopted by this invention to solve the technical problem is:

[0006] A time-domain simulation modeling method for parabolic shortwave propagation in anisotropic ionospheric regions is proposed. Based on the step-by-step Fourier transform algorithm, an atmospheric refractive index model is introduced to distinguish and model the propagation modes of ordinary and extraordinary waves. The channel transfer function between the transmitter and receiver is obtained through in-band sampling and multi-frequency scanning calculation. The frequency and time domain characteristic parameters of electromagnetic wave propagation are obtained by combining the Fourier synthesis method and the correlation function method.

[0007] In some possible implementations, the specific steps include:

[0008] Step S1: Construct the propagation geographic environment; specifically: using digital elevation maps and surface medium databases, and combining them with parabolic equation grid systems, establish a propagation geographic environment model and set surface boundary conditions;

[0009] Step S2: Based on the atmospheric layer structure and its mechanism of action on electromagnetic waves, establish an atmospheric refractive index model for the propagation of electromagnetic waves in the atmosphere.

[0010] Step S3: Calculate the multi-frequency point of the spatial electromagnetic field to obtain the channel transfer function between the transmitting and receiving points;

[0011] Step S4: Obtain time-frequency domain information characterizing the propagation features of electromagnetic waves, generate propagation feature parameters, and complete the simulation.

[0012] In some possible implementations, step S1 specifically includes the following steps:

[0013] Step S11: Based on the location of the transmitting and receiving antennas, use spatial interpolation methods to extract terrain elevation data consistent with the parabolic equation grid system from the original digital elevation map;

[0014] Step S12: Combine the surface medium database and topographic elevation data to establish the mapping relationship between the lower boundary grid points of the computational domain and the surface medium, and set the surface boundary conditions according to the mapping relationship.

[0015] In some possible implementations, the atmospheric refractive index model includes a tropospheric atmospheric model and an ionospheric atmospheric model;

[0016] Step S2 specifically includes the following steps:

[0017] Step S21: Establish a tropospheric refractive index model;

[0018] Step S22: Introduce geomagnetic field components and establish an atmospheric refractive index model of the ionosphere.

[0019] In some possible implementations, step S21 specifically refers to:

[0020] Within the troposphere, a model of the tropospheric refractive index is established:

[0021] n t =1+313 -0.36z ×10 -6 (1);

[0022] Where z is the height variable.

[0023] In some possible implementations, step S22 specifically refers to:

[0024] In the region from the upper boundary of the troposphere to the maximum calculation height, an atmospheric refractive index model of the ionosphere is established using formulas (2) and (3);

[0025]

[0026]

[0027] Wherein, the subscripts O and X represent ordinary waves and extraordinary waves, respectively.

[0028] variable

[0029]

[0030]

[0031] χ = ν / 2πf;

[0032] m is the electron mass (kg);

[0033] e represents the electron charge (C);

[0034] ε0 is the dielectric constant (F / m);

[0035] electron concentration (m -3 );

[0036] v is the electron collision frequency (s) -1 );

[0037] B TThis is the projection of the Earth's magnetic field onto the direction perpendicular to the wave vector;

[0038] B L This represents the projection of the geomagnetic field onto the direction of the wave vector; where the geomagnetic field is obtained from the International Geomagnetic Reference Field Model.

[0039] In some possible implementations, step S3 specifically includes the following steps:

[0040] Step S31: Perform time-frequency conversion on the time-domain pulse signal, and determine the frequency based on the spectral function and the time-domain observation window length T. w The frequency point to be calculated is determined by the signal bandwidth B;

[0041]

[0042] Step S32: Calculate the sampling frequency f of each sampling point within the band using the following formula. i The corresponding electromagnetic field wave function;

[0043]

[0044] In the formula, Δx is the step value in the rectangular coordinate system (x,z);

[0045] k0 is the vacuum propagation constant;

[0046] and For Fast Fourier Transform and Inverse Fourier Transform;

[0047] For ordinary waves, take n = n o For unusual waves, take n=n X ;

[0048] Step S33: Calculate the channel transfer function between the transmitter and receiver.

[0049] H(f)=u(x r ,z r ,f) (5);

[0050] Wherein, the subscript r represents the receiving antenna.

[0051] In some possible implementations, step S4 specifically includes the following steps:

[0052] Step S41: Calculate the spatial radio wave propagation loss using formula (6);

[0053]

[0054] In the formula, u0 is the wave function under free space conditions;

[0055] L0 is the free space propagation loss;

[0056] r is a distance variable.

[0057] Step S42: Calculate the pulse waveform at the receiving end using formula (7);

[0058]

[0059] In the formula, F(f) is the signal spectrum function;

[0060] Step S43: Calculate the electromagnetic wave propagation delay information.

[0061] In some possible implementations, step S43 specifically includes the following steps:

[0062] Step S431: Let u ref =u(x t ,z t (t) represents the reference signal; where the subscript t represents the transmitting antenna;

[0063] Step S432: Put u r with u ref Perform related operations, where the related function can be expressed as:

[0064]

[0065] Step S433: By searching the peak of the relevant function, obtain the time when R(τ) reaches its maximum value;

[0066] τ add =argmax{R(τ)} (9);

[0067] According to the definition of the relevant function, τ add For u r with u ref The relative time delay between them;

[0068] Step S434: Since the wave function u does not contain the phase term of the electromagnetic wave that changes rapidly in the x-direction, the total propagation delay is:

[0069]

[0070] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0071] This invention distinguishes between ordinary and unusual waves by using a birefringence index model. By combining Fourier synthesis and correlation function methods, it can effectively characterize phenomena such as attenuation, dispersion, birefringence, and time delay caused by the ionosphere, thereby greatly improving the electromagnetic simulation capability and accuracy of skywave propagation.

[0072] Compared to traditional simulation models, this invention supports time-domain feature descriptions including propagation delay and pulse envelope, thereby helping to improve the multi-domain electromagnetic simulation capabilities of skywave propagation. Attached Figure Description

[0073] Figure 1 This is a flowchart of the process of the present invention;

[0074] Figure 2 This is a flowchart illustrating the implementation of the present invention.

[0075] Figure 3 Propagation loss calculated using traditional simulation modeling methods;

[0076] Figure 4 The propagation loss obtained by simulation calculation in this invention;

[0077] Figure 5 The received pulse obtained through simulation in this invention. Detailed Implementation

[0078] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. The terms "first," "second," and similar terms used in this application do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, "a" or "one," etc., do not indicate a quantity limitation, but rather indicate the existence of at least one. In the implementation of this application, "and / or" describes the association relationship of related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more. For example, multiple positioning posts refer to two or more positioning posts. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0079] The present invention will now be described in detail.

[0080] like Figures 1-2 As shown:

[0081] A time-domain simulation modeling method for parabolic shortwave propagation in anisotropic ionospheric regions is proposed. Based on the step-by-step Fourier transform algorithm, it introduces atmospheric refractive index models and ionospheric atmospheric refractive index models to distinguish and model the propagation modes of ordinary and extraordinary waves. The channel transfer function between the transmitter and receiver is obtained through in-band sampling and multi-frequency scanning calculation. The frequency and time domain characteristic parameters of electromagnetic wave propagation are obtained by combining the Fourier synthesis method and the correlation function method.

[0082] This invention distinguishes between ordinary and unusual waves by using a birefringence index model, and by combining Fourier synthesis and other techniques, it can characterize phenomena such as attenuation, dispersion, birefringence and time delay generated by the ionosphere.

[0083] In some possible implementations, the specific steps include:

[0084] Step S1: Construct the propagation geographic environment; specifically, using digital elevation maps and surface medium databases, and combining them with a parabolic equation grid system, establish a propagation geographic environment model and set surface boundary conditions; this includes the following steps:

[0085] Step S11: Based on the location of the transmitting and receiving antennas, use spatial interpolation methods to extract terrain elevation data consistent with the parabolic equation grid system from the original digital elevation map;

[0086] Step S2: Based on the atmospheric layering structure and its mechanism of action on electromagnetic waves, establish an atmospheric refractive index model for electromagnetic wave propagation in the atmosphere; specifically including the following steps:

[0087] Step S21: Establish a tropospheric refractive index model; specifically:

[0088] Within the troposphere, a model of the tropospheric refractive index is established:

[0089] n t =1+313 -0.36z ×10 -6 (1);

[0090] Where z is the height variable.

[0091] Step S22: Based on the ionospheric electron concentration, ionospheric electron collision frequency, and geomagnetic field components, establish an ionospheric atmospheric refractive index model; specifically:

[0092] In the region from the upper boundary of the troposphere to the maximum calculation height, an atmospheric refractive index model of the ionosphere is established using formulas (2) and (3);

[0093]

[0094]

[0095] Wherein, the subscripts O and X represent ordinary waves and extraordinary waves, respectively;

[0096] variable χ = ν / 2πf;

[0097] m is the electron mass (kg);

[0098] e represents the electron charge (C);

[0099] ε0 is the dielectric constant (F / m);

[0100] electron concentration (m -3 );

[0101] v is the electron collision frequency (s) -1 );

[0102] B T T is the projection of the Earth's magnetic field in the direction perpendicular to the wave vector.

[0103] B L T is the projection of the geomagnetic field onto the direction of the wave vector; the geomagnetic field is obtained from the International Geomagnetic Reference Field Model (IGRF).

[0104] Step S3: Calculate the multi-frequency point of the spatial electromagnetic field to obtain the channel transfer function between the transmitting and receiving points; specifically, it includes the following steps:

[0105] Step S31: Perform time-frequency conversion on the time-domain pulse signal, and determine the frequency based on the spectral function and the time-domain observation window length T. w The frequency point to be calculated is determined by the signal bandwidth B;

[0106] f i i = 1, 2, 3, ..., N f ), N f =T w ;

[0107] Step S32: Calculate the sampling frequency f of each sampling point within the band using the following formula. i The corresponding electromagnetic field wave function;

[0108]

[0109] In the formula, Δx is the step value in the rectangular coordinate system (x,z), and k0 is the vacuum propagation constant. and This represents the Fast Fourier Transform and Inverse Fourier Transform, where n = n for ordinary waves. o For unusual waves, take n=n X ;

[0110] Step S33: Calculate the channel transfer function between the transmitter and receiver.

[0111] H(f)=u(x r ,z r ,f) (5);

[0112] Wherein, the subscript r represents the receiving antenna.

[0113] Step S4: Obtain time-frequency domain information characterizing electromagnetic wave propagation features from the multi-frequency calculation results of the spatial electromagnetic field, transmit propagation characteristic parameters, and complete the simulation; specifically, this includes the following steps:

[0114] Step S41: Calculate the spatial radio wave propagation loss using formula (6);

[0115]

[0116] In the formula, u0 is the wave function under free space conditions;

[0117] L0 is the free space propagation loss;

[0118] r is a distance variable.

[0119] Step S42: Calculate the pulse waveform at the receiving end using formula (7);

[0120]

[0121] In the formula, F(f) is the signal spectrum function;

[0122] Step S43: Calculate the electromagnetic wave propagation delay information; Step S43 specifically includes the following steps:

[0123] Step S431: Let u ref =u(x t ,z t (t) represents the reference signal; where the subscript t represents the transmitting antenna;

[0124] Step S432: Put u r with u ref Perform related operations, where the related function can be expressed as:

[0125]

[0126] Step S433: By searching the peak of the relevant function, obtain the time when R(τ) reaches its maximum value;

[0127] τ add =argmax{R(τ)}(9);

[0128] According to the definition of the relevant function, τ add For u r with uref The relative time delay between them;

[0129] Step S434: Since the wave function does not contain a phase term that changes rapidly in the direction of the electromagnetic wave, the total propagation delay is:

[0130]

[0131] This invention proposes a time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionospheric regions to improve the electromagnetic simulation capability and accuracy of skywave propagation.

[0132] This invention is achieved through four main steps: propagation geographic environment modeling, atmospheric refractive index modeling, multi-frequency calculation of the space electromagnetic field, and generation of propagation characteristic parameters. Specifically, propagation geographic environment modeling refers to establishing a physical model of the surface reflection boundary during multi-hop propagation of electromagnetic waves; atmospheric refractive index modeling involves establishing an atmospheric refractive index model for electromagnetic wave propagation in the atmosphere, based on the atmospheric layering structure and its mechanism of action on electromagnetic waves, including tropospheric and ionospheric models; multi-frequency calculation of the space electromagnetic field involves solving for the spatial field distribution corresponding to multiple sampling frequency points within the band to obtain the channel transfer function between the transmitting and receiving points; and generation of propagation characteristic parameters involves obtaining time-frequency domain information characterizing the propagation characteristics of electromagnetic waves from the results of the multi-frequency calculation of the space electromagnetic field. Compared to traditional simulation models, this invention supports time-domain feature descriptions including propagation delay and pulse envelope, which helps improve the multi-domain electromagnetic simulation capabilities of skywave propagation. This invention distinguishes between ordinary and extraordinary waves through a birefringence index model, and, in conjunction with techniques such as Fourier synthesis, can characterize phenomena such as attenuation, dispersion, birefringence, waveform distortion, and time delay generated by the ionosphere.

[0133] To compare the simulation accuracy of this invention with existing traditional simulation methods, a comparison is made between the propagation loss of a city in Northwest China (denoted as X) and a city in the southern coastal region of China (denoted as G). Figure 3 The propagation loss is calculated using traditional simulation modeling methods. Figure 4 The propagation loss is calculated using the simulation modeling method of this invention; see reference. Figure 3 and Figure 4 As can be seen, compared with traditional simulation modeling methods, this invention takes into account the influence of the geomagnetic field and can characterize the non-reciprocity of the electromagnetic wave propagation process, thus achieving higher electromagnetic simulation accuracy.

[0134] Figure 5 The received pulse obtained through simulation in this invention; traditional simulation models based on single-frequency point processing methods cannot characterize the time-domain characteristics of electromagnetic signals propagating in the ionosphere. This invention enables the calculation of the received pulse envelope and time delay information.

[0135] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionospheric regions, characterized in that, Based on the step-by-step Fourier transform algorithm, an atmospheric refractive index model is introduced to distinguish and model the propagation modes of ordinary and extraordinary waves. The channel transfer function between the transmitting and receiving points is obtained through in-band sampling and multi-frequency scanning calculations. Combining the Fourier synthesis method and the correlation function method, the frequency and time domain characteristic parameters of electromagnetic wave propagation are obtained, specifically including the following steps: Step S1: Construct the propagation geographic environment; specifically: using digital elevation maps and surface medium databases, and combining them with parabolic equation grid systems, establish a propagation geographic environment model and set surface boundary conditions; Step S2: Based on the atmospheric layering structure and its mechanism of action on electromagnetic waves, establish an atmospheric refractive index model for electromagnetic wave propagation in the atmosphere; the atmospheric refractive index model includes a tropospheric atmospheric model and an ionospheric atmospheric model; specifically, it includes the following steps: Step S21: Establish a tropospheric refractive index model; Step S22: Establish an atmospheric refractive index model for the ionosphere; specifically: In the region from the upper boundary of the troposphere to the maximum calculation height, an atmospheric refractive index model of the ionosphere is established using formulas (2) and (3); （2）； （3）； Among them, subscript and They are ordinary waves and extraordinary waves, respectively; variable ; ； ； ； For electronic quality; For electron charge; It is the dielectric constant; Electron concentration; The electron collision frequency; This is the projection of the Earth's magnetic field onto the direction perpendicular to the wave vector; This represents the projection of the geomagnetic field onto the direction of the wave vector; the geomagnetic field is obtained from the International Geomagnetic Reference Field Model. Step S3: Calculate the multi-frequency point of the spatial electromagnetic field to obtain the channel transfer function between the transmitting and receiving points; specifically, it includes the following steps: Step S31: Perform time-frequency conversion on the time-domain pulse signal, and determine the frequency based on the spectral function and the length of the time-domain observation window. and signal bandwidth Determine the frequency point to be calculated; ， ； Step S32: Calculate the sampling frequency points within the band sequentially using the following formula. The corresponding electromagnetic field wave function; （4）； In the formula, Cartesian coordinate system The step value in the middle; The vacuum propagation constant; and For Fast Fourier Transform and Inverse Fourier Transform; For ordinary wave Unusual wave ; Step S33: Calculate the channel transfer function between the transmitter and receiver. （5）； Among them, subscript For receiving antennas; Step S4: Obtain time-frequency domain information characterizing the propagation features of electromagnetic waves, generate propagation feature parameters, and complete the simulation.

2. The time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionosphere according to claim 1, characterized in that, Step S1 specifically includes the following steps: Step S11: Based on the location of the transmitting and receiving antennas, use spatial interpolation methods to extract terrain elevation data consistent with the parabolic equation grid system from the original digital elevation map; Step S12: Combine the surface medium database and topographic elevation data to establish the mapping relationship between the lower boundary grid points of the computational domain and the surface medium, and set the surface boundary conditions according to the mapping relationship.

3. The time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionosphere according to claim 2, characterized in that, Step S21 specifically refers to: Within the troposphere, a model of the tropospheric refractive index is established: （1）； Where z is the height variable.

4. The time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionosphere according to claim 3, characterized in that, Step S4 specifically includes the following steps: Step S41: Calculate the spatial radio wave propagation loss using formula (6); （6）； In the formula, The wave function under free space conditions; For free space propagation loss; For distance variables; Step S42: Calculate the pulse waveform at the receiving end using formula (7); （7）； In the formula, It is a signal spectrum function; Step S43: Calculate the electromagnetic wave propagation delay information.

5. The time-domain simulation modeling method for parabolic equations of shortwave propagation in anisotropic ionosphere according to claim 4, characterized in that, Step S43 specifically includes the following steps: Step S431: Let For reference signal; where, subscript For transmitting antenna; Step S432: ... and Perform related operations, where the related function can be expressed as: （8）； Step S433: Obtain the peak value through the correlation function. The moment when the maximum value is reached; （9）； According to the definition of the relevant functions, for and The relative time delay between them; Step S434: Due to the wave function Contains no electromagnetic waves For phase terms that change direction rapidly, the total propagation delay is: （10）。

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