Troposphere scattering sea sweeping channel modeling and analyzing method based on parabolic equation

Abstract

The invention relates to a troposphere scattering sea sweeping channel modeling and analyzing method based on a parabolic equation, and belongs to the technical field of wireless communication. The method comprises the following steps: firstly, acquiring meteorological data of a scatter communication channel modeling area based on WRF meteorological data mode inversion, including three meteorological parameters of air pressure, temperature and humidity, calculating and correcting an atmospheric refractive index M, and solving an atmospheric correction refractive index profile na; secondly, calculating a refractive index vertical gradient M'according to the atmospheric correction refractive index M, representing an atmospheric refractive index structure constant # imgabs0 #, then substituting # imgabs1 # into refractive index disturbance caused by turbulence, and describing random disturbance nf; and finally, substituting the atmosphere correction refractive index profile na and the random disturbance nf into a Fit-Fleck type wide-angle parabolic equation derived through a two-dimensional Helmholtz equation, performing numerical solution by using a step-by-step Fourier transform method, and constructing a troposphere scattering model. The method represents the problem of influence of atmospheric turbulence on radio wave propagation.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communications and relates to a tropospheric scattering sea-skimming channel modeling and analysis method based on a parabolic equation. Background Art

[0002] Tropospheric scatter propagation is an important way of over-the-horizon radio wave propagation. It mainly uses radio waves in ultra-short wave and microwave frequency bands to transmit energy for hundreds to thousands of kilometers in tropospheric phenomena such as atmospheric turbulence and horizontal stratification. This propagation mode is almost unaffected by the geographical environment. The single-hop communication distance can reach hundreds of kilometers, and the longest can reach thousands of kilometers, and it has a large transmission capacity. Due to the frequent occurrence of complex weather phenomena such as cold and warm air convection storms and clouds at sea, it is very easy to form tropospheric scattering phenomena such as atmospheric turbulence and sharp refractive index change layers, which make radio waves propagate over a long distance, forming tropospheric scattering propagation. With the development of computer technology, it has produced important interactions with electromagnetic field and electromagnetic wave theory, and computational electromagnetics has been generated. With the help of computers, numerical calculation methods can help better simulate the propagation characteristics of electromagnetic waves in different atmospheric physical environments, and consider the influence of different factors on the propagation characteristics. Constructing a propagation model with the help of parabolic equations is the core of mastering the influence of atmospheric environment on radio wave propagation, and it is also the application target of physical measurement technology and mesoscale simulation to obtain meteorological research data.

[0003] Traditional tropospheric scatter channel modeling is mainly based on empirical formulas and statistical models, such as the long ellipse scattering model, the Clarkes and Jakes model, the ITU-R P.617 model, etc. Although these methods can describe the average characteristics of signal propagation to a certain extent, their accuracy and adaptability in dynamic environments are poor. In addition, traditional models often ignore the impact of factors such as complex terrain and meteorological conditions on channel propagation characteristics, which limits their practical applications.

[0004] In recent years, physics-based deterministic channel modeling methods have received widespread attention. As an efficient wave propagation calculation method, the parabolic equation (PE) method can accurately simulate the propagation characteristics of signals in complex environments. The parabolic equation efficiently calculates the refraction and scattering effects of radio waves in different media by approximating the wave equation. Using the parabolic equation to construct a tropospheric scattering channel model can accurately characterize the propagation characteristics of radio waves, and is particularly suitable for describing complex terrain and dynamic environments.

[0005] However, the current tropospheric scattering channel modeling method based on parabolic equations still faces some technical difficulties. The first is how to characterize the atmospheric refractive index distribution and surface reflection characteristics, and the second is how to optimize the computational efficiency through numerical methods. To solve these problems, a tropospheric scattering sea-skimming channel modeling and analysis method based on parabolic equations is proposed, aiming to build a more accurate and efficient channel model to meet the needs of modern wireless communications. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a tropospheric scattering sea-skimming channel modeling and analysis method based on parabolic equations, aiming to solve the problems of insufficient accuracy, poor adaptability to dynamic environments and low computational efficiency in existing tropospheric scattering channel modeling. This method introduces the parabolic equation theory, combines the physical characteristics of the troposphere and environmental parameters, and establishes a channel model that can accurately describe the signal propagation characteristics, which is suitable for tropospheric scattering communications under complex terrain and dynamic meteorological conditions.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A parabolic equation-based tropospheric scatter sea-skimming channel modeling and analysis method, the method comprising the following steps:

[0009] Step 1: Environmental inversion: Invert the meteorological data of the scattering area based on the WRF meteorological data model, including real-time meteorological parameters of air pressure, temperature, and humidity, and calculate the atmospheric refractive index distribution;

[0010] Step 2: Atmospheric refractive index modeling: Combine the inverted meteorological parameters to establish a dynamic refractive index distribution model. Use a hierarchical modeling method to integrate meteorological parameters and random disturbances to characterize the change of atmospheric refractive index with height. Smooth the refractive index distribution and discretize the continuous refractive index distribution in the height direction so that each step height corresponds to an atmospheric refractive index to adapt to the subsequent parabolic equation algorithm.

[0011] Step 3: Parabolic equation scattering channel modeling: In the Feit-Fleck wide-angle scattering parabolic equation, based on the approximate wave equation, the impedance boundary of the atmospheric turbulence profile structure is derived, the boundary conditions and initial field are set, and the surface reflection coefficient is introduced considering the radio wave polarization mode to ensure the physical meaning of the channel model while ensuring the stability of the numerical solution;

[0012] Step 4: Numerical solution of parabolic equations: Use the split-step fourier transform (SSFT) method to discretely solve the parabolic equations; divide the appropriate grid in the space-time dimension according to the scattering communication channel modeling area and communication frequency; gradually calculate the tropospheric radio wave propagation path and intensity, including refraction, scattering and reflection paths;

[0013] Step 5: Scattering loss analysis: Consider the scattering of radio waves caused by turbulence and calculate the path loss;

[0014] Step 6: Comparative analysis of channel characteristics: Compare the proposed scattering channel model with the ITU model and measured data to verify the accuracy and effectiveness of the proposed model.

[0015] Further, the step 1 is specifically as follows:

[0016] Step 1-1: Atmospheric parameter collection: Introduce the turbulent atmospheric structure model and use the atmospheric refractive index structure constant Determine the intensity of environmental disturbances:

[0017]

[0018] Where: r is a random number uniformly distributed between [0,1]; S n (k) is the refractive index power spectrum; k = 2π / L 0 .a 2 is a constant, about 2.8; α' is the ratio of the turbulent diffusion coefficient, which does not change much (approximately 1); L 0 is the outer flow scale, the test scale is about tens of meters, and M' is calculated by steps one to three.

[0019] Step 1-2: Invert the meteorological data of the tropospheric scatter channel modeling area, including parameters such as air pressure, temperature, and humidity, and calculate the atmospheric refractive index distribution. The relationship between humidity U, pressure P, and temperature T in a certain area and height h is as follows:

[0020]

[0021] P=P 0 exp(-1.256×10 -4 h) (37)

[0022] T=t 0 -0.006047h (h<12970m) (38)

[0023] Where, h is the height from the ground, in meters, U 0 is the relative humidity near the ground, P 0 is the surface pressure, t 0 is the surface temperature. Under standard atmospheric conditions, the surface temperature is 15°C, so t 0 =15℃, pressure P 0 =1013.25hPa, relative humidity is generally between 50% and 80%, taking about 76.8%.

[0024] Step 1-3: The relationship between atmospheric refractive index and atmospheric temperature T, water vapor pressure e, and pressure P is:

[0025]

[0026] Where T is the absolute temperature of the troposphere, in K; e is the water vapor pressure, in hPa; P is the atmospheric pressure, in hPa, expressed as:

[0027]

[0028] Usually, the atmospheric refractive index N is defined to characterize the effect of the tropospheric atmosphere on radio wave propagation, and the unit is N-units. The relationship between the atmospheric refractive index N and the atmospheric refractive index n can be expressed as:

[0029] N=(n-1)×10 6 (41)

[0030] By taking the derivative of equation (39) with respect to h, we can obtain the vertical rate of change of atmospheric refractive index with height, which is called the refractive index gradient:

[0031]

[0032] Using Snell's law in spherical layered media, the corrected refractive index is obtained:

[0033]

[0034] Where h is the height above the ground, in meters; R is the radius of the earth, R = 6371 km. Using the relationship in equation (9), the corrected average refractive index profile n can be obtained: a =1+M×10 -6 , Substituting equation (39) into equation (43) and taking the derivative with respect to h, we obtain:

[0035]

[0036] Substituting equation (44) into equation (35), we can obtain the atmospheric refractive index structure constant:

[0037] Further, the step three is specifically as follows:

[0038] Step 3-1: In the two-dimensional rectangular coordinate system (x, z), assume that the time harmonic factor of the electromagnetic field is e -iwt , the electric or magnetic field component ψ(x,z) satisfies the two-dimensional scalar Helmholtz equation of the following form:

[0039]

[0040] In the formula, k 0is the free space wave number, n is the atmospheric refractive index. The wave function in the positive x direction is defined as:

[0041]

[0042] Substituting into equation (45) and factorizing it, we get:

[0043]

[0044] Where: Q is called the pseudo differential operator

[0045]

[0046] Considering only the forward propagation of electromagnetic waves, we get the forward parabolic equation:

[0047]

[0048] Using the Feit-Fleck approximation for operator Q and substituting it into equation (49), we can obtain the wide-angle parabolic equation in the following form:

[0049]

[0050] Step 3-2: Use the Leontovich impedance boundary condition to deal with the lower boundary of the parabolic equation calculation area:

[0051]

[0052] Among them, z is the coordinate value in the height direction, u is the electric field value, and α reflects the impedance characteristics of the lower boundary condition. Under the conditions of horizontal polarization and vertical polarization of electromagnetic waves, the following relationships are satisfied respectively:

[0053]

[0054] Among them, i, k represent the corresponding grid point positions in the x and z directions, θ i is the antenna elevation angle, ε r is the relative complex permittivity of the lower boundary and satisfies the following relationship:

[0055] ε r =ε g +i60σλ (53)

[0056] Among them, ε g and σ represent the relative permittivity and conductivity of the lower boundary respectively, and λ represents the wavelength of the electromagnetic wave.

[0057] Step 3-3: Use the window function to set the absorption layer at the upper boundary. All the upward propagating waves are attenuated to zero by the absorption layer without reflection. The expression of the commonly used Cosine-taper window function W(z) is as follows:

[0058]

[0059] Where Z is the vertical height of the computational domain and z is the coordinate value in the height direction.

[0060] Step 3-4: Use Gaussian source as the initial field. The expression of Gaussian antenna is:

[0061]

[0062] Here p = ksinθ and according to the half-wave width θ bW We get w as:

[0063]

[0064] The parabolic equation represents the initial aperture field as:

[0065]

[0066] Substituting the Gaussian pattern gives the initial aperture field, in which case the Fourier transform can be determined. 0 , launch elevation angle α, maximum calculated height z max , the emission source of the Gaussian pattern is:

[0067]

[0068] According to the mirror theory, the initial field of the upper half space is placed in the ideal reflecting terrain to meet the mirror symmetry condition. The initial field expression is:

[0069] u(0,z)=u fs (0,z)-u fs (0,-z) (59)

[0070] Steps 3-5: Polarization modes are divided into horizontal polarization and vertical polarization. Different polarization modes have different reflection coefficients:

[0071]

[0072] Where α is the incident angle, sinα is the sine of the incident angle, sinα=p / k 0 , p is the spectral domain variable, k 0 is the wave number, ε r is the relative dielectric constant.

[0073] Further, the step 4 is specifically as follows:

[0074] Step 4-1: Use the split-step Fourier transform (SSFT) method to discretize the parabolic equation (50):

[0075]

[0076] In the formula, ζ and ζ -1 Fourier transform and inverse transform respectively, p = k 0 sinθ is the spatial frequency, and θ is the angle between the electromagnetic wave and the horizontal direction. 0 ,z), we can use equation (61) to get the field distribution u(x 0 +Δx,z), thereby iteratively obtaining the field distribution in the entire space.

[0077] Step 4-2: Substitute the random perturbation factor n obtained in step 1 f Add the average refractive index profile n a Substituting into the parabolic equation, we obtain the tropospheric scatter channel model based on the parabolic equation.

[0078] Further, the step five is specifically as follows:

[0079] Step 5-1: After obtaining the simplified field u(x,z) at each location in space in step 4, the transmission loss can be obtained:

[0080] L=32.44+20logf+20logd-10logF 2 (62)

[0081] In the formula, f is the communication frequency in MHz; d is the propagation distance in km, that is, the step distance x, and F is the propagation factor. For the parabolic equation, Hitney pointed out the relationship between the propagation factor F and the simplified function field u(x,z), which is expressed as:

[0082] F 2 =xu(x,z) 2 (63)

[0083] Substituting equation (63) into equation (62), we can obtain the transmission loss of the tropospheric scatter channel:

[0084] L=32.44+20log f+10logd-20logu(x,z) (64)

[0085] The beneficial effects of the present invention are:

[0086] 1. Higher modeling accuracy: The present invention combines the parabolic equation method and the turbulent atmospheric structure model to effectively capture the impact of random refractive index perturbations and turbulent characteristics on the channel during tropospheric scattering. Compared with traditional empirical models and statistical models, the present invention can more accurately describe channel characteristics in complex environments.

[0087] 2. Stronger adaptability: Based on the meteorological data of WRF real-time forecast, the more accurate atmospheric refractive index in different regions is inverted, which can accurately reflect the real scattering channel characteristics. The model of the present invention can be dynamically adjusted according to different environmental conditions (such as temperature, humidity, and air pressure) and is applicable to a variety of terrain and climate conditions.

[0088] 3. Significantly improved computational efficiency: The present invention optimizes the numerical solution of parabolic equations and adopts efficient algorithms such as the Split-Step Fourier Method (SSFT), which significantly reduces the computational time while ensuring the stability and accuracy of the solution.

[0089] 4. Comprehensive consideration of multiple physical effects: The present invention not only takes into account the refraction and scattering effects of radio waves, but also combines the multipath effect, surface reflection and turbulence effects, and comprehensively simulates various propagation characteristics in tropospheric scatter communications, providing comprehensive support for system design and performance prediction.

[0090] 5. High reliability of model verification: The present invention verifies the validity of the model through simulation comparison with the ITU standard model. The results show that the model of the present invention has higher accuracy in terms of channel characteristics such as path loss and bit error rate.

[0091] 6. Wide scope of application: The present invention is not only applicable to tropospheric scatter communication, but can also be extended to scenarios of long-distance radio communication, radar system and beyond-line-of-sight transmission, providing a highly versatile modeling method for related fields.

[0092] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0094] Figure 1 Flowchart for modeling tropospheric scatter channels based on parabolic equations;

[0095] Figure 2 This is a comparison chart of transmission loss between tropospheric scatter and free space;

[0096] Figure 3 The transmission loss comparison diagram with and without turbulence at different transformation points N;

[0097] Figure 4 This is a comparison chart of the transmission loss between the tropospheric scatter parabolic equation and the ITU-R P.617 model;

[0098] Figure 5 is the turbulence effect under different transformation point numbers N. DETAILED DESCRIPTION

[0099] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0100] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0101] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0102] See also Figure 1 to Figure 5 The parabolic equation-based tropospheric scatter channel modeling method of the present invention comprises the following steps:

[0103] Step 1: Environmental inversion: Invert the meteorological data of the channel modeling area based on the WRF meteorological data model, including the three meteorological parameters of air pressure, temperature and humidity, and calculate the atmospheric refractive index distribution;

[0104] Step 2: Atmospheric refractive index modeling: Combine the inverted meteorological parameters to establish a dynamic refractive index distribution model. Use a hierarchical modeling method to integrate meteorological parameters and random disturbances to characterize the change of atmospheric refractive index with height. Smooth the refractive index distribution and discretize the continuous refractive index distribution in the height direction so that each step height corresponds to an atmospheric refractive index to adapt to the subsequent parabolic equation algorithm.

[0105] Step 3: Parabolic equation scattering channel modeling: In the Feit-Fleck wide-angle scattering parabolic equation, based on the approximate wave equation, the impedance boundary of the atmospheric turbulence profile structure is derived, the boundary conditions and initial field are set, and the surface reflection coefficient is introduced considering the radio wave polarization mode to ensure the physical meaning of the channel model while ensuring the stability of the numerical solution;

[0106] Step 4: Numerical solution of parabolic equations: Use the split-step fourier transform (SSFT) method to discretely solve the parabolic equations; divide the appropriate grid in the space-time dimension according to the scattering communication channel modeling area and communication frequency; gradually calculate the tropospheric radio wave propagation path and intensity, including refraction, scattering and reflection paths;

[0107] Step 5: Scattering loss analysis: Consider the scattering of radio waves caused by turbulence and calculate the path loss;

[0108] Step 6: Comparative analysis of channel characteristics: Compare the proposed scattering channel model with the ITU model and measured data to verify the accuracy and effectiveness of the proposed model.

[0109] In this embodiment, step 1 includes: environmental inversion: inverting the meteorological data of the channel modeling area based on the meteorological data model of WRF, including the three meteorological parameters of air pressure, temperature and humidity, and calculating the atmospheric refractive index distribution;

[0110] Step 1-1: Atmospheric parameter collection: Introduce the turbulent atmospheric structure model and use the atmospheric refractive index structure constant Determine the intensity of environmental disturbances:

[0111]

[0112] Where: r is a random number uniformly distributed between [0,1]; S n (k) is the refractive index power spectrum; k = 2π / L 0 .a 2 is a constant, about 2.8; α' is the ratio of the turbulent diffusion coefficient, which does not change much (approximately 1); L 0 is the outer flow scale, the test scale is about tens of meters, and M' is calculated by steps one to three.

[0113] Step 1-2: Invert the meteorological data of the tropospheric scatter channel modeling area, including parameters such as air pressure, temperature, and humidity, and calculate the atmospheric refractive index distribution. The relationship between humidity U, pressure P, and temperature T in a certain area and height h is as follows:

[0114]

[0115] P=P 0 exp(-1.256×10 -4 h) (69)

[0116] T=t 0 -0.006047h (h<12970m) (70)

[0117] Where, h is the height from the ground, in meters, U 0 is the relative humidity near the ground, P 0 is the surface pressure, t 0 is the surface temperature. Under standard atmospheric conditions, the surface temperature is 15°C, so t 0 =15℃, pressure P 0 =1013.25hPa, relative humidity is generally between 50% and 80%, taking about 76.8%.

[0118] Step 1-3: The relationship between atmospheric refractive index and atmospheric temperature T, water vapor pressure e, and pressure P is:

[0119]

[0120] In the formula, T is the absolute temperature of the troposphere, in K; e is the water vapor pressure, in hPa; P is the atmospheric pressure, in hPa. The expressions of each parameter are as follows:

[0121]

[0122] The atmospheric refractive index N is usually defined to characterize the influence of the tropospheric atmosphere on the propagation effect. Its unit is N-units. The relationship between the atmospheric refractive index N and the atmospheric refractive index n can be expressed as:

[0123] N=(n-1)×10 6 (73)

[0124] By differentiating equation (71) with respect to h, we can obtain the vertical rate of change of atmospheric refractive index along the height, which is called the refractive index gradient:

[0125]

[0126] Using Snell's law in spherical layered media, the corrected refractive index is obtained:

[0127]

[0128] Where h is the height above the ground in meters; R is the radius of the earth, R = 6371 km. Using the relationship in equation (73), the corrected average refractive index profile n can be obtained: a =1+M×10 -6 , substituting equation (71) into equation (75) and taking the derivative with respect to h, we obtain:

[0129]

[0130] Substituting equation (76) into equation (67) we can obtain the atmospheric refractive index structure constant:

[0131] In this embodiment, step three includes: parabolic equation scattering channel modeling: in the Feit-Fleck type wide-angle scattering parabolic equation, based on the approximate wave equation, the impedance boundary of the atmospheric turbulence profile structure is derived, and the boundary conditions and initial fields are set to ensure the physical meaning of the channel model while ensuring the stability of the numerical solution;

[0132] Step 3-1: In the two-dimensional rectangular coordinate system (x, z), assume that the time harmonic factor of the electromagnetic field is e -iwt , the electric or magnetic field component ψ(x,z) satisfies the two-dimensional scalar Helmholtz equation of the following form:

[0133]

[0134] In the formula, k 0 is the free space wave number, n is the atmospheric refractive index. The wave function in the positive x direction is defined as:

[0135]

[0136] Substituting into equation (72) and factorizing it, we get:

[0137]

[0138] Where: Q is called the pseudo differential operator

[0139]

[0140] Considering only the forward propagation of electromagnetic waves, we get the forward parabolic equation:

[0141]

[0142] Using the Feit-Fleck approximation for operator Q and substituting it into equation (81), we can obtain the wide-angle parabolic equation in the following form:

[0143]

[0144] Step 3-2: Use the Leontovich impedance boundary condition to deal with the lower boundary of the parabolic equation calculation area:

[0145]

[0146] Among them, z is the coordinate value in the height direction, u is the electric field value, and α reflects the impedance characteristics of the lower boundary condition. Under the conditions of horizontal polarization and vertical polarization of electromagnetic waves, the following relationships are satisfied respectively:

[0147]

[0148] Among them, i, k represent the corresponding grid point positions in the x and z directions, θ i is the antenna elevation angle, ε r is the relative complex permittivity of the lower boundary and satisfies the following relationship:

[0149] ε r =ε g +i60σλ (85)

[0150] Among them, ε g represents the relative permittivity of the lower boundary, σ represents the conductivity of the lower boundary, and λ represents the wavelength of the point wave.

[0151] Step 3-3: Use the window function to set the absorption layer at the upper boundary. All the upward propagating waves are attenuated to zero by the absorption layer without reflection. The commonly used Cosine-taper window function W(z) is expressed as:

[0152]

[0153] Where Z is the vertical height of the computational domain and z is the coordinate value in the height direction.

[0154] Step 3-4: Use Gaussian source as the initial field. The expression of Gaussian antenna is:

[0155]

[0156] Here p = ksinθ and according to the half-wave width θ bW We get w as:

[0157]

[0158] The parabolic equation represents the initial aperture field as:

[0159]

[0160] Substituting the Gaussian pattern gives the initial aperture field, in which case the Fourier transform can be determined. 0 , launch elevation angle α, maximum calculated height z max , the emission source of the Gaussian pattern is:

[0161]

[0162] According to the mirror theory, the initial field of the upper half space is placed in the ideal reflecting terrain to meet the mirror symmetry condition. The initial field expression is:

[0163] u(0,z)=u fs (0,z)-u fs (0,-z) (91)

[0164] Steps 3-5: Polarization modes are divided into horizontal polarization and vertical polarization. Different polarization modes have different reflection coefficients:

[0165]

[0166] Where α is the incident angle, sinα is the sine of the incident angle, sinα=p / k 0 , p is the spectral domain variable, k 0 is the wave number, ε r is the relative dielectric constant.

[0167] In this embodiment, step four includes: numerical solution of the parabolic equation: using the distributed Fourier transform SSFT algorithm to perform discrete solution on the parabolic equation.

[0168] Step 4-1: Use the split-step Fourier transform (SSFT) method to discretize the parabolic equation (82):

[0169]

[0170] In the formula, ζ and ζ -1 Fourier transform and inverse transform respectively, p = k 0 sinθ is the spatial frequency, and θ is the angle between the electromagnetic wave and the horizontal direction. 0 ,z), we can use equation (92) to get the field distribution u(x 0 +Δx,z), thereby iteratively obtaining the field distribution in the entire space.

[0171] Step 4-2: Substitute the random perturbation factor n obtained in step 1 f Add the corrected average refractive index profile n aSubstituting into the parabolic equation, we obtain the tropospheric scatter channel model based on the parabolic equation.

[0172] In this embodiment, step five includes: calculating the path loss; and introducing the surface reflection coefficient according to different polarization modes.

[0173] Step 5-1: After obtaining the simplified field u(x,z) at each location in space in step 4, the transmission loss can be obtained:

[0174] L=32.44+20logf+20logd-10logF 2 (94)

[0175] In the formula, f is the communication frequency in MHz; d is the propagation distance in km, that is, the step distance x, and F is the propagation factor. For the parabolic equation, Hitney pointed out the relationship between the propagation factor F and the simplified function field u(x,z), which is expressed as:

[0176] F 2 =xu(x,z) 2 (95)

[0177] Substituting equation (94) into equation (93), we can obtain the transmission loss of tropospheric scatter:

[0178] L=32.44+20logf+10logd-20logu(x,z) (96)

[0179] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A tropospheric scatter sea-skimming channel modeling and analysis method based on parabolic equations, characterized by: The method comprises the following steps: Step 1: Environmental inversion: Invert the meteorological data of the scattering area based on the WRF meteorological data model, including real-time meteorological parameters of air pressure, temperature, and humidity, and calculate the atmospheric refractive index distribution; Step 2: Atmospheric refractive index modeling: Combine the inverted meteorological parameters to establish a dynamic refractive index distribution model. Use a hierarchical modeling method to integrate meteorological parameters and random disturbances to characterize the change of atmospheric refractive index with height. Smooth the refractive index distribution and discretize the continuous refractive index distribution in the height direction so that each step height corresponds to an atmospheric refractive index to adapt to the subsequent parabolic equation algorithm. Step 3: Parabolic equation scattering channel modeling: In the Feit-Fleck wide-angle scattering parabolic equation, based on the approximate wave equation, the impedance boundary of the atmospheric turbulence profile structure is derived, the boundary conditions and initial field are set, and the surface reflection coefficient is introduced considering the radio wave polarization mode to ensure the physical meaning of the channel model while ensuring the stability of the numerical solution; Step 4: Numerical solution of parabolic equations: Use the split-step Fourier transform (SSFT) method to discretely solve the parabolic equations; divide the appropriate grid in the space-time dimension according to the scattering communication channel modeling area and communication frequency; gradually calculate the tropospheric radio wave propagation path and intensity, including refraction, scattering and reflection paths; Step 5: Scattering loss analysis: Consider the scattering of radio waves caused by turbulence and calculate the path loss; Step 6: Comparative analysis of channel characteristics: Compare the proposed scattering channel model with the ITU model and measured data to verify the accuracy and effectiveness of the proposed model.

2. The method for modeling and analyzing tropospheric scatter sea-skimming channels based on parabolic equations according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: Atmospheric parameter collection: Introduce the turbulent atmospheric structure model and use the atmospheric refractive index structure constant Determine the intensity of environmental disturbances: Where: r is a random number uniformly distributed between [0,1]; S n (k) is the refractive index power spectrum; k = 2π / L0.a 2 is a constant, about 2.8; α' is the ratio of the turbulent diffusion coefficient, which does not change much (approximately 1); L0 is the flow outer scale, the test scale is about tens of meters, and M' is calculated by steps one to three; Step 1-2: Invert the meteorological data of the tropospheric scatter channel modeling area, including the parameters of air pressure, temperature and humidity, and calculate the atmospheric refractive index distribution. The relationship between humidity U, pressure P, and temperature T in a certain area and the height h is as follows: P=P0exp(-1.256×10 -4 h) (5) T=t0-0.006047h (h<12970m) (6) Where, h is the height from the ground, in meters, U0 is the relative humidity near the ground, P0 is the pressure near the ground, and t0 is the temperature near the ground. Under standard atmospheric conditions, the temperature near the ground is 15°C, so t0 = 15°C, pressure P0 = 1013.25hPa, and relative humidity is generally between 50% and 80%, taking about 76.8%; Step 1-3: The relationship between atmospheric refractive index and atmospheric temperature T, water vapor pressure e, and pressure P is: Where T is the absolute temperature of the troposphere, in K; e is the water vapor pressure, in hPa; P is the atmospheric pressure, in hPa, expressed as: The atmospheric refractive index N is defined to characterize the effect of the tropospheric atmosphere on radio wave propagation. The unit is N-units. The relationship between the atmospheric refractive index N and the atmospheric refractive index n is expressed as: N=(n-1)×10 6 (9) By taking the derivative of equation (7) with respect to h, we can obtain the vertical rate of change of atmospheric refractive index with height, which is called the refractive index gradient: Using Snell's law in spherical layered media, the corrected refractive index is obtained: Where h is the height above the ground, in meters; R is the radius of the earth, R = 6371 km; the corrected average refractive index profile n is obtained using the relationship in equation (9): a =1+M×10 -6 , Substituting equation (7) into equation (11) and taking the derivative with respect to h, we obtain: Substituting equation (12) into equation (3), we can obtain the atmospheric refractive index structure constant:

3. The method for modeling and analyzing tropospheric scatter sea-skimming channels based on parabolic equations according to claim 1, characterized in that: The step three is specifically as follows: Step 3-1: In the two-dimensional rectangular coordinate system (x, z), assume that the time harmonic factor of the electromagnetic field is e -iwt , the two-dimensional scalar Helmholtz equation satisfied by the electric or magnetic field component ψ(x,z) is expressed as: Where k0 is the free space wave number, n is the atmospheric refractive index; the wave function in the positive x direction is defined as: Substituting into equation (13) and factoring it, we get: Where: Q is called the pseudo differential operator Considering only the forward propagation of electromagnetic waves, we get the forward parabolic equation: Using the Feit-Fleck approximation operator Q, substituting it into equation (17), we get the wide-angle parabolic equation, expressed as: Step 3-2: Use the Leontovich impedance boundary condition to deal with the lower boundary of the parabolic equation calculation area: Among them, z is the coordinate value in the height direction, u is the electric field value, and α reflects the impedance characteristics of the lower boundary condition. Under the conditions of horizontal polarization and vertical polarization of electromagnetic waves, the following relationships are satisfied respectively: Among them, i, k represent the grid point positions in the x and z directions, θ i is the antenna elevation angle, ε r is the relative complex permittivity of the lower boundary and satisfies the following relationship: e r =e g +i60sl (21) Among them, ε g and σ represent the relative permittivity and conductivity of the lower boundary, respectively, and λ represents the wavelength of the electromagnetic wave; Step 3-3: Use the window function to set the absorption layer at the upper boundary. All the upward propagating waves are attenuated to zero by the absorption layer without reflection. The commonly used Cosine-taper window function W(z) is expressed as: Where Z is the vertical height of the computational domain, and z is the coordinate value in the height direction; Step 3-4: Use Gaussian source as the initial field. The expression of Gaussian antenna is: Here p = ksinθ and according to the half-wave width θ bW We get w as: The parabolic equation represents the initial aperture field as: Substitute the Gaussian pattern to get the initial aperture field and clarify the Fourier transform; for the antenna height z0 and the transmission elevation angle α, calculate the maximum height z max , the emission source of the Gaussian pattern is: According to the mirror theory, the initial field of the upper half space is placed in the ideal reflecting terrain to meet the mirror symmetry condition. The initial field expression is: u(0,z)=u fs (0,z)-u fs (0,-z) (27) Steps 3-5: Polarization modes are divided into horizontal polarization and vertical polarization. Different polarization modes have different reflection coefficients: Where α is the incident angle, sinα is the sine of the incident angle, sinα=p / k0, p is the spectral domain variable, k0 is the wave number, ε r is the relative dielectric constant.

4. The method for modeling and analyzing tropospheric scatter sea-skimming channels based on parabolic equations according to claim 1, characterized in that: The step 4 is specifically as follows: Step 4-1: Use the split-step Fourier transform (SSFT) method to discretize the parabolic equation (18): In the formula, ζ and ζ -1 are Fourier transform and inverse transform respectively, p=k0sinθ is the spatial frequency, θ is the angle between the electromagnetic wave and the horizontal direction; when the initial field distribution u(x0,z) is given, the field distribution u(x0+Δx,z) at the next step is obtained by applying formula (29), thereby iteratively obtaining the field distribution in the entire space; Step 4-2: Substitute the random perturbation factor n obtained in step 1 f Add the corrected average refractive index profile n a Substituting into the parabolic equation, we obtain the tropospheric scatter channel model based on the parabolic equation.

5. The method for modeling and analyzing tropospheric scatter sea-skimming channels based on parabolic equations according to claim 1, characterized in that: The step five is specifically as follows: Step 5-1: After obtaining the simplified field u(x,z) at each location in space in step 4, the transmission loss is obtained: L=32.44+20logf+20logd-10logF 2 (30) Where f is the communication frequency in MHz; d is the propagation distance in km, i.e. the step distance x, and F is the propagation factor. For the parabolic equation, Hitney pointed out the relationship between the propagation factor F and the simplified function field u(x,z), which is expressed as: F 2 =xu(x,z) 2 (31) Substituting equation (31) into equation (30), we can obtain the transmission loss of the tropospheric scatter channel: L=32.44+20logf+10logd-20logu(x,z) (32).

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