CN107783086B - Method for diagnosing distorted position of antenna array aperture amplitude phase field - Google Patents

Method for diagnosing distorted position of antenna array aperture amplitude phase field Download PDF

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CN107783086B
CN107783086B CN201710966768.8A CN201710966768A CN107783086B CN 107783086 B CN107783086 B CN 107783086B CN 201710966768 A CN201710966768 A CN 201710966768A CN 107783086 B CN107783086 B CN 107783086B
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antenna
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CN107783086A (en
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陈玉林
胡元奎
于丁
张大海
范忠亮
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CETC 38 Research Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4004—Means for monitoring or calibrating of parts of a radar system
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/021—Auxiliary means for detecting or identifying radar signals or the like, e.g. radar jamming signals

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Abstract

The invention provides a method for diagnosing the distortion position of an antenna array aperture amplitude-phase field, which comprises the steps of firstly carrying out near field-plane spectrum transformation on near field data to obtain a plane spectrum component of a k space, then carrying out directional diagram correction of a probe and a unit on the k space plane spectrum, and finally carrying out plane spectrum-aperture field inverse transformation to obtain aperture field distribution. Finally, in order to obtain more accurate data, the aperture field needs to be reconstructed, and the amplitude-phase distribution of the actual physical position on the aperture surface is obtained, so that the position where the aperture field or the excitation current is distorted and the corresponding radiation unit are judged, and the purpose of diagnosing the antenna is achieved. The method can accurately position the position of the antenna failure unit, timely troubleshoot faults, save a large amount of test time, and improve the quality of the directional diagram in an inversion compensation mode. In addition, the invention uses Fast Fourier Transform (FFT) to carry out high-efficiency calculation, thereby having stronger engineering practicability.

Description

Method for diagnosing distorted position of antenna array aperture amplitude phase field
Technical Field
The invention relates to the technical field of antenna near field testing, in particular to a method for diagnosing the distortion position of an antenna array aperture amplitude phase field.
Background
In recent years, array antennas, and in particular phased array antennas, have been developed rapidly and are widely used in various military and civilian radio systems. At present, the research and development tasks of domestic array antennas, especially phased array antennas, are quite heavy, but due to the reasons of processing and manufacturing and the like, the antennas have a large number of inevitable errors in actual design, and besides, the vibration of the arrays, the coupling among antenna units, the aging of active devices, the change of temperature characteristics of the active devices and the like can introduce unpredictable errors into the antennas or cause failure units, so that the amplitude and phase of the radar antennas need to be diagnosed and debugged to determine the amplitude and phase distribution condition of currents on each radiation unit of the antennas.
At present, when a large array antenna is diagnosed and debugged in China, two methods are mainly used: the first is to approximate the antenna array with a probe, roughly measuring the area of failed elements or singular changes in the array. The method cannot accurately measure the amplitude-phase distribution of the antenna aperture surface, because a strong multiple reflection effect exists between the probe and the AUT, the effect changes along with the sampling motion of the probe on the scanning surface, so that a great diagnosis error is caused, and the method needs to continuously move the probe manually and record data manually, so that a great deal of labor and time cost is consumed. The second one is to use the caliber inversion module nested with the business software of the American NSI company to diagnose the caliber field amplitude phase, but the caliber inversion module is used as the business secret abroad, the principle and the source code are not disclosed, the external world can not know the inversion principle, mode and path, and can not learn, reference or even enhance and optimize on the basis; moreover, the caliber inversion module is mainly used on radars, relates to the national defense industry, and has the risk of radar parameter disclosure by completely using foreign software; finally, the caliber inversion module is packaged and exported as part of software, so that the caliber inversion module is expensive and cannot be independently applied at home. From the perspective of independent research and development, independent intellectual property, ensuring the confidentiality of radar test parameters, or from the perspective of secondary product development, reducing production cost and shortening manufacturing period, a set of technical scheme which is suitable for the actual needs of radars (antenna arrays) in China and has complete intellectual property is required to be provided, and only source codes compiled on the basis have safety and the backdoor is avoided.
Aiming at the problems, a large number of domestic scientific research institutions carry out beneficial research, exploration and attempt, and currently, an equivalent magnetic current method and a plane wave spectrum method are mainly used. However, in practical application, the method of the invention still has the limitation of use environment, specifically:
the main disadvantage of the equivalent magnetic current method is that the directional diagram of the probe is not corrected, so that the method is limited to be practical. In addition, in the method, because the limitation of the computer memory cannot consider the contribution of the equivalent magnetic current in the whole plane when the equivalent magnetic current is determined by the near-field data, the contribution of the equivalent magnetic current in the aperture surface or a slightly larger area of the antenna to be measured can only be considered, and the influence of the limited scanning surface in the plane near-field measurement is added, so that the accuracy of the aperture field distribution obtained by the method is limited. In addition, the method needs to solve a matrix equation when the equivalent magnetic current is determined by the near field data, so that when the aperture surface and the scanning surface of the antenna to be measured are both large, so that matrix elements are many, the calculation efficiency is not high, and the time cost is increased. The existing plane wave spectrum rule can be used only when the horizontal direction diagram and the vertical direction are both odd number of points. In actual antenna test, due to factors such as frequency, sampling surface, distance between the probe and the antenna, the number of sampling points may be even or odd, which causes the use of the traditional method in China to be greatly limited.
Disclosure of Invention
In order to solve the technical defects in the prior art, the invention provides a method for diagnosing the distorted position of the antenna array aperture amplitude-phase field.
The invention is realized by the following technical scheme:
the method is used for diagnosing the distortion position of an aperture amplitude phase field of an antenna array, wherein the antenna array comprises more than 4 radiation units, the radiation units respectively generate and emit excitation currents, and the excitation currents jointly form the aperture amplitude phase field; the method comprises the following steps:
the method comprises the following initial steps:
acquiring plane near-field test data of the antenna array;
a correction step:
performing near field-plane spectrum transformation of probe directional diagram correction on the plane near field test data to obtain a plane spectrum component of a k space subjected to probe correction and obtain a plane spectrum directional diagram of the k space subjected to correction;
and (3) inversion step:
carrying out plane spectrum-aperture field inverse transformation on the corrected plane spectrum directional diagram of the k space to obtain an inverted aperture amplitude phase field distribution diagram;
and (3) comparison:
and measuring the actual physical position of each radiation unit of the antenna array, and comparing the actual physical position of each radiation unit with the position in the inverted aperture amplitude-phase field distribution diagram to obtain the amplitude-phase distribution of each radiation unit of the antenna array, thereby judging the position where distortion occurs and the corresponding radiation unit.
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention can judge the distortion position of the aperture field or the excitation current and the corresponding radiation unit by measuring the distribution of the antenna near field and reversely deducing the distribution of the antenna aperture field or the excitation current of each radiation unit of the antenna, thereby achieving the purpose of 'diagnosing' the antenna.
(2) The method can accurately position the position of the antenna failure unit, timely troubleshoot faults, save a large amount of test time, and improve the quality of the directional diagram in an inversion compensation mode. In addition, the invention uses Fast Fourier Transform (FFT) to carry out high-efficiency calculation, thereby having stronger engineering practicability.
(3) The invention thoroughly overcomes the defect that when the large array antenna is diagnosed and debugged in China, the probe is mainly used for approaching the array surface of the antenna manually, and the invalid units or singular change areas in the array are roughly measured. The method solves the problem that the amplitude-phase distribution of the antenna aperture surface cannot be accurately measured by adopting the method, and greatly reduces the diagnosis error.
(4) The invention firstly provides a method for diagnosing the distortion position of the antenna array aperture amplitude-phase field by adopting a computer inversion mode, and breaks through the business monopoly of high-precision technology in China abroad. The technical scheme has high simulation degree, high inversion efficiency and wide application range, avoids errors caused by human introduction, and software based on the method has complete intellectual property and no risk of backdoor.
(5) The software based on the method can be independently operated on a computer, thereby reducing the purchase cost and having the upgrading advantages of redevelopment and redevelopment.
(6) The invention realizes the inversion and diagnosis of the antenna array surface amplitude phase in the plane near-field test, realizes the independent intellectual property right in the near-field diagnosis in China, can be nested in the near-field test system as an independent module, and lays a solid foundation for the construction of the near-field test system in China.
(7) The invention realizes the inversion and diagnosis of the antenna array surface amplitude phase in the plane near-field test, realizes the independent intellectual property right in the near-field diagnosis in China, can be nested in the near-field test system as an independent module, and lays a solid foundation for the construction of the near-field test system in China.
(8) The method overcomes the defects of an equivalent magnetic flow method and the existing plane wave spectrum method, considers the influence of a probe directional diagram, uses quick FFT conversion in the calculation process, is suitable for any type of sampling points, and has the advantages of high precision, high calculation speed, universality and the like. In other words, the invention can simultaneously solve the problems of low accuracy of array antenna aperture field amplitude-phase diagnosis, low calculation speed, poor algorithm applicability and the like.
Drawings
Fig. 1 is a general flow chart of the method for diagnosing the distorted position of the antenna array aperture phase field according to the present invention.
Fig. 2 is a diagram showing the correspondence between the probe coordinate system and the antenna coordinate system when the probe is horizontally linearly polarized.
FIG. 3 is a drawing showing
Figure GDA0002795964630000041
Schematic diagram of vector in space coordinate system.
Fig. 4 is a diagram showing the corresponding relationship between the probe coordinate system and the antenna coordinate system when the probe is vertically linearly polarized.
FIG. 5 is a drawing showing
Figure GDA0002795964630000042
Schematic diagram of vector in space coordinate system.
Fig. 6 is a three-dimensional amplitude pattern using embodiment 1 of the present invention.
Fig. 7 is a caliber field horizontal amplitude distribution curve of example 1 using the present invention.
Fig. 8 is a horizontal phase distribution curve of the aperture field of example 1 to which the present invention is applied.
Fig. 9 is a plot of the amplitude distribution to each cell for localization using example 1 of the present invention.
Fig. 10 is a three-dimensional amplitude pattern using embodiment 2 of the present invention.
Fig. 11 is a horizontal amplitude distribution curve of the aperture field of example 2 using the present invention.
FIG. 12 is a horizontal phase distribution curve of aperture field of example 2 using the present invention.
Figure 13 uses example 2 of the present invention to locate the amplitude profile to each cell.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, the method for diagnosing the distortion position of the aperture amplitude phase field of the antenna array comprises more than 4 radiation units, wherein the radiation units respectively generate and emit excitation currents, and the excitation currents jointly form the aperture amplitude phase field; the method is characterized by comprising the following steps:
step S1, initial step:
and acquiring plane near-field test data of the antenna array.
Step S2, correction step:
and performing near field-plane spectrum transformation of probe directional diagram correction on the plane near field test data to obtain a plane spectrum component of the k space subjected to probe correction, and obtaining a plane spectrum directional diagram of the k space subjected to correction.
Specifically, the correcting step specifically includes:
the main electric field polarization of the probe is oriented along the x direction, and the probe is scanned on a plane z ═ d, so that a function of the relation between near-field data acquired when the probe is horizontally polarized and an antenna spectrum is obtained:
Figure GDA0002795964630000051
wherein, the meaning of the parameter is that k is wave number;
Figure GDA0002795964630000052
Bxthe signal measured on the z-d plane when the probe is horizontally polarized; f [ B ]x]Is BxPerforming two-dimensional Fourier inverse transformation;
Figure GDA0002795964630000053
is the plane wave spectrum of the antenna and has
Figure GDA0002795964630000054
Figure GDA0002795964630000055
The plane wave spectrum when the probe is horizontally polarized is
Figure GDA0002795964630000056
Normalizing the function to a11Ax+a12Ay＝IxAn equation relating to the plane spectral component;
the main electric field polarization of the probe is oriented along the y direction, and the probe is scanned on a plane z ═ d, so that a function of the relation between near-field data acquired when the probe is vertically polarized and an antenna spectrum is obtained:
Figure GDA0002795964630000057
wherein the parameters are each ByThe signal measured on the z ═ d plane when the probe is vertically polarized; f [ B ]y]Is ByPerforming two-dimensional Fourier inverse transformation;
Figure GDA0002795964630000058
the plane wave spectrum when the probe is vertically polarized is
Figure GDA0002795964630000059
Normalizing the function to a21Ax+a22Ay＝IyAnother equation for the plane spectral component;
the 2 equations of the plane spectral components are combined to obtain the following system of equations:
Figure GDA00027959646300000510
a can be obtained by the above formulaxAnd AyFurther, it obtains AzThereby obtaining the plane wave spectrum after the directional diagram correction of the probe
Figure GDA00027959646300000511
Tangential component of
Figure GDA00027959646300000512
Further obtain
Figure GDA00027959646300000513
The value of (c).
In other words, in step S1, the main electric field of the probe is scanned in only one direction, so that no plane spectrum component is obtained, and only if the two cases are combined to form a two-dimensional equation set, the plane spectrum can be obtained.
Further, the correcting step further comprises:
referring to fig. 2, let B be the signal measured when the probe main electric field polarization is oriented in the x-direction and scanned on the z-d planex(x, y, d), the coupling formula measured by the planar near-field antenna can be obtained
Figure GDA0002795964630000061
Wherein k is the wave number; k is a radical ofzIs the component of k in the z direction;
Figure GDA0002795964630000062
is a vector in the k direction;
Figure GDA0002795964630000063
is the plane wave spectrum of the antenna;
Figure GDA0002795964630000064
the plane wave spectrum when the probe is horizontally polarized; f [ B ]x(x,y,d)]Is BxThe two-dimensional inverse Fourier transform of (x, y, d) is as follows:
Figure GDA0002795964630000065
wherein pi is 3.14159; k is a radical ofxAnd kyX and y components of k, respectively;
the relationship between the probe coordinate system and the antenna coordinate system is as follows:
Figure GDA0002795964630000066
with reference to figure 3 of the drawings,
Figure GDA0002795964630000067
the relation of the vector in the space coordinate system is as follows:
Figure GDA0002795964630000068
here, the first and second liquid crystal display panels are,
Figure GDA0002795964630000069
is composed of
Figure GDA00027959646300000610
A unit vector of (a);
while
Figure GDA00027959646300000611
Then, the equations 303, 304 and 305 can be used,
Figure GDA00027959646300000612
from the above formula, one can obtain:
Figure GDA00027959646300000613
namely, the method comprises the following steps:
Figure GDA0002795964630000071
then in (formula 301)
Figure GDA0002795964630000072
It can be in the form of:
Figure GDA0002795964630000073
of formula (II) to'θ′Is composed of
Figure GDA0002795964630000074
In that
Figure GDA0002795964630000075
The component of the direction is that of the direction,
Figure GDA0002795964630000076
is composed of
Figure GDA0002795964630000077
In that
Figure GDA0002795964630000078
A component of direction;
by substituting formula 309 into formula 301 and then obtaining formula 303
Figure GDA0002795964630000079
Because the antenna is located in the passive area during the test, there are:
Figure GDA00027959646300000710
and because the relation between the electric field and the spectrum is:
Figure GDA00027959646300000711
in the formula, a0Represents the complex amplitude of the incident wave;
by substituting formula 312 into formula 311
Figure GDA00027959646300000712
Namely, it is
Figure GDA00027959646300000713
Namely, it is
Figure GDA00027959646300000714
Then can obtain
Figure GDA00027959646300000715
Will be provided with
Figure GDA00027959646300000716
In the formula 310, there are:
Figure GDA0002795964630000081
from formula 309 can give A'x′，A′y′，A′z′And A'θ′，
Figure GDA00027959646300000818
The relationship of (1) is:
Figure GDA0002795964630000082
Figure GDA0002795964630000083
A′z′＝-A′θ′sin theta' (formula 320)
Because the far field pattern of the probe can be approximated by:
Figure GDA0002795964630000084
also, we know that the relationship between the normalized far-field pattern function and the plane spectrum is:
Figure GDA0002795964630000085
therefore:
Figure GDA0002795964630000086
Figure GDA0002795964630000087
in the above two formulas, the first and second groups,
Figure GDA0002795964630000088
is far field pattern
Figure GDA0002795964630000089
A component at θ';
Figure GDA00027959646300000810
is far field pattern
Figure GDA00027959646300000811
In that
Figure GDA00027959646300000812
Component of (a), (b), (c) and (d)E(theta') and fH(θ') normalizing the far field pattern functions for the E-plane and the H-plane of the probe, respectively; then there is
Figure GDA00027959646300000813
Figure GDA00027959646300000814
When the above two formulas are substituted into the formulas 318, 319 and 320, there are
Figure GDA00027959646300000815
Figure GDA00027959646300000816
Figure GDA00027959646300000817
Order to
Figure GDA0002795964630000091
Figure GDA0002795964630000092
Figure GDA0002795964630000093
Equation 317 may be in the form:
a11Ax+a12Ay＝Ix(formula 333)
The above equation is an equation for the planar spectral component, and the equation has two unknowns AxAnd AyThe probe is required to rotate once to measure and then an equation is established to solve simultaneously to obtain AxAnd Ay。
Further, the correcting step further comprises:
let the main probe electric field polarization be oriented in the y-direction and the measured signal when scanning on the z-d plane be By(x, y, d), then the coupling equation measured by the planar near-field antenna can be derived:
Figure GDA0002795964630000094
in the formula (I), the compound is shown in the specification,
Figure GDA0002795964630000095
the plane wave spectrum is obtained when the probe is vertically polarized;
Figure GDA0002795964630000096
is By(x, y, d) is inverse two-dimensional Fourier transform, namely
Figure GDA0002795964630000097
Referring to fig. 4, in this case, that is, in the case where equation 401 corresponds to, the relationship between the probe coordinate system and the antenna coordinate system is:
Figure GDA0002795964630000098
with reference to figure 5 of the drawings,
Figure GDA0002795964630000099
the vector is in a space coordinate system:
then
Figure GDA00027959646300000910
And under the current coordinate system, the coordinate system,
Figure GDA00027959646300000911
then, from equations 403, 404 and 405,
Figure GDA0002795964630000101
can be obtained from the above formula
Figure GDA0002795964630000102
Namely have
Figure GDA0002795964630000103
Then in formula 401
Figure GDA0002795964630000104
It can be in the form of:
Figure GDA0002795964630000105
in the formula, Aθ"is a
Figure GDA0002795964630000106
In that
Figure GDA0002795964630000107
The component of the direction is that of the direction,
Figure GDA0002795964630000108
is composed of
Figure GDA0002795964630000109
In that
Figure GDA00027959646300001010
A component of direction;
by substituting formula 409 into formula 401 and then obtaining formula 403, the following formula can be obtained
Figure GDA00027959646300001011
Will be provided with
Figure GDA00027959646300001013
Substituting the formula into the formula, then:
Figure GDA00027959646300001012
a "obtained from formula 409x″，A″y″，A″z″And A ″)θ″，
Figure GDA0002795964630000111
In a relationship of
Figure GDA0002795964630000112
Figure GDA0002795964630000113
A″z″＝-A″θ″sin theta' (formula 414)
And because the far field pattern of the probe can be approximated by:
Figure GDA0002795964630000114
also, we know that the relationship between the normalized far-field pattern function and the plane spectrum is:
Figure GDA0002795964630000115
therefore, it is not only easy to use
Figure GDA0002795964630000116
Figure GDA0002795964630000117
In the above two formulas, the first and second groups,
Figure GDA0002795964630000118
is far field pattern
Figure GDA0002795964630000119
A component at θ ";
Figure GDA00027959646300001110
is far field pattern
Figure GDA00027959646300001111
In that
Figure GDA00027959646300001112
Component of (a), (b), (c) and (d)E(theta') and fH(θ ") normalizing the far field pattern functions for the E-plane and the H-plane of the probe, respectively; so that there are
Figure GDA00027959646300001113
Figure GDA00027959646300001114
When the above two formulas are substituted into the formulas 412, 413 and 414, there are
Figure GDA00027959646300001115
Figure GDA00027959646300001116
Figure GDA00027959646300001117
Order to
Figure GDA00027959646300001118
Figure GDA0002795964630000121
Figure GDA0002795964630000122
Equation 411 may be in the form: a is21Ax+a22Ay＝Iy(formula 427).
Combining 333 with 427, the system of equations is obtained as follows:
Figure GDA0002795964630000123
a can be obtained by the above formulaxAnd AyFurther, it obtains AzThereby obtaining the plane wave spectrum after the directional diagram correction of the probe
Figure GDA0002795964630000124
Tangential component of
Figure GDA0002795964630000125
Further obtain
Figure GDA0002795964630000126
The value of (c).
Step S3, inversion step:
and carrying out plane spectrum-aperture field inverse transformation on the corrected plane spectrum directional diagram of the k space to obtain an inverted aperture amplitude phase field distribution diagram.
Specifically, the inversion step specifically includes:
obtaining the plane wave spectrum after the probe directional diagram correction
Figure GDA0002795964630000127
Tangential component of
Figure GDA0002795964630000128
And calculating the tangential component of the plane near field, and extracting the value of the plane near field at each unit position on the array antenna aperture surface, wherein the specific implementation mode is as follows:
from the planar wave expansion of the field generated by the antenna, the tangential component of the electric field in the z-h plane is obtained
Figure GDA0002795964630000129
Will be parameter
Figure GDA00027959646300001210
By Fourier transformation, into tangential components of the electric field
Figure GDA00027959646300001211
Further, the parameters are
Figure GDA00027959646300001212
Through Fourier transform into
Figure GDA00027959646300001213
The method comprises the following specific steps:
Figure GDA00027959646300001214
wherein, Deltax is the sampling interval in the x direction, Deltay is the sampling interval in the y direction, N is the number of sampling points in the x direction, M is the number of sampling points in the y direction,
Figure GDA00027959646300001215
so that the tangential component of the electric field at each uniform grid point on the z-h plane is
Figure GDA0002795964630000131
In the formula, p and q are integers and are numbers corresponding to each sampling point;
Figure GDA0002795964630000132
if h is 0, an array is obtainedThe tangential electric field on the antenna aperture surface can obtain the inverted aperture amplitude phase field distribution
Figure GDA0002795964630000133
Step S4, comparison step.
And measuring the actual physical position of each radiation unit of the antenna array, and comparing the actual physical position of each radiation unit with the position in the inverted aperture amplitude-phase field distribution diagram to obtain the amplitude-phase distribution of each radiation unit of the antenna array, thereby judging the position where distortion occurs and the corresponding radiation unit.
And after inversion, obtaining 2 sets of three-dimensional data about position and amplitude phase values, wherein one set is an amplitude value, and the other set is a phase value, and inserting the position of the radiation unit into the three-dimensional data through an interpolation method to obtain the amplitude phase value of each radiation unit.
Specifically, the comparison step specifically comprises:
measuring the actual physical position of each radiating element of the antenna array, and carrying out the inversion step
Figure GDA0002795964630000134
And (4) carrying out interpolation to obtain the amplitude-phase distribution of each radiation unit of the antenna array, and further judging the position where distortion occurs and the corresponding radiation unit.
Example 1
In order to ensure the accuracy of the diagnosis method provided by the invention on the diagnosis of the wavefront failure unit, the test is carried out on a certain L-waveband vertical linear polarization antenna in a darkroom. The number of horizontal elements of the tested wavefront was 42, the horizontal element pitch was 0.138m, the number of elements in the vertical direction was 1, and the test frequency was 990 Mhz. And introducing failure units at the 36 th unit position and the 40 th unit position simultaneously, testing and carrying out inversion diagnosis by using a program algorithm, wherein the obtained results and analysis are as follows:
fig. 6 is a three-dimensional stereo amplitude pattern, and fig. 7 and 8 are a caliber field horizontal amplitude distribution graph and a caliber field horizontal phase distribution graph, respectively. Fig. 9 is a graph of the amplitude distribution localized to each cell.
As can be seen from fig. 7 and 8, after the introduction of the failure unit, the corresponding amplitude phase distribution is changed, and the amplitude value is significantly decreased at the corresponding position. The positions of the failed unit can be accurately diagnosed as 36 th and 40 th units from the positioning graph 9, so that the correctness of the algorithm for diagnosing the failed unit is proved.
Example 2
And (3) carrying out failure unit diagnosis test on a certain S-band array antenna, wherein the test frequency is 3140MHz, the number of horizontal units is 128, and the unit interval is 0.046 m. And (4) directly introducing a failure unit at the positions of the 5 th unit and the 100 th unit, and carrying out near-field active state testing. The inversion diagnosis result and analysis of the test result by using the invention are as follows:
fig. 10, 11, and 12 are an aperture field amplitude distribution diagram, an aperture field horizontal amplitude distribution diagram, and an aperture field horizontal phase distribution diagram, respectively. Fig. 13 is a graph of the amplitude distribution localized to each cell.
Fig. 10-12 reflect the aperture field distribution after introduction of the failed element, and the location of the failed element can be substantially determined. The positioning curves in fig. 13 accurately diagnose the positions of the failed units as the 5 th and 100 th units, thereby further proving the accuracy of the algorithm of the present invention in diagnosing the failed units.
Compared with the prior art, the beneficial effects of the invention are shown in table 1:
table 1 advantageous effects of the invention over the prior art
Figure GDA0002795964630000141
Figure GDA0002795964630000151
It will be understood by those skilled in the art that the foregoing is merely a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included within the scope of the present invention.

Claims (3)

1. The method is used for diagnosing the distortion position of an aperture amplitude phase field of an antenna array, wherein the antenna array comprises more than 4 radiation units, the radiation units respectively generate and emit excitation currents, and the excitation currents jointly form the aperture amplitude phase field; the method is characterized by comprising the following steps:
the method comprises the following initial steps:
acquiring plane near-field test data of the antenna array;
a correction step:
performing near field-plane spectrum transformation of probe directional diagram correction on the plane near field test data to obtain a plane spectrum component of a k space subjected to probe correction and obtain a plane spectrum directional diagram of the k space subjected to correction;
the correction step specifically comprises:
the main electric field polarization of the probe is oriented along the x direction, and the probe is scanned on a plane z ═ d, so that a function of the relation between near-field data acquired when the probe is horizontally polarized and an antenna spectrum is obtained:
Figure FDA0002795964620000011
wherein, the meaning of the parameter is that k is wave number;
Figure FDA0002795964620000012
Bxthe signal measured on the z-d plane when the probe is horizontally polarized; f [ B ]x]Is BxPerforming two-dimensional Fourier inverse transformation;
Figure FDA0002795964620000013
is the plane wave spectrum of the antenna and has
Figure FDA0002795964620000014
Figure FDA0002795964620000015
The plane wave spectrum when the probe is horizontally polarized is
Figure FDA0002795964620000016
Normalizing the function to a11Ax+a12Ay＝IxAn equation relating to the plane spectral component;
the main electric field polarization of the probe is oriented along the y direction, and the probe is scanned on a plane z ═ d, so that a function of the relation between near-field data acquired when the probe is vertically polarized and an antenna spectrum is obtained:
Figure FDA0002795964620000017
wherein the parameters are each ByThe signal measured on the z ═ d plane when the probe is vertically polarized; f [ B ]y]Is ByPerforming two-dimensional Fourier inverse transformation;
Figure FDA0002795964620000018
the plane wave spectrum when the probe is vertically polarized is
Figure FDA0002795964620000019
Normalizing the function to a21Ax+a22Ay＝IyAnother equation for the plane spectral component;
the 2 equations of the plane spectral components are combined to obtain the following system of equations:
Figure FDA0002795964620000021
a can be obtained by the above formulaxAnd AyFurther, it obtains AzThereby obtaining the plane wave spectrum after the directional diagram correction of the probe
Figure FDA0002795964620000022
Tangential component of
Figure FDA0002795964620000023
Further obtain
Figure FDA0002795964620000024
A value of (d);
the correcting step further comprises:
let the main electric field polarization of the probe be oriented in the x-direction and the measured signal when scanning on the z-d plane be Bx(x, y, d), the coupling formula measured by the planar near-field antenna can be obtained
Figure FDA0002795964620000025
Wherein k is the wave number; k is a radical ofzIs the component of k in the z direction;
Figure FDA0002795964620000026
is a vector in the k direction;
Figure FDA0002795964620000027
is the plane wave spectrum of the antenna;
Figure FDA0002795964620000028
the plane wave spectrum when the probe is horizontally polarized; f [ B ]x(x,y,d)]Is BxThe two-dimensional inverse Fourier transform of (x, y, d) is as follows:
Figure FDA0002795964620000029
wherein pi is 3.14159; k is a radical ofxAnd kyX and y being respectively kAn amount;
the relationship between the probe coordinate system and the antenna coordinate system is as follows:
Figure FDA00027959646200000210
Figure FDA00027959646200000211
the relation of the vector in the space coordinate system is as follows:
Figure FDA00027959646200000212
here, the first and second liquid crystal display panels are,
Figure FDA00027959646200000213
is composed of
Figure FDA00027959646200000214
A unit vector of (a);
while
Figure FDA00027959646200000215
Then, the equations 303, 304 and 305 can be used,
Figure FDA0002795964620000031
from the above formula, one can obtain:
Figure FDA0002795964620000032
namely, the method comprises the following steps:
Figure FDA0002795964620000033
then in (formula 301)
Figure FDA0002795964620000034
It can be in the form of:
Figure FDA0002795964620000035
of formula (II) to'θ′Is composed of
Figure FDA0002795964620000036
In that
Figure FDA0002795964620000037
The component of the direction is that of the direction,
Figure FDA0002795964620000038
is composed of
Figure FDA0002795964620000039
In that
Figure FDA00027959646200000310
A component of direction;
by substituting formula 309 into formula 301 and then obtaining formula 303
Figure FDA00027959646200000311
Because the antenna is located in the passive area during the test, there are:
Figure FDA00027959646200000312
and because the relation between the electric field and the spectrum is:
Figure FDA00027959646200000313
in the formula, a0Represents the complex amplitude of the incident wave;
by substituting formula 312 into formula 311
Figure FDA0002795964620000041
Namely, it is
Figure FDA0002795964620000042
Namely, it is
Figure FDA0002795964620000043
Then can obtain
Figure FDA0002795964620000044
Will be provided with
Figure FDA0002795964620000045
In the formula 310, there are:
Figure FDA0002795964620000046
from formula 309 can give A'x′，A′y′，A′z′And A'θ′，
Figure FDA0002795964620000047
The relationship of (1) is:
Figure FDA0002795964620000048
Figure FDA0002795964620000049
A′z′＝-A′θ′sin theta' (formula 320)
Because the far field pattern of the probe can be approximated by:
Figure FDA00027959646200000410
also, we know that the relationship between the normalized far-field pattern function and the plane spectrum is:
Figure FDA00027959646200000411
therefore:
Figure FDA00027959646200000412
Figure FDA00027959646200000413
in the above two formulas, the first and second groups,
Figure FDA00027959646200000414
is far field pattern
Figure FDA00027959646200000415
At theta′A component of (a);
Figure FDA00027959646200000416
is far field pattern
Figure FDA00027959646200000417
In that
Figure FDA00027959646200000418
Component of (a), (b), (c) and (d)E(theta') and fH(θ') normalizing the far field pattern functions for the E-plane and the H-plane of the probe, respectively; then there is
Figure FDA00027959646200000419
Figure FDA0002795964620000051
When the above two formulas are substituted into the formulas 318, 319 and 320, there are
Figure FDA0002795964620000052
Figure FDA0002795964620000053
Figure FDA0002795964620000054
Order to
Figure FDA0002795964620000055
Figure FDA0002795964620000056
Figure FDA0002795964620000057
Equation 317 may be in the form:
a11Ax+a12Ay＝Ix(formula 333)
The above equation is an equation for the planar spectral component;
the correcting step further comprises:
let the main probe electric field polarization be oriented in the y-direction and the measured signal when scanning on the z-d plane be By(x, y, d), then the coupling equation measured by the planar near-field antenna can be derived:
Figure FDA0002795964620000058
in the formula (I), the compound is shown in the specification,
Figure FDA0002795964620000059
the plane wave spectrum is obtained when the probe is vertically polarized; f [ B ]y(x,y,d)]Is By(x, y, d) is inverse two-dimensional Fourier transform, namely
Figure FDA00027959646200000510
In this case, that is, in the case where equation 401 corresponds to, the relationship between the probe coordinate system and the antenna coordinate system is:
Figure FDA00027959646200000511
Figure FDA00027959646200000512
the vector is in a space coordinate system:
then
Figure FDA0002795964620000061
And under the current coordinate system, the coordinate system,
Figure FDA0002795964620000062
then, from equations 403, 404 and 405,
Figure FDA0002795964620000063
can be obtained from the above formula
Figure FDA0002795964620000064
Namely have
Figure FDA0002795964620000065
Then in formula 401
Figure FDA0002795964620000066
It can be in the form of:
Figure FDA0002795964620000067
in the formula, A ″)θ″Is composed of
Figure FDA0002795964620000068
In that
Figure FDA0002795964620000069
The component of the direction is that of the direction,
Figure FDA00027959646200000610
is composed of
Figure FDA00027959646200000611
In that
Figure FDA00027959646200000612
A component of direction;
by substituting formula 409 into formula 401 and then obtaining formula 403, the following formula can be obtained
Figure FDA00027959646200000613
Will be provided with
Figure FDA0002795964620000071
Substituting the formula into the formula, then:
Figure FDA0002795964620000072
a "obtained from formula 409x″，A″y″，A″z″And A ″)θ″，
Figure FDA0002795964620000073
In a relationship of
Figure FDA0002795964620000074
Figure FDA0002795964620000075
A″z″＝-A″θ″sin theta' (formula 414)
And because the far field pattern of the probe can be approximated by:
Figure FDA0002795964620000076
also, we know that the relationship between the normalized far-field pattern function and the plane spectrum is:
Figure FDA0002795964620000077
therefore, it is not only easy to use
Figure FDA0002795964620000078
Figure FDA0002795964620000079
In the above two formulas, the first and second groups,
Figure FDA00027959646200000710
is far field pattern
Figure FDA00027959646200000711
A component at θ ";
Figure FDA00027959646200000712
is far field pattern
Figure FDA00027959646200000713
In that
Figure FDA00027959646200000714
Component of (a), (b), (c) and (d)E(theta') and fH(θ ") normalizing the far field pattern functions for the E-plane and the H-plane of the probe, respectively; so that there are
Figure FDA00027959646200000715
Figure FDA00027959646200000716
When the above two formulas are substituted into the formulas 412, 413 and 414, there are
Figure FDA00027959646200000717
Figure FDA00027959646200000718
Figure FDA00027959646200000719
Order to
Figure FDA0002795964620000081
Figure FDA0002795964620000082
Figure FDA0002795964620000083
Equation 411 may be in the form: a is21Ax+a22Ay＝Iy(formula 427);
and (3) inversion step:
carrying out plane spectrum-aperture field inverse transformation on the corrected plane spectrum directional diagram of the k space to obtain an inverted aperture amplitude phase field distribution diagram;
and (3) comparison:
and measuring the actual physical position of each radiation unit of the antenna array, and comparing the actual physical position of each radiation unit with the position in the inverted aperture amplitude-phase field distribution diagram to obtain the amplitude-phase distribution of each radiation unit of the antenna array, thereby judging the position where distortion occurs and the corresponding radiation unit.
2. The method for diagnosing the distorted position of the antenna array aperture phase field as claimed in claim 1, wherein the inverting step specifically comprises:
obtaining the plane wave spectrum after the probe directional diagram correction
Figure FDA0002795964620000084
Tangential component of
Figure FDA0002795964620000085
And calculating the tangential component of the plane near field, and extracting the value of the plane near field at each unit position on the array antenna aperture surface, wherein the specific implementation mode is as follows:
from the planar wave expansion of the field generated by the antenna, the tangential component of the electric field in the z-h plane is obtained
Figure FDA0002795964620000086
Will be parameter
Figure FDA0002795964620000087
By Fourier transformation, into tangential components of the electric field
Figure FDA0002795964620000088
Further, the parameters are
Figure FDA0002795964620000089
Through Fourier transform into
Figure FDA00027959646200000810
The method comprises the following specific steps:
Figure FDA00027959646200000811
in the formula, Δ x is the sampling interval in the x direction, Δ y is the sampling interval in the y direction, N is the number of sampling points in the x direction, and M is the number of sampling points in the x directionThe number of sampling points in the y-direction,
Figure FDA0002795964620000091
so that the tangential component of the electric field at each uniform grid point on the z-h plane is
Figure FDA0002795964620000092
In the formula, p and q are integers and are numbers corresponding to each sampling point;
Figure FDA0002795964620000093
if h is 0, the tangential electric field on the aperture surface of the array antenna can be obtained, and the inverted aperture amplitude-phase field distribution can be obtained
Figure FDA0002795964620000094
3. The method for diagnosing the distorted position of an antenna array aperture phase field as claimed in claim 1, wherein the comparing step specifically comprises:
measuring the actual physical position of each radiating element of the antenna array, and carrying out the inversion step
Figure FDA0002795964620000095
And (4) carrying out interpolation to obtain the amplitude-phase distribution of each radiation unit of the antenna array, and further judging the position where distortion occurs and the corresponding radiation unit.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10536226B1 (en) * 2018-07-16 2020-01-14 Litepoint Corporation System and method for over-the-air (OTA) testing to detect faulty elements in an active array antenna of an extremely high frequency (EHF) wireless communication device
CN109521374B (en) * 2018-10-18 2020-10-27 北京航空航天大学 Resonance tangential electric field probe embedded with integrated balun and loaded improved dipole
CN111044802A (en) * 2019-12-04 2020-04-21 上海霍莱沃电子系统技术股份有限公司 Phased array antenna unit amplitude and phase balancing method and device based on aperture field
CN111812418B (en) * 2020-07-17 2021-09-28 中国汽车工程研究院股份有限公司 Tire pressure monitoring antenna performance testing system and method
US11982761B2 (en) * 2021-06-22 2024-05-14 Src, Inc. Method for calibrating a phased array
CN113589051A (en) * 2021-08-04 2021-11-02 西安电子科技大学 Clutter suppression field electromagnetic measurement device and method
CN118501563A (en) * 2023-02-06 2024-08-16 中兴通讯股份有限公司 Planar near field test method and device, electronic equipment and readable storage medium

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5343204A (en) * 1993-07-29 1994-08-30 Unisys Corporation Auto-focusing correction for rotational acceleration effects on inverse synthetic aperture radar images
GB2318941A (en) * 1996-10-07 1998-05-06 Advantest Corp Radio hologram image reconstruction using fast fourier transforms
CN1664611A (en) * 2005-03-24 2005-09-07 武汉大学 Method for correcting passive channels based on non-linear antenna array
CN103411528A (en) * 2013-08-26 2013-11-27 中国科学院空间科学与应用研究中心 Method for calculating electric field probe rotation offset through circular polarization antenna axial ratio directional diagram
CN103424066A (en) * 2013-08-26 2013-12-04 中国科学院空间科学与应用研究中心 Method for using circularly polarized antenna far field phase difference for calculating rotation offset of electric field probe
CN103698753A (en) * 2013-12-19 2014-04-02 武汉大学 Passive passage correcting method of small-size array
CN104765022A (en) * 2015-03-18 2015-07-08 中船重工鹏力（南京）大气海洋信息系统有限公司 Methods for characteristic value probability statistics model establishment and antenna self-check based on echo spectra
CN105717493A (en) * 2016-03-17 2016-06-29 哈尔滨工程大学 Passive radar radiation source polarization identification and direction-finding system based on synthesis polarization method
CN106526562A (en) * 2016-10-17 2017-03-22 西北工业大学 Antenna directional pattern-based method for correcting RCS of calculation target

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5809063A (en) * 1996-10-25 1998-09-15 General Electric Company Coherent detection architecture for remote calibration of coherent systems using direct sequence spread spectrum transmission of reference and calibration signals
US5726656A (en) * 1996-12-19 1998-03-10 Hughes Electronics Atmospheric correction method for interferometric synthetic array radar systems operating at long range
CN104063544B (en) * 2014-06-25 2017-11-24 电子科技大学 Near-field effect error analysis method
CN106169654B (en) * 2016-06-08 2019-03-08 中国电子科技集团公司第三十八研究所 A kind of broadband active multibeam antenna system
CN106546828A (en) * 2016-10-31 2017-03-29 西北工业大学 A kind of sphere Multi probe antenna measurement data processing method based on microwave network analysis

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5343204A (en) * 1993-07-29 1994-08-30 Unisys Corporation Auto-focusing correction for rotational acceleration effects on inverse synthetic aperture radar images
GB2318941A (en) * 1996-10-07 1998-05-06 Advantest Corp Radio hologram image reconstruction using fast fourier transforms
CN1664611A (en) * 2005-03-24 2005-09-07 武汉大学 Method for correcting passive channels based on non-linear antenna array
CN103411528A (en) * 2013-08-26 2013-11-27 中国科学院空间科学与应用研究中心 Method for calculating electric field probe rotation offset through circular polarization antenna axial ratio directional diagram
CN103424066A (en) * 2013-08-26 2013-12-04 中国科学院空间科学与应用研究中心 Method for using circularly polarized antenna far field phase difference for calculating rotation offset of electric field probe
CN103698753A (en) * 2013-12-19 2014-04-02 武汉大学 Passive passage correcting method of small-size array
CN104765022A (en) * 2015-03-18 2015-07-08 中船重工鹏力（南京）大气海洋信息系统有限公司 Methods for characteristic value probability statistics model establishment and antenna self-check based on echo spectra
CN105717493A (en) * 2016-03-17 2016-06-29 哈尔滨工程大学 Passive radar radiation source polarization identification and direction-finding system based on synthesis polarization method
CN106526562A (en) * 2016-10-17 2017-03-22 西北工业大学 Antenna directional pattern-based method for correcting RCS of calculation target

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
《Near-field probe used as a diagnostic tool to locate defective elements in an array antenna》;J.J. Lee ; E.M. Ferren ; D.P. Woollen ; K.M. Lee;《 IEEE Transactions on Antennas and Propagation》;19880630;第36卷(第6期);884-889 *
《带探头补偿近场-口径场的反演与诊断》;陈玉林、李刚;《雷达科学与技术》;20131215(第6期);第668-670页 *
《平面近场测量和诊断技术的研究》;潘宇虎;《中国优秀博硕士学位论文全文数据库 (硕士) 信息科技辑》;20050815(第4期);第5页、第18页和第25-26页 *
《平面近场测量技术及误差分析》;王彬虎;《中国优秀硕士学位论文全文数据库 信息科技辑》;20111215(第S2期);I136-8 *
潘宇虎.《平面近场测量和诊断技术的研究》.《中国优秀博硕士学位论文全文数据库 (硕士) 信息科技辑》.2005,(第4期),第5页、第18页和第25-26页. *

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