Antenna gain calculation method for phase-free measurement under finite plane sampling
By constructing a virtual array model and solving the excitation information using the nonlinear least squares method, combined with the extended field form, the problem of inaccurate antenna gain calculation in small sampling areas is solved, and efficient and accurate antenna gain measurement is achieved.
Patent Information
- Application Number
- CN202510954853.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-11
- Publication Date
- 2025-09-12
AI Technical Summary
Existing planar near-field phase-free measurement technology has insufficient measurement accuracy in a small sampling area and is sensitive to the environment, resulting in inaccurate antenna gain calculation, high testing costs, and high system complexity.
A virtual array model is constructed. By obtaining amplitude information in a finite plane sampling area, the nonlinear least squares method is used to solve the equivalent array model excitation, and the antenna gain is calculated in combination with the extended field form, the system complexity is reduced and the test accuracy is improved.
Accurate measurement of antenna gain is achieved in a small sampling area, which reduces test cost and system complexity, improves test efficiency and reliability, and reduces interference of environmental changes on measurement.
Smart Images
Figure CN120639205A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of wireless communication technology, and in particular to a method for calculating antenna gain based on phase-free measurement under finite plane sampling. Background Art
[0002] With the rapid development of emerging technologies such as 5G / 6G and satellite internet, modern communication systems are placing increasingly stringent demands on antennas. In this context, antenna gain, a core metric for measuring the concentration of radiated energy, essentially reflects the antenna's directivity and energy conversion efficiency, and its importance is becoming increasingly prominent. Therefore, accurately measuring and optimizing gain has become an essential step in antenna design, testing, and application.
[0003] The demand for antenna accuracy and performance indicators has made antenna testing increasingly important in the design process, and high-precision measurement methods are gaining increasing attention. Among the many methods for measuring antenna gain, planar near-field measurement technology is widely used due to its simple mechanical structure and low algorithm complexity. However, we have found that when using planar near-field technology to obtain antenna field distribution and then calculate antenna gain, the size of the sampling surface has a significant impact on measurement accuracy. As the sampling surface decreases, the gain error gradually increases. In particular, when the sampling area is smaller than the aperture size of the antenna to be measured, the gain calculated using the field distribution data at this time loses its reference value.
[0004] In near-field measurements, phase information acquisition typically relies on precision instruments such as vector network analyzers. While these devices can provide highly accurate phase data, they are extremely sensitive to environmental conditions. Furthermore, changes in ambient temperature and mechanical vibration can cause phase data drift. For example, a slight deviation in probe position (a displacement of 0.1 mm) can introduce a phase error of up to 10°. Furthermore, at high frequencies, phase information measurement is highly susceptible to noise interference, resulting in unstable data, further increasing measurement difficulty and cost. To address the inherent shortcomings of traditional phase measurement methods, phase-free measurement technology has emerged. The core of phase-free measurement technology lies in indirectly reconstructing phase information using only amplitude data, thereby enabling near-field antenna measurements.
[0005] Existing planar near-field phase-free measurement techniques primarily involve collecting amplitude information from two planes using Fourier iteration to calculate phase, using multi-probe sampling to determine the reference phase, and using the equivalent source method to determine the radiation source characteristics and recover phase information. These methods have drawbacks due to their sensitivity to noise and high test equipment requirements. Furthermore, we have found that within existing planar near-field phase-free measurement techniques, little research has focused on obtaining reliable antenna radiation information as the sampling area is gradually reduced. Summary of the Invention
[0006] To solve the above technical problems, the present invention provides an antenna gain calculation method for phase-free measurement under finite plane sampling, so as to significantly reduce the complexity and cost of the measurement system and improve the test efficiency and reliability.
[0007] To achieve the above object, the technical solution of the present invention is as follows:
[0008] A method for calculating antenna gain for phase-free measurement under finite plane sampling comprises the following steps:
[0009] Step 1: Measure the size of the radiation aperture of the antenna to be tested, and obtain the amplitude information of the plane field distribution of a finite size at a distance d from the antenna to be tested through the antenna test system;
[0010] Step 2: Select an appropriate number and spacing of virtual array elements to construct an equivalent array model, so that the aperture of the equivalent array model is larger than the radiation aperture size of the original antenna to be tested, and establish a forward transmission equation based on the position of each array element, the sampling distance d, and the coordinates of the sampling plane;
[0011] Step 3: Using the obtained amplitude information, a nonlinear least square method is used to solve the optimal solution for the excitation of the equivalent array model, and the position, excitation amplitude, and phase information of each array element in the equivalent array model are obtained;
[0012] Step 4: Select the appropriate extended field form based on the characteristics of the different antennas under test. Use the position of each array element in the new equivalent array model, the amplitude and phase information of the excitation, and the coordinates of the sampling points of the extended field to establish a new forward transmission equation to obtain the complete field distribution on the extended field.
[0013] Step 5: Calculate the antenna gain value by using the complete field distribution on the extended field.
[0014] In the above scheme, in step 2, assume that the number of array elements in the x and z directions of the equivalent array model is n respectively. x and n z , the array element spacing in the x-direction and z-direction is d x and d z , and the size of the equivalent array model must be greater than the minimum plane size surrounding the original antenna radiation structure to be tested, that is, n x *d x >L x And n z *d z >L z , L x and L z are respectively the length and width of the original radiation aperture of the antenna to be tested.
[0015] In the above scheme, in step 2, the forward transmission equation established is as follows:
[0016] The forward transmission matrix T is constructed using the free-space Green's function G. Then the forward transmission matrix is expressed as T = F·G, where F represents the far-field pattern of the complex electric field of the equivalent array model.
[0017] Assuming that the array elements of the equivalent array model are omnidirectional ideal point sources, that is, F is the same in all directions, then T = G, where
[0018]
[0019] Where k represents the wave number, and r represents the distance from a certain array element to the sampling point in the equivalent array model, which can be expressed as Where (X, Y, Z) represents the coordinates of the array element, and (xp, d, zp) represents the coordinates of the sampling point.
[0020] In the above solution, step 3 is as follows:
[0021] Assume that a virtual equivalent array consisting of N array elements is used to replace the original antenna under test. The total number of sampling points in the planar near field is M. In phase-free measurement, the amplitude information of the planar near field distribution of the antenna under test can be expressed as the amplitude of the superposition of the electromagnetic waves radiated by each array element in the virtual array. The formula is:
[0022] |F M×1 |=|T M×N ·x N×1 |
[0023] Among them, |F M×1 | represents the amplitude information of M points in the planar near field area, |T M×N | is the forward transmission equation established based on the free-space Green's function and the radiation characteristics of the virtual array unit, |x N×1 | represents the complex excitation coefficient vector of the virtual array element;
[0024] Taking the square of both sides of the above equation yields:
[0025] |F| 2 =(Re{T·x}) 2 +(Im{T·x}) 2
[0026] In the above formula, the following relationship exists:
[0027]
[0028] Among them, Re{·} means taking the real part, Im{·} means taking the imaginary part; redefine [Re{T},-Im{T}] as K1 M×2N , redefine [Im{T},Re{T}] as K2M×2N ,Bundle Redefining L 2N×1 , then the above formula can be re-expressed as:
[0029] |F| 2 =(K1·L) 2 +(K2·L) 2
[0030] Wherein, L represents the excitation information of the equivalent array model to be solved;
[0031] In order to obtain the optimal solution of L in a limited area, the objective function is expressed as:
[0032]
[0033] The above optimization problem is solved by nonlinear least square method to obtain an optimal solution of L, so that the original antenna to be tested can be replaced by an equivalent array model.
[0034] In the above scheme, in step 4, the horn antenna and high-gain antenna select the plane field as the form of the extended field, the wide-beam antenna selects the cylindrical field as the form of the extended field, and the omnidirectional or complex radiation pattern antenna selects the spherical field as the form of the extended field.
[0035] In the above scheme, in step 4, a new forward transmission equation is established as follows:
[0036] The new forward transmission equation T′ is constructed using the free-space Green's function G′, and T′ can be expressed as T′=F′·G′, where F′ represents the far-field pattern of the complex electric field of the new equivalent array model.
[0037] In the above scheme, in step 5, the method for calculating the antenna gain value by using the complete field distribution on the extended field is as follows:
[0038]
[0039] Among them, G a Indicates the gain of the antenna to be tested, M a represents the mismatch factor, Δx and Δz represent the sampling interval of the sampling surface, A represents the plane wave spectrum obtained by two-dimensional Fourier transform of the field distribution data, G p represents the gain of the probe, and λ represents the wavelength of the antenna to be tested.
[0040] Through the above technical solution, the present invention provides a method for calculating antenna gain for phase-free measurement under finite plane sampling, which has the following beneficial effects:
[0041] (1) This invention constructs a virtual array model to perform an equivalent test on the antenna under test, enabling accurate gain values to be obtained in a small sampling area. This solves the problem of inaccurate gain calculation in the planar near field when the sampling range is insufficient, reduces test costs, and improves test efficiency. This method only requires obtaining amplitude information when obtaining the field distribution of the antenna planar near field, thus simplifying the complexity of the test system, reducing interference with the phase caused by environmental changes and other issues, and further improving test accuracy.
[0042] (2) After obtaining the amplitude and phase data of the virtual equivalent array excitation, the present invention can select an appropriate expansion field form (plane, cylindrical, or spherical) based on the characteristics of the antenna when expanding the field. It should be noted that the actual sampling surface is always a plane, which allows us to obtain a more flexible expansion field shape without changing the mechanical structure.
[0043] (3) The virtual array constructed by the method proposed in the present invention has flexible array element selection, and can use any antenna such as an ideal point source, a dipole antenna, a waveguide antenna, a Vivaldi antenna, etc. The arrangement mode is also adaptable to arrays of any arrangement type, such as rectangular uniform arrangement, circular arrangement, polygonal arrangement, and random distribution. The method proposed in the present invention is flexible in implementation and has strong applicability.
[0044] In summary, the present invention proposes a method for accurately measuring antenna gain using only amplitude information collected under limited sampling area conditions. The core of this method is to collect the amplitude information of the antenna to be measured only through the near field, and inversely deduce the amplitude and phase of the excitation of the constructed virtual array unit, so that the amplitude information generated by the near field can match the amplitude data obtained by the actual small sampling surface, thereby effectively expanding the field information of the small area sampling area to a larger space, and finally realizing the accurate calculation of the antenna gain. The method of the present invention can realize accurate phase-free gain measurement technology under a small sampling area, which can significantly reduce the complexity and cost of the measurement system and improve test efficiency and reliability. BRIEF DESCRIPTION OF THE DRAWINGS
[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for describing the embodiments or the prior art.
[0046] Figure 1 The present invention discloses a flow chart of a method for calculating antenna gain for phase-free measurement under finite plane sampling. DETAILED DESCRIPTION
[0047] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.
[0048] The present invention provides a method for calculating antenna gain for phase-free measurement under finite plane sampling, such as Figure 1 As shown, the following steps are included:
[0049] Step 1: Measure the size of the radiation aperture of the antenna to be tested, and obtain amplitude information of a plane field distribution of finite size at a distance d from the antenna to be tested through an antenna test system.
[0050] Taking the rectangular waveguide as an example, use a ruler to measure the length L of the radiation port. x and L z , use the antenna near-field test system to measure the amplitude information corresponding to each sampling point in the plane near field with an area of S at a distance d from the antenna to be tested.
[0051] Step 2: Select the appropriate number and spacing of virtual array elements to construct an equivalent array model, so that the aperture size of the equivalent array model is larger than the radiation aperture size of the original antenna to be tested, and establish the forward transmission equation based on the position of each array element, the sampling distance d, and the coordinates of the sampling plane.
[0052] Assume that the number of array elements in the x and z directions of the equivalent array model is n respectively. x and n z , the array element spacing in the x-direction and z-direction is d x and d z , and the size of the equivalent array model must be greater than the minimum plane size surrounding the original antenna radiation structure to be tested, that is, n x *d x >L x And n z *d z >L z , L x and L z are respectively the length and width of the original radiation aperture of the antenna to be tested.
[0053] The forward transmission equation established is as follows:
[0054] The forward transmission matrix T is constructed using the free-space Green's function G. Then the forward transmission matrix is expressed as T = F·G, where F represents the far-field pattern of the complex electric field of the equivalent array model.
[0055] Assuming that the array elements of the equivalent array model are omnidirectional ideal point sources, that is, F is the same in all directions, then T = G, where
[0056]
[0057] Where k represents the wave number, and r represents the distance from a certain array element to the sampling point in the equivalent array model, which can be expressed as Where (X, Y, Z) represents the coordinates of the array element, and (xp, d, zp) represents the coordinates of the sampling point.
[0058] Step 3: Using the obtained amplitude information, a nonlinear least square method is used to solve the optimal solution of the equivalent array model excitation, and the position of each array element in the equivalent array model, the amplitude and phase information of the excitation are obtained.
[0059] Assume that a virtual equivalent array consisting of N array elements is used to replace the original antenna under test. The total number of sampling points in the planar near field is M. In phase-free measurement, the amplitude information of the planar near field distribution of the antenna under test can be expressed as the amplitude of the superposition of the electromagnetic waves radiated by each array element in the virtual array. The formula is:
[0060] |F M×1 |=|T M×N ·x N×1 |
[0061] Among them, |F M×1 | represents the amplitude information of M points in the planar near field area, |T M×N | is the forward transmission equation established based on the free-space Green's function and the radiation characteristics of the virtual array unit, |x N×1 | represents the complex excitation coefficient vector of the virtual array element;
[0062] Taking the square of both sides of the above equation gives:
[0063] |F| 2 =(Re{T·x}) 2 +(Im{T·x}) 2
[0064] In the above formula, the following relationship exists:
[0065]
[0066] Among them, Re{·} means taking the real part, Im{·} means taking the imaginary part; redefine [Re{T},-Im{T}] as K1 M×2N , redefine [Im{T},Re{T}] as K2 M×2N ,Bundle Redefining L 2N×1 , then the above formula can be re-expressed as:
[0067] |F| 2 =(K1·L) 2 +(K2·L) 2
[0068] Wherein, L represents the excitation information of the equivalent array model to be solved;
[0069] In order to obtain the optimal solution of L in a limited area, the objective function is expressed as:
[0070]
[0071] The above optimization problem is solved by nonlinear least square method to obtain an optimal solution of L, so that the original antenna to be tested can be replaced by an equivalent array model.
[0072] Step 4: Select the appropriate form of the extended field according to the characteristics of the different antennas to be tested, and use the positions of each array element, the amplitude and phase information of the excitation, and the coordinates of the sampling points of the extended field in the new equivalent array model to establish a new forward transmission equation to obtain the complete field distribution on the extended field.
[0073] Select the appropriate extended field form according to the type of antenna. For example, for horn antennas and high-gain antennas, choose a planar field as the extended field form; for wide-beam antennas, choose a cylindrical field as the extended field form; and for omnidirectional or complex radiation pattern antennas, choose a spherical field as the extended field form.
[0074] The new forward transmission equation is established as follows:
[0075] Using the free-space Green's function G', we construct a new forward propagation equation T'. T' can then be expressed as T' = F'·G', where F' represents the far-field pattern of the complex electric field of the new equivalent array model. This is similar to step 2, except that the number and location of the new extended field sampling points differ, resulting in different matrix sizes and Green's function values.
[0076] Step 5: Calculate the antenna gain value by using the complete field distribution on the extended field.
[0077] The calculation method is as follows:
[0078]
[0079] Among them, G a Indicates the gain of the antenna to be tested, M a represents the mismatch factor, Δx and Δz represent the sampling interval of the sampling surface, A represents the plane wave spectrum obtained by two-dimensional Fourier transform of the field distribution data, G p represents the gain of the probe, and λ represents the wavelength of the antenna to be tested.
[0080] In order to evaluate the accuracy of the gain calculation method of the present invention, the gain error is defined as follows:
[0081]
[0082] Among them, ε o represents the gain error obtained by the method of the present invention, ε prepresents the gain error obtained by the traditional plane wave spectrum method, G our represents the calculation gain obtained by the method of the present invention, G p represents the calculation gain obtained using the traditional plane wave spectrum method, G ref Indicates the actual gain of the antenna under test.
[0083] Based on the above indicators, three types of antennas to be tested were simulated and verified using FEKO and MATLAB:
[0084] (1) A horn antenna is selected as the antenna to be tested, with an operating frequency of f = 10 GHz, a direct distance from the sampling surface of 150 mm, and an aperture size of 138 mm × 107 mm.
[0085] β is defined as the ratio of the sampling area to the antenna aperture. Five sampling planes of different sizes are selected with a sampling interval of 10 mm. The gain errors calculated by the method of the present invention and the traditional plane wave spectrum method are compared. The results are shown in Table 1, where ε o and ε p They represent the gain errors calculated by the method of the present invention and the traditional plane wave spectrum method respectively.
[0086] Table 1 Comparison of gain errors of horn antennas with different sampling areas
[0087] β 2.71 3.91 6.09 7.83 9.78 <![CDATA[ε o ]]> 0.0785dB -0.0379dB 0.0158dB 0.0194dB 0.0338dB <![CDATA[ε p ]]> 0.4219dB -0.6785dB 0.3436dB -0.2311dB 0.1072dB
[0088] (2) An 11×11 microstrip array antenna is selected as the antenna to be tested, with an operating frequency of f=1.5 GHz, a direct distance from the sampling surface of 800 mm, and an aperture size of 1000 mm×1000 mm.
[0089] β is defined as the ratio of the sampling area to the antenna aperture. Three sampling planes of different sizes are selected with a sampling interval of 50 mm. The gain errors calculated using the method of the present invention and the traditional plane wave spectrum method are compared. The results are shown in Table 2.
[0090] Table 2 Comparison of gain errors of 11×11 microstrip antenna arrays with different sampling areas
[0091] β 1.44 2.25 4 <![CDATA[ε o ]]> -0.1163dB 0.0849dB 0.0396dB <![CDATA[ε p ]]> -0.3615dB 0.4766dB -0.2234dB
[0092] (3) An 11×3 microstrip array antenna is selected as the antenna to be tested, with an operating frequency of f=1.5 GHz, a direct distance from the sampling surface of 800 mm, and an aperture size of 1000 mm×300 mm.
[0093] β is defined as the ratio of the sampling area to the antenna aperture. Four sampling planes of different sizes are selected with a sampling interval of 50 mm. The gain errors calculated by the method of the present invention are compared with those calculated by the traditional plane wave spectrum method when the expanded field is a plane and a cylinder, respectively. The results are shown in Table 3.
[0094] Table 3 Comparison of gain error of 11×3 microstrip antenna array with different sampling areas
[0095] β 4.8 7.5 9.3 13.3 <![CDATA[e o (plague)]]> 0.0437dB 0.1662dB 0.1394dB 0.0058dB <![CDATA[ε o (cylinder)]]> -0.0269dB 0.1027dB 0.0801dB -0.0228dB <![CDATA[ε p ]]> -0.4351dB 0.4687dB 0.1991dB -0.1707dB
[0096] Based on the above three sets of simulations, the following conclusions can be drawn:
[0097] For different types of antennas, whether single antennas or array antennas, whether electrically large or electrically small, the method of the present invention can achieve a calculated gain error within ±0.1dB using only a sampling area several times larger than the antenna aperture, greatly improving both efficiency and accuracy compared to the traditional plane wave spectrum method.
[0098] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for calculating antenna gain for phase-free measurement under finite plane sampling, characterized in that: The steps include: Step 1: Measure the size of the radiation aperture of the antenna to be tested, and obtain the amplitude information of the plane field distribution of a finite size at a distance d from the antenna to be tested through the antenna test system; Step 2: Select an appropriate number and spacing of virtual array elements to construct an equivalent array model, so that the aperture of the equivalent array model is larger than the radiation aperture size of the original antenna to be tested, and establish a forward transmission equation based on the position of each array element, the sampling distance d, and the coordinates of the sampling plane; Step 3: Using the obtained amplitude information, a nonlinear least square method is used to solve the optimal solution for the excitation of the equivalent array model, and the position, excitation amplitude, and phase information of each array element in the equivalent array model are obtained; Step 4: Select the appropriate extended field form based on the characteristics of the different antennas under test. Use the position of each array element in the new equivalent array model, the amplitude and phase information of the excitation, and the coordinates of the sampling points of the extended field to establish a new forward transmission equation to obtain the complete field distribution on the extended field. Step 5: Calculate the antenna gain value by using the complete field distribution on the extended field.
2. The method for calculating antenna gain for phase-free measurement under finite plane sampling according to claim 1, characterized in that: In step 2, assume that the number of array elements in the x and z directions of the equivalent array model is n respectively. x and n z , the array element spacing in the x-direction and z-direction is d x and d z , and the size of the equivalent array model must be greater than the minimum plane size surrounding the original antenna radiation structure to be tested, that is, n x *d x >L x And n z *d z >L z , L x and L z are respectively the length and width of the original radiation aperture of the antenna to be tested.
3. The method for calculating antenna gain for phase-free measurement under finite plane sampling according to claim 1, characterized in that: In step 2, the forward transmission equation is established as follows: The forward transmission matrix T is constructed using the free-space Green's function G. Then the forward transmission matrix is expressed as T = F·G, where F represents the far-field pattern of the complex electric field of the equivalent array model. Assuming that the array elements of the equivalent array model are omnidirectional ideal point sources, that is, F is the same in all directions, then T = G, where Where k represents the wave number, and r represents the distance from a certain array element to the sampling point in the equivalent array model, which can be expressed as Where (X, Y, Z) represents the coordinates of the array element, and (xp, d, zp) represents the coordinates of the sampling point.
4. The method for calculating antenna gain for phase-free measurement under finite plane sampling according to claim 1, characterized in that: Step 3 is as follows: Assume that a virtual equivalent array consisting of N array elements is used to replace the original antenna under test. The total number of sampling points in the planar near field is M. In phase-free measurement, the amplitude information of the planar near field distribution of the antenna under test can be expressed as the amplitude of the superposition of the electromagnetic waves radiated by each array element in the virtual array. The formula is: |F M×1 |=|T M×N ·x N×1 | Among them, |F M×1 | represents the amplitude information of M points in the planar near field area, |T M×N | is the forward transmission equation established based on the free-space Green's function and the radiation characteristics of the virtual array unit, |x N×1 | represents the complex excitation coefficient vector of the virtual array element; Taking the square of both sides of the above equation gives: |F| 2 =(Re{T·x}) 2 +(Im{T·x}) 2 In the above formula, the following relationship exists: Among them, Re{·} means taking the real part, Im{·} means taking the imaginary part; redefine [Re{T},-Im{T}] as K1 M×2N , redefine [Im{T},Re{T}] as K2 M×2N ,Bundle Redefining L 2N×1 , then the above formula can be re-expressed as: |F| 2 =(K1·L) 2 +(K2 L) 2 Wherein, L represents the excitation information of the equivalent array model to be solved; In order to obtain the optimal solution of L in a limited area, the objective function is expressed as: The above optimization problem is solved by nonlinear least square method to obtain an optimal solution of L, so that the original antenna to be tested can be replaced by an equivalent array model.
5. The method for calculating antenna gain for phase-free measurement under finite plane sampling according to claim 1, characterized in that: In step 4, the horn antenna and high-gain antenna select a plane field as the form of the extended field, the wide-beam antenna selects a cylindrical field as the form of the extended field, and the omnidirectional or complex radiation pattern antenna selects a spherical field as the form of the extended field.
6. The method for calculating antenna gain for phase-free measurement under finite plane sampling according to claim 1, characterized in that: In step 4, a new forward transmission equation is established as follows: The new forward transmission equation T′ is constructed using the free-space Green's function G′, and T′ can be expressed as T′=F′·G′, where F′ represents the far-field pattern of the complex electric field of the new equivalent array model.
7. The method for calculating antenna gain for phase-free measurement under finite plane sampling according to claim 1, characterized in that: In step 5, the antenna gain value is calculated by the complete field distribution on the extended field as follows: Among them, G a Indicates the gain of the antenna to be tested, M a represents the mismatch factor, Δx and Δz represent the sampling interval of the sampling surface, A represents the plane wave spectrum obtained by two-dimensional Fourier transform of the field distribution data, G p represents the gain of the probe, and λ represents the wavelength of the antenna to be tested.