A method for reconstructing the diffraction field of an antenna aperture based on similarity principle

Abstract

The invention discloses a method for reconstructing the diffraction field of an antenna aperture face based on a similarity principle, comprising the following steps: step 1. enabling a probe to collect aperture face near field data; step 2. collecting aperture face field data; step 3. using a spatial convolution formula to perform convolution processing on the aperture face field data at two frequency points; step 4. using a data set as a similar data set providing complete interpolation information; randomly extracting part of the sampled data from the data set as a defective data set to be interpolated; performing feature division using a K-means and Voronoi cell division method; step 5. collecting data on a two-dimensional diffraction field at one of the frequency points; step 6. calculating a two-dimensional plane error and a correlation coefficient to obtain a relatively accurate reconstruction result, and the method can effectively save the plane near field test time and cost expenditure at a frequency point with data defect. The invention realizes the data reconstruction work of the aperture face diffraction field with data defect problems at different frequency points.

Description

Technical Field

[0001] The invention relates to the technical field of microwave measurement, and in particular to a method for reconstructing an antenna aperture diffraction field based on a similarity principle. Background Art

[0002] It can be seen from the far-field test conditions of the antenna that for an electrically large antenna, the far-field test distance is large, so it is difficult to directly complete the far-field test of the antenna to be tested in a limited indoor environment. It is necessary to collect the two-dimensional planar near-field data near the antenna aperture through a planar near-field measurement system, and obtain the far-field radiation information of the antenna through a planar near-field conversion algorithm. In addition, since the radiation field on the antenna aperture and other observation surfaces satisfies the physical optical relationship, that is, the planar field strength information on different observation surfaces can be inferred using the antenna aperture field, so studying the planar near-field diffraction problem of the antenna aperture is conducive to promoting the development of compact field test technology (Compact Antenna Test Range, CATR). In the process of planar near-field data acquisition, the test system or the antenna to be tested may have missing or abnormal data at different test frequencies. For an antenna with an electrically large size and a high operating frequency, the overall number of near-field samples is large, so it is very time-consuming to re-measure the planar near-field data of a certain frequency point and infer the plane wave information on the target observation surface. Therefore, it is a very important research task to reconstruct the aperture diffraction field data at the frequency to be measured without repeated measurement and by interpolating the aperture field strength information at other frequencies.

[0003] The diffraction field of the antenna changes with the distance between the observation surface and the aperture. Currently, the aperture diffraction field of electrically large-sized antennas can be calculated using physical optics methods. However, as the number of grid divisions increases, the overall calculation process becomes very complicated and time-consuming. Summary of the invention

[0004] In order to overcome the above technical problems, the present invention proposes a method for reconstructing the antenna aperture diffraction field based on the similarity principle. The method utilizes the characteristic that the diffraction field has a high similarity at N times the frequency and N times the observation distance to obtain a group of similar data sets that can provide complete interpolation information. At the same time, the K-means and Voronoi cell partitioning methods are used to divide the defective data set into feature areas, and sample points that need deep interpolation and shallow interpolation are distinguished according to the data characteristics of each area. Then, the interpolation information required for the defective data set is extracted from the similar data set, thereby effectively supplementing the plane field strength information of the defective data set, and significantly reducing the time and cost overhead of repeated testing, thereby realizing the data reconstruction of the aperture diffraction field with data missing problems at different frequency points.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for reconstructing the diffraction field of an antenna aperture based on a similarity principle comprises the following steps:

[0007] Step 1. Align the array antenna 101 to be tested with the mobile scanning frame 104 in the planar near-field darkroom, and control the scanning frame 104 to complete the planar near-field scanning of the array antenna 101 to be tested by the probe 103. Meanwhile, the absorbing material 102 is used to absorb the reflected interference in the environment, so that the probe 103 can collect more accurate near-field data of the mouth surface;

[0008] Step 2. For f 1 =28GHz and f 2 =30.8GHz aperture field data is collected, and the distance between the probe 103 and the aperture is d 0 =50mm, the scanning area of ​​the mouth surface is 32cm×32cm, with 0.5λ 1 (λ 1 =c / f 1 , c is the speed of light) is the sampling interval along the x and y directions of the antenna aperture surface for f 1 =28 GHz frequency point to collect two-dimensional near-field data, and record the collected data set as X 1 ; with 0.4λ 2 (λ 1 =c / f 1 ) is the sampling interval along the x and y directions of the antenna aperture for f 2 =20.8 GHz frequency point to collect two-dimensional near-field data, and record the collected data set as X 2 ;

[0009] Step 3. Use the spatial convolution formula to transform X 1 and X 2 Perform convolution processing to obtain the distance d from the antenna aperture. 1 =20λ 1 = Data set X′ on the observation surface of 214.286 mm 1 , and the distance from the antenna aperture d 2 =1.1×20λ 1 = Data set X′ on the observation surface of 235.714 mm 2 ;

[0010] Step 4. Transform the dataset X′ 1 As a similar dataset that provides complete interpolation information; from the dataset X′ 2 Randomly select some sample data as the defective data set to be interpolated, denoted as X″ 2 ; Use K-means and Voronoi cell partitioning to calculate X″ 2 Perform feature partitioning and use X′ 1 The complete interpolation information provided is X″2 The feature area is interpolated and X″ 2 The interpolated data set is denoted as X″′ 2 ;

[0011] Step 5. At a distance d from the antenna 2 =1.1×20λ 1 =235.714mm, with 0.2λ 2 is the sampling interval, for f 2 = The two-dimensional diffraction field at the frequency point of 30.8 GHz is used for data collection, and the collected data set is recorded as X 3 ;

[0012] Step 6. X 3 As a comparison data set, and the interpolated reconstructed X″′ 2 Compare and calculate X 3 and X″′ 2 The two-dimensional plane error and correlation coefficient between them are shown, which shows that the similarity principle and cluster interpolation method can obtain more accurate reconstruction results, and this method can effectively save the time and cost of planar near-field testing at the frequency point of data loss.

[0013] In step 2, the two test frequency points f 1 =28GHz and f 2 =30.8GHz satisfies a multiple relationship of 1.1, and the antenna aperture field at the two frequency points is scanned in the near field, with a scanning distance d 0 =50mm, the scanning range along the x and y directions is (-16cm, 16cm); in order to satisfy the Nyquist sampling theorem (Δx≤λ / 2, Δy≤λ / 2) and reduce the number of samples and test time, the scanning range is 0.5λ respectively. 1 and 0.4λ 2 is the sampling interval f 1 =28GHz and f 2 =30.8GHz aperture field data collection, and obtain the corresponding complete data set X 1 and X 2 .

[0014] In step 3, since f 1 With f 2 There is a multiple correspondence relationship between them 2 / f 1 =1.1, so from the similarity principle of the aperture diffraction field, we can know that the frequency f 1 and f 2 The corresponding observation plane S 1 106 and S 2 The distance from 107 to the antenna aperture also needs to satisfy the multiple relationship d2 / d 1 =1.1, then when S 1 The distance between 106 and the antenna aperture is d 1 =214.286mm, S 2 The distance between 107 and the antenna aperture should be d 2 =235.714mm;

[0015] From the extrapolation formula of the aperture diffraction field, we know that if the tangential component of the antenna aperture field is E x (x',y') and E y (x',y'), then the two-dimensional tangential field component on a certain observation surface in space can be expressed as

[0016]

[0017]

[0018] Among them, the constant z is the distance between the observation plane and the antenna aperture, k = 2π / λ, R is the Euclidean distance from a point in space to the aperture, and satisfies

[0019] By observing equations (1) and (2), we can find that the two equations differ only in the transformed field component, and the other parameters remain the same. Therefore, let

[0020] f(x,y)=E x,y (x,y) (3)

[0021]

[0022] in, Substituting (3) and (4) into (1) and (2) for simplification, we can obtain

[0023] F(x,y)=f(x,y)*g(x,y)=∫∫f(x',y')g(x-x',y-y')dx'dy' (5)

[0024] Among them, f(x, y) represents the aperture field, g(x, y) represents the convolution kernel, and F(x, y) represents the tangential electric field component on the observation surface. Therefore, using formula (5), the aperture field can be transferred to the observation surface S 1 106 and S 2 The convolution process on 107 is used to obtain the distance d from the antenna aperture. 1 =20λ 1 = Data set X′ at 214.286 mm 1 , and the distance from the antenna aperture d 2 =1.1×20λ 1= Data set X′ at 235.714 mm 2 .

[0025] In step 4, to simulate the impact of the instability of the test system on the data collection and storage process under complex conditions, it is necessary to perform a 2 Random data collection is performed. The random sampling process reflects the impact of system random errors on the measurement results. The data set after random sampling is recorded as X″ 2 , and the data set X′ 1 As a complete similarity data set for X″ 2 Interpolate the data to get X″ 2 Add more valid data information, due to the data set X″ 2 It is a set of feature points randomly extracted from a complete data set, so it is necessary to 2 The overall sampling data is clustered and the characteristics of the sampling points within each cluster are analyzed to obtain more accurate interpolation results.

[0026] Using K-means method to 2 Perform clustering and divide X″ 2 Divide it into several feature categories, and then use Voronoi cells to analyze the data features of the sample points in each cluster. 2 In the sample space of , k sample centers are randomly selected, and k clustering results are generated accordingly. The i-th cluster A i The cluster center of (1≤i≤k) is denoted as a i , calculate the Euclidean distance between each cluster center and all sample points, and divide each sample into the cluster with the smallest Euclidean distance. Find the best sample center and clustering result through multiple iterations. The calculation method of the above cluster centers is as follows

[0027]

[0028] Among them, N i and x j Respectively represent the i-th cluster A i The total number of samples and the jth sample in the clustering result corresponding to the current cluster number k are used to calculate the overall error sum of all clusters.

[0029]

[0030] Change the number of clusters k, recalculate the values ​​of (6) and (7), and convert E under different cluster numbers into k Compare and select the E with obvious numerical inflection point change. k As the best clustering result, the corresponding k value is the optimal number of clusters.

[0031] In order to further analyze the data characteristics of samples within each cluster and complete the corresponding data interpolation work for different feature areas, the Voronoi cell division method is used to calculate the characteristic parameters of the sample points in each cluster area. The calculated characteristic parameters include the cell area and the gradient between cells. Assuming that the current sample point is x m , then the corresponding cell area is s(x m ), and the cell area is normalized

[0032]

[0033] Among them, M sum Represents data set X″ 2 The number of all samples in . The inter-cell gradient needs to be selected with the current x m Multiple adjacent cells are calculated. Assume that one of the adjacent cells is x n , then the inter-cell gradient can be expressed as

[0034]

[0035] will be with x m The gradients between all adjacent cells are modulo summed to obtain

[0036]

[0037] Among them, N sum Represents x m The total number of adjacent cells. Normalizing the cell gradient, we can get

[0038]

[0039] The above two parameters S(x m ) and D(x m ) and multiply each by the coefficient q 1 and q 2 , get a comprehensive parameter index

[0040] L(x m )=q 1 (1+S(x m ))+q 2 (1+D(x m )) (12)

[0041] For a cluster, the cell area or gradient parameter within the cluster may be close. By adjusting the weight coefficient of each parameter, the overall parameter index L(x m ), if L(x m) is too large, it means that the sample point belongs to the under-sampling area, and the interpolation data near the sampling point should be increased. Otherwise, it belongs to the non-under-sampling area, and less interpolation data can meet the data needs of the area. After determining the under-sampling and non-under-sampling areas, the complete data set X′ is used to 1 X″ 2 Data interpolation is performed on each feature area to obtain the interpolated data set X″′ 2 .

[0042] In step 5, in order to compare with the interpolated data set X″′ 2 To perform error analysis and comparison, it is necessary to 2 = 235.714mm position with 0.2λ 2 f is the sampling interval 2 =Complete diffraction field data at 30.8 GHz frequency point, this distance is consistent with the observation surface S in step 3 2 107 is the same distance from the mouth surface, and d 2 The complete theoretical diffraction field at the distance is denoted as X 3 .

[0043] In step 6, the interpolated data set X″′ 2 With observation surface S 2 The complete theoretical diffraction field on 107X 3 Perform two-dimensional error calculation, obtain the two-dimensional error distribution by calculating all sample differences on the entire two-dimensional plane, and 2 With X 3 Calculate the correlation

[0044]

[0045] Among them, v and w represent the overall sample number on the two-dimensional plane. By comparing the two-dimensional plane error and correlation coefficient, it can be shown that the complete similarity matrix X′ can be effectively used. 1 Complete the data missing matrix X″ 2 The data interpolation work is carried out and the result is very close to the complete theoretical diffraction field on the observation plane. The interpolation method saves the time of f 2 The data measurement work at each frequency point effectively reduces the overall test time and cost.

[0046] Beneficial effects of the present invention:

[0047] The antenna aperture diffraction field reconstruction method described in the present invention combines the similarity principle of the aperture diffraction field with the interpolation method, obtains the diffraction field distribution at different frequency points on the target observation plane by convolution extrapolation, clusters and divides the overall sample data of the defective diffraction field by using K-means and Voronoi cell partitioning, and supplements and interpolates the data in the complete similar data set into the defective data set according to the sample characteristics of each divided area, thereby effectively realizing the recovery and reconstruction of the diffraction field data at the target frequency point.

[0048] The diffraction field similarity principle described in the present invention can effectively combine the diffraction fields at different frequencies and observation distances. For two diffraction fields with the same frequency and observation distance, their two-dimensional field intensity distributions have a high degree of similarity, so the data on one observation surface can be used to supplement the data on the other observation surface. The data supplementation and interpolation process utilizes the existing complete information on other frequency points, thereby avoiding the data measurement work of the secondary aperture field or observation surface of the target frequency point, effectively reducing the overall test time consumption, and solving the problem of random data collection and storage failure caused by system stability, thereby improving the overall utilization rate of multi-frequency aperture data. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the structure of a planar near-field test environment adopted in an embodiment of the present invention.

[0050] Figure 2 It is a schematic diagram of the similarity principle of the aperture diffraction field adopted in the embodiment of the present invention.

[0051] Figure 3 The embodiment of the present invention is 0.5λ 1 f is the sampling interval 1 = aperture field X at 28 GHz 1 The plane field intensity spectrum ( Figure 3 (a)) and phase spectrum ( Figure 3 (b)).

[0052] Figure 4 The embodiment of the present invention is 0.4λ 2 f is the sampling interval 2 = aperture field X at 30.8 GHz 2 The plane field intensity spectrum ( Figure 4 (a)) and phase spectrum ( Figure 4 (b)).

[0053] Figure 5 The embodiment of the present invention converts the mouth surface field X into 1 Transform to d 1 = Data set X′ on the 214.286 mm observation surface1 The plane field intensity spectrum ( Figure 5 (a)) and phase spectrum ( Figure 5 (b)).

[0054] Figure 6 The embodiment of the present invention converts the mouth surface field X into 2 Transform to d 2 = Data set X′ on the observation surface of 235.714 mm 2 The plane field intensity spectrum ( Figure 6 (a)) and phase spectrum ( Figure 6 (b)).

[0055] Figure 7 The embodiment of the present invention is from the data set X′ 2 Randomly select some sample data as the defective data set X″ to be interpolated 2 Plane field strength amplitude spectrum.

[0056] Figure 8 is the overall error square sum curve obtained by processing in the embodiment of the present invention ( Figure 8 (a)) and K-means clustering results ( Figure 8 (b)).

[0057] Fig. 9 , which is the Voronoi cell diagram obtained by processing according to the embodiment of the present invention.

[0058] Fig.10 These are the deep interpolation and shallow interpolation methods used in the embodiments of the present invention.

[0059] Fig.11 is the data set X″′ after interpolation and reconstruction in the embodiment of the present invention 2 The plane field intensity spectrum ( Fig.11 (a)) and phase spectrum ( Fig.11 (b)).

[0060] Fig.12 The embodiment of the present invention is at a distance d from the antenna aperture. 2 =235.714mm, at 0.2λ 2 f is the sampling interval 2 = Two-dimensional diffraction field X at 30.8 GHz 3 The plane field intensity spectrum ( Fig.12 (a)) and phase spectrum ( Fig.12 (b)).

[0061] Fig.13 In this embodiment of the present invention, the data set X 3 and the interpolated reconstructed dataset X″′ 2 For comparison, the normalized two-dimensional plane error is obtained. DETAILED DESCRIPTION

[0062] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0063] The overall test environment of the embodiment of the present invention is as follows Figure 1 As shown, the array antenna 101 is placed in a darkroom environment, and its aperture is aligned parallel to the planar near-field scanning frame 104. The data collection of the aperture field of the array antenna 101 to be tested is completed by controlling the probe 103 on the scanning frame 104. The absorbing material 102 in the test environment can effectively suppress multipath reflection interference, so that the probe 103 can collect more accurate near-field data information. Since the planar near-field scanning needs to satisfy the Nyquist sampling theorem, when scanning the antenna aperture, the sampling interval along the x and y directions of the aperture should be less than or equal to λ / 2, that is, Δx≤λ / 2, Δy≤λ / 2. The following describes the aperture field data acquisition, the principle of diffraction field similarity, and the cluster interpolation technology, and verifies the effectiveness of the reconstruction method.

[0064] On the observation surface 50 mm away from the antenna aperture, the antenna aperture field data is collected using the sampling probe 103. Two test frequency points f are selected. 1 =28GHz and f 2 =30.8GHz, the scanning area of ​​the probe 103 on the antenna aperture is 32cm×32cm. 1 The sampling interval of f 1 The data of the aperture field at the frequency point is collected, then Δx = Δy = 5.36mm, and a 61×61 data set X is formed. 1 The amplitude and phase distribution of the aperture field are as follows: Figure 3 (a)(b) As shown; with 0.4λ 2 The sampling interval of f 2 The data of the aperture field at the frequency point is collected, then Δx = Δy = 3.89 mm, and a 82×82 data set X is formed. 2 The amplitude and phase distribution of the aperture field are as follows: Figure 4 As shown in (a)(b).

[0065] After completing the data collection of the aperture field, it is necessary to deduce the aperture field to the target observation surface through the similarity principle and obtain the diffraction field distribution with similar relationship at different frequency points. Figure 2 This is a schematic diagram of the extrapolation of the aperture diffraction field and the application of similarity principles. 0 is the scanning distance of the aperture field, d 1 Yes 1 The extrapolated distance of the aperture diffraction field corresponds to the observation plane S 1 106;d 2 Yes 2The extrapolated distance of the aperture diffraction field corresponds to the observation plane S 2 107, and the above parameters satisfy d 2 / d 1 =f 2 / f 1 =1.1.

[0066] Next, we use the aperture diffraction formula to calculate d 0 The surface field at the distance is extrapolated to obtain the observation surface S 1 106 and S 2 The field distribution on 107. Assume that the tangential electric field component of the aperture field is E x (x',y') and E y (x',y'), the coordinates of any point P in space are (x,y,z), then from Maxwell's equations and the vector potential A m From the expression, we can see that the field strength at point P in space can be expressed as

[0067]

[0068] Among them, J m is the equivalent magnetic flux of the aperture field, G is the Green function in free space, and the Euclidean distance between any point P in space and the aperture sampling point can be expressed as Therefore, the electric field component on the observation surface can be expressed as

[0069]

[0070]

[0071] Where z is the distance between the observation plane and the antenna aperture, and the beam k = 2π / λ. 1 When , the observation surface S is obtained by using formula (2) (3) 1 106 diffraction field, when z = d 2 When , the observation surface S is obtained by using formula (2) (3) 2 107 diffraction field. If the antenna aperture field is expressed as the excitation function f(x,y), and the Green function is expressed as the network response function g(x,y), then

[0072] f(x,y)=E x,y (x,y) (4)

[0073]

[0074] in, Substituting equations (4) and (5) into equations (2) and (3) for simplification, the diffraction field F(x, y) on the observation surface can be expressed as

[0075] F(x,y)=f(x,y)*g(x,y)=∫∫f(x',y')g(x-x',y-y')dx'dy' (6)

[0076] From equation (6), we can see that the aperture diffraction field F(x, y) is the spatial convolution result of the aperture field f(x, y) and the Green's function g(x, y). Therefore, the calculation process of extrapolating the aperture field to the observation surface is also called the spatial convolution process. 1 and f 2 The corresponding observation surface S 1 106 and S 2 The field distribution on 107 is as follows Figure 5 and Figure 6 As shown, Figure 5 The result is recorded as data set X′ 1 , Figure 6 The result is recorded as data set X′ 2 .

[0077] In the actual measurement phase, for electrically large size and high frequency antennas, the number of near-field sampling is large, so the data collection and storage process of the planar near-field system is more time-consuming, and as the amount of data and test time increase, the stability of the system will be affected to a certain extent, resulting in some missing or abnormal data in the collected near-field data. In this regard, this method treats the interpolation data set X′ 2 Perform random sampling from the existing data set X′ 2 Randomly select 55% of the data as the missing data set X″ 2 , used to reflect data loss and abnormal problems caused by system stability, such as Figure 7 shown.

[0078] In order to 2 To effectively supplement data, the present invention uses K-means clustering and Voronoi cell partitioning to 2 The sample characteristics are analyzed to effectively identify the interpolation method required for each sample under different clustering results. The interpolation process requires the use of a similar data set X′ with complete information. 1 X′ obtained by formula (6) 1 and X′ 2 Satisfy d in terms of frequency and observation distance 2 / d 1 =f 2 / f 1 =1.1, so X′ 1 With X″ 2 The field distribution has good similarity, so we use X′ 1 To provide X″ 2 The sample information required for interpolation can better reconstruct S2 Field strength distribution on 107.

[0079] Using K-means clustering method, X″ 2 Divide into multiple clusters, assuming that the current 2 Perform k cluster divisions, then there are k sample centers in total, and the i-th cluster A i The sample center of (1≤i≤k) is denoted as a i , then calculate the Euclidean distance between each cluster center and the sample, and obtain the overall error sum of squares within all k clusters

[0080]

[0081] where x j Represents the i-th cluster A i The jth sample in . Record the E of k clusters at this time k Then change the cluster number k, reselect k sample centers, and calculate the Euclidean distance between all samples and k cluster centers. At this time, each sample corresponds to k distances, find the smallest distance, and divide each sample point into the cluster corresponding to the smallest distance. Use the sample distribution under the current clustering results to calculate each cluster center.

[0082]

[0083] Where N i Represents the i-th cluster A i The total number of samples in (8). Recalculate the distance between each sample and each cluster center in (8), and re-divide each sample into the cluster corresponding to the minimum distance. Repeat (8) and perform new clustering on the samples until the cluster centers converge and stabilize. At this time, calculate E of (7) corresponding to the current number of clusters k. k From multiple groups of different cluster numbers k, select E with significant change inflection points k Values, such as Figure 8 As shown in (a), the corresponding cluster number k is X″ 2 The best number of clusters is k = 5, and the clustering results are as follows: Figure 8 (b) as shown.

[0084] For the sake of Figure 8 In order to analyze the sample characteristics within each cluster in (b), the Voronoi cell partitioning method is needed to calculate the Voronoi cell area and inter-cell gradient parameters of each sample point. The Voronoi cell partitioning result is shown in Fig. 9 Assume that the current sample point is x m , then the cell area after Voronoi cell division can be expressed as s(x m), for s(x m ) is normalized to get

[0085]

[0086] Among them, M sum It is X″ 2 The gradient calculation method that characterizes the rate of cell change needs to find the value that is related to the current sample point x. m Adjacent cells with common cell walls or common vertices are assumed to be m One of the adjacent sample points is x n , then the two-dimensional plane gradient between the two can be expressed as

[0087]

[0088] At this time, all m The adjacent cell gradients are modulo summed, then

[0089]

[0090] Among them, N sum represents all m The number of adjacent cells. m ) is normalized, we can get

[0091]

[0092] In order to form a unified criterion in each cluster, the parameter S(x m ) and D(x m ) to obtain the comprehensive index L(x m )

[0093] L(x m )=q 1 (1+S(x m ))+q 2 (1+D(x m )) (13)

[0094] where q 1 and q 2 is the parameter coefficient, and q 1 +q 2 =1. Using L(x m ) can select the interpolation method within each cluster. If L(x m ) is too large, it belongs to the under-sampling area, otherwise it belongs to the non-under-sampling area. m ) parameter is too large, it means that the cluster belongs to the high dynamic area, and it is impossible to accuratelym ) to determine whether the area is an under-sampling area, so it is necessary to reduce q 2 value and improve q 1 Weights are used to determine the appropriate interpolation method for this region based on the cell area.

[0095] For under-sampled and non-under-sampled areas, the present invention example adopts Fig.10 The deep and shallow interpolation methods shown, that is, if the sample point x m The cell belongs to the under-sampling area, then in x m Add 24 interpolation data around, otherwise only x m The eight data points around are interpolated. The interpolated and reconstructed data set X″ 2 Note it as X″′ 2 , the results are as follows Fig.11 As shown, at this time, the data set X″′ 2 is a 164×164 array. In order to reconstruct X″′ after interpolation 2 To compare and illustrate the accuracy and effectiveness of the reconstruction method, 0.2λ 2 is the sampling interval (Δx = Δy = 1.95 mm) from the antenna aperture d 2 = f at the position of 235.714 mm 2 = The complete diffraction field data at the frequency point of 30.8 GHz is sampled, and the obtained data set is recorded as X 3 ,like Fig.12 shown.

[0096] The dataset X 3 and the interpolated reconstructed dataset X″′ 2 Perform two-dimensional error calculation, and its two-dimensional error distribution is as follows Fig.13 As shown in the figure, the error distribution results show that the interpolated and reconstructed data set X″′ 2 With the complete theoretical data set X 3 There is good similarity, which shows the effectiveness of the method described in the present invention. At the same time, X″′ is calculated 2 With X 3 Planar correlation

[0097]

[0098] Wherein, v and w represent the overall sample number on the two-dimensional plane. The calculated result is 0.9964, so the correlation between the reconstruction result and the theoretical value is very high, indicating that the invention method has a good reconstruction effect.

[0099] The method of the present invention can use the field strength information at different frequencies and observation distances to effectively supplement the data missing problems caused by system failure or poor system stability, and the error between the data set after interpolation and reconstruction and the theoretical value is small, which shows the effectiveness and practicality of the method. In addition, the method can improve the utilization rate of the mouth field data under continuous frequency point testing, effectively complement the information of similar fields, thereby reducing the secondary data measurement work at certain frequency points, saving test time and cost.

[0100] The present invention selects the aperture field at different frequencies for convolution calculation and obtains the diffraction field distribution on the target observation surface at different frequencies, thereby illustrating the applicability of the diffraction field similarity theory when the frequency and the distance between the observation surface and the aperture are both increased by N times.

[0101] In the multi-frequency planar near-field measurement system, the number of planar near-field samples of electrically large size and high-frequency antennas is large, so the overall measurement process of the system will be time-consuming. In addition, as the number of system samples, test time and data storage volume increase, the stability of the near-field system will be affected to a certain extent, resulting in missing and abnormal data at certain frequency points or sampling areas.

[0102] In order to solve the problem of missing data, the near-field information of the plane is supplemented by an adaptive sampling method, or the field distribution characteristics of different sample areas are divided by machine learning, and different interpolation methods are used for each characteristic area, so as to obtain more accurate field strength information. The present invention combines the similarity principle of the aperture diffraction field with the data missing problem at different frequency points, and clusters the missing plane data to be interpolated by the K-means and Voronoitessellation division methods, and uses the diffraction field with N times the frequency and observation distance as a similar data set, and uses this data set to interpolate the missing data set after clustering, so as to obtain more complete and accurate target plane field strength information.

[0103] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for reconstructing the diffraction field of an antenna aperture based on similarity principle. It is characterized in that The steps include: Step 1. Align the array antenna (101) to be tested with the mobile scanning frame (104) of the planar near-field darkroom, and complete the planar near-field scanning of the array antenna (101) to be tested by the probe (103) by controlling the scanning frame (104). Meanwhile, the absorbing material (102) is used to absorb the reflected interference in the environment, so that the probe (103) can collect more accurate near-field data of the mouth surface; Step 2. For f 1 =28GHz and f 2 =30.8 GHz aperture field data is collected, and the distance between the probe (103) and the aperture is d 0 =50mm, the scanning area of ​​the mouth surface is 32cm×32cm, with 0.5λ 1 is the sampling interval along the x and y directions of the antenna aperture for f 1 =28GHz frequency point to collect two-dimensional near-field data, λ 1 =c / f 1 , c is the speed of light; The collected data set is recorded as X 1 ; with 0.4λ 2 is the sampling interval along the x and y directions of the antenna aperture for f 2 =30.8 GHz frequency point to collect two-dimensional near-field data, and record the collected data set as X 2 ; l 2 =c / f 2 ; Step 3. Use the spatial convolution formula to transform the two frequency points f 1 =28GHz and f 2 = Aperture field data X at 30.8 GHz 1 and X 2 Perform convolution processing to obtain the distance d from the antenna aperture. 1 =20λ 1 = Data set X′ on the observation surface of 214.286 mm 1 , and the distance from the antenna aperture d 2 =1.1×20λ 1 = Data set X' on the observation surface of 235.714 mm 2 ; Step 4. Transform the dataset X′ 1 As a similar dataset that provides complete interpolation information; from dataset X' 2 Randomly select some sample data as the defective data set to be interpolated, denoted as X″ 2 ; Use K-means and Voronoi cell partitioning to calculate X″ 2 Perform feature partitioning and use X′ 1 The complete interpolation information provided is X″ 2 The feature area is interpolated and X″ 2 The interpolated data set is denoted as X″' 2 ; Step 5. At a distance d from the antenna 2 =1.1×20λ 1 =235.714mm, with 0.2λ 2 is the sampling interval, for f 2 = The two-dimensional diffraction field at the frequency point of 30.8 GHz is used for data collection, and the collected data set is recorded as X 3 ; Step 6. X 3 As a comparison data set, and the interpolated reconstructed X'" 2 Compare and calculate X 3 and X'" 2 The two-dimensional plane error and correlation coefficient between them are calculated, and accurate reconstruction results are obtained by using similarity principle and cluster interpolation method.

2. According to the method for reconstructing the diffraction field of an antenna aperture based on the similarity principle as described in claim 1, It is characterized in that In step 2, the two test frequency points f 1 =28GHz and f 2 =30.8GHz satisfies a multiple relationship of 1.1, and the antenna aperture field at the two frequency points is scanned in the near field, with a scanning distance d 0 =50mm, the scanning range along the x and y directions is (-16cm, 16cm); in order to satisfy the Nyquist sampling theorem and reduce the number of samples and test time, the scanning range is 0.5λ respectively. 1 and 0.4λ 2 is the sampling interval f 1 =28GHz and f 2 =30.8GHz aperture field data collection, and obtain the corresponding complete data set X 1 and X 2 .

3. According to the method for reconstructing the antenna aperture diffraction field based on the similarity principle as described in claim 2, It is characterized in that In step 3, since f 1 With f 2 There is a multiple correspondence relationship between them 2 / f 1 =1.1, so from the similarity principle of the aperture diffraction field, we can know that the frequency f 1 and f 2 The corresponding observation plane S 1 106 and S 2 The distance from 107 to the antenna aperture also needs to satisfy the multiple relationship d 2 / d 1 =1.1, then when S 1 The distance between 106 and the antenna aperture is d 1 =214.286mm, S 2 The distance between 107 and the antenna aperture should be d 2 =235.714mm; From the extrapolation formula of the aperture diffraction field, we know that if the tangential component of the antenna aperture field is E x (x',y') and E y (x',y'), then the two-dimensional tangential field component on a certain observation surface in space can be expressed as Among them, the constant z is the distance between the observation plane and the antenna aperture, k = 2π / λ, R is the Euclidean distance from a point in space to the aperture, and satisfies By observing equations (1) and (2), we find that the two equations differ only in the transformed field component, and the other parameters remain the same. Therefore, let f(x,y)=E x,y (x,y) (3) in, Substituting (3) and (4) into (1) and (2) for simplification, we can obtain F(x,y)=f(x,y)*g(x,y)=∫∫f(x',y')g(x-x',y-y')dx'dy' (5) Among them, f(x, y) represents the aperture field, g(x, y) represents the convolution kernel, and F(x, y) represents the tangential electric field component on the observation surface. Therefore, using formula (5), the aperture field can be transferred to the observation surface S 1 106 and S 2 The convolution process on 107 is used to obtain the distance d from the antenna aperture. 1 =20λ 1 = Data set X′ at 214.286 mm 1 , and the distance from the antenna aperture d 2 =1.1×20λ 1 = Data set X' at 235.714 mm 2 .

4. According to the method for reconstructing the antenna aperture diffraction field based on the similarity principle as claimed in claim 3, It is characterized in that In step 4, to simulate the impact of the instability of the test system on the data collection and storage process under complex conditions, it is necessary to perform a 2 Random data collection is performed. The random sampling process reflects the impact of system random errors on the measurement results. The data set after random sampling is recorded as X″ 2 , and the data set X′ 1 As a complete similarity data set for X″ 2 Interpolate the data to get X″ 2 Add more valid data information, due to the data set X″ 2 It is a set of feature points randomly extracted from a complete data set, so it is necessary to 2 The overall sampling data is clustered and the characteristics of the sampling points within each cluster are analyzed to obtain accurate interpolation results.

5. According to the method for reconstructing the diffraction field of an antenna aperture based on the similarity principle as claimed in claim 4, It is characterized in that Using K-means method to 2 Perform clustering and divide X″ 2 Divide it into several feature categories, and then use Voronoi cells to analyze the data features of the sample points in each cluster. 2 In the sample space, k are randomly selected n sample center points, then k corresponding n clustering results, and the i-th cluster A i (1≤i≤k n ) is denoted as a i , calculate the Euclidean distance between each cluster center and all sample points, and divide each sample into the cluster with the smallest Euclidean distance. Find the best sample center and clustering result through multiple iterations. The calculation method of the above cluster centers is as follows Among them, N i and x j Respectively represent the i-th cluster A i The total number of samples and the jth sample in the cluster, for the current number of clusters k n The corresponding clustering results calculate the overall sum of square errors within all clusters; Changing the number of clusters k n , recalculate the values ​​of (6) and (7) and convert the values ​​of Compare and select the ones with obvious numerical inflection point changes As the best clustering result, its corresponding k n The value is the optimal number of clusters.

6. The antenna aperture diffraction field reconstruction method based on similarity principle according to claim 5, It is characterized in that In order to further analyze the data characteristics of samples within each cluster and complete the corresponding data interpolation work for different feature areas, the Voronoi cell division method is used to calculate the characteristic parameters of the sample points in each cluster area. The calculated characteristic parameters include the cell area and the gradient between cells. Assuming that the current sample point is x m , then the corresponding cell area is s(x m ), and the cell area is normalized; Among them, M sum Represents data set X″ 2 The number of samples in the cell-to-cell gradient needs to be selected according to the current x m Multiple adjacent cells are calculated. Assume that one of the adjacent cells is x n , then the inter-cell gradient can be expressed as will be with x m The gradients between all adjacent cells are modulo summed to obtain Among them, N sum Represents x m The total number of adjacent cells, normalizing the cell gradient, can be obtained The above two parameters S(x m ) and D(x m ) and multiply each by the coefficient q 1 and q 2 , get a comprehensive parameter index L(x m )=q 1 (1+S(x m ))+q 2 (1+D(x m )) (12) For a cluster, the cell area or gradient parameter within the cluster may be close. By adjusting the weight coefficient of each parameter, the overall parameter index L(x m ), if L(x m ) is too large, it means that the sample point belongs to the under-sampling area, and the interpolation data near the sampling point should be increased. Otherwise, it belongs to the non-under-sampling area, and less interpolation data can meet the data needs of the area. After determining the under-sampling and non-under-sampling areas, the complete data set X′ is used to 1 X″ 2 Data interpolation is performed on each feature area to obtain the interpolated data set X″′ 2 .

7. The antenna aperture diffraction field reconstruction method based on similarity principle according to claim 6, It is characterized in that In step 5, in order to compare with the interpolated data set X″′ 2 To perform error analysis and comparison, it is necessary to 2 =235.714Gmm position with 0.2λ 2 f is the sampling interval 2 = Complete diffraction field data at 30.8GGHz, and the observation surface S in step 3 2 107 is the same distance from the mouth surface, and d 2 The complete theoretical diffraction field at the distance is denoted as X 3 .

8. According to the method for reconstructing the antenna aperture diffraction field based on similarity principle as claimed in claim 7, It is characterized in that In step 6, the interpolated data set X″′ 2 With observation surface S 2 The complete theoretical diffraction field on 107X 3 Perform two-dimensional error calculation, obtain the two-dimensional error distribution by calculating all sample differences on the entire two-dimensional plane, and 2 With X 3 Calculate the correlation Among them, v and w represent the overall sample number on the two-dimensional plane. By comparing the two-dimensional plane error and correlation coefficient, it can be shown that the complete similarity matrix X′ can be effectively used. 1 Complete the data missing matrix X″ 2 The data interpolation work is carried out and the result is very close to the complete theoretical diffraction field on the observation plane. The interpolation method saves the time required for f 2 The data measurement work at each frequency point effectively reduces the overall test time and cost.

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