Method for Obtaining Wideband RCS of Electrically Large Targets Based on Communication Base Stations

Abstract

This invention proposes a method for obtaining the broadband RCS of electrically large targets based on a communication base station. The implementation steps are as follows: 1) dividing the surface of the electrically large target into sections; 2) defining RWG basis functions on the triangular facets; 3) initializing parameters; 4) calculating the Chebyshev frequency sampling points within the frequency band f based on CAT; 5) calculating the surface current at each Chebyshev frequency sampling point using the equivalent dipole moment method and the method of moments; 6) calculating the wavenumber k at each frequency point within the band. a Surface current; 7) Obtain the radar cross section (RCS) of electrically large targets. Based on the Chebyshev approximation method (CAT), this invention combines the equivalent dipole moment method to significantly reduce the calculation time of the impedance matrix and improve the calculation efficiency of the broadband radar cross section of electrically large targets.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic simulation technology, and further relates to a method for obtaining the broadband RCS of electrically large targets based on communication base stations, which can be applied to fields such as target recognition. Background Technology

[0002] The radar cross section (RCS) is a physical quantity that measures the intensity of the echo scattering produced by a target under radar wave illumination. In practical engineering applications, modern radar detection systems use signals from non-cooperative radiation sources such as radar signals, communication base station signals, and FM radio signals. Among these, communication base station signals are characterized by wide distribution, large signal coverage, and wide frequency bands, making radar detection systems based on communication base stations extremely valuable. When electrically large targets such as aircraft and automobiles are moving at high speeds, the ability to quickly calculate the radar cross section over a wide frequency band is crucial for accurate target detection. Therefore, researching rapid analysis of the broadband radar cross section of electrically large targets based on communication base stations has significant practical application value. While the traditional method of moments (MoM) can guarantee high accuracy in calculating the broadband radar cross section of electrically large targets, the large physical size of these targets leads to high complexity in impedance matrix calculation, placing excessive demands on computing power. Furthermore, calculating the broadband radar cross section requires calculating the current at each frequency point, resulting in low computational efficiency.

[0003] To rapidly calculate the broadband radar cross section (RCS) of electrically large targets, Xi'an University of Electronic Science and Technology disclosed a method for rapidly calculating the broadband RCS in its patent application, "A Method for Obtaining the Broadband RCS of Electrically Large Targets Based on ACA and CAT" (Application Publication No.: CN 114755652A). The main steps of this method are: 1) dividing the surface of the electrically large target into segments; 2) defining RWG basis functions on the segmented target surface; 3) grouping the RWG basis functions of the electrically large target surface; 4) dividing the impedance matrix into near-field and far-field blocks; 5) determining the broadband Chebyshev sampling points; 6) filling the far-field and near-field blocks of the impedance matrix at the sampling points respectively; 7) filling the excitation vector of the sampling points with the incident wave electric field; 8) solving for the surface induced current at each Chebyshev sampling point; 9) calculating the surface current at each frequency point within the broadband; and 10) obtaining the broadband radar cross section of the electrically large target. In this method, when calculating the current at the sampling point of Chebyshev frequency, the ACA method is used to divide the RWG basis function of the electrically large target surface into far-field and near-field blocks to calculate the impedance matrix. Compared with the traditional method of moments, this reduces the dimension of the impedance matrix calculation. However, since multiple integrals still need to be solved in the far-field and near-field blocks of the impedance matrix calculation, the calculation process is complicated, resulting in a low efficiency in calculating the broadband radar cross section of electrically large targets. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the prior art by proposing a method for obtaining the broadband RCS of electrically large targets based on communication base stations, thereby solving the technical problem of low efficiency due to computational complexity in the prior art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Surface segmentation of electrically large target:

[0007] The surface of a electrically large target is triangulated to obtain a set of D triangular facets S = {S1, S2, ..., S...} d ,...,S D}, where D≥4 and is even, S d This represents the d-th triangular facet;

[0008] (2) Define RWG basis functions on the triangular facet:

[0009] For each triangular facet S d Pair the triangles that share a common edge with the triangles to obtain U pairs of triangles. Define RWG basis functions on each pair of triangles to obtain the RWG basis function set Ω = {Ω1,...,Ω...} u ,...,Ω U}, where Ω u The center position coordinates are Γ u ={Γ u 1,Γ u 2,Γ u 3} The u-th RWG basis function, Γ u 1、Γ u 2、Γ u 3 represent the x, y, and z coordinates of the center position of the u-th RWG basis function, respectively;

[0010] (3) Initialize parameters:

[0011] The electric field and frequency band of a broadband uniform plane wave irradiated by an initial communication base station onto the surface of an electrically large target are E in f, where f contains a start frequency of f1 and a cutoff frequency of f. A A frequency points, the a-th frequency point f a ∈[f1,f A The corresponding wavenumber and wavelength are k, respectively. a , λ a The frequency point corresponding to the a-th frequency point after coordinate transformation is The Chebyshev polynomial has E terms in its expansion, where A≥4 and E≥3.

[0012] (4) Calculate the Chebyshev frequency sampling points within the frequency band f based on CAT:

[0013] Calculate each Chebyshev polynomial Chebyshev nodes And the Chebyshev approximation method CAT is used to... and the starting frequency f1 and the cutoff frequency f of frequency band f. A The corresponding wave numbers k1 and k A Calculate the frequency band within f Corresponding Chebyshev frequency sampling points

[0014] (5) The surface current at each Chebyshev frequency sampling point is calculated using the equivalent dipole moment method and the method of moments:

[0015] (5a) Calculate the basis functions for every two RWGs With Ω U，χ Distance between judge Compared with the preset threshold of 0.15λ A Does it meet the requirements? If so, use the equivalent dipole moment method (EDM) to calculate the first... element Otherwise, the method of moments is used to calculate the first... element The obtained U×U elements are used to form the e-th Chebyshev frequency sampling point. Impedance matrix of dimension U×U in, χ∈[1,U], Representing the impedance matrix The Middle The element in row x, column x;

[0016] (5b) Through a broadband uniform plane wave electric field E in Calculate each Chebyshev frequency sampling point Excitation vector at point and through and impedance matrix Calculate each Chebyshev frequency sampling point Surface current at

[0017] (6) Calculate k at the wavenumber corresponding to each frequency point. a Surface current:

[0018] Through each Chebyshev frequency sampling point Current coefficient at Calculate the wavenumber k at each frequency point within the frequency band f.a Surface current I(k a ):

[0019]

[0020]

[0021] Among them, c e Chebyshev frequency sampling points representing the E-order Chebyshev polynomial The coefficient at the location, Represents wave number k a The values ​​after coordinate transformation. Indicates in The E-order Chebyshev polynomial at the location;

[0022] (7) Obtain the radar cross section (RCS) of electrically large targets:

[0023] Based on the wavenumber k corresponding to each frequency point within frequency band f a Surface current I(k) at the location a Calculate the scattered electric field E generated by the target at the far-field receiving radar. Scat (k a ), and according to E Scat (k a Calculate the wavenumber k corresponding to each frequency point within the frequency band f. a Radar cross section (RCS) of electrically large targets a ), thus obtaining the broadband radar cross section set RCS={RCS(k1),...,RCS(k a ),...,RCS(k A )};

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] This invention, based on the wideband signal of a communication base station, calculates the Chebyshev frequency sampling points within frequency band f, and, according to preset conditions, calculates the impedance matrix at each Chebyshev frequency sampling point using both the Equivalent Dipole Moment (EDM) method and the Method of Moments (MoM) method. ACA requires dividing the impedance matrix into near and far fields and calculating the impedance matrix using the MoM method, making the calculation process complex. The Equivalent Dipole Moment (EDM) method, on the other hand, eliminates the need for near and far field division and simplifies the calculation process. This invention avoids the high complexity of existing technologies that require multiple double integrations after dividing electrically large targets into near and far fields for impedance matrix calculation. Compared to existing technologies, this invention effectively improves computational efficiency while maintaining computational accuracy. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0027] Figure 2 This is a schematic diagram of the electrically large target used in this invention. Detailed Implementation

[0028] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0029] Reference Figure 1 The present invention includes the following steps:

[0030] Step 1) Mesh the electrically large target surface:

[0031] In this embodiment, an aircraft model is used as an electrically large target, and its structural diagram is as follows: Figure 2 As shown, the fuselage is 6m long and 1.5m wide. The physical dimensions of the aircraft are more than 200 times the radar wavelength. The model is made of an ideal conductor. The aircraft model is triangularly divided to obtain a set of triangular facets S = {S1, S2, ..., S...}. d ,...,S D}, where D≥4, in this embodiment, D=72640, S d This represents the d-th triangular facet.

[0032] Step 2) Define RWG basis functions on the triangular facet:

[0033] For each triangular facet S d Pair the triangles that share a common edge with the triangles to obtain U pairs of triangles. Define RWG basis functions on each pair of triangles to obtain the RWG basis function set Ω = {Ω1,...,Ω...} u ,...,Ω U In this embodiment, U = 108960, where Ω u The center position coordinates are Γ u ={Γ u 1,Γ u 2,Γ u 3} The u-th RWG basis function, Γ u 1、Γ u 2、Γ u 3 represent the x, y, and z coordinates of the center position of the u-th RWG basis function, respectively;

[0034] Step 3) Initialize parameters:

[0035] In this example, the broadband uniform plane wave electric field illuminating the electrically large target surface by the communication base station is initialized as E. inA uniform plane wave is an electromagnetic wave whose field vector changes only along its propagation direction. Within an infinitely large plane perpendicular to the propagation direction, the direction, amplitude, and initial phase of the electric field strength E and magnetic field strength H remain constant. A broadband uniform plane wave has a frequency band f containing 91 frequencies from a starting frequency of 1 GHz to a cutoff frequency of 10 GHz, with an incident angle of θ = 0°. The electric field polarization is θ polarization, and the direction of the far-field receiving radar is θ = 0°. The a-th frequency f a ∈[f1,f A The corresponding wavenumber and wavelength are k, respectively. a =2πc / f a , λ a =c / f a The speed of light, c = 3 × 10 9 m / s, the order of the Chebyshev polynomial expansion is 21;

[0036] Step 4) Calculate the Chebyshev frequency sampling points within frequency band f based on CAT:

[0037] First, calculate each Chebyshev polynomial within the frequency band f. Chebyshev nodes and within the frequency band f Corresponding Chebyshev frequency sampling points

[0038]

[0039]

[0040] in, Let π represent the e-th Chebyshev frequency sampling point within the wideband, π represent pi, and cos represents the cosine function. The Chebyshev polynomial described in this example... It is determined by the following recursive relation:

[0041]

[0042] in, Indicates in The e-order Chebyshev polynomial at the location;

[0043] Step 5) Calculate the surface current at each Chebyshev frequency sampling point:

[0044] Step 5a) Calculate any two RWG basis functions With Ω u，χ Distance between judge The relationship between the magnitude and the preset threshold, if The equivalent dipole moment method (EDM) is used to calculate the first... The element is not specified; otherwise, the method of moments is used to calculate the element. There are elements, among which... χ∈[1,U], Representing the impedance matrix The Middle The formulas for calculating the distance, equivalent dipole moment, and method of moments for the element in row x and column x are as follows:

[0045]

[0046]

[0047]

[0048] Indicates the first basis functions The x, y, z coordinates of the center position, Γ u,χ 1、Γ u,χ 2、Γ u,χ 3 represents the x-th basis function Ω u，χ The x, y, z coordinates of the center position, η represents the wave impedance in free space, and j is the imaginary unit. express The distance vector between the centroids of the two upper triangular facets and Ω u，χ The vector difference between the distances of the centroids of the two upper triangular facets to the vector. express The distance vector between the centroids of the two upper triangular facets and Ω u，χ The magnitude of the vector difference between the distances of the centroids of the two upper triangular facets to the vector. express The corresponding equivalent dipole moment vector, m u,χ Represents Ω u，χ The corresponding equivalent dipole moment vector, where C is a variable. r indicates The source point location in Ω, r′ represents the source point location. u，χ The location of the field point in the middle, Let G(r,r′) denote the Hamiltonian operator, and G(r,r′) denote the Green's function. S • Indicates the area integral operation.

[0049] When calculating the impedance matrix, the distance between basis functions is determined based on a set threshold. The coupling relationship between basis functions is then equivalent to an electric dipole moment based on the distance between them. Using this equivalent relationship to calculate the impedance matrix avoids the process of dividing the basis functions into near and far fields and performing multiple double integrals, thus simplifying the calculation steps and improving the calculation efficiency of the impedance matrix.

[0050] Step 5b) Passing through a broadband uniform plane wave electric field of E n in Calculate each Chebyshev frequency sampling point Excitation vector at point pass and impedance matrix Calculate each Chebyshev frequency sampling point Current coefficient at

[0051]

[0052]

[0053] in, This represents the current at the e-th Chebyshev frequency sampling point within the wide bandwidth. Let ∫∫ represent the impedance matrix at the e-th Chebyshev frequency sampling point within the frequency band. S • indicates area integral operation, × indicates cross product operation;

[0054] Step 6) Through Calculate the surface current at the wavenumber corresponding to each frequency point within the frequency band f:

[0055]

[0056]

[0057] Where I(k) a ) represents the corresponding wave number k a Surface current at c e Chebyshev frequency sampling points representing the E-order Chebyshev polynomial The coefficient at the location;

[0058] Step 7) Obtain the radar cross section (RCS) of electrically large targets:

[0059] Based on the wavenumber k corresponding to each frequency point within frequency band f a Surface current I(k) at the location a Calculate the scattered electric field E generated by the target at the far-field receiving radar. Scat (k a ), and according to E Scat (k a Calculate the wavenumber k corresponding to each frequency point within the frequency band f. a Radar cross section (RCS) of electrically large targets a ), thus obtaining the broadband radar cross section set RCS={RCS(k1),...,RCS(k a ),...,RCS(kA )}:

[0060]

[0061]

[0062] Among them, RCS(k a ) represents the wave number k a The radar cross section at point j represents the imaginary unit symbol, η represents the wave impedance in free space, and R represents the position vector between the far-field receiving radar and the electrically large target. Let |R| represent the position vector of the electrically large target, |R| represent the distance between the far-field radar and the electrically large target, R' represent the position vector of the far-field receiving radar, and S represent the area of ​​the outer surface of the electrically large target. S • Represents the area integral operation, I(k) a ) represents the surface current of a large-size target, e represents the natural constant, |·| 2 This indicates the operation of squaring the modulo value.

[0063] The technical effects of this invention will be further explained below with reference to simulation experiments:

[0064] 1. Experimental conditions

[0065] The aircraft model of this invention was simulated using the simulation software Feko2020; the processor was an Intel i7-7700K CPU with a main frequency of 2.9GHz and 48.0GB of memory. The software platform was Windows 10 operating system and Intel Visual Fortran 2017; the aircraft model used in the simulation experiment was an electrically large-scale aircraft model.

[0066] 2. Simulation content and result analysis.

[0067] The computational efficiency of the present invention and existing methods for obtaining the broadband RCS of electrically large targets based on ACA and CAT were compared and simulated, and the results are shown in Table 1.

[0068] Table 1

[0069] Calculation method Calculation time (s) Existing technology 32603.9 This invention 11933.2

[0070] As shown in Table 1, the calculation time of this invention is reduced by 63.4% compared to the existing ACA-CAT technology. This proves that this invention can quickly obtain the broadband radar cross section (RCS) of electrically large targets in a shorter time.

Claims

1. A method for wideband RCS acquisition of large size targets based on a communication base station, characterized in that, Includes the following steps: (1) Mesh the electrically large target surface: The surface of the electrically large target is triangulated to obtain... A set of triangular facets ,in, And it is an even number. Indicates the first A triangular facet; (2) Define RWG basis functions on the triangular facet: pairing each triangle patch with the triangle patch sharing a common edge with it, obtaining triangle patch pairs, and defining RWG basis functions on each triangle patch pair, obtaining a RWG basis function set wherein, denotes the center position coordinates the RWG basis function, , , denotes the coordinate of the center position of the RWG basis function, respectively. (3) Initialize parameters: The electric field and frequency band of a broadband uniform plane wave irradiated by an initial communication base station onto the surface of an electrically large target are as follows: , , The starting frequency is included. Cutoff frequency is of The frequency point, the first frequency points The corresponding wavenumbers and wavelengths are respectively , , No. After coordinate transformation, the corresponding frequency points are: The number of terms in the Chebyshev polynomial expansion is ,in, , ; (4) Calculate frequency band based on CAT Chebyshev frequency sampling points within: Calculate each Chebyshev polynomial Chebyshev nodes And using the Chebyshev approximation method CAT, through and frequency band starting frequency and cutoff frequency Corresponding wave number and Calculate the frequency band Inside Corresponding Chebyshev frequency sampling points ; (5) The surface current at each Chebyshev frequency sampling point was calculated using the equivalent dipole moment method and the method of moments: (5a) Calculate the basis functions for every two RWGs and Distance between ,judge With a preset threshold Does it meet the requirements? If so, the equivalent dipole moment method (EDM) is used to calculate the first... element Otherwise, the method of moments is used to calculate the first... element and will arrive The elements form the first Chebyshev frequency sampling points The dimension is impedance matrix ,in The equivalent dipole moment method (EDM) is used to calculate the first... element And the method of moments is used to calculate the first element The calculation formulas are as follows: ； ； ； in, , , Representing the impedance matrix The Middle Line number Column elements; , , Indicates the first basis functions central position coordinate, , , Indicates the first basis functions central position coordinate, Represents wave impedance in free space. The imaginary unit, express The distance vector between the centroids of the two upper triangular patches and The vector difference between the distances of the centroids of the two upper triangular facets to the vector. express The distance vector between the centroids of the two upper triangular patches and The magnitude of the vector difference between the distances of the centroids of the two upper triangular facets to the vector. express The corresponding equivalent dipole moment vector, express The corresponding equivalent dipole moment vector, As variables, , express The source point location in the middle, express The location of the field point in the middle, Represents the Hamiltonian operator. Represents the Green's function. This represents the area integral operation; (5b) Through a broadband uniform plane wave electric field Calculate each Chebyshev frequency sampling point Excitation vector at point and through and impedance matrix Calculate each Chebyshev frequency sampling point Surface current at ; (6) Calculate the wavenumber corresponding to each frequency point. Surface current: Through each Chebyshev frequency sampling point Current coefficient at Calculate the frequency band Each frequency point corresponds to a wavenumber. Surface current : ； ； in, express Chebyshev frequency sampling points of the Chebyshev polynomial of order The coefficient at the location, Wave number The values ​​after coordinate transformation. Indicates in place Chebyshev polynomial; (7) Obtain the radar cross section (RCS) of electrically large targets: According to frequency band Wavenumber corresponding to each frequency point Surface current at Calculate the scattered electric field generated by the target at the far-field receiving radar. and according to Calculate the frequency band Wavenumber corresponding to each frequency point Radar cross section of electrically large targets The broadband radar cross section set is obtained. .

2. The method for obtaining the broadband RCS of electrically large targets based on a communication base station according to claim 1, characterized in that, In step (3) The formula for coordinate transformation of individual frequency points is as follows: 。 3. The method for obtaining the broadband RCS of electrically large targets based on a communication base station according to claim 2, characterized in that, Each Chebyshev polynomial described in step (4) Chebyshev nodes and frequency band Inside Corresponding Chebyshev frequency sampling points The calculation formulas are as follows: ； ； in, Represents pi (π). This represents the cosine function.

4. The method for obtaining the broadband RCS of electrically large targets based on a communication base station according to claim 3, characterized in that, The excitation vector described in step (5b) and current coefficient The calculation formulas are as follows: ； ； This indicates the cross product operation.

5. The method for obtaining the broadband RCS of electrically large targets based on a communication base station according to claim 4, characterized in that, The step (7) described above, based on the frequency band Wavenumber corresponding to each frequency point Surface current at Calculate the scattered electric field generated by the target at the far-field receiving radar. and according to Calculate the frequency band Wavenumber corresponding to each frequency point Radar cross section of electrically large targets The calculation formula is expressed as follows: ； ； in, Wave number The radar cross section at that location This represents the position vector between the far-field receiving radar and the electrically large target. Represents the position vector of electrically large targets. This indicates the distance between the far-field receiving radar and the electrically large target. This represents the position vector of the far-field receiving radar. The area of ​​the outer surface of the electrically large target. This represents the surface current of electrically large targets. Represents the natural constant. This indicates the operation of squaring the modulo value.

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