Doppler frequency shift calculation method based on short wave signal path

Abstract

The invention discloses a Doppler frequency shift calculation method based on a short-wave signal path. The Doppler frequency shift calculation method comprises the following steps: step 1, ray path calculation; step 2, refractive index calculation; 3, calculating a geomagnetic field; 4, solving a ray tracing equation; and step 5, Doppler frequency shift calculation. Simulation analysis of Doppler frequency shift in the prior art stays at a theoretical level, and no specific calculation method exists. According to the method disclosed by the invention, the problem is solved, the Doppler frequency shift of any short wave channel can be calculated in real time according to the real-time ionosphere condition, and the Doppler frequency shift comprises a ground-to-air link, a ground-to-ground sky wave link and an air-to-air link.

Description

Technical Field

[0001] The present invention belongs to the field of shortwave communication, and particularly relates to a Doppler frequency shift calculation method based on a shortwave signal path in the field, and more particularly to a Doppler frequency shift calculation method from a shortwave emission point to any point on the signal path. Background Art

[0002] The Doppler effect is a significant factor affecting shortwave channels, directly impacting the performance of receiving equipment. Ionospheric magnetic storms and sudden ionospheric disturbances can severely impact shortwave signals, even causing signal interruption. Therefore, detecting shortwave channels and studying the interaction between the ionosphere and electromagnetic waves is a crucial tool for studying radio wave propagation, ionospheric characteristics, and their state. It also provides a theoretical foundation for the development of modern scientific and technological fields such as space physics, aerospace, and defense.

[0003] There are two main causes of Doppler shift: one is the change of the transmission medium, such as the rise, fall or disturbance of the ionosphere. In practice, the high-frequency Doppler shift caused by the movement of the ionosphere is at most a few hertz; the other is the change in the relative position of the target and the signal transmission point. For fixed targets, this item is 0, and for high-speed moving targets such as hypersonic aircraft, this item can be as high as 100-200Hz.

[0004] In 1995, Ning Baiqi and others from the Wuhan Institute of Physics, Chinese Academy of Sciences, conducted observational research on shortwave single-hop skywave signals (the distance between transmitter and receiver was 670 km) for five consecutive years (1986-1990). They gave the annual, monthly and daily variations in the Doppler frequency shift and broadening of the 10MHz and 15MHz signal echoes, as well as the influence of magnetic storm activities on them, and explored the reasons for the changes in these parameters from the perspective of ionospheric radio wave propagation.

[0005] Jiang Yuzhong and others from the Naval University of Engineering assumed that the movement of the ionosphere is two different kinds of movement: the regular layer and the inhomogeneous clusters, and derived the expression of the Doppler frequency shift.

[0006] Davies et al. pointed out the proportional relationship between high-frequency Doppler shift and the virtual height of the radio wave reflection point, and Bertel et al. gave the relationship between the apparent velocity of the radio wave reflection point and the high-frequency Doppler shift.

[0007] The shortwave signal transmission beam has a certain width. After refraction and reflection from the transmission medium, the signal received at the receiving point is composed of multiple paths. This not only causes random variations in the signal amplitude at the receiving end, but also causes the signal phase to fluctuate. Moreover, even with only a single mode of propagation, the length of the propagation path constantly changes due to the frequent rapid movement of the ionosphere and the rapid changes in the height of the reflector layer, causing the signal phase to fluctuate. Because of these phase fluctuations, the frequency structure of the transmitted signal changes, and the spectrum is distorted. Simulation calculations of Doppler shift have traditionally primarily relied on empirical models formed from empirical data, without incorporating real-time channel sounding data to form real-time Doppler calculations. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a Doppler frequency shift calculation method based on a shortwave signal path.

[0009] The present invention adopts the following technical solutions:

[0010] A Doppler frequency shift calculation method based on a shortwave signal path is improved in that it includes the following steps:

[0011] Step 1, ray path calculation:

[0012] The three-dimensional ray tracing method is used to construct the radio wave propagation trajectory of a point-to-point radio wave propagation link with a specified radio wave frequency and a specified departure elevation angle based on the Haselgrove equation.

[0013] Step 2, refractive index calculation;

[0014] Step 3, calculation of the geomagnetic field;

[0015] Step 4, solving the ray tracing equation;

[0016] Step 5, Doppler shift calculation:

[0017]

[0018] In the above formula, Δf is the Doppler shift, k = 80.5, c is the speed of light in a vacuum, f0 is the frequency of the radio wave, s is the propagation path of the radio wave, ΔN e is the rate of change of electron concentration.

[0019] Furthermore, the step 1 specifically includes:

[0020] Let P(r,θ,φ) be a point on the ray in spherical coordinates, and express the wave vector of this point as Then the Hamiltonian equation of the ray is:

[0021]

[0022] In the above formula, τ is the independent variable, n is the phase refractive index, and the independent variable is taken as the ray group path P', then:

[0023]

[0024] In the above formula, H is the Hamiltonian operator, ω is the angular frequency of the radio wave, r, θ, is the coordinate of the point on the ray path in the spherical coordinate system, k r 、k θ 、 are the three components of the wave vector in spherical coordinates:

[0025]

[0026] The relationship between the Hamiltonian operator H and the wave vector and phase refractive index n is:

[0027]

[0028] Furthermore, the step 2 specifically includes:

[0029] The refractive index μ of the medium is:

[0030]

[0031] In the above formula:

[0032]

[0033]

[0034] ω p is the ionospheric plasma frequency, ω H is the electron magnetic rotation frequency, ω1 is the incident wave frequency, and v is the electron collision frequency;

[0035] υ=υ en +υ ei

[0036]

[0037] In the above formula, [N2], [O2], [O] are densities, T e is the electron temperature, n e is the electron density.

[0038] Furthermore, the step 3 specifically includes:

[0039] The Earth's magnetic field is approximately represented by a dipole, and the magnetic rotation frequency f H and the magnetic inclination I are:

[0040]

[0041] tgI=2ctgλ

[0042] In the above formula, r0 is the radius of the earth; h is the height from the ground; λ is the geomagnetic latitude; f H0 is the magnetic rotation frequency at the Earth's surface at the magnetic equator.

[0043] Furthermore, the step 4 specifically includes:

[0044]

[0045] In the above formula, f() represents a differential equation, x and y are two variables, i represents the i-th tracked trajectory point, i is a natural number greater than or equal to 1, and ΔX is the integration step size, which is given as follows:

[0046]

[0047] In the above formula, f n is the plasma frequency, f is the operating frequency, and l is the coefficient.

[0048] The beneficial effects of the present invention are:

[0049] Existing simulations and analyses of Doppler shift remain at the theoretical level, lacking specific calculation methods. The method disclosed in the present invention addresses this problem by enabling real-time calculation of the Doppler shift of any shortwave channel, including ground-to-air links, ground-to-ground skywave links, and air-to-air links, based on real-time ionospheric conditions. By calculating the Doppler shift of shortwave channels, the frequency and time selective fading problems caused by the dynamics and mobility of the ionosphere can be addressed, providing a basis for key technologies such as signal synchronization, channel equalization, and system adaptation, ultimately improving the reliability and efficiency of shortwave communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a Doppler calculation flow chart for a specified azimuth and elevation angle;

[0051] Figure 2 This is the Doppler calculation result diagram of multiple path points. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0053] Example 1: This embodiment discloses a method for calculating Doppler frequency shift based on a shortwave signal path, comprising the following steps:

[0054] Step 1, ray path calculation:

[0055] The three-dimensional ray tracing method is used to construct the radio wave propagation trajectory of a point-to-point radio wave propagation link with a specified radio wave frequency and a specified departure elevation angle based on the Haselgrove equation.

[0056] Let P(r,θ,φ) be a point on the ray in spherical coordinates, and express the wave vector of this point as Then the Hamiltonian equation of the ray is:

[0057]

[0058]

[0059] In the above formula, τ is the independent variable, n is the phase refractive index, and the independent variable is taken as the ray group path P', then:

[0060]

[0061] In the above formula, H is the Hamiltonian operator, ω is the angular frequency of the radio wave, r, θ, is the coordinate of the point on the ray path in the spherical coordinate system, k r 、k θ 、 are the three components of the wave vector in spherical coordinates:

[0062]

[0063] The relationship between the Hamiltonian operator H and the wave vector and phase refractive index n is:

[0064]

[0065] The ray tracing process is to solve the above-mentioned ray differential equations to obtain the coordinate vectors and wave vectors at different points on the ray propagation path of a ray emitted at a certain location with a certain frequency, a certain exit elevation angle and a certain azimuth angle under a given ionospheric environment, and obtain the trajectory and main parameters of the ray propagation path, such as group path, great circle distance, propagation mode, etc.

[0066] Step 2, refractive index calculation;

[0067] Taking into account the magnetic field and collisions, the refractive index μ of the medium is:

[0068]

[0069] In the above formula:

[0070]

[0071] ωp is the ionospheric plasma frequency, ω H is the electron magnetic rotation frequency, ω1 is the incident wave frequency, and v is the electron collision frequency;

[0072] υ=υ en +υ ei

[0073]

[0074] In the above formula, [N2], [O2], [O] are densities, T e is the electron temperature, n e is the electron density.

[0075] Step 3, calculation of the geomagnetic field;

[0076] The Earth's magnetic field is approximately represented by a dipole with its center at the center of the Earth, the South Pole at 78.6°N, 70.1°W, and the North Pole at 78.6°S, 109.9°E. The magnetic rotation frequency f is H and the magnetic inclination I are:

[0077]

[0078] tgI=2ctgλ

[0079] In the above formula, r0 is the radius of the earth; h is the height from the ground; λ is the geomagnetic latitude; f H0 is the magnetic rotation frequency at the Earth's surface at the magnetic equator.

[0080] Step 4, solving the ray tracing equation;

[0081]

[0082] In the above formula, f() represents a differential equation, x and y are two variables, i represents the i-th tracked trajectory point, i is a natural number greater than or equal to 1, and ΔX is the integration step size, which is given as follows:

[0083]

[0084] In the above formula, f n is the plasma frequency, f is the operating frequency, and l is the coefficient.

[0085] Step 5, Doppler shift calculation:

[0086]

[0087] In the above formula, Δf is the Doppler shift, k = 80.5, c is the speed of light in a vacuum, f0 is the frequency of the radio wave, s is the propagation path of the radio wave, ΔNe is the rate of change of electron concentration.

[0088] The time resolution of Doppler depends on the time resolution of the ionospheric state.

[0089] The shortwave communication link's transmission point A has an elevation angle of 1° to 89°, with a 1° interval, and an operating frequency of 70 MHz. The receiving point is any point on the ground within a distance of -1000 to 1000 km. A Doppler calculation model for the shortwave communication channel was used to simulate the trajectory points along the path of each link (with a maximum hop count of 2). Figure 1 It is a Doppler calculation flow chart for a specified azimuth and elevation angle;

[0090] Figure 2 The calculated Doppler shift of the high-frequency propagation trajectory point under the normal ionosphere is shown in Figure 2. In the normal ionosphere, the Doppler shift is very small; only after some complex multiple scattering will a relatively large Doppler shift occur.

Claims

1. A Doppler frequency shift calculation method based on a shortwave signal path, characterized in that: The steps include: Step 1, ray path calculation: The three-dimensional ray tracing method is used to construct the radio wave propagation trajectory of a point-to-point radio wave propagation link with a specified radio wave frequency and a specified departure elevation angle based on the Haselgrove equation. Step 2, refractive index calculation; Step 3, calculation of the geomagnetic field; Step 4, solving the ray tracing equation; Step 5, Doppler shift calculation: In the above formula, Δf is the Doppler shift, k = 80.5, c is the speed of light in a vacuum, f0 is the frequency of the radio wave, s is the propagation path of the radio wave, ΔN e is the rate of change of electron concentration.

2. The Doppler frequency shift calculation method based on the shortwave signal path according to claim 1, characterized in that: The step 1 specifically includes: Let P(r,θ,φ) be a point on the ray in spherical coordinates, and express the wave vector of this point as Then the Hamiltonian equation of the ray is: In the above formula, τ is the independent variable, n is the phase refractive index, and the independent variable is taken as the ray group path P', then: In the above formula, H is the Hamiltonian operator, ω is the angular frequency of the radio wave, r, θ, is the coordinate of the point on the ray path in the spherical coordinate system, k r 、k θ 、 are the three components of the wave vector in spherical coordinates: The relationship between the Hamiltonian operator H and the wave vector and phase refractive index n is:

3. The Doppler shift calculation method based on the shortwave signal path according to claim 2, characterized in that: The step 2 specifically includes: The refractive index μ of the medium is: In the above formula: ω p is the ionospheric plasma frequency, ω H is the electron magnetic rotation frequency, ω1 is the incident wave frequency, and v is the electron collision frequency; υ=υ en +u ei In the above formula, [N2], [O2], [O] are densities, T e is the electron temperature, n e is the electron density.

4. The Doppler frequency shift calculation method based on the shortwave signal path according to claim 3, characterized in that: The step 3 specifically includes: The Earth's magnetic field is approximately represented by a dipole, and the magnetic rotation frequency f H and the magnetic inclination I are: tgI=2ctgλ In the above formula, r0 is the radius of the earth; h is the height from the ground; λ is the geomagnetic latitude; f H0 is the magnetic rotation frequency at the Earth's surface at the magnetic equator.

5. The Doppler shift calculation method based on the shortwave signal path according to claim 4, characterized in that: The step 4 specifically includes: In the above formula, f() represents a differential equation, x and y are two variables, i represents the i-th tracked trajectory point, i is a natural number greater than or equal to 1, and ΔX is the integration step size, which is given as follows: In the above formula, f n is the plasma frequency, f is the operating frequency, and l is the coefficient.

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