Spherical near-field antenna measurement truncation error correction method based on mode filtering and cosine window function

Abstract

The invention provides a spherical near-field antenna measurement truncation error correction method based on mode filtering and a cosine window function. The method comprises the following implementation steps: calculating a spherical wave mode expansion coefficient of an antenna to be measured; optimizing the spherical near-field electric field data based on mode filtering and a cosine window function; and obtaining a correction result of the measurement truncation error of the spherical near-field antenna. Mode filtering is performed on expansion coefficients of TE and TM modes of a spherical wave of a to-be-tested antenna, interference information introduced by zero charging of spherical near-field data of an unsampled area is filtered out, and then windowing is performed on the spherical near-field electric field data obtained by performing iterative updating on the spherical near-field electric field data by using near-near field transformation through a cosine window function, so that the near-field electric field data of the to-be-tested antenna is obtained. According to the method, data near a truncation area is smoother, the defects that useful information in a part of sampling near field is not fully utilized, interference information cannot be effectively filtered out, and the windowing range is limited to part of spherical near field data in the prior art are overcome, and the calculation precision of an antenna far field pattern is improved.

Description

A Method for Correcting Truncation Errors in Spherical Near-Field Antenna Measurements Based on Mode Filtering and Cosine Window Function Technical Field

[0001] This invention belongs to the field of antenna measurement technology and relates to a method for correcting the truncation error of spherical near-field antenna measurements based on mode filtering and cosine window function. It can be applied to the design, development and maintenance of various antennas under rapid measurement conditions. Background Technology

[0002] Antenna measurement methods can be broadly classified into two categories: direct methods and indirect methods. Direct methods include far-field methods, focusing methods, and compact field methods. However, the testing efficiency and accuracy of direct methods are insufficient for the requirements of modern antennas. Indirect methods, also known as near-field measurement methods, are further divided into planar near-field measurement, cylindrical near-field measurement, and spherical near-field measurement, depending on the shape of the scanning surface of the probe during near-field measurement. The principle of spherical near-field measurement involves using a probe with known characteristics in an anechoic chamber, under computer control, to measure the antenna under test with a radius of [missing information]. On the surface of the sphere, along the latitude angle and longitude angle A scan is performed to measure the amplitude and phase distribution of the electric field on the scanned sphere. Then, the far-field pattern of the antenna is calculated based on the measurement data and probe characteristics. The spherical near-field antenna measurement method has higher accuracy, greater flexibility, and wide bandwidth adaptability. The antenna far-field pattern is an important indicator of the antenna, which can clearly characterize key antenna parameters such as the directivity, main lobe width, and sidelobe level.

[0003] However, in actual spherical near-field antenna measurements, the sampling sphere is not a complete sphere due to the antenna's support structure (antenna turntable) and cable obstruction. Furthermore, most antenna measurements only focus on forward radiation. Therefore, to improve testing efficiency, in practice, only partial spherical sampling is performed, i.e., only the near-field electric field data of the upper hemisphere or a portion thereof is collected, while the uncollected near-field electric field data is zeroed out. This not only causes sudden discontinuities in the near-field data at the scanning plane boundary but also introduces interference, particularly affecting higher-order modes in the spherical wave mode expansion coefficients. Consequently, errors occur in the calculated far-field radiation characteristics of the antenna, especially noticeable near the scanning plane boundary. This error, caused by the non-complete sampling sphere and the zeroing out of unsampled areas, is called truncation error. Especially for phased array antennas, in beam scanning, when the maximum radiation direction is close to the scanning plane boundary measured by the spherical near-field antenna, a large truncation error is often introduced.

[0004] To reduce the impact of traditional methods that only zero-fill and window the unsampled spherical near-field electric field data on the accuracy of the calculated antenna far-field pattern, for example, Ma Di disclosed a method for correcting truncation error in his 2024 master's thesis "Research on Measurement and Diagnosis Methods of Phase-Free Spherical Near-Field Antennas". This method first samples the spherical near-field electric field data of the antenna under test, then zero-fills the unsampled spherical near-field data and optimizes the zero-filled spherical near-field electric field data using near-near-field transformation, then windows the sampled spherical near-field data, and finally obtains the far-field pattern of the antenna under test. Compared to the traditional method of calculating the far-field radiation pattern by zeroing the spherical near-field electric field data of the unsampled region and then windowing it, this method adds a near-near-field transformation, which optimizes the zeroed spherical near-field electric field data and makes the calculated antenna far-field radiation pattern more accurate. However, it does not fully utilize the useful information contained in the sampled part of the spherical near-field electric field data when calculating the mode expansion coefficients of the spherical wave. At the same time, it cannot filter out the interference information introduced by zeroing part of the spherical near-field electric field data, and the windowing range is limited to the sampled part of the spherical near-field electric field data, which will change the spherical near-field electric field data near the scanning surface boundary and affect the further improvement of the antenna far-field radiation pattern calculation accuracy. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects of the prior art and propose a method for correcting the truncation error of spherical near-field antenna measurements based on mode filtering and cosine window function, which is used to solve the technical problem of low measurement accuracy of antenna far-field radiation pattern in the prior art.

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

[0007] (1) Calculate the spherical wave mode expansion coefficients of the antenna under test:

[0008] Using a spherical coordinate system centered at the center of the antenna under test, along the latitude angle... and longitude angle Spherical near-field electric field data , Calculate the expansion coefficients of the TE and TM modes of the spherical wave from the antenna under test. , ;

[0009] (2) Optimization of near-field electric field data of sphere based on mode filtering and cosine window function:

[0010] Based on mode filtering function Expansion coefficients of TE and TM modes , Mode filtering is performed, and the expansion coefficients of the TE and TM modes of the spherical wave after mode filtering are calculated. , Calculate the filtered near-field electric field data of the sphere , A near-near-field transformation is performed, followed by iterative updates to the near-field electric field data of the spherical surface after the near-near-field transformation. A cosine window function is then used to update the iteratively updated near-field electric field data of the spherical surface. , Windowing was applied to obtain optimized near-field electric field data for the spherical surface. , ;

[0011] (3) Obtain the correction results for the measurement truncation error of the spherical near-field antenna:

[0012] Optimized spherical near-field electric field data , Calculate the expansion coefficients of the TE and TM modes of the optimized spherical wave. , Then through and Calculate the far-field radiation pattern of the antenna .

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] 1. This invention utilizes the expansion coefficients of the TE and TM modes of the spherical wave from the antenna under test. , By performing mode filtering to remove error information in higher-order modes, the information contained in the collected partial spherical near-field electric field data can be utilized to the greatest extent, and interference information introduced by zeroing the spherical near-field electric field data in unsampled areas can be filtered out. Compared with existing technologies, this improves the calculation accuracy of the antenna far-field radiation pattern.

[0015] 2. This invention calculates the near-near-field transformation of the filtered spherical near-field electric field data by calculating the expansion coefficients of the TE and TM modes of the spherical wave after mode filtering. Then, it applies a cosine window function to the spherical near-field electric field data that has been iteratively updated using the near-near-field transformation. This makes the spherical near-field data smoother near the truncation region, avoiding the shortcomings of existing technologies that do not fully utilize the useful information obtained from some sampled electric fields, cannot effectively filter out interference information, and have a windowing range limited to a portion of the spherical near-field electric field data. This invention recovers the portion of the spherical near-field electric field data that was not collected outside the scanning plane boundary, thus improving the calculation accuracy of the antenna far-field radiation pattern. Attached Figure Description

[0016] Figure 1 is a flowchart of the implementation of the present invention.

[0017] Figure 2 is a comparison of the simulation results of the antenna E-plane radiation pattern after the truncation error correction of the present invention and the prior art. Detailed Implementation

[0018] The present invention will now be described in further detail with reference to the accompanying drawings and specific implementation steps.

[0019] Referring to Figure 1, the present invention includes the following steps:

[0020] Step 1) Calculate the spherical wave mode expansion coefficients of the antenna under test:

[0021] Using a spherical coordinate system with the center of the antenna under test as the center, respectively... , For intervals along latitude angles Longitude angle The direction is centered on the center of the antenna under test with a radius of 1000. The sampling sphere is divided into grids, and the probe is used to perform the grid division. , The polarization method applies to the multiple grid points formed by the mesh division. Near-field electric field data of each grid point were sampled to obtain near-field electric field data of a portion of the sphere. , Simultaneously, the near-field electric field data of the remaining grid points are zeroed out, resulting in a dimension of of , Near-field electric field data of spherical surfaces with polarization , .

[0022] Sampling radius latitude angle Longitude angle Grid division interval and Need to meet , , , , This represents the circumferential angle of the probe rotation during near-field electric field sampling on a spherical surface. Indicates the wavelength of electromagnetic waves. This represents the minimum spherical radius surrounding the antenna under test. The near-field electric field data of the sampled portion of the sphere refers to the data obtained by the probe along the latitude angle in this coordinate system. The region for directional sampling is only , Along the longitude angle The directional sampling area remains unchanged, while the mesh generation creates... grid points and dimensions spherical near-field electric field data , , The expansion coefficients of the TE and TM modes of the spherical wave from the antenna under test , The first in Line number Column elements , The calculation formulas are as follows:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] in, This represents the highest order of the spherical wave mode expansion coefficients. express index, , and , , This represents the wave number of the electromagnetic wave emitted by the antenna under test. , To indicate a variable, , express index, , This represents the maximum angular modulus of the spherical wave mode expansion coefficients. , express Hankel function of the second kind of sphere, Indicates to exist , Perform double integral operations on it. and They represent respectively to and Differential operations, The imaginary unit, This represents the base of the exponential function. express Step The first kind of associated Legendre function To represent factorial operation, Indicates to The derivative of .

[0034] At this time, because the probe is along the latitude angle The sampling area in the direction is only Therefore, the sampled near-field electric field data of the sphere is not complete near-field electric field data of the sphere, and it is in There is data truncation in the direction, and truncation error will occur when the unsampled area is filled with zeros.

[0035] Step 2) Optimize the near-field electric field data of the sphere based on mode filtering and cosine window function:

[0036] Based on mode filtering function Expansion coefficients of TE and TM modes , Mode filtering is performed, and the expansion coefficients of the TE and TM modes of the spherical wave after mode filtering are calculated. , Calculate the filtered near-field electric field data of the sphere , A near-near-field transformation is performed, followed by iterative updates to the near-field electric field data of the spherical surface after the near-near-field transformation. A cosine window function is then used to update the iteratively updated near-field electric field data of the spherical surface. , Windowing was applied to obtain optimized near-field electric field data for the spherical surface. , Among them, the optimized near-field electric field data of the spherical surface is obtained. , The specific steps are as follows:

[0037] (2a) Initialize the number of iterations to be The maximum number of iterations is The error function is , and order ;

[0038] (2b) Based on mode filtering function Expansion coefficients of TE and TM modes of spherical waves , Perform mode filtering to obtain the spherical wave mode expansion coefficients after mode filtering. , Among them, the expansion coefficients of the TE and TM modes of spherical waves , The Middle Line number Column elements , The formulas for mode filtering are as follows:

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] in, Represents a cosine-like function. , The expansion coefficients of the TE and TM modes of the spherical wave after mode filtering. , The Middle Line number Column elements, This refers to the range of influence of the cosine-like function in pattern filtering. This represents the minimum possible order of the spherical wave mode expansion coefficients.

[0045] Since the sampling yields partial spherical near-field electric field data, the unsampled regions are zeroed out. This process not only causes sudden discontinuities in the near-field data at the scanning surface boundary but also introduces interference information when calculating the spherical wave mode expansion coefficients of the antenna, especially affecting the higher-order modes in the spherical wave mode expansion coefficients. Furthermore, in order to fully utilize the sampled partial spherical near-field electric field data, several additional orders are calculated when setting the order of the spherical wave mode expansion coefficients. However, the interference information in the additionally calculated mode expansion coefficients far outweighs the effective information. Therefore, mode filtering is used to remove the interference information.

[0046] (2c) Spherical wave mode expansion coefficients after mode filtering , Calculate the near-field electric field data of the spherical surface after mode filtering. , and to , Perform a near-near field transformation to obtain the spherical near-field electric field data of the near-near field transformation in this iteration. , Among them, , The specific steps for performing a near-near field transformation are as follows:

[0047] (2c1) Spherical near-field electric field data after mode filtering , Calculate the first The TE and TM mode expansion coefficients of the spherical wave of the antenna under test in the next iteration , ,in , The Middle Line number The elements of the column are , ;

[0048] (2c2) By using the TE and TM mode expansion coefficients of the spherical wave of the antenna under test in this iteration , Perform mode filtering to obtain the first... TE and TM mode expansion coefficients of the spherical wave after mode filtering by the antenna under test in the next iteration , ,in , The Middle Line number The elements of the column are , ;

[0049] (2c3) TE and TM mode expansion coefficients of the spherical wave after mode filtering by the antenna under test in this iteration , No. Line number Column elements , Calculate the spherical near-field electric field data for the near-near field transformation in this iteration. , :

[0050] ;

[0051] .

[0052] (2d) Near-field electric field data through a partial spherical surface , For the same in this iteration , Spherical near-field electric field data obtained by near-near-field transformation at grid coordinate points , Perform the replacement and determine... or Is it true? If so, then the first... Replacement result of the next iteration , As the iteratively updated near-field electric field data of the sphere, proceed to step (2e); otherwise, let , , and perform step (2c), where The calculation formula is:

[0053] ;

[0054] Near-near-field transformation can utilize the spherical wave mode coefficients as a link to calculate the global surface near-field electric field data from near-field electric field data of a portion of the sphere. However, the near-field information in the zero-charge region contains errors, especially after multiple near-near-field transformation iterations, which accumulate and increase, eventually making the near-field electric field data outside the sampling area unreliable. Therefore, we introduce a filtering function in the near-near-field transformation to filter out erroneous higher-order modes, preserving their correct information to the maximum extent. Furthermore, in each near-near-field transformation, we also use the sampled partial spherical near-field electric field data to replace the near-near-field electric field data obtained at the same location, ensuring that no errors are introduced into the sampled partial spherical near-field electric field data. This makes the near-field electric field data in the unsampled region after near-near-field transformation iterations also have a certain degree of reliability, thereby increasing the windowing range when windowing the iteratively updated spherical near-field electric field data in the next step.

[0055] (2e) Applying a cosine window function to the iteratively updated near-field electric field data of the sphere , Windowing was applied to obtain optimized near-field electric field data for the spherical surface. , The cosine window function is used to iteratively update the near-field electric field data of the sphere. , The formula for calculating windowing is:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] in, Represents the cosine window function The window function used on the amplitude of near-field electric field data. Represents the cosine window function A window function used on the phase of near-field electric field data. yes The windowed area in the direction occupies the sampling range The ratio, It is the maximum phase delay of the cosine window function.

[0062] The cosine window function is a complex window that includes both amplitude and phase. Since near-field data is also complex, it's necessary to consider windowing both amplitude and phase. The cosine window function is just one typical example among various window functions. Because its main lobe is slightly wider and its peak side lobes are significantly reduced in the Fourier transform, and the function has a smooth taper at the edges of the scanning plane, introducing a cosine window function is a good choice to reduce the impact of truncation error. It can smoothly reduce the near-field electric field data near the scanning plane boundary. However, the windowing process causes the data at the sampling plane edge to gradually decrease, leading to errors in the originally accurate partial spherical near-field electric field data. Therefore, in the previous step, we increased the confidence level of the unsampled region, which allows us to expand the windowing range and avoid introducing errors into the sampled partial spherical near-field electric field data.

[0063] Step 3) Obtain the correction results for the truncation error of the spherical near-field antenna measurement:

[0064] Optimized spherical near-field electric field data , Calculate the expansion coefficients of the optimized TE and TM modes. , The Line number Column elements , ,as well as and Far-field pattern function of the component and and through and Calculate the far-field radiation pattern of the antenna :

[0065] ;

[0066] ;

[0067] ;

[0068] in, and They represent and The unit vector of direction.

[0069] The technical effects of the present invention will be further explained below with reference to simulation results:

[0070] 1. Experimental conditions and contents:

[0071] The far-field E-plane radiation pattern of the antenna after truncation error correction was compared and simulated using MATLAB 2022a software. The results are shown in Figure 2(a) and (b).

[0072] 2. Analysis of experimental results:

[0073] Referring to Figure 2, where Figure 2(a) and (b) show the spherical area sampled by the antenna under test without beam scanning, respectively. , and beam scanning And the sampled spherical area is , In the case of correcting the near-field electric field data of a partial spherical surface, the far-field radiation pattern of the antenna is obtained, with the horizontal axis representing the far-field radiation of the antenna under test. The vertical axis represents the amplitude value of the E-plane radiation pattern of the antenna under test. The blue solid line in the figure represents the amplitude value of the theoretical far-field E-plane radiation pattern of the antenna under test. The red solid line represents the amplitude value of the E-plane radiation pattern of the antenna under test calculated by the prior art after recovering the truncated near-field electric field data. The black solid line represents the amplitude value of the E-plane radiation pattern of the antenna under test calculated by the present invention after recovering the truncated near-field electric field data.

[0074] As can be seen from Figure 2(a), when the spherical near-field electric field data is truncated, the far-field radiation pattern of the antenna calculated using existing technology to correct for the truncation error has an error of 1.3 dB between the left and right second sidelobe levels and the theoretical far-field radiation pattern. Angle is The amplitude value has an error of 2dB compared to the theoretical far-field pattern. The angle is further away The error between the amplitude value and the theoretical far-field radiation pattern is constantly increasing; however, the antenna far-field radiation pattern calculated after correcting the truncation error using the method of this invention has an error of 1.1 dB in the level of the left and right second sidelobes compared to the theoretical far-field radiation pattern. Angle is The error only just appeared, and the error was basically less than 0.7dB.

[0075] As can be seen from Figure 2(b), the near-field electric field data of the sphere is truncated and the antenna under test is subjected to... In the case of beam scanning, the far-field radiation pattern of the antenna calculated after correcting for truncation errors using existing technology shows a 2dB error in the level of the second sidelobe on the right compared to the theoretical far-field radiation pattern. Angle greater than The amplitude values ​​gradually show a significant error compared to the theoretical far-field pattern, reaching a maximum of 10 dB. Angle less than The amplitude values ​​gradually show a significant error compared to the theoretical far-field radiation pattern, reaching a maximum of 2dB; however, the antenna far-field radiation pattern calculated using this invention after correcting for the truncation error shows a more pronounced error. There is no obvious error within, only Errors only appear when the angle deviates further, and the errors are generally less than 2dB.

[0076] The simulation results above fully demonstrate that, in the case of truncation error in spherical near-field antenna measurement, the present invention significantly improves the accuracy of calculating the far-field radiation pattern of the antenna under test compared to the prior art when the beam is scanned. For the case where the beam is not scanned, it also shows some improvement in calculation accuracy and stability.

Claims

1. A method for correcting measurement truncation errors of a spherical near-field antenna based on mode filtering and a cosine window function, characterized in that, The steps include: (1) Calculating the spherical wave mode expansion coefficient of the antenna under test: using a spherical coordinate system with the center of the antenna under test as the center of the sphere along the latitude angle. and longitude angle Spherical near-field electric field data 、 Calculate the expansion coefficients of the TE and TM modes of the spherical wave from the antenna under test. 、 (2) Optimization of near-field electric field data of sphere based on mode filtering and cosine window function: based on mode filtering function Expansion coefficients of TE and TM modes 、 Mode filtering is performed, and the expansion coefficients of the TE and TM modes of the spherical wave after mode filtering are calculated. 、 Calculate the filtered near-field electric field data of the sphere 、 A near-near-field transformation is performed, followed by iterative updates to the near-field electric field data of the spherical surface after the near-near-field transformation. A cosine window function is then used to update the iteratively updated near-field electric field data of the spherical surface. 、 Windowing was applied to obtain optimized near-field electric field data for the spherical surface. 、 (3) Obtain the correction results of the truncation error of the spherical near-field antenna measurement: through the optimized spherical near-field electric field data 、 Calculate the expansion coefficients of the TE and TM modes of the optimized spherical wave. 、 Then through and Calculate the far-field radiation pattern of the antenna 。 2. The method according to claim 1, characterized in that, The spherical near-field electric field data mentioned in step (1) 、 The implementation steps are as follows: (The rest of the text appears to be a list of steps and doesn't translate directly.) 、 For intervals along latitude angles Longitude angle The direction is centered on the center of the antenna under test with a radius of 1000. The sampling sphere is divided into grids, and the probe is used to perform the grid division. 、 The polarization method applies to the multiple grid points formed by the mesh division. Near-field electric field data of each grid point were sampled to obtain near-field electric field data of a portion of the sphere. 、 Simultaneously, the near-field electric field data of the remaining grid points are zeroed out, resulting in a dimension of of 、 Near-field electric field data of spherical surfaces with polarization 、 ,in: ； ； ； ； ； ； ； ； ;in, This represents the circumferential angle of the probe rotation during near-field electric field sampling on a spherical surface. Indicates the wavelength of electromagnetic waves. This represents the minimum spherical radius surrounding the antenna under test. Indicates the probe along the latitude angle The range of the near-field electric field data region of the directional sampling sphere.

3. The method according to claim 2, characterized in that, The expansion coefficients of the TE and TM modes of the spherical wave of the antenna under test mentioned in step (1) 、 ,in 、 The first in Line 1 Column elements 、 The calculation formulas are as follows: ； ； ； ； ； ； ;in, This represents the highest order of the spherical wave mode expansion coefficients. express index, ， and ， ， This represents the wave number of the electromagnetic wave emitted by the antenna under test. ， To indicate a variable, ， express index, ， This represents the maximum angular modulus of the spherical wave mode expansion coefficients. ， express Hankel function of the second kind of sphere, Indicates to exist ， Perform double integral operations on it. and They represent respectively to and Differential operations, The imaginary unit, This represents the base of the exponential function. express Step The first kind of associated Legendre function To represent factorial operation, Indicates to The derivative of .

4. The method according to claim 3, characterized in that, The optimized spherical near-field electric field data described in step (2) 、 The steps to obtain the results are as follows: (2a) Initialize the number of iterations to be... The maximum number of iterations is The error function is ， and order ； (2b) Based on mode filtering function Expansion coefficients of TE and TM modes of spherical waves 、 Perform mode filtering to obtain the spherical wave mode expansion coefficients after mode filtering. 、 (2c) Spherical wave mode expansion coefficients after mode filtering 、 Calculate the near-field electric field data of the spherical surface after mode filtering. 、 and to 、 Perform a near-near field transformation to obtain the spherical near-field electric field data of the near-near field transformation in this iteration. 、 (2d) Near-field electric field data through a portion of the sphere 、 For the same in this iteration 、 Spherical near-field electric field data obtained by near-near-field transformation at grid coordinate points 、 Perform the replacement and determine... or Is it true? If so, then the first... Replacement result of the next iteration 、 As the iteratively updated near-field electric field data of the sphere, proceed to step (2e); otherwise, let ， ， and perform step (2c), where The calculation formula is: (2e) The near-field electric field data of the sphere after iterative update is processed by a cosine window function. 、 Windowing was applied to obtain optimized near-field electric field data for the spherical surface. 、 。 5. The method according to claim 4, characterized in that, The expansion coefficients of the TE and TM modes described in step (2b) 、 Perform mode filtering, where... 、 The Middle Line number Column elements 、 The formulas for mode filtering are as follows: ； ； ； ； ;in, Represents a cosine-like function. 、 The expansion coefficients of the TE and TM modes of the spherical wave after mode filtering. 、 The Middle Line number Column elements, This refers to the range of influence of the cosine-like function in pattern filtering. This represents the minimum possible order of the spherical wave mode expansion coefficients.

6. The method according to claim 4, characterized in that, The step (2c) described above 、 The near-near field transformation is performed by the following steps: (2c1) spherical near-field electric field data after mode filtering. 、 Calculate the first The TE and TM mode expansion coefficients of the spherical wave of the antenna under test in the next iteration 、 ,in 、 The Middle Line number The elements of the column are 、 (2c2) By expanding the TE and TM modes of the spherical wave of the antenna under test in this iteration. 、 Perform mode filtering to obtain the first... TE and TM mode expansion coefficients of the spherical wave after mode filtering by the antenna under test in the next iteration 、 ,in 、 The Middle Line number The elements of the column are 、 (2c3) TE and TM mode expansion coefficients of the spherical wave after mode filtering by the antenna under test in this iteration. 、 The Line number Column elements 、 Calculate the spherical near-field electric field data for the near-near field transformation in this iteration. 、 ： ； 。 7. The method according to claim 4, characterized in that, The optimized spherical near-field electric field data described in step (2e) 、 The calculation formula is: ； ； ； ； ;in, Represents the cosine window function The window function used on the amplitude of near-field electric field data. Represents the cosine window function A window function used on the phase of near-field electric field data. yes The windowed area in the direction occupies the sampling range The ratio, It is the maximum phase delay of the cosine window function.

8. The method according to claim 7, characterized in that, The far-field pattern described in step (3) The implementation steps are as follows: using optimized spherical near-field electric field data 、 Calculate the expansion coefficients of the optimized TE and TM modes. 、 The Line number Column elements 、 ,calculate and Far-field pattern function of the component and and through and Calculate the far-field radiation pattern of the antenna ： ； ； ;in, and They represent and The unit vector of direction.

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