CN114818935A - Planar near-field antenna pattern reconstruction method - Google Patents
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Abstract
The invention discloses a planar near-field antenna directional pattern reconstruction method, which comprises the following steps of; carrying out plane near-field scanning on the mouth surface of the antenna to be detected to obtain plane near-field electric field data; selecting a planar near-field scan surface S 1 At S 1 The upper control probe scans along the X and y directions of the aperture surface of the antenna to be detected to obtain a plane near field data set X under different sampling intervals 1 ，X 2 And X 3 (ii) a From data set X 2 Randomly selecting partial sampling data as an initial data set X 'to be interpolated and reconstructed' 2 ；X 1 Finish Pair X 'as complete dataset' 2 Is interpolated and X 'is interpolated' 2 The interpolated result was denoted as X' 2 '; to X' 2 'iterative processing to obtain data set X' 2 ", will X 3 Far field and interpolated reconstructed X' 2 "the far field of the images is compared; far field side of antenna to be measured for reducing truncation errorDirecting a graph; will S 1 The increase in the scanning area is denoted as S 2 And obtaining a plane near-field data set X by sampling 4 Prepared from X' 2 "and X 4 Is compared with the far field pattern of S 2 And (4) the result of the similar far-field pattern on the sampling surface. The invention reduces the truncation error of the plane data and improves the accuracy of measurement.
Description
Technical Field
The invention belongs to the technical field of microwave measurement, and particularly relates to a planar near-field antenna directional pattern reconstruction method.
Background
The plane near-field measurement technology is widely applied to the field of antenna near-field measurement due to a concise numerical calculation method. The plane near-field measurement system comprises a support frame, a mechanical arm, a probe, an antenna to be tested and a wave-absorbing material, wherein the antenna to be tested and the probe are respectively fixed on the support frame and the mechanical arm, and the probe is used for scanning the aperture surface of the antenna to be tested by controlling the moving position of the mechanical arm, so that two-dimensional plane electric field data of the antenna to be tested under the near-field condition are obtained. Because the actual scanning range of the plane near-field measurement is limited, the radiation energy of the antenna aperture surface obtained by the probe scanning has a truncation error, and the confidence included angle between the antenna aperture surface and the near-field scanning surface is related to the size of the scanning surface and the vertical distance of the near-field scanning, so that the area of the plane near-field scanning surface is generally required to be increased in order to obtain the plane near-field electric field data with a small truncation error and a large confidence interval. However, increasing the sampling area makes the whole measurement process time-consuming, and in some cases, the scanning range and accuracy of the testing instrument are limited, so that the scanning area and the number of sampling points are also limited, and even data defects exist on some sampling points. Therefore, it is a very important research work on how to reduce the truncation error and accurately interpolate and reconstruct the far-field radiation pattern of the antenna to be measured under the condition of fewer initial sampling points.
By referring to the measurement method of the antenna to be measured in different darkroom environments, the method can play an important guiding role in the reconstruction work of the plane near field data. At present, the number of near-field samples and the measuring time can be effectively reduced by a spiral scanning method in a spherical near-field measuring environment; in order to improve the accuracy of the overall data, the minimum distribution of the data samples acquired in the data grid can be determined by an adaptive sampling method, and the overall radiation characteristic of the system can be represented; when the original data acquisition is inaccurate or data loss occurs at some sampling points, the switch probe can be used for completing uniform data acquisition, and the data information of the point to be compensated is estimated through adjacent sampling data; in addition, under the traditional spherical near-field acquisition system, through a clustering analysis and self-adaptive interpolation method, data supplement can be carried out on a spherical high dynamic region and other regions to be interpolated by effectively utilizing partial spherical near-field data, so that data expansion and reconstruction of a far-field directional diagram are completed. The method uses the research content of the near-field data interpolation and reconstruction work as reference, carries out cluster division on all plane near-field initial sampling points by a K-means clustering method, calculates the area of the cell to which each sampling point belongs and the gradient between adjacent sampling points by using a Vono cell division method, and divides the deep interpolation area and the shallow interpolation area in each cluster by using the cell area and the gradient parameters under different weights, thereby obtaining an accurate data interpolation result.
Since the planar near-field measurement may introduce truncation errors due to the limited coverage of the scanning area, in order to improve the accuracy of the measurement, it is necessary to reduce the influence of the truncation errors by increasing the sampling area. However, increasing the sampling area increases the sampling time, and an effective data processing algorithm is needed to reduce the sampling time and improve the measurement accuracy. At present, the influence caused by mis-sampling can be effectively reduced by utilizing a smooth window function to carry out edge filtering on plane near-field data, but the method also reduces the range of an effective area; although the equivalent current on the aperture surface of the antenna to be measured can be obtained by the source reconstruction method to complete numerical analysis and reconstruction of the directional diagram, the method consumes more time on the antenna with large electrical size.
Disclosure of Invention
In order to overcome the technical problems, the invention aims to provide a planar near-field antenna directional pattern reconstruction method, which utilizes a K-means clustering and Voronoi tesselation (Voronoi tesselation) dividing method to perform clustering division on initial small amount of sampling data, completes data supplement of a deep interpolation area and a shallow interpolation area through distinguishing parameters, and simultaneously utilizes a GP (GP) algorithm to perform iterative processing on the planar near-field data after interpolation, thereby reducing the truncation error of the planar data and improving the accuracy of measurement.
In order to achieve the purpose, the invention adopts the technical scheme that:
a planar near-field antenna directional pattern reconstruction method comprises the following steps;
step 1: placing an antenna 102 to be tested on a support 104, placing a probe 101 on a mechanical arm 103, controlling the mechanical arm 103 to move, and performing plane near-field scanning on the mouth surface of the antenna 102 to be tested, so as to obtain plane near-field electric field data;
step 2: selecting the area of 16 multiplied by 16cm 2 Planar near field scan surface S 1 And is in S 1 The probe 101 is controlled to scan along the X and y directions of the aperture of the antenna 102 to be measured by taking 0.5 lambda, 0.4 lambda and 0.2 lambda as intervals respectively, and a plane near field data set X under different sampling intervals is correspondingly obtained 1 ，X 2 And X 3 ；
And step 3: from data set X 2 Randomly selecting partial sampling data as an initial data set X 'to be interpolated and reconstructed' 2 ；X 1 Finish Pair X 'as complete dataset' 2 Is interpolated and X 'is interpolated' 2 The interpolated result is denoted as X ″ 2 ；
And 4, step 4: using GP algorithm to X ″) 2 Iterative processing is carried out to obtain a data set X 'with reduced truncation error' 2 And X is 3 Far field and interpolated reconstructed X' 2 Comparing the far fields of the two images; obtaining a far-field directional diagram of the antenna to be tested 102 with reduced truncation error;
and 5: will S 1 Is increased to 30 x 30cm 2 Is recorded as S 2 And sampling at 0.5 lambda interval to obtain planar near-field data set X 4 Prepared from X' 2 And X 4 Is compared with the far-field directional diagram of S 2 And (4) the result of the similar far-field pattern on the sampling surface.
In the step 2, the mechanical arm 103 controls the probe 101 to scan the mouth surface of the antenna 102 to be measured, and selects an S formed by x: (-8cm,8cm) and y: (-8cm,8cm) of the plane near field 1 The scanning area is 16 x 16cm 2 As known from the planar near-field sampling theorem, the minimum interval of near-field scanning should satisfy Δ x ≦ λ/2 and Δ y ≦ λ/2, so to reduce the sampling time, 0.5 λ and 0.4 λ are selected as the step length of planar near-field sampling, and corresponding complete data are obtainedCollection X 1 And an initial data set X 2 。
In step 3, to form an initial small number of incomplete original data sets, X is subjected to 2 Carrying out random sampling and obtaining an initial small data set X 'to be interpolated' 2 (ii) a Due to X' 2 The data of (1) is a random sampling result, the difference between sampling values is large, and the defective sampling data cannot be supplemented by directly performing linear interpolation on the sampling values, so that another complete data set X needs to be used 1 Carrying out reasonable data interpolation on the data;
the interpolation method adopts a method of K-means clustering and Weino cell element division, wherein the K-means clustering method divides an initial data set X' 2 Performing cluster division, respectively calculating the 2 norm (Euclidean distance) of the field intensity of each sample point and the field intensity of each cluster center, selecting the minimum Euclidean distance corresponding to each sample point, thereby dividing the sample point into cluster clusters corresponding to the minimum Euclidean distance, assuming that k clusters are divided in total, wherein the jth cluster is C j (j is more than or equal to 1 and less than or equal to k) and the clustering center is c j Repeating the above calculation process until the clustering center converges, thereby obtaining a stable clustering center
Wherein n is j Represents the jth cluster C j The total number of samples in, then calculate the Sum of the Squares of the errors (SSE) inside all the current clusters
Selecting different clustering numbers k, recalculating the values of the equations (1) and (2), and when a significant inflection point appears at a certain k value of the SSE error curve, indicating that the k at the moment is the optimal region division number;
then, using a Veno cell embedding method to divide the cell of the sampling points in each cluster, and calculating the area of each cell and each sampleEvaluating the data density in each cluster and the corresponding interpolation method by the field intensity gradient change between the points to ensure that each sampling point x n ,n＝1,2,...,N sample The corresponding cell area is A (x) n ) The distribution density S (x) of the samples near the current sampling point n ) Can be expressed as follows
Selecting two sample points x having a common cell wall or vertex n And x m Calculating corresponding field intensity gradients
Calculate and x simultaneously n The field intensity change gradients of adjacent sampling points are calculated, and x is obtained n Sum of absolute values of all gradients in the vicinity
Wherein M is sample Is represented by the formula n The total number of adjacent sample points. Normalized field strength gradient value of
The two parameters S (x) are combined n ) And G (x) n ) Combining to obtain an overall evaluation parameter J (x) n )
J(x n )＝h 1 (1+S(x n ))+h 2 (1+G(x n )) (7)
Wherein h is 1 And h 2 Is a parameter coefficient, and h 1 +h 2 The values of the two are dynamically adjusted in different cluster, if the whole G (x) in the cluster is as follows n ) On the larger side, increase h should be added appropriately 1 On the contrary, h should be decreased 1 Finally, if the overall evaluation parameter J (x) n ) If the data point is larger than the preset threshold, more interpolation data need to be added to the area where the data point is located, and the data set X is used 1 The X 'subjected to cluster division and cell division' 2 Interpolation is performed if J (x) of the sample point n ) If smaller, only 8 data points are added around the point, otherwise 24 data points are added, and the newly added data points are selected from the data set X 1 And (4) obtaining.
In the step 4, for reducing the truncation error, the GP algorithm is adopted for S 1 Performing iterative processing on the interpolation data on the Plane to improve the accuracy of a far-field directional diagram after interpolation, reserving Plane field intensity information and a Plane Wave Spectrum (PWS) in a confidence interval in a Wave number domain filtering and space domain filtering mode, and simultaneously expanding the range of a reliable interval by a circular iteration method to reduce the influence of truncation errors of the unreliable interval, wherein the GP algorithm firstly converts Plane near-field scanning information into the PWS through Fourier transform
Wherein k is x ，k y And k z Is the wave number along the x, y and z axes, E x,y (x, y, d) is the in-plane electric field strength at d from the antenna aperture plane, while defining the reliable region of the wavenumber domain as
Wherein, theta x And theta y Is the angle, η, of the confidence interval x And η y Greater than 1 to account for more modes, for which spectral filtering may be expressed as
The filtered PWS can be represented as
Wherein n represents the number of iterations, the PWS after wave number domain filtering is transformed into the electric field strength of the spatial domain by means of inverse Fourier transform,
then, for the field intensity of formula (12)
Performing spatial domain filtering
Wherein
Of the formula (13)
Fourier transform to PWS
In this case, P 'of formula (15)' x,y (k x ,k y ) Is P 'obtained by one-time wave-domain filtering and spatial-domain filtering of PWS and then equation (15)' x,y (k x ,k y ) Substituting into (11) - (15) again, realizing the effect of reducing truncation error through multiple cycle iteration, and finally substituting PWS after multiple iteration operation into the calculation formula of the far-field directional diagram of the antenna to obtain the antenna with reduced truncation errorThe far field pattern of the antenna under test 102;
in the step 5, the sampling plane S corresponding to the step 1 to the step 4 is used 1 Increased to an area of 30X 30cm 2 Near field scanning surface S 2 At this time, if sampling is performed at a maximum sampling interval of 0.5 λ, 61 × 61 groups of data X can be obtained 4 X in an actual measurement environment 4 Is about 180min, and S 1 X on the sampling plane 1 And X 2 It takes only 30min and 60min to convert X 2 Interpolated reconstructed X' 2 Far field pattern and X 4 The far field patterns are compared, and the method of the invention is used for finding S 1 After interpolation reconstruction is carried out on the initial small amount of data on the sampling surface, the sum S can be obtained 2 The result of the extrapolated far field patterns on the sampling plane being similar, and S 1 The time consumption on the sampling surface is less, so that the method can effectively reduce the whole data volume and save the measurement time under the condition of similar truncation errors.
The invention has the beneficial effects that:
the plane near-field antenna directional pattern reconstruction method combines a K-means clustering method and a Vono cell division method, performs clustering division and regional interpolation on plane near-field data through parameter discrimination, and obtains a far-field directional pattern of the antenna to be measured 102 with a reduced truncation error through a GP iterative algorithm.
The plane near-field interpolation reconstruction method can effectively perform cluster division on a small amount of initial data and perform reasonable interpolation aiming at the parameter characteristics of the Vono cell element, thereby obtaining an interpolation array with more complete data quantity. The interpolation process solves the influence caused by the limitation of the scanning position of the mechanical arm and the defect of data acquired by the probe in the process of plane near-field scanning. Meanwhile, the method can reduce the influence caused by truncation errors in a smaller sampling area by adopting a GP iterative algorithm, and can obviously reduce the sampling number compared with a far-field directional diagram result corresponding to a larger scanning surface, thereby saving the whole sampling time.
On the basis of a band-limited signal extrapolation theory, the method effectively reduces the truncation error of the plane near-field data and improves the far-field radiation pattern of the antenna to be measured by using a GP (Gerchberg-Papoulis) iterative algorithm on the premise of not increasing the scanning area of the plane near-field.
Drawings
FIG. 1 is a schematic diagram of a planar near-field test environment according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of the geometric parameters and structure of the planar near-field scanning according to the embodiment of the present invention.
FIG. 3 is a data set X acquired by an embodiment of the present invention 1 (FIG. 3(a)) and X' 2 (FIG. 3(b)) in-plane electric field magnitude spectrum.
Fig. 4 shows the L-curve (fig. 4(a)) and the K-means clustering result (fig. 4(b)) obtained by the processing of the embodiment of the present invention.
Figure 5 is a graph of a voronoi cell processed according to an embodiment of the invention.
FIG. 6 illustrates a planar near-field depth interpolation and a shallow interpolation method according to an embodiment of the present invention.
FIG. 7 is an interpolated data set X 'processed according to an embodiment of the present invention' 2 (FIG. 7(a)), and two contrast data sets X 3 (FIG. 7(b)) and X 4 (FIG. 7(c)) in-plane near-field electric field intensity magnitude spectrum.
FIG. 8 is a graph of the normalized planar near-field energy iterative difference of an embodiment of the present invention.
FIG. 9 shows the theoretical far field (FIG. 9(a)) and X obtained by the planar near-far-field transformation algorithm according to the embodiment of the present invention 3 (FIG. 9(b)), X' 2 (FIG. 9(c)), X' 2 (FIG. 9(d)) and X 4 (FIG. 9(e)) comparison of far-field three-dimensional patterns.
FIG. 10 is a diagram of theoretical far field, X, of an embodiment of the present invention 3 Far field, X' 2 Far field, X' 2 Far field and X 4 The far field was compared between the E plane (fig. 10(a)) and the H plane (fig. 10 (b)).
FIG. 11 is the present inventionBright embodiments separate theoretical far field from X' 2 And X' 2 And comparing the far fields to obtain the error result of the normalized radiation pattern.
Fig. 12 is a flowchart of a planar near-field antenna pattern reconstruction algorithm employed in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, in the overall test environment of the embodiment of the present invention, an antenna 102 to be tested is mounted on a support 104, a measurement probe 101 is mounted on a mechanical arm 103, and the probe 101 on the mechanical arm 103 is controlled by a control system to complete a planar near-field scanning operation on the antenna 102 to be tested. In order to verify the effectiveness of the interpolation reconstruction method, the embodiment of the invention verifies the interpolation method of random initial sampling data and GP iteration algorithm under the environment of the plane near-field darkroom.
Firstly, a plane near-field sampling surface S is formed 1 The discrete grids are generated at different sampling intervals at 106, as shown in fig. 2, and the planar near-field data is acquired at different grid densities. The working frequency of the antenna 102 to be tested is selected to be 30GHz, and the sampling theorem shows that the minimum sampling interval of the spatial domain should satisfy that Deltax is not more than lambda/2, so three different sampling intervals satisfying the sampling theorem are set, namely 0.5 lambda, 0.4 lambda and 0.2 lambda, and the corresponding sampling array is defined as X 1 ，X 2 And X 3 . Wherein, X 1 Is a complete set of basic sample data sets, as shown in FIG. 3(a), X 2 Providing discrete data to be interpolated, X 3 Then is with X 2 The data set obtained by comparing the interpolation reconstruction results of the data set to be interpolated is shown in fig. 7 (b).
From data set X 2 In random extraction of N sample A discrete data point, denoted
As shown in FIG. 3(b), with X 1 Data set complete to X' 2 The interpolation of the data of (2). In order to obtain accurate interpolation result by the data characteristics of the initial sampling point, the method needs to be applied toThis N sample And carrying out cluster analysis on the sampling points. According to the method, X 'is subjected to K mean value unsupervised machine learning' 2 And performing cluster division. X 'is calculated first' 2 And 2 norms (Euclidean distances) of the electric field intensity between each sampling point and each clustering center, and dividing each sampling point into clustering clusters corresponding to the minimum 2 norms. Now assume that there are k clusters in total, where the jth cluster is C j (j is more than or equal to 1 and less than or equal to k), and the clustering center c j Is composed of
Wherein n is j Represents the jth cluster C j (1. ltoreq. j. ltoreq.k) and then calculating the sum of the squares of errors (SSE) for all clusters present
The above process is repeated until the cluster center positions converge. Selecting different clustering numbers k, and recalculating c j And F k When F of the SSE error curve (L curve) k When a significant inflection point appears at a certain value of k, the k at this time is the optimal clustering number. Fig. 4(a) is an SSE error curve (L curve), and since an inflection point appears in the L curve when k is 5, the optimum clustering number is 5, and X 'corresponds to the number' 2 The results of class division of 5 types are shown in FIG. 4 (b).
After obtaining the proper cluster division, adopting a proper interpolation judgment method to carry out initial random sampling data set X 'in each cluster' 2 And (6) carrying out interpolation. The main discrimination parameters of data interpolation include sample distribution density and sample change rate. The sample distribution density can be judged by the area of the voronoi cell where the initial sampling point is located, and the sample change rate can be represented by the field intensity gradient between adjacent sampling points with the same voronoi cell edge and vertex.
Next, solve S 1 106 discrete sampled data
As shown in fig. 5, each sampling point corresponds to a cell, wherein the cell with larger area indicates that the area where the sampling point is located belongs to the under-sampled area, and therefore, the number of sampling points near the area needs to be increased. Each sample point x n (n＝1,2,...,N sample ) The corresponding cell area is A (x) n ) Near the sampling point x n Can be expressed as
To calculate a sampling point x n The method first selects x and the adjacent gradient change n Adjacent sample points x with common apex and cell wall m The field intensity gradient between two sampling points is expressed as
Wherein, the first and the second end of the pipe are connected with each other,
representing the absolute value of the field strength gradient, and close to x n The field intensity variation gradient of other adjacent sampling points is also calculated by the formula (4), and is compared with x n All gradient values with the same cell wall and apex are denoted B (x) n )
Wherein M is sample Is represented by the formula n The total number of adjacent sampling points, and the corresponding normalized field strength gradient value G (x) n ) Is composed of
Larger G (x) n ) Value representing x n The field intensity around the field changes more violently and belongs to a high dynamic area, so that more interpolation points need to be added around the point, and conversely, the interpolation number can be reduced because the point belongs to a low dynamic area. Combining the above formulas (3) and (6) to obtain an overall discrimination parameter J (x) n )
J(x n )＝h 1 (1+S(x n ))+h 2 (1+G(x n )) (7)
Wherein h is 1 And h 2 Are the area and gradient weight coefficients, respectively, satisfying h 1 +h 2 Within a cluster, if all cells of a point belong to a high dynamic region, it is difficult to pass the gradient parameter G (x) again n ) Judging the interpolation mode, at this time, h needs to be increased 1 Is weighted and reduced by h 2 The weight of (c). When the overall discrimination parameter J (x) n ) If the sampling point is larger, the sampling point belongs to an under-sampling area, more interpolation data needs to be added, otherwise, only a small amount of interpolation data needs to be added.
The method of the invention is directed to J (x) n ) In both cases of large and small, two ways of depth interpolation and shallow interpolation are used, as shown in FIG. 6, if the sampling point x n Belongs to the under-sampled region, it should be in x n Add 24 interpolation data at the same interval around, i.e. depth interpolation method, otherwise only at x n And 8 pieces of interpolation data are added around the periphery, namely a shallow interpolation method. By the method shown in FIG. 6
Data interpolation is carried out, and the original data can be N 1 ×N 1 Becomes (2N) 1 -1)×(2N 1 -1) grid data, hence the number of effective interpolations of the whole
Satisfy the requirement of
The interpolation result is shown in FIG. 7(a), and in FIG. 7(b), S is measured at intervals of 0.2. lambda. 1 106, the amount of the planar near-field data obtained by sampling is (2N) 1 -1)×(2N 1 -1) and may thus be taken as X' 2 X "of interpolation result 2 The comparison data of (1).
In order to effectively reduce the influence of truncation errors caused by a limited near-field scanning surface, the method adopts a GP iteration algorithm to process interpolation data obtained by the formulas (1) - (7). Firstly, the interpolated plane electric field is converted into a plane wave spectrum PWS through two-dimensional Fourier transform
Wherein, E x,y (x, y, d) is the planar electric field intensity after the processing of the formulas (1) to (7), and the plane S is scanned 1 106 are at a distance d from the antenna under test 102,
the observation surface is scanned from the scanning surface S 1 106 to the face of the antenna 102 to be tested, and
k＝2πf 0 /c
where M1, 2, a, M, N1, 2, a, N, M and N denote fourier transform numbers along x and y directions of the aperture plane of the antenna under test 102, and Δ x and Δ y denote planar near-field scanning intervals smaller than a half wavelength.
The scan geometry of the planar near field is shown in FIG. 2, where L x And L y Respectively a scan plane S 1 Size of (D) x And D y Is the aperture size, O, of the antenna 102 to be measured 1 And O 2 Respectively a scan plane S 1 106 and center of the aperture plane of the antenna to be tested 102, and theta x ＝arctan((L x -D x )/2d)，θ y ＝arctan((L y -D y )/2d)。
Because the plane near-field scanning surface only belongs to valid data in a credible area, and the data outside the credible area can generate truncation error influence, the credible interval of a space domain is converted into a wavenumber domain through Fourier transform, and the corresponding credible area is defined as follows
Wherein theta is x And theta y Is the angle of confidence interval, eta, as shown in FIG. 2 x And η y Greater than 1 to preserve more modes for numerical operations. Thus, in U 0 And (4) the interval belongs to the credible data needing to be reserved, otherwise, filtering is carried out. In this regard, spectral filtering in the wavenumber domain may be expressed as
The filtered wavenumber spectrum can be expressed as
Wherein n is the number of loop iterations of the GP algorithm,
is the initial PWS of equation (8), the filtered PWS is converted into the electric field intensity on the aperture surface of the antenna to be measured 102 by the inverse Fourier transform
Antenna aperture electric field for equation (13)
In other words, the electric field information in the trusted region of the antenna aperture should be preserved, while the electric field outside the aperture should be 0, so that the aperture electric field filtering in the spatial domain is defined as
For this reason, the aperture electric field intensity of the antenna to be measured 102 after spatial domain aperture filtering is
The electric field intensity on the aperture surface of the antenna to be measured 102 subjected to the spatial domain and wavenumber domain filtering processing of the expressions (12) to (15) is converted into a corresponding PWS by using Fourier transform
P 'obtained from the formula (16)' x,y (k x ,k y ) Of alternative formula (12)
The PWS with reduced truncation error is obtained by iterative processes of equations (12) - (16) a plurality of times. However, the above calculation processes of equations (12) to (16) need to be performed for a limited number of iterations, and therefore, an appropriate iteration stop point needs to be selected. Due to different PWS components
Thus, P' z (k x ,k y ) P 'solved by equation (16)' x,y (k x ,k y ) The far-field pattern can be determined by substituting formula (17) and is represented by P' x,y,z (k x ,k y ) To obtain
Wherein r is more than 0 and less than infinity,
and as the initial value of the credible interval comprises an accurate value and an error part, and as the iteration times are increased, the accurate value is gradually converged and the error part is gradually diverged, the whole plane near-field error is reduced and then increased. The method of the invention adopts a method of comparing errors of far field pattern of the sub data set to determine the optimal iteration stop point. Assuming a planar near field E x,y (x, y, d) are common
A far field obtained after Num times of iteration is
n 1 Num, simultaneously from E x,y (x, y, d) extraction
Obtaining far-field directional diagram after Num times of iteration
n 2 Num, when the pattern error between the two is 1
Since the two data sets are acquired on the same near-field scan surface, they have relatively stable iteration stop points, i.e., the minimum energy difference between the two data sets corresponds to the far-field pattern of the two data sets
And
best stop iteration point n 1 And n 2 . For X ″' by the method described in formula (19) 2 Data extraction is performed to obtain different data subsets, and data sets X' are shown in FIGS. 8(a) (b), respectively 2 With its two data subsets X 5 And X 6 Iterative energy difference between, wherein X 5 Is from X ″) 2 Decimate a sub data set of 33X 33 data, and X 6 Is from X ″) 2 And extracting a sub data set obtained by 41 × 41 data. X' can be seen 2 The optimal iteration point is stabilized at 20 times, so that the GP iteration algorithm can obtain better reconstruction effect after being executed for 20 times, and the final iteration result X ″ 'is obtained' 2 。
In order to comparatively illustrate the effectiveness of the GP iterative algorithm adopted by the method and the advantage of saving sampling time, the size of the original sampling plane needs to be changed, S 1 106 area is changed from original 16X 16cm 2 Expanding to 30X 30cm 2 Is recorded as S 2 And sampling at 0.5 lambda interval to obtain planar near-field data set X 4 The planar near-field scanning electric field intensity is shown in FIG. 7 (c).
Finally, the theoretical far-field pattern (fig. 9(a)) and X of the antenna 102 to be measured are measured 3 The near-field-to-far-field pattern (FIG. 9(b)) of (X' 2 The near-field-to-far-field pattern of (FIG. 9(c)), X ″' 2 The near-field to far-field pattern (FIG. 9(d)) and X 4 The two-dimensional E-plane and H-plane comparison results are shown in fig. 10, and the curves S1, S2, S3, S4 and S5 in fig. 10(a) and (b) correspond to fig. 9(a) to (E) in sequence. By comparison, it can be seen that the theoretical far field (FIG. 9(a), curve S1 in FIG. 10) is compared with the initial small random data set X' 2 There is a clear difference between the inferred far fields (fig. 9(c), curve S3 in fig. 10); and data set X 'after iteration by interpolation and GP' 2 The far field of (fig. 9(d), curve S4 in fig. 10) has a good similarity to the theoretical far field; at the same time, data set X 4 Far field (FIG. 9(e), curve S5 in FIG. 10) with data set X ″. 2 The far fields (fig. 9(d), curve S4 in fig. 10) are all very close to the theoretical far field, but X 4 Is higher than completion X '(about 180 minutes)' 2 The time (about 90 minutes) consumed by reconstruction work, therefore, the method can reduce the whole sampling time of the plane near field while ensuring the reconstruction precision. FIGS. 11(a) and (b) are theoretical far field and initial small random data set X ', respectively' 2 And interpolated reconstructed data set X' 2 The projection of the energy difference value between the far fields on a two-dimensional plane can be seen through comparison, the radiation error of a far field directional diagram can be effectively reduced, and the measurement accuracy is improved. Finally, the overall concept and algorithm flow of the method of the present invention are summarized in fig. 12.
In the invention, in a plane near-field measurement environment, reasonable interpolation is carried out on a small amount of initial plane near-field data by a K-means clustering and Voronoi diagram division method, and the influence of truncation errors generated by a limited sampling plane is effectively reduced by using a GP iterative algorithm, so that related research contents have positive significance for perfecting a plane near-field antenna measurement technology.
Claims (5)
1. A planar near-field antenna directional pattern reconstruction method is characterized by comprising the following steps;
step 1: placing an antenna (102) to be tested on a support (104), placing a probe (101) on a mechanical arm (103), controlling the mechanical arm (103) to move, and performing plane near-field scanning on the mouth surface of the antenna (102) to be tested so as to obtain plane near-field electric field data;
step 2: selecting the area of 16 multiplied by 16cm 2 Planar near field scan surface S 1 And is in S 1 The probe (101) is controlled to scan along the X and y directions of the mouth surface of the antenna to be measured 102 by respectively taking 0.5 lambda, 0.4 lambda and 0.2 lambda as intervals, and a plane near-field data set X under different sampling intervals is correspondingly obtained 1 ，X 2 And X 3 ；
And step 3: from data set X 2 Medium random selection of partial miningSample data as an initial data set X 'to be interpolated' 2 ；X 1 Finish Pair X 'as complete dataset' 2 Is interpolated and X 'is interpolated' 2 The interpolated result is denoted as X ″ 2 ；
And 4, step 4: using GP algorithm to X ″) 2 Iterative processing is carried out to obtain a data set X' with reduced truncation error 2 And X is 3 Far field and interpolated reconstructed X ″) 2 Comparing the far fields of the two images; obtaining a far-field directional diagram of the antenna to be tested (102) with the truncation error reduced;
and 5: will S 1 Is increased to 30 x 30cm 2 Is recorded as S 2 And sampling at 0.5 lambda interval to obtain planar near-field data set X 4 Mixing X ″) 2 And X 4 Is compared with the far-field directional diagram of S 2 And (4) the result of the similar far-field pattern on the sampling surface.
2. The method as claimed in claim 1, wherein in step 2, the mechanical arm (103) controls the probe (101) to scan the aperture of the antenna (102) to be measured, and the planar near field is selected to have a scanning range of x: ((-8 cm,8cm), y: ((-8 cm,8cm) to form S 1 The scanning area is 16 x 16cm 2 As can be known from the planar near-field sampling theorem, the minimum interval of the near-field scanning should satisfy the conditions that Deltax is less than or equal to lambda/2 and Delay is less than or equal to lambda/2, so that in order to reduce the sampling time, 0.5 lambda and 0.4 lambda are selected as the step length of the planar near-field sampling, and a corresponding complete data set X is obtained 1 And an initial data set X 2 。
3. The method as claimed in claim 1, wherein in step 3, to form an initial small number of incomplete original data sets, X pairs are selected 2 Carrying out random sampling and obtaining an initial small data set X 'to be interpolated' 2 ；
The interpolation method adopts a method of K-means clustering and Voronoi cell element division, wherein the K-means clustering method divides an initial data set X′ 2 Performing cluster division, respectively calculating the 2 norm (Euclidean distance) of the field intensity of each sample point and the field intensity of each cluster center, selecting the minimum Euclidean distance corresponding to each sample point, thereby dividing the sample point into cluster clusters corresponding to the minimum Euclidean distance, assuming that k clusters are divided in total, wherein the jth cluster is C j (j is more than or equal to 1 and less than or equal to k) and the clustering center is c j Repeating the above calculation process until the clustering center converges, thereby obtaining a stable clustering center
Wherein n is j Represents the jth cluster C j The total number of samples in, then calculate the Sum of the Squares of the errors (SSE) inside all the current clusters
Selecting different clustering numbers k, recalculating the values of the equations (1) and (2), and when a significant inflection point appears at a certain k value of the SSE error curve, indicating that the k at the moment is the optimal region division number;
then, carrying out cell division on sampling points in each cluster by using a Veno cell embedding method, and evaluating the data density in each cluster and a corresponding interpolation method by calculating the area of each cell and the field intensity gradient change between sampling points to ensure that each sampling point x n ,n＝1,2,...,N sample The corresponding cell area is A (x) n ) The distribution density S (x) of the samples near the current sampling point n ) Can be expressed as follows
Selecting two sample points x having a common cell wall or vertex n And x m Calculate correspondencesField intensity gradient
Calculate and x simultaneously n The field intensity change gradients of adjacent sampling points are calculated, and x is obtained n Sum of absolute values of all gradients in the vicinity
Wherein M is sample Is represented by the formula n The total number of adjacent sample points. Normalized field strength gradient value of
The two parameters S (x) are combined n ) And G (x) n ) Combining to obtain an overall evaluation parameter J (x) n )
J(x n )＝h 1 (1+S(x n ))+h 2 (1+G(x n )) (7)
Wherein h is 1 And h 2 Is a parameter coefficient, and h 1 +h 2 The values of the two are dynamically adjusted in different cluster, if the whole G (x) in the cluster is as follows n ) On the larger side, increase h should be added appropriately 1 On the contrary, h should be decreased 1 Finally, if the overall evaluation parameter J (x) n ) If the data point is larger than the preset threshold, more interpolation data need to be added to the area where the data point is located, and the data set X is used 1 The X 'subjected to cluster division and cell division' 2 Interpolation is performed if J (x) of the sample point n ) If smaller, only 8 data points are added around the point, otherwise 24 data points are added, and the newly added data points are selected from the data set X 1 And (4) obtaining.
4. According to claim1, the method for reconstructing the directional diagram of the planar near-field antenna is characterized in that in the step 4, a GP algorithm is adopted to perform S 1 Performing iterative processing on interpolation data on a Plane, reserving Plane field intensity information and a Plane Wave Spectrum (PWS) in a confidence interval in a Wave number domain filtering and space domain filtering mode, and converting Plane near-field scanning information into the PWS by a GP algorithm through Fourier transform
Wherein k is x ，k y And k z Is the wave number along the x, y and z axes, E x,y (x, y, d) is the in-plane electric field strength at d from the antenna aperture plane, while defining the reliable region of the wavenumber domain as
Wherein, theta x And theta y Is the angle, η, of the confidence interval x And η y Greater than 1 to account for more modes, for which spectral filtering may be expressed as
The filtered PWS can be represented as
Wherein n represents the number of iterations, the PWS after wave number domain filtering is transformed into the electric field strength of the spatial domain by means of inverse Fourier transform,
then, for the field intensity of formula (12)
Performing spatial domain filtering
Wherein
Of the formula (13)
Fourier transform to PWS
In this case, P 'of formula (15)' x,y (k x ,k y ) Is P 'obtained by one-time wave-domain filtering and spatial-domain filtering of PWS and then equation (15)' x,y (k x ,k y ) Substituting into (11) - (15) again, realizing the effect of reducing truncation errors through multiple cycle iterations, and finally substituting PWS after multiple iteration operations into a calculation formula of an antenna far-field pattern to obtain the far-field pattern of the antenna to be measured 102 with reduced truncation errors;
5. the method as claimed in claim 1, wherein in step 5, the samples corresponding to steps 1-4 are sampledPlane S 1 The increase is 30X 30cm 2 Near field scanning surface S 2 At this time, if sampling is performed at a maximum sampling interval of 0.5 λ, 61 × 61 groups of data X can be obtained 4 X in an actual measurement environment 4 Is about 180min, and S 1 X on the sampling plane 1 And X 2 It takes only 30min and 60min to convert X 2 Interpolated reconstructed X ″) 2 Far field pattern and X 4 Is compared with the far field pattern of S by said method 1 After interpolation reconstruction is carried out on the initial small amount of data on the sampling surface, the sum S can be obtained 2 And (4) the result of the similar far-field pattern on the sampling surface.
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| CN117665414A (en) * | 2024-01-31 | 2024-03-08 | 深圳大学 | Near field measurement method, device, terminal and readable storage medium |
| CN117665414B (en) * | 2024-01-31 | 2024-04-26 | 深圳大学 | Near field measurement method, device, terminal and readable storage medium |
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