Method for Obtaining Periodic Structure Wideband RCS Based on CBFM and CAT

Abstract

The present invention proposes a method for obtaining the broadband RCS of a periodic structure based on CBFM and CAT, and the implementation steps are as follows: 1) Divide the periodic structure target; 2) Obtain the incident wave electric field of each sub-region; 3) Calculate the Chebyshev frequency sampling points within the frequency band f; 4) Use the characteristic basis function method CBFM to solve the induced current at each Chebyshev frequency sampling point; 5) Use the Chebyshev approximation method CAT to calculate the surface current at the wave number corresponding to each frequency within the frequency band f; 6) Obtain the radar cross section RCS(ks) of the periodic structure target at the wave number corresponding to each frequency. The present invention divides the periodic structure target into N sub-regions, uses the Chebyshev approximation method to calculate the induced current at each frequency sampling point, represents each sub-region with a characteristic basis function, compresses the impedance matrix into an N-dimensional matrix, solves the problem of large computing memory when calculating the periodic structure, and improves the computing efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic simulation, and particularly relates to a method for obtaining the broadband radar cross section (RCS) of a periodic structure by combining the characteristic basis function method (CBFM) with the Chebyshev approximation method (CAT). Background Technique

[0002] The radar cross section (RCS) is a physical quantity that measures the echo scattering intensity generated by a target under the illumination of radar waves. A periodic structure is a structure formed by arranging units according to a certain rule, and it has some important electromagnetic characteristics, such as miniaturization, bandgap structure, local resonance, etc., which have attracted extensive research. When detecting and identifying a target by radar, it is necessary to calculate and analyze the radar cross section of the target. However, due to the limitations of traditional radomes in electromagnetic wave regulation, it cannot well meet the electromagnetic performance requirements of the new generation of communication antenna systems. With the rapid development of current periodic structures, it is of great significance to quickly and accurately calculate the broadband radar cross sections of periodic structures such as phased array antennas, frequency selective surfaces, and electromagnetic bandgap structures.

[0003] The frequency selective surfaces used in engineering are all of finite size, and most of them are conformal with the rest of the models in the system. For this type of periodic structure, traditional calculation and analysis methods based on the theory of infinite periodic structures, including the periodic boundary conditions of an infinite plane, are no longer applicable, or rather, they are no longer completely applicable. There are two difficulties in calculating the broadband radar cross section of a finite periodic structure by existing methods: one is to obtain a periodic structure by arranging and combining units. In order to relatively accurately describe its surface current, in addition to meeting the requirements of their respective numerical analysis methods, the meshing size of the periodic structure target may need to be further refined, so that each periodic structure can meet the requirement of being able to describe singular currents, which leads to a large increase in the number of unknowns. The other is that when calculating the broadband radar cross section of the target, it is necessary to calculate one by one for each frequency. However, the scattering characteristics of the periodic structure target change violently with frequency, and it is necessary to calculate at a small frequency interval, which reduces the calculation efficiency.

[0004] For example, the patent application with the publication number CN 113567943 and the title "Method for Obtaining Broadband RCS of Carrier Platform Based on SAIM and CAT" discloses a method for obtaining the broadband radar cross section (RCS) of a carrier platform based on SAIM and CAT. The method first divides the complex carrier platform target into multiple sub-regions and retains the common virtual surfaces between adjacent sub-regions; then triangulates all the closed sub-regions and establishes Cartesian grids for each sub-region; calculates the Chebyshev sampling points of the broadband radar cross section (RCS) and uses AIM to calculate the initial surface induced current of the sub-region at the Chebyshev sampling points; imposes boundary conditions on the virtual surfaces of adjacent sub-regions to update the excitation vector and update the surface induced current of the sub-region at the Chebyshev sampling points until convergence; finally, uses the Merry approximation to improve the current accuracy and obtain the broadband radar cross section of the complex carrier platform, improving the calculation efficiency. However, its drawback is that when calculating the surface current at each frequency, due to too many basis functions, the impedance matrix is too large, resulting in too high a requirement for computer memory. Even after dividing into multiple sub-regions, calculating the surface current is still complex, leading to a relatively low acquisition efficiency. Summary of the Invention

[0005] The object of the present invention is to propose a method for obtaining the broadband RCS of a periodic structure based on CBFM and CAT in view of the above deficiencies of the prior art, so as to solve the technical problem of relatively low acquisition efficiency caused by large memory occupation and long calculation time in the prior art.

[0006] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Divide the periodic structure target:

[0008] Divide the periodic structure target along the intervals of its surface array to obtain N sub-regions Ω = {Ω1, Ω2,..., Ω n ,..., Ω N}, where N ≥ 2 and Ω n represents the nth sub-region;

[0009] (2) Obtain the incident wave electric field of each sub-region:

[0010] Irradiate each sub-region Ω n with a broadband uniform plane wave in a frequency band f containing S frequencies to obtain the incident wave electric field E n corresponding to the sub-region Ω n in , where the starting frequency, ending frequency, and width of the frequency band f are f1, f S , [f1, f S , and the s-th frequency is fs The corresponding wavenumber is k s , and the wavenumber range corresponding to f is [k1, k S , s ∈ {1, 2, 3,..., S};

[0011] (3) Calculate the Chebyshev frequency sampling points within the frequency band f:

[0012] (3a) Calculate the q-th Chebyshev node of the Chebyshev polynomial of order Q

[0013] (3b) Transform from the interval [-1, 1] to the interval [f1, f S to obtain the q-th Chebyshev frequency sampling point k q within the frequency band f, where Q ≥ 2 and q ∈ {1, 2,..., Q};

[0014] (4) Use the characteristic basis function method (CBFM) to solve for the induced current at each Chebyshev frequency sampling point:

[0015] (4a) Construct the total matrix equation at each Chebyshev frequency sampling point k n through the excitation vector V n (k q ) of each sub-region Ω n , and the impedance matrix Z n' (k nn' ) between the n-th sub-region Ω q and the n'-th sub-region Ω q :

[0016] Z nn' (k q )I n (k q ) = V n (k q )

[0017] where I n (k q ) is the total induced current of the sub-region Ω n to be solved. When n = n', Z nn' (k q ) is the self-impedance matrix of the n-th sub-region Ω n ; when n ≠ n', Z nn' (k q ) is the mutual impedance matrix between the n-th sub-region Ω n and the n'-th sub-region Ω n' , and n' ∈ {1, 2, 3,..., N};

[0018] ​(4b) Through the q-th Chebyshev frequency sampling point k q at the excitation vector E n in (k q ), the impedance matrix Z nn' (k q ), the main characteristic basis function to be solved on the sub-region Ω n' the field generated on the sub-region Ω on the sub-region Ω n and the secondary characteristic basis function to be solved and construct the on the sub-region Ω n at k q the matrix equation of and the matrix equation of

[0019]

[0020]

[0021] (4c) Use LU decomposition to solve the matrix equations of the main characteristic basis function and the secondary characteristic basis function respectively, to obtain the main characteristic basis function and the secondary characteristic basis function

[0022] (4d) Use the Galerkin method to solve the total matrix equation in step (4a) through the main characteristic basis function and the secondary characteristic basis function to obtain the coefficients a n and b n , and calculate the induced current I n and b n at the Chebyshev frequency sampling point k n on the sub-region Ω q : n (k q )

[0023]

[0024] (5) Use the Chebyshev approximation method CAT to calculate the surface current at each frequency corresponding wavenumber within the frequency band f:

[0025] (5a) Through the induced current I n at the Chebyshev frequency sampling point kq on the n-th sub-region Ω n (k q ), construct the n at the s-th frequency f within the frequency band fs The surface current I at the corresponding wave number k s is given by the equation for n (k s ) as follows:

[0026]

[0027]

[0028]

[0029] where a n,l represents the first unknown coefficient at the Chebyshev nodes of the L - th order Chebyshev polynomial in the n - th sub - region Ω n , b represents the second unknown coefficient at the Chebyshev nodes of the M - th order Chebyshev polynomial in the n - th sub - region Ω n,m , b n = 1, c represents the third unknown coefficient at the Chebyshev nodes of the Q - th order Chebyshev polynomial in the n - th sub - region Ω n,0 , and n,q represents the Chebyshev nodes of the frequency f n ; (5b) Calculate the unknown coefficients a and b s of the n - th sub - region Ω

[0030] and obtain the surface current I n at each wave number k n,l corresponding to each frequency f n,m in the frequency band f of the n - th sub - region Ω n,l using a n,m and b n ; s (6) Obtain the radar cross - section RCS(k s ) of the periodic - structure target at each wave number corresponding to each frequency: n (k s ) as follows:

[0031] Calculate the scattered electric field generated by the sub - region Ω s at the far - field radar according to the target surface current I

[0032] corresponding to each sub - region Ω n at the wave number k s corresponding to the s - th frequency f s and calculate the total scattered electric field generated by the periodic - structure target at the far - field radar according to n (k s ) n and ; ​ Then, according to Calculate the wideband radar cross-section RCS(k s corresponding to the wave number k at each frequency f within the frequency band f of the periodic structure target s ). s )

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] The present invention is used to solve the technical problem of low acquisition efficiency in the prior art due to large memory occupation and long calculation time. First, the periodic structure target is segmented along the intervals of its surface array, and the Chebyshev approximation technique is used to reduce the number of frequencies to be calculated within the frequency band. Then, the induced current at the Chebyshev sampling points is calculated to obtain the surface current at any frequency within the entire frequency band, and the method of characteristic basis functions is used to represent the surface current of each sub-region as a characteristic basis function, reducing the impedance matrix dimension to N×N dimension, avoiding the defect of difficult impedance matrix filling caused by too many basis functions, thereby reducing the memory for calculating the surface current and greatly improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the implementation flowchart of the present invention;

[0036] Figure 2 is the structural schematic diagram of the periodic structure target adopted by the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0038] Referring to Figure 1 , the present invention includes the following steps:

[0039] Step 1) Divide the area of the periodic structure target:

[0040] In this embodiment, the periodic structure target adopted is a conical FSS radome, and its structure is as shown in Figure 2 (a). The periodic structure target is divided along the separation between each layer of periodic surface FSS units. Each layer of periodic surface FSS unit is a region, and 6 sub-regions composed of periodic units are obtained, Ω = {Ω1, Ω2,..., Ω n ,..., Ω N}, and the division of sub-regions is as shown in Figure 2 (b), where N = 6, Ω nIt represents the nth sub-region; the periodic structure target consists of 6 layers of FSS units, and the number of FSS units in each layer is 16, 15, 15, 12, 9, and 8 respectively. For the conical FSS radome model, an initial FSS unit is first established on the xoz plane, with its normal parallel to the x-axis. The angle between the conical generatrix and the xoy plane is measured, and the FSS unit is rotated to be parallel to the conical generatrix according to the angle size. Then the FSS unit is swept so that it vertically penetrates the conical surface and intersects with the extensible surface. By deleting the remaining extra parts, an FSS unit structure is finally obtained. According to the above FSS unit modeling method, FSS periodic units can be obtained by modeling at equal intervals along the conical generatrix direction. Then, each of them is rotated and copied clockwise around the z-axis to obtain the FSS periodic units of each layer, and finally the conical FSS radome is obtained.

[0041] Step 2) Obtain the incident wave electric field of each sub-region:

[0042] Irradiate each sub-region Ω with a broadband uniform plane wave in the frequency band f containing S = 16 frequencies n , and obtain the incident wave electric field E n corresponding to the sub-region Ω n in . A uniform plane wave means that the field vector of the electromagnetic wave only changes along its propagation direction. In an infinite plane perpendicular to the propagation direction of the electromagnetic wave, the directions, amplitudes, and initial phases of the electric field strength E and the magnetic field strength H remain unchanged. In this embodiment, the starting frequency and the ending frequency of the initialized frequency band f are f1 = 12 GHz and f S = 20 GHz respectively. The s-th frequency is f s , and the corresponding wave number is k s . The corresponding wave numbers are k1 = 2πc / f1 and k S = 2πc / f S , the speed of light c = 3×10 9 m / s, and the wave number range corresponding to f is [k1, k S , s ∈ {1, 2, 3,..., S};

[0043] Step 3) Calculate the Chebyshev frequency sampling points in the frequency band f:

[0044] (3a) Use the Chebyshev approximation method to calculate the induced current at the Chebyshev frequency sampling points to improve the calculation efficiency of the broadband RCS. First, calculate the Chebyshev nodes in the frequency band f and the q-th Chebyshev node of the Q-th order Chebyshev polynomial

[0045]

[0046]

[0047] The Chebyshev polynomial described in this embodiment is determined by the following recurrence relation:

[0048]

[0049] where denotes the q-th order Chebyshev polynomial at ;

[0050] (3b) Transform the q-th Chebyshev node of the Q-th order Chebyshev polynomial from the interval [-1, 1] to the interval [f1, f S to obtain the q-th Chebyshev frequency sampling point k q of the frequency band f:

[0051]

[0052] Step 4) Use the characteristic basis function method (CBFM) to solve the induced current at each Chebyshev frequency sampling point:

[0053] (4a) The characteristic basis function method is a variation based on the method of moments. It mainly reduces the dimension of the impedance matrix by dividing the target into sub-regions. For N sub-regions, the dimension of the impedance matrix is N×N. Through the excitation vector V n of each sub-region Ω n (k q ), and the impedance matrix Z n between the n-th sub-region Ω n' and the n'-th sub-region Ω nn' (k q ), construct the total matrix equation at each Chebyshev frequency sampling point k q :

[0054] Z nn' (k q )I n (k q ) = V n (k q )

[0055]

[0056] where I n (k q ) is the total induced current of the sub-region Ω n to be solved. When n = n', Z nn' (k q ) is the impedance matrix of the n-th sub-region Ω nThe self-impedance matrix; when n ≠ n', Z nn' (k q ) is the mutual impedance matrix between the nth sub-region Ω n and the n'th sub-region Ω n' , where n' ∈ {1, 2, 3,..., N};

[0057] (4b) According to the Foldy-Lax multipath scattering equation, the final excitation source of each scatterer should be equal to the incident source plus the scattered sources of all scatterers except this target. When constructing the characteristic basis functions of the periodic structure target, it should include the main characteristic basis functions representing the self-interaction of the sub-region itself, and the secondary characteristic basis functions representing the mutual coupling effect between sub-regions. That is, the main characteristic basis function of the nth sub-region Ω n is the surface induced current generated by the incident source on a sub-region. At this time, the contribution of the scattered fields of the remaining sub-regions to the induced current on the surface of the target sub-region should be ignored during the calculation. The secondary characteristic basis function can be obtained by superimposing the main characteristic basis functions on the remaining sub-regions, and using the scattered field generated by them on the required sub-region as the excitation source. Therefore, through the excitation vector E q at the qth Chebyshev frequency sampling point k n in (k q ), the impedance matrix Z nn' (k q ), the main characteristic basis function to be solved on the sub-region Ω n' generates the field on the sub-region Ω n and the secondary characteristic basis function to be solved constructs the matrix equation of at k n on the sub-region Ω q and the matrix equation of : The matrix equations of

[0058]

[0059]

[0060] (4c) Use LU decomposition to solve the matrix equations of the main characteristic basis function and the matrix equation of the secondary characteristic basis function respectively, to obtain the main characteristic basis function and the secondary characteristic basis function Then use the Galerkin method through the main characteristic basis function and the secondary characteristic basis function Solve the total matrix equation in step (4a) to obtain the total matrix equation after applying the Galerkin method and obtain the coefficients a n and b n , and calculate the induced current I n and b n at the Chebyshev frequency sampling point k n on the sub-region Ω q using the following formula: n (k q ), where [·]

[0061]

[0062]

[0063]

[0064] denotes the transpose operation; T Step 5) Use the Chebyshev approximation method CAT to calculate the surface current at each frequency corresponding wavenumber within the frequency band f:

[0065] (5a) In this embodiment, construct the equation for the surface current I

[0066] (k n ) at the Chebyshev frequency sampling point k q on the sub-region Ω n (k q ) obtained in step 4) for the sth frequency f n within the frequency band f corresponding to the wavenumber k s : s where a n (k s ) represents the first unknown coefficient at the Chebyshev node of the L-th order Chebyshev polynomial for the n-th sub-region Ω

[0067]

[0068]

[0069]

[0070] n,l n , b n,m represents the second unknown coefficient at the Chebyshev node of the M-th order Chebyshev polynomial for the n-th sub-region Ω , b n,0 n n,0 = 1, and c represents the n-th sub-region Ω n,0 n,q n ​​The unknown coefficient of the third term at the Chebyshev nodes of the Q - order Chebyshev polynomial where, the Chebyshev nodes representing the frequency f s are;

[0071] (5b) Calculate the unknown coefficients a n and b n,l of the n - th sub - region Ω n,m , and use a n,l and b n,m to obtain the surface current I n at each frequency f s corresponding to the wave number k s in the frequency band f of the n - th sub - region Ω n (k s ). The unknown coefficients a n and b n,l of the n - th sub - region Ω n,m are calculated by the formula:

[0072]

[0073] where, represents the p - order Chebyshev polynomial at ;

[0074] Step 6) Obtain the radar cross - section RCS(k s ) of the periodic - structure target at the wave number corresponding to each frequency:

[0075] According to the target surface current I n corresponding to the s - th frequency f s and the wave number k s in each sub - region Ω n (k s ), calculate the scattered electric field n generated by the sub - region Ω at the far - field radar and calculate the total scattered electric field generated by the periodic - structure target at the far - field radar according to Then, according to calculate the broadband radar cross - section RCS(k s ) at the wave number k s corresponding to each frequency f s in the frequency band f of the periodic - structure target. The calculation formula is as follows:

[0076]

[0077]

[0078]

[0079] Among them, represents taking the limit operation on the distance R between the far-field radar and the periodic structure, π represents the pi, j represents the imaginary unit symbol, and Z0 represents the wave impedance in the air. represents the unit vector of the radar position vector r′, × represents the cross product operation, S n is the area of the outer surface of the sub-region Ω n of. represents the surface integral operation, f n (r n ) represents the nth eigenbasis function defined by the sub-region Ω n of the periodic structure target, r n represents the field point vector in the nth eigenbasis function of the periodic structure, |·| 2 represents taking the square of the modulus value operation, and e represents the natural constant.

[0080] The technical effects of the present invention will be further described below in combination with simulation experiments:

[0081] 1. Simulation experiment conditions:

[0082] The hardware platform for the simulation experiment is: the processor is an Intel i7-10700 CPU with a main frequency of 2.9 GHz and a memory of 64 GB. The software platform is: Windows 10 operating system and Intel Visual Fortran2017.

[0083] 2. Simulation content and result analysis:

[0084] A comparative simulation is carried out on the CBFM-CAT technology of the present invention and the existing SAIM-CAT technology, and the results are shown in Table 1. The technology conducts a comparative analysis on the computing memory and computing time for obtaining the broadband radar cross section (RCS) of the periodic structure target. The periodic structure target model used in the simulation experiment of the present invention is a conical FSS radome model, the material of the model is an ideal conductor material, the incident direction of the radiation source is θ = 0°, the electric field polarization mode is θ polarization, and the receiving direction is θ = 60°. Then, the SAIM-CAT method and the CBFM-CAT method are respectively used to calculate the broadband RCS of the periodic structure target in the 12-20 GHz frequency band.

[0085] In order to prove the technical effects of the present invention, the simulation results of the two methods are analyzed and compared using the following two indicators (computing memory, computing time). The results of the computing memory and the computing time are plotted in Table 1.

[0086] Table 1 Comparison table of simulation effects of the method of the present invention and the existing technology

[0087] Calculation method Calculation memory (MB) Calculation time (min) SAIM-CAT 41.22 58.6 The present invention 27.648 52.2

[0088] As can be seen from Table 1, the computing time of the present invention is shortened by 10.92% compared with the prior art, and the computing memory is reduced by 32.92%, which proves that the present invention can obtain the broadband radar cross section (RCS) of the periodic structure target more quickly with less memory occupied.

Claims

1. A method for obtaining the broadband RCS of a periodic structure based on CBFM and CAT, characterized in that It includes the following steps: (1) Divide the periodic structure target: The periodic structure target is segmented at intervals along its curved surface array to obtain N sub-regions composed of periodic units Ω = {Ω1, Ω2,..., Ω n ,..., Ω N}, where N ≥ 2, and Ω n represents the nth sub-region; (2) Obtain the incident wave electric field of each sub-region: Irradiate each sub-region Ω with a broadband uniform plane wave whose frequency band f contains S frequencies n to obtain the incident wave electric field E n corresponding to the sub-region Ω n in , where the starting frequency, ending frequency, and width of the frequency band f are f1, f S , [f1, f S , and the s-th frequency is f s corresponding to the wave number k s , the wave number range corresponding to f is [k1, k S , s ∈ {1, 2, 3,..., S}; (3) Calculate the Chebyshev frequency sampling points within the frequency band f: (3a) Calculate the q-th Chebyshev node of the Q-th Chebyshev polynomial of the q-th Chebyshev node (3b) Convert from the interval [-1, 1] to the interval [f1, f S , and obtain the q-th Chebyshev frequency sampling point k in the frequency band f q , where Q ≥ 2 and q ∈ {1, 2,..., Q}; (4) Use the characteristic basis function method (CBFM) to solve for the induced current at each Chebyshev frequency sampling point: (4a) Through each sub-region Ω n 's excitation vector V n (k q ), and the impedance matrix Z n of the nth sub-region Ω n' and the n'th sub-region Ω nn' (k q ), construct the total matrix equation at each Chebyshev frequency sampling point k q : Z nn' (k q )I n (k q )=V n (k q ) Among them, I n (k q ) is the total induced current of the sub-region Ω n . When n = n', Z nn' (k q ) is the self-impedance matrix of the nth sub-region Ω n ; when n ≠ n', Z nn' (k q ) is the mutual impedance matrix between the nth sub-region Ω n and the n'th sub-region Ω n' , where n' ∈ {1, 2, 3,..., N}; (4b) through the q-th Chebyshev frequency sampling point k q at the excitation vector E n in (k q ), the impedance matrix Z nn' (k q ), the main eigenfunction to be solved in the sub-region Ω n' the field generated on the sub-region Ω on the sub-region Ω n and the secondary eigenfunction to be solved Construct the matrix equation of k on the sub-region Ω n at q and the matrix equation of : (4c) Use LU decomposition to solve the matrix equations of the primary eigenbasis functions and the secondary eigenbasis functions respectively, and obtain the primary eigenbasis functions and the secondary eigenbasis functions (4d) Solve the total matrix equation in step (4a) using the Galerkin method through the primary eigenbasis functions and the secondary eigenbasis functions to obtain the coefficients a n and b n , and calculate the induced current I n and b n at the Chebyshev frequency sampling points k n on the sub-region Ω q : n (k q ): (5) Use the Chebyshev approximation method (CAT) to calculate the surface current at the wavenumber corresponding to each frequency within the frequency band f: (5a) Through the nth sub-region Ω n The Chebyshev frequency sampling point k q The induced current I at n (k q ), construct Ω n The s-th frequency f in the frequency band f s The corresponding wave number k s The surface current I at n (k s ) equation: where a n,l represents the nth sub-region Ω n at the Chebyshev nodes of the Lth-order Chebyshev polynomial, b is the first unknown coefficient, b n,m represents the nth sub-region Ω n at the Chebyshev nodes of the Mth-order Chebyshev polynomial, b is the second unknown coefficient, b n,0 = 1, c n,q represents the nth sub-region Ω n at the Chebyshev nodes of the Qth-order Chebyshev polynomial, c is the third unknown coefficient, represents the Chebyshev nodes of the frequency f s ; (5b) Calculate the unknown coefficients a n and b n,l of the nth sub-region Ω n,m , and use a n,l and b n,m to obtain the surface current I n at each frequency f s in the frequency band f corresponding to the wave number k s at the nth sub-region Ω n (k s ); (6) Obtain the radar cross section RCS(k s ) of the periodic structure target at the wavenumber corresponding to each frequency: According to each sub-region Ω n at the s-th frequency f s corresponding to the wave number k s the corresponding target surface current I n (k s ), calculate the scattered electric field generated by the sub-region Ω n at the far-field radar and according to calculate the total scattered electric field generated by the periodic structure target at the far-field radar Then according to calculate the wideband radar cross section RCS(k s corresponding to the wave number k s ) at each frequency f in the frequency band f s ) 2. The method for obtaining the periodic structure broadband RCS based on CBFM and CAT according to claim 1, characterized in that, The Q-th order Chebyshev polynomial described in step (3a) is determined by the following recurrence relation: Among them, represents the q-th order Chebyshev polynomial at 3. The method for obtaining the periodic structure broadband RCS based on CBFM and CAT according to claim 1, characterized in that The q-th Chebyshev node described in step (3b) and the q-th Chebyshev frequency sampling point k q , and the calculation formula is:

4. The method for obtaining the periodic structure broadband RCS based on CBFM and CAT according to claim 1, characterized in that The frequency f described in step (5a) s of the Chebyshev nodes The calculation formula is:

5. The method for obtaining the periodic structure broadband RCS based on CBFM and CAT according to claim 1, wherein The unknown coefficients a n and b n,l of the nth sub-region Ω n,m to be solved in step (5b) are calculated by the formula: Among them, represents the p-th Chebyshev polynomial at 6. The method for obtaining the periodic structure broadband RCS based on CBFM and CAT according to claim 1, characterized in that The broadband radar cross section RCS(k s ) corresponding to the wave number k s at each frequency f within the frequency band f of the calculated periodic structure target described in step (6) is calculated by the following formula: s corresponding to the wave number k s at the broadband radar cross section RCS(k s ), the calculation formula is: Among them, represents taking the limit operation on the distance R between the far-field radar and the periodic structure, π represents the pi, j represents the imaginary unit symbol, and Z0 represents the wave impedance in air. represents the unit vector of the radar position vector r′, × represents the cross product operation, S n is the area of the outer surface of the sub-region Ω n outside. represents the surface integral operation, f n (r n ) represents the nth eigenbasis function defined by the sub-region Ω n of the periodic structure target, r n represents the field point vector in the nth eigenbasis function of the periodic structure, |·| 2 represents taking the square of the modulus value, and e represents the natural constant.

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