Antenna Radiation Field Modeling Method Based on Planar Uniformly Distributed Dipole Model

Abstract

The present invention provides a method for modeling the antenna radiation field of a planar uniformly distributed dipole model, comprising: placing dipoles at uniform grid points within a normal plane of the antenna radiation aperture of the antenna test radiation field, wherein the type, position, and orientation of the dipoles are known parameters, and the x, y, and z axes of the dipoles are oriented parallel to the x, y, and z axes of the antenna's geometric coordinate system, respectively; establishing a linear matrix equation between the spherical wave expansion coefficients and the dipole moment parameters of the antenna test radiation field based on a transformation matrix from the dipoles' local coordinate system to the global coordinate system, thereby estimating the dipole moment parameters from the spherical wave expansion coefficients; and establishing a dipole equivalent antenna radiation field model based on the type, position, and orientation of the dipoles and the estimated dipole moment parameters. This modeling method provides high accuracy for modeling the antenna radiation field and is easy to test.

Description

Technical Field

[0001] The present invention relates to the technical field of radar near-field target characteristic analysis and recognition, and in particular to a method for modeling antenna radiation fields of a planar uniformly distributed dipole model. Background Art

[0002] The near-field electromagnetic scattering characteristics of targets observed by radar are closely related to the antenna pattern. Variations in antenna pattern gain were incorporated into the definition of the target's near-field radar cross section in the 1990s. In the near-field, the antenna pattern and observation distance determine the form of the incident electromagnetic wave, resulting in non-uniform or localized illumination of the target surface. Furthermore, the form of the target's scattered echo received by the antenna is also influenced by the antenna pattern. Therefore, the target's near-field characteristics are closely related to the antenna's characteristics.

[0003] To decorrelate the target's near-field characteristics from the antenna pattern, an infinitesimal dipole can be used to model the antenna pattern. By transforming the target's near-field characteristics under dipole incidence, the target's near-field characteristics under different radar antenna incidences can be obtained. The unification of radar antenna forms is primarily based on the antenna's electromagnetic radiation characteristics. The varying charge and current on the antenna serve as the radiation source for excited electromagnetic waves, which themselves constitute dipole radiation. An actual antenna can be viewed as a combination of many dipoles, and the electromagnetic field excited by the antenna can be viewed as the superposition of the electromagnetic fields excited by these dipoles. According to the principle of electromagnetic field superposition, any incident or scattered electromagnetic field can be decomposed into a combination of the radiation fields of infinitesimal ideal electric or magnetic dipoles.

[0004] At present, the dipole modeling method for antenna radiation field, on the one hand, sets the dipole type, position, orientation and parameters to be changed, and adopts the heuristic global optimization modeling method; on the other hand, a constrained dipole model is used to model the antenna radiation test near field, constraining the dipole type, position and orientation parameters, and using the radiation measurement near field data to estimate the dipole moment parameters; in addition, for the estimation of the number of modeled dipoles and moment parameters, an orthogonal matching pursuit algorithm, There are many methods such as norm sparse constraint algorithm; the above methods all have problems such as low accuracy or difficulty in testing.

[0005] Therefore, in view of the problems of the prior art, it is necessary to provide a modeling method for antenna radiation field, which has high modeling accuracy and is easy to test. Summary of the Invention

[0006] The present invention provides an antenna radiation field modeling method of a planar uniformly distributed dipole model, which has high modeling accuracy for the antenna radiation field and is easy to test.

[0007] To achieve the above-mentioned and other related purposes, the present invention provides a method for modeling the antenna radiation field of a planar uniformly distributed dipole model, comprising:

[0008] Dipoles are placed at uniform grid points in the normal plane of the antenna radiation aperture of the antenna test radiation field, where the type, position, and orientation of the dipoles are all known parameters, and the x, y, and z axes of the dipoles are respectively parallel to the x, y, and z axes of the antenna's geometric coordinate system;

[0009] Based on the transformation matrix of the dipole from the local coordinate system to the global coordinate system, a linear matrix equation between the spherical wave expansion coefficient of the antenna test radiation field and the dipole moment parameter is established, so as to estimate the dipole moment parameter through the spherical wave expansion coefficient;

[0010] A dipole equivalent antenna radiation field model is established based on the type, position and orientation of the dipole and the estimated dipole moment parameters.

[0011] Preferably, the transformation matrix of the dipole from the local coordinate system to the global coordinate system is used to establish a linear matrix equation between the spherical wave expansion coefficient of the antenna test radiation field and the dipole moment parameter, specifically including:

[0012] The spherical wave expansion of the antenna test radiation field is expressed as:

[0013]

[0014] Where k = 2π / λ represents the spatial wave number, λ is the antenna radiation wavelength; ζ represents the intrinsic admittance of the medium, which is the reciprocal of the intrinsic impedance of the free space medium; J max The maximum truncation coefficient of the spherical wave expansion is related to the minimum radius of the sphere surrounding the antenna; F j (r) represents the normalized spherical vector wave function, Q j It represents the spherical wave expansion coefficient;

[0015] First, assume that the antenna test radiation field is represented by L current element radiation modes. Each current element radiation mode consists of six dipoles with the same position and orientation in the x, y, and z axes. The modal radiation field of the L current elements in the spherical coordinate system is expressed by spherical wave expansion as follows:

[0016]

[0017] in,

[0018]

[0019]

[0020] represents the dipole parameter of the i current element position, represents the transformation coefficient from the local coordinate system of the i-th current element to the global coordinate system, which is calculated according to the translation and rotation superposition theorem of the spherical wave expansion coefficient;

[0021] Using the L component current element radiation field to equate to the antenna radiation field, we can get from equations (1) and (2)

[0022]

[0023] Using F j (r) The orthogonal characteristics of the function, the transmission coefficients on both sides of the above equation are equal, then the linear matrix equation between the spherical wave expansion coefficient and the dipole moment parameter is obtained as follows:

[0024] Q=ΦX

[0025] in,

[0026]

[0027]

[0028] X=[S1,S2,...,S L ] T

[0029] Φ represents the transformation coefficient matrix of the spherical wave function from the local coordinate system of the current element to the global coordinate system of the antenna, with a dimension of J max ×6L; X represents the dipole moment parameter of the L component current elements.

[0030] Preferably, estimating the dipole moment parameters by using the spherical wave expansion coefficients specifically includes performing least squares estimation on the dipole moment parameters using a singular value decomposition method to obtain the dipole moment parameters.

[0031] Preferably, the matrix Φ is decomposed by SVD:

[0032]

[0033] in, represents a left singular matrix, V=[v1,v2,...,v 6L ] represents a right singular matrix, Σ=diag(σ1,...,σ r ,0,...,0) represents the singular value diagonal matrix, r = rank{Φ} represents the matrix rank, and the superscript "H" represents the conjugate transpose, so the least squares estimate of X is:

[0034]

[0035] Preferably, it is characterized in that the transformation coefficients of the matrix Φ are calculated by the rotation and translation theorem of spherical wave expansion.

[0036] Preferably, the method further includes evaluating the modeling accuracy of the dipole model of the antenna test radiation field, and the evaluation method is:

[0037] The relative error changes between the antenna radiation field modeled by the dipole model and the antenna test radiation field are compared, and the accuracy of the antenna radiation field modeled by the dipole model is evaluated using an evaluation method.

[0038] Preferably, the antenna radiation field of the dipole model is The antenna test radiation field is The normalized root mean square error of the antenna radiation field for dipole modeling is defined as:

[0039]

[0040] Preferably, the dipole is an electric dipole and / or a magnetic dipole.

[0041] In summary, the dipole of the present invention directly models the antenna radiation field, and the test data of the modeled antenna radiation field has the characteristics of good accuracy and high efficiency. The antenna radiation field equivalent dipole model can realize the change prediction of the antenna radiation field at any target observation distance. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic flow chart of a method for modeling antenna radiation fields using a planar uniformly distributed dipole model according to an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of a uniformly distributed dipole model of an antenna radiation field provided by an embodiment of the present invention;

[0044] Figure 3 A schematic diagram of coordinate system translation transformation provided by an embodiment of the present invention;

[0045] Figure 3 (a) is a schematic diagram of a horn antenna model provided by an embodiment of the present invention;

[0046] Figure 3 (b) is a schematic diagram of the spherical wave expansion coefficients of a horn antenna provided by an embodiment of the present invention;

[0047] Figure 4a The equivalent electric dipole distribution of the horn antenna radiation field provided by one embodiment of the present invention;

[0048] Figure 4b The equivalent electric dipole distribution of the horn antenna radiation field provided by one embodiment of the present invention;

[0049] Figure 5a and Figure 5b A schematic diagram comparing the radiation field of a horn antenna and the radiation field of a dipole modeling provided in one embodiment of the present invention. DETAILED DESCRIPTION

[0050] Combined with attachment Figure 1 -5 and the specific implementation method further describe in detail the antenna radiation field modeling method of the planar uniformly distributed dipole model proposed in the present invention. According to the following description, the advantages and features of the present invention will be clearer. It should be noted that the drawings are in a very simplified form and are not in precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the implementation of the present invention. In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, please refer to the drawings. It should be noted that the structure, proportion, size, etc. illustrated in the drawings of this specification are only used to match the content disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the implementation conditions of the present invention, so they have no technical significance. Any modification of the structure, change in the proportional relationship or adjustment of the size should still fall within the scope of the technical content disclosed by the present invention without affecting the efficacy and purpose that can be achieved by the present invention.

[0051] See Figure 1 An embodiment of the present invention provides a method for modeling antenna radiation fields of a planar uniformly distributed dipole model, comprising:

[0052] S100, placing dipoles at uniform grid points in a normal plane of the antenna radiation aperture of the antenna test radiation field, wherein the type, position, and orientation of the dipoles are all known parameters, and the x-, y-, and z-axes of the dipoles are respectively parallel to the x-, y-, and z-axes of the antenna's geometric coordinate system;

[0053] S200, establishing a linear matrix equation between the spherical wave expansion coefficient and the dipole moment parameter of the antenna test radiation field based on a transformation matrix of the dipole from the local coordinate system to the global coordinate system, thereby estimating the dipole moment parameter through the spherical wave expansion coefficient;

[0054] S300: Establishing a dipole equivalent antenna radiation field model based on the type, position, and orientation of the dipole and the estimated dipole moment parameters.

[0055] The above method of the present invention is described in detail below.

[0056] Using an infinitesimal dipole model as an equivalent approximation for antenna test radiation fields has become an effective inverse modeling approach. From a forward analysis of antenna radiation characteristics, the varying charge and current on the antenna serve as the radiation source for excited electromagnetic waves, which themselves constitute dipole radiation. By decomposing the radar antenna into multiple dipole antenna combinations, the target area's illumination field distribution under different antenna beams can be synthesized. The following study, from the perspective of inverse modeling of antenna radiation fields, examines the conversion method from basic near-field scattering to radar near-field scattering, achieving antenna decorrelation of radar target near-field characteristics.

[0057] The constrained dipole model is used to model the antenna radiation field, that is, electric dipoles or magnetic dipoles oriented in the x, y, and z axes are placed at uniform grid points in the normal plane of the antenna radiation aperture, such as Figure 2 As shown in Figure 1, here, the type, position, and orientation of each dipole are fixed, and only the dipole moment parameter varies. By varying the dipole moment parameter, the radiation field distribution is altered, and the radiation fields of all dipoles are combined to achieve equivalent modeling of the radiation field of any antenna.

[0058] The uniformly distributed dipole parameters used in antenna radiation modeling are closely related to the spherical wave expansion coefficients of the antenna test radiation field. Therefore, in step S200, the transformation matrix from the dipole's local coordinate system to the global coordinate system is used to establish a linear matrix equation between the spherical wave expansion coefficients of the antenna radiation field and the dipole moment parameters, specifically including:

[0059] It is known that the antenna radiation field E AUT The relationship between (r) and its spherical wave expansion coefficient is expressed as:

[0060]

[0061] Where k = 2π / λ represents the spatial wave number, λ is the antenna radiation wavelength; ζ represents the intrinsic admittance of the medium, which is the reciprocal of the intrinsic impedance of the free space medium; J max The maximum truncation coefficient of the spherical wave expansion is related to the minimum radius of the sphere surrounding the antenna; F j (r) represents the normalized spherical vector wave function, Q j It represents the spherical wave expansion coefficient;

[0062] First, assume that the antenna radiation field is represented by L current element radiation modes, each current element radiation mode is composed of 6 dipoles with the same position and orientation in the x, y, and z axes respectively. The modal radiation field E of the L current element radiation modes in the spherical coordinate system is mod (r) is expressed as:

[0063]

[0064] in,

[0065]

[0066]

[0067] represents the dipole parameter of the i current element position, represents the transformation coefficient from the local coordinate system of the i-th current element to the global coordinate system, which is calculated according to the translation and rotation superposition theorem of the spherical wave expansion coefficient;

[0068] Using the L component current element radiation field to equate to the antenna radiation field, we can get from equations (1) and (2)

[0069]

[0070] Using F j (r) The orthogonal characteristics of the function, the transmission coefficients on both sides of the above equation are equal, and the relationship between the spherical wave expansion coefficient and the dipole moment parameter is obtained:

[0071] Q=ΦX (4)

[0072] in,

[0073]

[0074]

[0075] X=[S1,S2,...,S L ] T (7) Φ represents the transformation coefficient matrix of the spherical wave function from the local coordinate system of the current element to the global coordinate system of the antenna, with a dimension of J max ×6L; X represents the dipole moment parameter of the L component current elements.

[0076] In this embodiment, Equation (4) establishes an overdetermined linear matrix equation between the spherical wave coefficient Q of the antenna radiation field and the current element dipole parameter X, that is, J max >6L, theoretically, the least squares method can be used directly for estimation. However, since the matrix Φ is generally a non-full rank matrix, that is, rank(Φ)=r<6L, it is necessary to calculate Φ H Therefore, this paper uses the singular value decomposition (SVD) method to perform the least squares estimation of X.

[0077] Perform SVD decomposition on the matrix Φ

[0078]

[0079] in, represents a left singular matrix, V=[v1,v2,...,v 6L ] represents a right singular matrix, Σ=diag(σ1,...,σ r ,0,...,0) represents the singular value diagonal matrix, r = rank{Φ} represents the matrix rank, and the superscript "H" represents the conjugate transpose, so the least squares estimate of X is:

[0080]

[0081] In this embodiment, the transformation coefficients of the matrix Φ can be calculated using the rotation and translation theorem of spherical wave expansion. Figure 3 、 Figure 3 (a) and Figure 3 As shown in (b), o(x, y, z) represents the global coordinate system, corresponding to the spherical coordinate system o′(x′, y′, z′) represents the dipole local coordinate system, corresponding to the spherical coordinate system The rotation and translation transformation from coordinate system o'(x',y',z') to o(x,y,z) is decomposed into the following three steps: First, rotate the rectangular system o(x,y,z) around the z axis Then rotate θ0 around the y-axis so that the z-axis direction of the coordinate system coincides with the r0 direction after rotation; secondly, translate the distance r0 along the z-axis direction, where r0 = |r0|; finally, perform the inverse rotation transformation on the translated coordinate system, that is, rotate -θ0 around the y-axis and rotate around the z-axis Obtain the rectangular coordinate system o′(x′, y′, z′).

[0082] According to the rotation and translation theorem of spherical wave function, let the spherical coordinate system be The spherical wave expansion coefficient is F smn (r′), which can be expressed as a spherical wave function F σμν (r) After the rotation-translation-inverse rotation transformation, that is

[0083]

[0084] Among them, the rotation coefficient Expressed as

[0085]

[0086]

[0087] The above formula can also be written as

[0088]

[0089] in, Represents Jacobi polynomials.

[0090] Translation coefficient Expressed as

[0091]

[0092] Among them, j p (x) represents the spherical Bessel function; a(μ,n,-μ,ν,p) is called the linear coefficient and represents the product of two non-normalized associated Legendre functions

[0093]

[0094] In addition, a(μ,n,-μ,ν,p) can also be written in the form of Wigner 3-j notation, that is,

[0095]

[0096] When n+v+p is an odd number, we can get

[0097]

[0098] Therefore, the summation terms in equation (14) only need to calculate the terms p = |n-ν|, |nv|+2, ..., n+v-2, n+v.

[0099] Directly calculating the coefficient a(μ,n,-μ,v,p) of formula (14) is still relatively inefficient. We can use the recursive relationship between the coefficients to calculate it. Define a p ≡a(μ,n,-μ,v,p),p=n+v,n+v-2,...,|nv|, then we have the recursive relation

[0100] α p-3 a p-4 -(α p-2 +α p-1 -4μ 2 )a p-2 +α p a p =0 (16)

[0101] in

[0102]

[0103] The calculation results of the initial terms p=n+ν and p=n+ν-2 in formula (16) are

[0104]

[0105]

[0106] Where, (2q-1)! ! = (2q-1)(2q-3)…3·1, (-1)! ! ≡1.

[0107] For the z-axis electric dipole of the i-th current element, in the local coordinate system The spherical wave expansion of the radiation field is expressed as

[0108]

[0109] Transform it to the radiation field representation in the global coordinate system

[0110]

[0111] Among them, j=2[ν(ν+1)+l-1]+σ, J tr =2ν max (ν max +2),

[0112] In an embodiment, it also includes evaluating the modeling accuracy of the dipole model of the antenna radiation field, and the evaluation method is: comparing the relative error change between the antenna radiation field modeled by the dipole model and the antenna radiation field, and using the evaluation method to evaluate the accuracy of the antenna radiation field modeled by the dipole model.

[0113] Taking the horn antenna radiation field as an example, a dipole model is performed on the horn antenna radiation field to evaluate the modeling accuracy of the dipole combination model for the antenna radiation field. The horn antenna is shown on the left side of Figure 4. The aperture size is 55mm×42.8mm, the operating frequency is 16GHz, and the minimum spherical radius surrounding the antenna is r min ≈4λ. Taking the antenna coordinate center as the origin, the simulated antenna is at a radius of r meas =70λ measures the radiation field on the spherical surface, where the elevation angle measurement range is 0°≤θ≤120° and the azimuth angle measurement range is Angle sampling interval Calculate the spherical wave expansion coefficient Q of the antenna radiation field, as shown on the right side of Figure 4.

[0114] According to the minimum spherical radius r of the antenna enclosed area min ,get Therefore, the truncated number J of the spherical wave expansion coefficient of the antenna radiation field is max =2N tr (N tr +2)=2736. Figure 3 As shown in (b), as j increases, Q j Gradually decreases, when j>J max When |Q j |<10-10 W 1 / 2 Dipole current elements are set at equal intervals in the plane where the antenna aperture is located. The current element position interval is 0.3λ, and the variation range is 2.4λ×3λ. A total of L=99 current elements are obtained. Each current element contains 3 electric dipoles and 3 magnetic dipoles. Therefore, the number of dipoles modeled in the antenna radiation field is 6L=594.

[0115] According to the antenna spherical wave expansion coefficient Q, the parameter X of the dipole model is calculated, and the equivalent dipole model distribution of the horn antenna radiation field is obtained as shown in Figure 4. Among them, Figure 4(a) shows the electric dipole distribution, and the arrow length represents the dipole equivalent current. Figure 4(b) shows the magnetic dipole distribution, and the arrow length represents the dipole equivalent magnetic current.

[0116] The Normalized Root Mean Square Error (NRMSE) is used to evaluate the modeling accuracy of the dipole model of the antenna radiation field. Assume that the antenna radiation field modeled by the dipole model is The radiation field of the Horn antenna is The NRMES of the antenna radiation field modeled by the dipole model is defined as

[0117]

[0118] The error of the dipole model modeling antenna radiation field evaluated by NRMSE is 0.75%, so the accuracy of the dipole model modeling Horn antenna radiation field is 99.25%.

[0119] like Figure 5a and Figure 5b As shown, further comparison and The radiation field distribution of the horn antenna and the dipole modeling at the antenna spherical measurement position, where: The NRMSE of dipole modeling is 1.13%, The NRMSE of the dipole modeling is 0.55%. Therefore, the accuracy of the equivalent dipole modeling of the horn antenna shows that the constrained dipole model can achieve an equivalent approximation of the horn antenna radiation field with high accuracy.

[0120] In this embodiment, the dipole is an electric dipole or a magnetic dipole.

[0121] In summary, the advantages of the present invention are that the dipole directly models the antenna radiation field, the test data of the modeled antenna radiation field has the characteristics of good accuracy and high efficiency, and the antenna radiation field equivalent dipole model can realize the prediction of antenna radiation field changes at any target observation distance.

[0122] Although the present invention has been described in detail through the above preferred embodiments, it should be understood that the above description is not intended to limit the present invention. After reading the above description, various modifications and substitutions of the present invention will become apparent to those skilled in the art. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for modeling antenna radiation fields of a planar uniformly distributed dipole model, characterized in that: include: Dipoles are placed at uniform grid points in the normal plane of the antenna radiation aperture of the antenna test radiation field, where the type, position, and orientation of the dipoles are all known parameters, and the x, y, and z axes of the dipoles are respectively parallel to the x, y, and z axes of the antenna's geometric coordinate system; Based on the transformation matrix of the dipole from the local coordinate system to the global coordinate system, a linear matrix equation between the spherical wave expansion coefficient of the antenna test radiation field and the dipole moment parameter is established, so as to estimate the dipole moment parameter through the spherical wave expansion coefficient; A dipole equivalent antenna radiation field model is established based on the type, position and orientation of the dipole and the estimated dipole moment parameters.

2. The antenna radiation field modeling method of the planar uniformly distributed dipole model according to claim 1, characterized in that: The transformation matrix from the local coordinate system to the global coordinate system of the dipole is used to establish a linear matrix equation between the spherical wave expansion coefficient of the antenna test radiation field and the dipole moment parameter, specifically including: The spherical wave expansion of the antenna test radiation field is expressed as: Where k = 2π / λ represents the spatial wave number, λ is the antenna radiation wavelength; ζ represents the intrinsic admittance of the medium, which is the reciprocal of the intrinsic impedance of the free space medium; J max The maximum truncation coefficient of the spherical wave expansion is related to the minimum radius of the sphere surrounding the antenna; F j (r) represents the normalized spherical vector wave function, Q j It represents the spherical wave expansion coefficient; First, assume that the antenna test radiation field is represented by L current element radiation modes. Each current element radiation mode consists of six dipoles with the same position and orientation in the x, y, and z axes. The modal radiation field of the L current elements in the spherical coordinate system is expressed by spherical wave expansion as follows: in, represents the dipole parameter of the i current element position, represents the transformation coefficient from the local coordinate system of the i-th current element to the global coordinate system, which is calculated according to the translation and rotation superposition theorem of the spherical wave expansion coefficient; Using the L component current element radiation field to equate to the antenna radiation field, we can get from equations (1) and (2) Using F j (r) The orthogonal characteristics of the function, the transmission coefficients on both sides of the above equation are equal, then the linear matrix equation between the spherical wave expansion coefficient and the dipole moment parameter is obtained as follows: Q=ΦX in, X=[S1,S2,K,S L ] T Φ represents the transformation coefficient matrix of the spherical wave function from the local coordinate system of the current element to the global coordinate system of the antenna, with a dimension of J max ×6L; X represents the dipole moment parameter of the L component current elements.

3. The antenna radiation field modeling method of the planar uniformly distributed dipole model according to claim 2, characterized in that: The method of estimating the dipole moment parameters by using the spherical wave expansion coefficients specifically includes performing least square estimation on the dipole moment parameters by using a singular value decomposition method to obtain the dipole moment parameters.

4. The antenna radiation field modeling method of the planar uniformly distributed dipole model according to claim 3, characterized in that: Perform SVD decomposition on the matrix Φ: in, Represents a left singular matrix, V=[v1,v2,K,v 6L ] represents a right singular matrix, Σ=diag(σ1,K,σ r ,0,K,0) represents the singular value diagonal matrix, r=rank{Φ} represents the matrix rank, and the superscript "H" represents the conjugate transpose, so the least squares estimate of X is:

5. The antenna radiation field modeling method of a planar uniformly distributed dipole model according to any one of claims 2 to 4, characterized in that: The transformation coefficients of the matrix Φ are calculated using the rotation and translation theorem of spherical wave expansion.

6. The antenna radiation field modeling method of the planar uniformly distributed dipole model according to claim 1, characterized in that: The evaluation method is as follows: The relative error changes between the antenna radiation field modeled by the dipole model and the antenna test radiation field are compared, and the accuracy of the antenna radiation field modeled by the dipole model is evaluated using an evaluation method.

7. The antenna radiation field modeling method of the planar uniformly distributed dipole model according to claim 6, characterized in that: Assume that the antenna radiation field modeled by the dipole is The antenna test radiation field is The normalized root mean square error of the antenna radiation field for dipole modeling is defined as:

8. The antenna radiation field modeling method of the planar uniformly distributed dipole model according to claim 1, characterized in that: The dipole is an electric dipole and / or a magnetic dipole.

Images