A tropospheric scatter channel modeling method based on parabolic equation

Abstract

The present application relates to a kind of troposphere scattering channel modeling method based on parabolic equation, belong to wireless communication technical field.First, based on the meteorological data mode of WRF is obtained meteorological data in the modeling region of scattering communication channel, including three meteorological parameters such as air pressure, temperature, humidity, calculate correction atmospheric refractivity M, obtain atmospheric correction refractivity profile n a ;Second, according to atmospheric correction refractivity M, calculate refractivity vertical gradient M', atmospheric refractivity structure constant is characterized then, refractivity disturbance caused by turbulence is substituted, describe random disturbance n f ;Finally, atmospheric correction refractivity profile n a With random disturbance n f It is substituted into Feit-Fleck type wide-angle parabolic equation derived from two-dimensional Helmholtz equation, numerical solution is carried out using step Fourier transform method, constructs troposphere scattering model.The method characterizes the influence problem of atmospheric turbulence on radio wave propagation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication, and relates to a tropospheric scattering channel modeling method based on a parabolic equation. BACKGROUND

[0002] Tropospheric scattering propagation is an important over-the-horizon radio wave propagation method, which mainly transmits energy hundreds to thousands of kilometers through super short wave, microwave and other frequency bands of radio waves in atmospheric turbulence, horizontal stratification and other tropospheric phenomena. This propagation method is almost not affected by geographical environment, and the single-hop communication distance can reach hundreds of kilometers, and the farthest can reach thousands of kilometers, and has a large transmission capacity. Due to the frequent occurrence of cold and warm air convection storms, cloud clusters and other complex weather phenomena at sea, atmospheric turbulence and refractive index sharp change layer and other tropospheric scattering phenomena are easily formed to make the radio wave propagate a long distance, forming tropospheric scattering propagation. With the development of computer technology, important interactions with electromagnetic field and electromagnetic wave theory have occurred, resulting in computational electromagnetics. 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. With the help of parabolic equation to construct the propagation model, it is the core to master the influence of atmospheric environment on the propagation of radio waves, and is also the application target of physical measurement technology and mesoscale simulation to obtain meteorological research data.

[0003] Traditional tropospheric scattering channel modeling is mainly based on empirical formulas and statistical models, such as long elliptical scattering model, Clarkes and Jakes model, ITU-RP.617 model, etc. Although these methods can describe the average characteristics of signal propagation to some extent, they have poor accuracy and adaptability in dynamic environment. In addition, traditional models often ignore the influence of complex terrain, weather conditions and other factors on the propagation characteristics of the channel, which limits their application in practice.

[0004] In recent years, physical-based deterministic channel modeling methods have attracted 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 approximates the wave equation and efficiently calculates the refraction and scattering effects of radio waves in different media. Using the parabolic equation to construct the tropospheric scattering channel model can accurately characterize the propagation characteristics of radio waves, and is particularly suitable for describing complex terrain and dynamic environment.

[0005] However, the current tropospheric scattering channel modeling method based on the parabolic equation still faces some technical difficulties, one is how to represent the atmospheric refractive index distribution, the ground reflection characteristics, and the other is how to optimize the calculation efficiency through numerical method. In order to solve these problems, a tropospheric scattering channel modeling method based on the parabolic equation is proposed, which aims to build a more accurate and efficient channel model to meet the needs of modern wireless communication. SUMMARY

[0006] Therefore, the purpose of the present application is to provide a tropospheric scattering channel modeling method based on the parabolic equation, which aims to solve the problems of insufficient accuracy, poor dynamic environment adaptability and low calculation efficiency in the existing tropospheric scattering channel modeling. This method introduces the parabolic equation theory, combines the physical characteristics and environmental parameters of the troposphere, and establishes a channel model that can accurately describe the signal propagation characteristics, which is suitable for tropospheric scattering communication under complex terrain and dynamic weather conditions.

[0007] To achieve the above purpose, the present application provides the following technical scheme:

[0008] A tropospheric scattering channel modeling method based on the parabolic equation, the method comprising the following steps:

[0009] Step 1: Environmental inversion: Based on the WRF meteorological data model, the meteorological data of the scattering area is inverted, including real-time meteorological parameters such as air pressure, temperature and humidity, and the atmospheric refractive index distribution is calculated;

[0010] Step 2: Atmospheric refractive index modeling: Combine the inverted meteorological parameters to establish a dynamic refractive index distribution model, use the hierarchical modeling method, integrate meteorological parameters and random disturbance, represent the variation law 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 type 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, the ground reflection coefficient is introduced considering the polarization mode of the radio wave, to ensure the physical meaning of the channel model and the stability of the numerical solution;

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

[0013] Step five: scattering loss analysis: considering the scattering of radio waves caused by turbulence, the path loss is calculated;

[0014] Step six: channel characteristics comparative analysis: comparing the proposed scattering channel model with the ITU model and the measured data, the accuracy and effectiveness of the proposed model are verified.

[0015] Further, the step one is specifically:

[0016] Step one-one: atmospheric parameter acquisition: introduce the turbulence atmospheric structure model, and calculate the atmospheric refractive index structure constant Determine the environmental disturbance intensity:

[0017]

[0018] In the formula: 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 turbulence diffusion coefficient, the value changes little (approximately 1); L0 is the outflow scale, the order of magnitude of the test is about tens of meters, M' is calculated from step one-three.

[0019] Step one-two: inverse the meteorological data of the tropospheric scattering channel modeling area, including air pressure, temperature, humidity and other parameters, calculate the atmospheric refractive index distribution, the relationship between humidity U, pressure P, temperature T and height h in a certain area is as follows:

[0020]

[0021] P = P0exp(-1.256×10 -4 h) (37)

[0022] T = t0-0.006047h (h < 12970m) (38)

[0023] In the formula, h is the height from the ground, unit m, U0 is the relative humidity near the ground, P0 is the pressure near the ground, t0 is the temperature near the ground. Under the standard atmospheric conditions, the temperature near the ground is 15℃, so t0 = 15℃, the pressure P0 = 1013.25 hPa, the relative humidity is generally between 50% and 80%, about 76.8%.

[0024] Step one-three: the relationship between atmospheric refractive index and atmospheric temperature T, water vapor pressure e, pressure P is:

[0025]

[0026] where T is the absolute temperature of the tropospheric atmosphere in K, e is the water vapor pressure in hPa, and P is the atmospheric pressure in hPa, which is expressed as:

[0027]

[0028] Generally, the atmospheric refractive index N is defined to represent the influence of the tropospheric atmosphere on the effect of 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) x 10 6 (41)

[0030] Taking the derivative of formula (39) with respect to h, the vertical variation rate of the atmospheric refractive index with height, called the refractive index gradient, can be obtained:

[0031]

[0032] Using Snell's law in a spherical layered medium, the modified refractive index n is obtained:

[0033]

[0034] where h is the height from the ground in m, and R is the radius of the earth, taken as R = 6371 km. Using the relationship of formula (9), the modified average refractive index profile n a = 1 + M x 10 -6 is obtained. Substituting formula (39) into formula (43) and taking the derivative with respect to h, we obtain:

[0035]

[0036] Substituting formula (44) into formula (35), the atmospheric refractive index structure constant

[0037] Further, the third step specifically includes:

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

[0039]

[0040] where k0 is the free space wave number, and n is the atmospheric refractive index. Define the wave function in the positive x direction as:

[0041]

[0042] Substitute (45) into (44) and factor it to get

[0043]

[0044] where Q is called the pseudo-differential operator

[0045]

[0046] Considering only the forward propagation of electromagnetic waves, the forward parabolic equation is obtained as

[0047]

[0048] Substitute the Feit-Fleck approximation of Q into (49) to get the wide-angle parabolic equation as

[0049]

[0050] Step three-two: Leontovich impedance boundary condition is used to deal with the lower boundary of the parabolic equation calculation area

[0051]

[0052] where z is the coordinate value in the height direction, u is the electric field value, and a reflects the impedance characteristics of the lower boundary condition, which satisfies the following relationship under the conditions of electromagnetic wave horizontal polarization and vertical polarization respectively

[0053]

[0054] where i, k represent the corresponding grid point positions in the x, 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] where ε g and σ represent the relative permittivity and conductivity of the lower boundary respectively, and λ represents the wavelength of electromagnetic waves.

[0057] Step three-three: use a window function to set an absorbing layer at the upper boundary, all upward propagating electromagnetic waves are attenuated to zero by the absorbing layer without reflection, and 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 calculation domain, and z is the coordinate value in the height direction.

[0060] Step three-four: Using a Gaussian source as the initial field, the expression of the Gaussian antenna is:

[0061]

[0062] Here p = ksina and according to the half-wave width a bW The w is obtained as:

[0063]

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

[0065]

[0066] Substituting the Gaussian pattern, the initial aperture field is obtained, and in this case the Fourier transform can be explicitly determined. For the antenna height z0, the maximum calculation height z max , the emission source of the Gaussian pattern is:

[0067]

[0068] According to the mirror image theory, the initial field of the upper half space is placed in the ideal reflection terrain, which satisfies the mirror image symmetry condition, and the initial field expression is:

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

[0070] Step three-five: The polarization mode is divided into horizontal polarization and vertical polarization, and different reflection coefficients are selected for different polarization modes:

[0071]

[0072] In the formula, a is the incidence angle, sina is the incidence angle sine, sina = p / k0, p is the spectral domain variable, k0 is the wave number, e r is the relative dielectric constant.

[0073] Further, the step four is specifically:

[0074] Step four-one: using the split-step Fourier transform (SSFT) method to discretely solve the parabolic equation (50):

[0075]

[0076] In the formula, zeta and zeta -1are the Fourier transform and inverse transform respectively, p=k0sin0 is the spatial frequency, and 0 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+Ax,z) at the next step can be obtained by using equation (61), and thus the field distribution in the whole space can be iteratively calculated.

[0077] Step four-two: the random perturbation factor n f plus the average refractive index profile n a Substituted into the parabolic equation, the tropospheric scattering channel model based on the parabolic equation is obtained.

[0078] Further, the step five is specifically:

[0079] Step five-one: after obtaining the simplified field u(x,z) at each place in the space in step four, the transmission loss can be obtained:

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

[0081] In the formula, f is the communication frequency, unit: MHz; d is the propagation distance, unit: 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 =x|u(x,z)| 2 (63)

[0083] Substitute equation (63) into equation (62) to obtain the transmission loss of the tropospheric scattering channel:

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

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

[0086] 1. Higher modeling accuracy: The present application combines the parabolic equation method and the turbulent atmosphere structure model, effectively capturing the influence of refractive index random perturbation and turbulent characteristics on the channel in the tropospheric scattering process. Compared with traditional empirical models and statistical models, the present application can more accurately describe the channel characteristics in complex environments.

[0087] 2. Stronger adaptability: Based on the real-time weather data of WRF, more accurate atmospheric refractive index in different regions is obtained, which can accurately reflect the real scattering channel characteristics. The model of the present application can be dynamically adjusted according to different environmental conditions (such as temperature, humidity, air pressure), and is suitable for various terrains and climate conditions.

[0088] 3. Significant improvement in computational efficiency: The present application optimizes the numerical solution of the parabolic equation, using high-efficiency algorithms such as the split-step Fourier method (SSFT), significantly reducing the calculation time while ensuring the stability and accuracy of the solution.

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

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

[0091] 6. Wide range of applications: The present application is not only applicable to tropospheric scatter communication, but can also be extended to long-distance radio communication, radar systems, and over-the-horizon transmission scenarios, providing a highly versatile modeling method for related fields.

[0092] Other advantages, objects, and features of the present application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or can be learned by practice of the present application. The objects and other advantages of the present application can be realized and attained by the structure particularly pointed out in the description below. BRIEF DESCRIPTION OF DRAWINGS

[0093] In order to make the objects, technical solutions, and advantages of the present application clearer, the preferred detailed description of the present application will be made below in combination with the accompanying drawings, in which:

[0094] Figure 1 Flowchart for modeling the tropospheric scatter channel based on the parabolic equation;

[0095] Figure 2 Comparison chart of transmission loss for tropospheric scatter and free space;

[0096] Figure 3 Comparison chart of transmission loss with and without turbulence for different transform point numbers N;

[0097] Figure 4 Comparison chart of transmission loss for the tropospheric scatter parabolic equation and the ITU-R P.617 model;

[0098] Figure 5 Turbulence effect for different transform point numbers N. DETAILED DESCRIPTION

[0099] The present application is illustrated by way of example and not limitation in the figures of the accompanying drawings, in which like references indicate similar elements, and in which: BRIEF DESCRIPTION OF THE DRAWINGS

[0100] The drawings are merely schematic and are not drawn to scale. Any measurements are also not necessarily to scale, and the emphasis instead is placed upon illustrating the principles of the application. In the drawings, like reference numerals refer to like elements throughout.

[0101] The same or similar components in the drawings of the embodiments of the present application correspond to the same or similar components. In the description of the present application, it should be understood that the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "front", "back", etc. are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and therefore the terms indicating the positional relationships in the drawings should not be understood as indicating or implying that the devices or elements referred to must have a particular orientation, be constructed in a particular orientation, and be operated in a particular orientation. Therefore, the terms indicating the positional relationships in the drawings are only for illustrative purposes, and should not be understood as limiting the present application. For those skilled in the art, the specific meanings of the above terms can be understood according to the specific circumstances.

[0102] Referring to Figures 1-5 The tropospheric scatter channel modeling method based on the parabolic equation according to the present application comprises the following steps:

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

[0104] Step 2: Atmospheric refractive index modeling: Combined with the inverted meteorological parameters, a dynamic refractive index distribution model is established, a hierarchical modeling method is adopted, meteorological parameters and random disturbances are integrated, the variation law of atmospheric refractive index with height is represented, the refractive index distribution is smoothed and discretized 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 three: 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, the boundary conditions and the initial field are set, the ground reflection coefficient is introduced considering the polarization mode of the electric wave, and the stability of the numerical solution is ensured while ensuring the physical meaning of the channel model;

[0106] Step four: Numerical solution of parabolic equation: the split-step fourier transform (SSFT) method is used to discretely solve the parabolic equation; according to the scattering communication channel modeling area and the communication frequency, the appropriate grid is divided in the time and space dimensions; the tropospheric wave propagation path and intensity are calculated step by step, including refraction, scattering and reflection path;

[0107] Step five: Scattering loss analysis: considering the scattering of the electric wave caused by turbulence, the path loss is calculated;

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

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

[0110] Step one-one: atmospheric parameter acquisition: introduce the turbulence atmospheric structure model, and calculate the atmospheric refractive index structure constant Determine the environmental disturbance intensity:

[0111]

[0112] In the formula: 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 turbulence diffusion coefficient, which varies little (approximately 1); L0 is the outer scale, the order of magnitude of the test is about tens of meters, and M' is obtained by step one-three calculation.

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

[0114]

[0115] P = P0exp(-1.256 x 10 -4 h) (69)

[0116] T = t0- 0.006047h (h < 12970m) (70)

[0117] where h is the height from the ground, U0 is the relative humidity near the ground, P0 is the pressure near the ground, and t0 is the temperature near the ground. Under the standard atmospheric conditions, the temperature near the ground is 15°C, so t0 = 15°C, the pressure P0 = 1013.25 hPa, and the relative humidity is generally between 50% and 80%, taking about 76.8%.

[0118] Steps one-three: the relationship between the atmospheric refractive index and the atmospheric temperature T, water vapor pressure e, and pressure P is:

[0119]

[0120] where T is the absolute temperature of the troposphere, e is the water vapor pressure, and P is the atmospheric pressure. The expressions of the parameters are as follows:

[0121]

[0122] The atmospheric refractive index N is usually defined to represent the influence of the troposphere on the propagation effect, and 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) x 10 6 (73)

[0124] Taking the derivative of equation (71) with respect to h, the vertical variation rate of the atmospheric refractive index along the height, called the refractive index gradient, is obtained:

[0125]

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

[0127]

[0128] where h is the height from the ground, and R is the radius of the earth, taking R = 6371 km. Using the relationship of equation (73), the modified average refractive index profile n is obtained a = 1 + M x 10 -6 , and taking the derivative of equation (71) with respect to h, we get:

[0129]

[0130] Substituting equation (76) into equation (67), the atmospheric refractive index structure constant

[0131] In this embodiment, step three includes: parabolic equation scattering channel modeling: in 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, the boundary conditions and the initial field are set, and the stability of the numerical solution is ensured while ensuring the physical meaning of the channel model;

[0132] Step three-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 field or magnetic field component ψ(x, z) satisfies the following form of two-dimensional scalar Helmholtz equation:

[0133]

[0134] In the formula, k0 is the free space wave number, and n is the atmospheric refractive index. The wave function in the positive direction of x is defined as:

[0135]

[0136] Substitute formula (72) and factorize it to obtain:

[0137]

[0138] In the formula: Q is called a pseudo-differential operator

[0139]

[0140] Only the forward propagation of electromagnetic waves is considered, and the forward parabolic equation is obtained:

[0141]

[0142] The Feit-Fleck approximation is adopted for the operator Q, and substituted into formula (81) to obtain the following form of wide-angle parabolic equation:

[0143]

[0144] Step three-2: the Leontovich impedance boundary condition is used to process the lower boundary of the parabolic equation calculation area:

[0145]

[0146] Wherein, 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, which satisfies the following relationship under the conditions of horizontal polarization and vertical polarization of electromagnetic waves:

[0147]

[0148] where i, k represent the corresponding grid point position in x, z direction, 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] where ε g represents the relative permittivity of the lower boundary, σ represents the conductivity of the lower boundary, and λ represents the point wave wavelength.

[0151] Step three-three: use a window function to set the absorbing layer on the upper boundary, all upwardly propagating electromagnetic waves are attenuated to zero by the absorbing layer and no reflection, the commonly used Cosine-taper window function W(z) is expressed as:

[0152]

[0153] where Z is the vertical height of the calculation domain, and z is the coordinate value in the height direction.

[0154] Step three-four: use a Gaussian source as the initial field, the expression of the Gaussian antenna is:

[0155]

[0156] Here p = ks in θ and according to the half-wave number width θ bW w is obtained as:

[0157]

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

[0159]

[0160] Substituting the Gaussian pattern, the initial aperture field can be obtained, in this case the Fourier transform can be determined. For the antenna height z0, the maximum calculation height z max , the transmission source of the Gaussian pattern is:

[0161]

[0162] According to the mirror image theory, the initial field of the upper half space is placed in the ideal reflection terrain condition, which satisfies the mirror image symmetry condition, and the expression of the initial field is:

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

[0164] Step three-five: polarization mode is divided into horizontal polarization and vertical polarization, and 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 / k0, p is a spectral variable, k0 is a wave number, ε r is a relative dielectric constant.

[0167] In this embodiment, step four includes: numerical solution of the parabolic equation: using the split-step Fourier transform SSFT algorithm to discretely solve the parabolic equation.

[0168] Step four-one: using the split-step Fourier transform (SSFT) method to discretely solve the parabolic equation (82):

[0169]

[0170] where, ζ and ζ -1 are Fourier transform and inverse transform respectively, p = k0sinθ is a 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 can be obtained by using formula (92), so as to iteratively obtain the field distribution in the whole space.

[0171] Step four-two: add the random disturbance factor n f obtained in step one to the modified average refractive index profile n a , and substitute it into the parabolic equation to obtain the tropospheric scattering channel model based on the parabolic equation.

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

[0173] Step five-one: after obtaining the simplified field u(x,z) at each place in the space in step four, the transmission loss can be obtained:

[0174] L = 32.44 + 20logf + 20logd - 10logF 2 (93)

[0175] where, f is the communication frequency, unit: MHz; d is the propagation distance, unit: km, that is, the step distance x, 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 represented as:

[0176] F 2= x | u(x, z) 2 (94)

[0177] Substituting equation (94) into equation (93) gives the transmission loss of tropospheric scatter:

[0178] L = 32.44 + 20 log f + 10 log d - 20 log u(x, z) (95)

[0179] Finally, it should be pointed out that the above examples are merely intended to illustrate the technical solutions of the present application and not to limit the same. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalently replaced without departing from the spirit and scope of the present application, and all such modifications and equivalents should be encompassed within the scope of the claims of the present application.

Claims

1. A method for modeling tropospheric scattering channels based on parabolic equations, characterized in that: The method includes the following steps: Step 1: Environmental Inversion: Based on the WRF meteorological data model, invert meteorological data of the scattering region, including real-time meteorological parameters such as air pressure, temperature, and humidity, and calculate the atmospheric refractive index distribution; Step 2: Atmospheric refractive index modeling: Combine the retrieved meteorological parameters to establish a dynamic refractive index distribution model. The hierarchical modeling method is adopted, incorporating meteorological parameters and random perturbation factors to characterize the variation law of atmospheric refractive index with altitude. The refractive index distribution is smoothed and the continuous refractive index distribution is discretized in the altitude direction so that each step altitude corresponds to an atmospheric refractive index, in order to adapt to the subsequent parabolic equation algorithm. Step 3: 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, 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 the parabolic equation: Discretely solve the parabolic equation using the split-step Fourier transform (SSFT) method; divide the spatiotemporal dimensions into appropriate grids based on the scattering communication channel modeling region and communication frequency; calculate the propagation path and intensity of tropospheric radio waves step by step, 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 Six: Channel Characteristics Comparison and Analysis: The proposed scattering channel model is compared with the ITU model and measured data to verify the accuracy and effectiveness of the proposed model.

2. The tropospheric scattering channel modeling method based on parabolic equations according to claim 1, characterized in that: Step one specifically involves: Step 1.1: Atmospheric Parameter Acquisition: Introduce a turbulent atmospheric structure model, using the atmospheric refractive index structure constant... Determine the intensity of environmental disturbance: Where: n f S represents the random perturbation of the refractive index caused by turbulence; r is a random number uniformly distributed between [0,1]; n (k) represents the refractive index power spectrum; k = 2π / L0.a 2 α is a constant, which is 2.8; α' is the ratio of the turbulent diffusion coefficient, which does not change much and is approximately 1; L0 is the external scale, which is on the order of tens of meters in the experiment; M' is calculated from step 1.

3. Step 1.2: Invert meteorological data for the tropospheric scattering 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 with altitude h in a certain area is as follows: P=P0exp(-1.256×10 -4 h) (5) T=t0-0.006047h (h<12970m) (6) In the formula, h is the height above 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℃, t0 = 15℃, the pressure P0 = 1013.25hPa, and the relative humidity is generally between 50% and 80%, which is taken as 76.8%. Step 1.3: The relationship between atmospheric refractive index and atmospheric temperature T, water vapor pressure e, and pressure P is as follows: In the formula, T is the absolute temperature of the troposphere, in K; e is the water vapor pressure, in hPa; and P is the atmospheric pressure, in hPa, expressed as: The atmospheric refractive index N is defined to characterize the effect of the troposphere on radio wave propagation, and its unit is N-units. The relationship between the atmospheric refractive index N and the atmospheric refractive index n is expressed as follows: N=(n-1)×10 6 (9) Differentiating equation (7) with respect to h yields the vertical rate of change of atmospheric refractive index with altitude, known as the refractive index gradient: Using Snell's law in spherical layered media, the corrected refractive index is obtained: In the formula, h is the height above the ground in meters; R is the radius of the Earth, taken as R = 6371 km; the corrected average refractive index profile n is obtained using the relationship in formula (9). a =1 + M × 10 -6 Substituting equation (7) into equation (11) and differentiating with respect to h, we get: Substituting equation (12) into equation (3), we obtain the atmospheric refractive index structure constant.

3. The tropospheric scattering channel modeling method based on parabolic equations according to claim 1, characterized in that: Step three specifically involves: 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 components ψ(x,z) is expressed as: In the formula, k0 is the free-space wavenumber, and n is the atmospheric refractive index; the wave function in the positive x-direction is defined as: Substituting into equation (13) and factoring, we get: In the formula: Q is called the pseudo-differential operator. n(x,z) represents the atmospheric refractive index at spatial location (x,z); Considering only the forward propagation of electromagnetic waves, we obtain the forward parabolic equation: Using the Feit-Fleck approximation operator Q, substituting it into equation (17) yields the equation for the wide-angle parabola, expressed as: Step 3.2: Use Leontovich impedance boundary conditions to handle the lower boundary of the computational domain for the parabolic equation: Where 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, which satisfy the following relationships under the conditions of horizontal and vertical polarization of electromagnetic waves: Where i,k represent the grid point positions in the x,z directions, and θ i ε is the antenna elevation angle. r Let be the relative complex permittivity of the lower boundary and satisfy the following relationship: e r =e g +i60sl (21) Where, ε g σ 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 a window function to set up an absorption layer at the upper boundary. All upward-propagating electromagnetic waves are attenuated to zero by the absorption layer and are not reflected. 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: Using a Gaussian source as the initial field, the expression for the Gaussian antenna is: Here, p = ksinθ and according to the half-wavelength width θ bW The value of w is: The parabolic equation represents the initial field of the aperture as: z represents the spatial coordinate in the height direction; p z The vertical wavenumber component is represented by: k; α represents the transmit elevation angle; i represents the imaginary unit; z0 represents the antenna height; z max ζ represents the maximum height of the computational domain; A represents the complex amplitude function of the antenna's radiation characteristics in the spectral domain; -1 Indicates the inverse Fourier transform; Substituting the Gaussian radiation pattern into the initial aperture field, the Fourier transform is determined; for the antenna height z0 and the transmit elevation angle α, the maximum height z is calculated. max The emission source of the Gaussian pattern is: According to mirror theory, placing the initial field of the upper half-space in the case of an ideal reflecting terrain satisfies the mirror symmetry condition, and the expression for the initial field is: u(0,z)=u fs (0,z)-u fs (0,-z) (27) Step 3.5: Polarization is divided into horizontal polarization and vertical polarization. Different polarization methods result in different reflection coefficients. In the formula, 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 wavenumber, and ε r is the relative permittivity.

4. The tropospheric scattering channel modeling method based on parabolic equations according to claim 1, characterized in that: Step four specifically involves: Step 4.1: Use the split-step Fourier transform (SSFT) method to discretely solve the parabolic equation (18): In the formula, u(x0+Δx,z) represents the field distribution in the height direction z at the next step position x0+Δx in the propagation direction; x0 represents the current propagation position; Δx represents the step distance in the propagation direction; z represents the height direction; i represents the imaginary unit; k0 represents the free space wavenumber; n represents the atmospheric refractive index; u(x0,z) represents the field distribution in the height direction z at the current propagation position x0, and ζ and ζ -1 These are the Fourier transform and inverse transform, respectively. p = k0sinθ is the spatial frequency, and θ is the angle between the electromagnetic wave and the horizontal direction. Given the initial field distribution u(x0,z), use equation (29) to iteratively find the field distribution u(x0+Δx,z) at the next step, thereby finding the field distribution in the entire space. Step 4.2: The random perturbation factor n obtained in Step 1 f Adding the corrected mean refractive index profile n a Substituting into the parabolic equation, we obtain the tropospheric scattering channel model based on the parabolic equation.

5. The tropospheric scattering channel modeling method based on parabolic equations according to claim 1, characterized in that: Step five specifically involves: Step 5.1: After obtaining the simplified field u(x,z) at each point in space in Step 4, the transmission loss is obtained: L=32.44+20logf+20logd-10logF 2 (30) In the formula, 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, the relationship between the propagation factor F and the simplified function field u(x,z) is expressed as: F 2 =x|u(x,z)| 2 (31) Substituting equation (31) into equation (30), we obtain the transmission loss of the tropospheric scattering channel: L=32.44+20log f+10log d-20log|u(x,z)| (32).

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