CN115524541B - Arbitrary polarization line antenna array directional diagram measuring method based on quasi-far-field mode filtering - Google Patents

Arbitrary polarization line antenna array directional diagram measuring method based on quasi-far-field mode filtering Download PDF

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CN115524541B
CN115524541B CN202211496612.5A CN202211496612A CN115524541B CN 115524541 B CN115524541 B CN 115524541B CN 202211496612 A CN202211496612 A CN 202211496612A CN 115524541 B CN115524541 B CN 115524541B
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CN115524541A (en
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栗曦
张鹏
韩伟
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Shaanxi Shibei Communication Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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Abstract

The invention discloses a method for measuring an arbitrary polarization line antenna array directional diagram based on quasi-far field mode filtering, which is characterized by comprising the following technical steps of: the method comprises the following steps: determining a quasi-far field measurement distance of an antenna to be measured; step two: measuring the amplitude and phase on a surface at the quasi-far field position of the antenna; step three: correcting the detected directional diagram by a far-field directional diagram reconstruction technology; step four: and obtaining a final far-field directional diagram by a quasi-far-field mathematical absorption reflection suppression technology. The method is particularly suitable for quickly and accurately measuring the single-tangent-plane far-field pattern of the linear antenna, the linear antenna usually has a one-dimensional large size and a one-dimensional small size, and the linear antenna has good performance in the environment with scattering interference sources.

Description

Arbitrary polarization line antenna array directional diagram measuring method based on quasi-far-field mode filtering
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to a method for measuring an arbitrary polarization line antenna array directional diagram based on quasi-far field mode filtering.
Background
Linear antenna arrays with arbitrary polarization characteristics, such as 45 ° polarized base station antennas, typically have one dimension large and another dimension small; far-field measurements are faster and more efficient than near-field measurements. The Chinese patent with the granted publication number of CN 114966239B discloses a quasi-far-field measurement method based on separable excitation coefficient variables, which increases the universality of a quasi-far-field extrapolation algorithm: the method for measuring the two-dimensional antenna array based on cylindrical wave expansion increases the universality of a quasi far-field extrapolation algorithm, and the finally obtained far-field directional pattern of the antenna is accurate; the antenna test efficiency is obviously improved: the antenna test system is used for measuring in the quasi-far field range of the antenna to be tested, so that the problems of large test distance and low near field measurement efficiency required by far field measurement are solved, and the antenna test efficiency is remarkably improved. The measuring distance is significantly reduced: the distance between the antenna to be tested and the probe only needs to meet the quasi-far field condition, the testing distance is obviously reduced, and the cost of darkroom construction is greatly saved. However, this method is susceptible to interference from surface scattering of bare metal or walls and the like. For these antennas, developers have focused on only single-section far-field patterns (usually in the E and H planes), and therefore, it is necessary to have an efficient method for making measurements that meets the above requirements and does not require the use of large microwave darkrooms and can avoid multipath interference.
Disclosure of Invention
The invention aims to provide a method for measuring an arbitrary polarized linear antenna array directional diagram based on quasi far field mode filtering, so as to solve the problems in the prior art.
In order to achieve the above purpose, the invention provides the following technical scheme: the method for measuring the directional diagram of the arbitrary polarized linear antenna array based on the quasi-far field mode filtering comprises the following technical steps:
the method comprises the following steps: determining a quasi-far field measurement distance of an antenna to be measured;
step two: measuring the amplitude and phase on a surface at the quasi-far field position of the antenna;
step three: correcting the detected directional diagram by a far-field directional diagram reconstruction technology;
step four: and obtaining a final far-field directional diagram by a quasi-far-field mathematical absorption reflection suppression technology.
Preferably, in the first step, the distance between the antenna to be tested and the test probe is calculated, the quasi-far-field distance can meet the far-field distance of the antenna unit, and the antenna is placed on the turntable at the distance.
Preferably, in the second step, according to the sampling interval of the antenna to be tested, the control computer is used to control a test probe with a known characteristic and a same working frequency as the antenna to be tested, so as to measure the amplitude and phase distribution on a certain surface at the quasi-far-field position of the antenna.
Preferably, in the third step, the one-dimensional quasi far-field electric field measurement is performed under the condition that the measured antenna deviates from the origin point
Figure 866504DEST_PATH_IMAGE001
And
Figure 664827DEST_PATH_IMAGE002
wherein, in the step (A),
Figure 505744DEST_PATH_IMAGE003
andθall variables are variables in a standard coordinate system under a spherical coordinate, and the far field region of the antenna to be measured is obtained through the following formula (2 a) and formula (2 b)
Figure 220145DEST_PATH_IMAGE004
Component sum
Figure 821022DEST_PATH_IMAGE005
A component;
Figure 191960DEST_PATH_IMAGE006
（2a）
Figure 501981DEST_PATH_IMAGE007
（2b）
wherein, the first and the second end of the pipe are connected with each other,kas the number of free-space waves,kwhere = 2 pi/lambda is the wave number,jis the unit of an imaginary number,nin order to be able to set the integer number,eis the bottom of the index, and is,
Figure 263264DEST_PATH_IMAGE008
and
Figure 271759DEST_PATH_IMAGE009
is the coefficient of the cylindrical wave expansion,
Figure 575833DEST_PATH_IMAGE008
and
Figure 102760DEST_PATH_IMAGE009
is defined by the following equations (3 a) and (3 b):
Figure 836492DEST_PATH_IMAGE010
（3a）
Figure 169384DEST_PATH_IMAGE011
（3b）
wherein the content of the first and second substances,
Figure 921440DEST_PATH_IMAGE001
and
Figure 675726DEST_PATH_IMAGE002
respectively electric field
Figure 83705DEST_PATH_IMAGE004
Component sum
Figure 485867DEST_PATH_IMAGE005
Component, and can be obtained from equation (4):
Figure 889167DEST_PATH_IMAGE012
（4）
wherein the content of the first and second substances,
Figure 351372DEST_PATH_IMAGE013
and
Figure 308964DEST_PATH_IMAGE014
is defined as:
Figure 452500DEST_PATH_IMAGE015
（5）
Figure 507044DEST_PATH_IMAGE016
（6）
using the above expression, if the linear polarization mode of the antenna to be tested is linear polarization, the main polarization of the antenna to be tested is determined
Figure 812254DEST_PATH_IMAGE017
And cross polarization
Figure 725984DEST_PATH_IMAGE018
Expressed as:
Figure 938790DEST_PATH_IMAGE019
（7a）
Figure 785524DEST_PATH_IMAGE020
（7b）
wherein
Figure 261635DEST_PATH_IMAGE021
Is that
Figure 928240DEST_PATH_IMAGE004
Direction main polarization
Figure 210317DEST_PATH_IMAGE017
And cross polarization
Figure 380398DEST_PATH_IMAGE018
And, if the measured antenna polarization is circular polarization, the left-hand circular polarization and the right-hand circular polarization of the measured antenna can be expressed as:
Figure 355307DEST_PATH_IMAGE022
（8a）
Figure 571525DEST_PATH_IMAGE023
（8b）
preferably, in the fourth step, the measured antenna is converted back to the origin of the measurement coordinate system by applying the differential phase change and the formula (9), the converted mode coefficient is calculated as the formula (11), so that the measured antenna is conceptually located at the center of the measurement coordinate system, the band-pass filter function, namely the formula (12), is applied to suppress unnecessary high-order cylindrical mode coefficients, and the mathematical absorption and reflection suppression algorithm-filtered directional diagram is calculated from the cylindrical mode coefficients by using the formula (13);
Figure 651433DEST_PATH_IMAGE024
（9）
wherein, the first and the second end of the pipe are connected with each other,
Figure 410442DEST_PATH_IMAGE025
representing a distance offset vector between the measured coordinate system center and the measured antenna center,E t (r → ∞, θ) In order to test the electric field,E 0 (r →∞, θ) Representing the electric field centered at the center of the antenna being measured, the offset distance makes the source phase from the receiver at different locations significantly different, which enables us to remove the scattered field from the field, the angular separation of the data points being used
Figure 618569DEST_PATH_IMAGE026
It means that the following conditions should be satisfied:
Figure 994187DEST_PATH_IMAGE027
（10）
wherein the content of the first and second substances,
Figure 618067DEST_PATH_IMAGE028
is to bekρ 0 The function of rounding down is performed on the basis of the function,n 0 is set to 10, thus, fromE 0 (r →∞, θ) Is/are as follows
Figure 231582DEST_PATH_IMAGE005
And
Figure 282714DEST_PATH_IMAGE004
obtaining equivalent cylindrical mode coefficient from component
Figure 348890DEST_PATH_IMAGE029
And
Figure 838778DEST_PATH_IMAGE030
：
Figure 306799DEST_PATH_IMAGE031
（11a）
Figure 122308DEST_PATH_IMAGE032
（11b）
wherein the content of the first and second substances,
Figure 941360DEST_PATH_IMAGE033
satisfy the requirement ofΛ 2 + h 2 = k 2 ；
And can set an integernPolarization and fourier variableshIs complex, and effectively obtains settable integers from the measured data by using a one-dimensional fast Fourier transformnAnd polarization and Fourier variableshTherefore, the filter is stably eliminated by using the following filtering functionρ min Any cylindrical mode coefficient of the external field:
Figure 500517DEST_PATH_IMAGE034
（12）
where τ ∈ {1,2}. Therefore, a far-field pattern is obtained using the filtered cylindrical mode coefficients, see below:
Figure 88624DEST_PATH_IMAGE035
（13a）
Figure 481560DEST_PATH_IMAGE036
（13b）。
compared with the prior art, the invention has the beneficial effects that:
the measurement distance is significantly reduced: the distance between the antenna to be tested and the probe only needs to meet the quasi-far field condition, the testing distance is obviously reduced, and the cost of darkroom construction is greatly saved;
the reconstructed far-field directional diagram has high precision: the single-section far-field pattern extrapolation method based on the quasi-far-field mode filtering technology can inhibit multipath interference, solves the problem that the conventional antenna quasi-far-field measurement can only meet the measurement of a linear antenna array, cannot inhibit the influence of multipath interference and cannot accurately obtain an antenna pattern to be measured, and ensures that the final extrapolated far-field pattern of the antenna to be measured has high accuracy.
Drawings
FIG. 1 shows the present invention
Figure 912541DEST_PATH_IMAGE037
A schematic diagram of a coordinate system;
FIG. 2 is a simplified model diagram of an antenna under test according to the present invention;
FIG. 3 is a far-field pattern and a filtered far-field pattern in accordance with the present invention in a 45 degree linear polarization theory;
FIG. 4 is a diagram of the difference between the 45 linear polarization theoretical far field pattern and the filtered far field pattern of the present invention;
FIG. 5 is a far field pattern from the 45 linear polarization theory and a filtered far field pattern of the present invention;
fig. 6 is a diagram of the difference between the far-field pattern of the present invention in the 45 ° linear polarization theory and the filtered far-field pattern.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
One specific example is described below: near field data was provided by a linear array antenna consisting of an electric dipole antenna with a frequency of 3GHz, fig. 2 shows the architecture of the model,θmeans thatxozPlane andzincluded angle of the axes, offset vector of the measured antenna beingx a , y a , z a ) The number of electric dipole elements isN x × N y × N z The element antennas are spaced along the x-axis by a distance ofd x Is provided withN y = 1, N z = 2, becausezAntenna element spacing in the direction ofλ/4And each antenna element is equal in amplitude and 90 ° phase shifted, the antenna array is able to radiate in the + z direction, which will excitea i Interference source (normalized to measured) maximum excitation of the antenna) is placed inx i , y i , z i ) To simulate multipath interference, the interference source does not rotate with the antenna array, wherein the quasi-far field distance isρ 0 The parameter values are detailed in table 1;
Figure 885176DEST_PATH_IMAGE038
TABLE 1
The invention relates to a method for measuring any polarization line antenna array directional diagram based on quasi-far field mode filtering, which relates to an antenna to be measured arranged on a rotary table, a control computer, a test probe, a test instrument in an antenna measuring system and the like in the measuring process, wherein the characteristics of all the test probes are known before testing, the method combines the characteristics of a line antenna array with one-dimensional large electrical size and one-dimensional small electrical size to carry out antenna quasi-far field measurement, and comprises the following technical steps:
step one, determining a quasi-far-field measurement distance of an antenna to be measured: the invention is suitable for measuring a linear antenna array, the quasi-far-field distance measurement can meet the far-field distance of an antenna unit, the distance between the antenna to be measured and a test probe is calculated, and the antenna is placed on a turntable at the distance;
step two, measuring the amplitude and the phase on a certain surface at the quasi-far-field position of the antenna: controlling a test probe which is consistent with the working frequency of the antenna to be tested and has known characteristics by using a control computer according to the sampling interval of the antenna to be tested, and measuring the amplitude and phase distribution on a certain surface at the quasi-far-field position of the antenna;
thirdly, correcting the measured directional diagram through a far field directional diagram reconstruction technology: the measured antenna deviates from the original point and is measured by a one-dimensional quasi far field electric field
Figure 452424DEST_PATH_IMAGE001
And
Figure 219523DEST_PATH_IMAGE002
wherein, in the step (A),
Figure 809904DEST_PATH_IMAGE003
andθall variables are variables in a standard coordinate system under a spherical coordinate, and the far field region of the antenna to be measured is obtained through a formula (2 a) and a formula (2 b)
Figure 710864DEST_PATH_IMAGE004
Component sum
Figure 7984DEST_PATH_IMAGE005
A component;
as shown in fig. 1, the coordinates of the measured antenna with the characteristics of one dimension being large and the other dimension being small, the antenna is a linear array antenna designed along the x-axis, and the measuring plane is xoz, it can be seen that the length of the antenna is very long in the x-direction and very short in the y-direction, which indicates that the distance satisfying the far-field measurement in the y-direction, but for the x-direction, it will be very difficult, in fig. 1,
Figure 336197DEST_PATH_IMAGE037
is a typical cylindrical coordinate system, so that the y-axis is the polar axis of the cylinder around the antenna under test, and the antenna elements are along the x-axis
Figure 103557DEST_PATH_IMAGE039
Are uniformly arranged with the associated radiation pattern in the xoz plane, i.e., y = 0; the cylinder is deformed into a circle in the plane xoz, wherein,
Figure 480311DEST_PATH_IMAGE003
andθare all variables in a standard coordinate system under spherical coordinates, and therefore the radius of a cylinder centered at the origin and surrounding the entire antenna under test is used
Figure 22151DEST_PATH_IMAGE003
The radius of the smallest cylinder, centered at the center of the array and surrounding the entire antenna under test, is marked as
Figure 396632DEST_PATH_IMAGE040
。
Exceed
Figure 23922DEST_PATH_IMAGE003
The electric field of (a) is written as:
Figure 142051DEST_PATH_IMAGE041
（1）
wherein
Figure 538397DEST_PATH_IMAGE042
And
Figure 83779DEST_PATH_IMAGE043
is the coefficient of the number of the first and second,
Figure 198366DEST_PATH_IMAGE044
and
Figure 854606DEST_PATH_IMAGE045
a function of a vector wave is represented,hfor the polarization and the fourier variables,
Figure 371038DEST_PATH_IMAGE046
for differential operators in calculus, and, in addition, for deriving electric fieldsE θ (ρ, θ, 0) AndE y (ρ, θ, 0) Given by:
Figure 87321DEST_PATH_IMAGE047
（2a）
Figure 689204DEST_PATH_IMAGE048
（2b）
wherein the content of the first and second substances,kis a function of the wave number in free space,kwhere = 2 pi/lambda is the wave number,jis the unit of an imaginary number,nin order to be able to set the integer number,eis the bottom of the index, and is,
Figure 149135DEST_PATH_IMAGE008
and
Figure 520074DEST_PATH_IMAGE009
is the coefficient of expansion of the cylindrical wave,
Figure 407258DEST_PATH_IMAGE008
and
Figure 230858DEST_PATH_IMAGE009
is defined by the following formula (3 a) and formula (3 b)
Figure 494480DEST_PATH_IMAGE008
And
Figure 719925DEST_PATH_IMAGE009
is defined as:
Figure 43590DEST_PATH_IMAGE010
（3a）
Figure 495431DEST_PATH_IMAGE011
（3b）
wherein, the first and the second end of the pipe are connected with each other,E θ (ρ 0 , θ0) andE y (ρ 0 , θ0) are respectively electric fields
Figure 421799DEST_PATH_IMAGE004
Component sum
Figure 642696DEST_PATH_IMAGE005
Component, and can be obtained by:
Figure 996317DEST_PATH_IMAGE049
（4）
wherein the content of the first and second substances,
Figure 935454DEST_PATH_IMAGE013
and
Figure 399933DEST_PATH_IMAGE014
is defined as:
Figure 475337DEST_PATH_IMAGE015
（5）
Figure 265438DEST_PATH_IMAGE016
（6）
by using the above expression, if the linear polarization mode of the antenna to be measured is linear polarization, the main polarization of the antenna to be measured is
Figure 426292DEST_PATH_IMAGE017
And cross polarization
Figure 694463DEST_PATH_IMAGE018
Expressed as:
Figure 618513DEST_PATH_IMAGE019
（7a）
Figure 579516DEST_PATH_IMAGE020
（7b）
wherein
Figure 696508DEST_PATH_IMAGE021
Is that
Figure 768369DEST_PATH_IMAGE004
Direction main polarization
Figure 818364DEST_PATH_IMAGE017
And cross polarization
Figure 684689DEST_PATH_IMAGE018
And if the measured antenna polarization mode is circular polarization, the left-hand circular polarization and the right-hand circular polarization of the measured antenna can be expressed as:
Figure 820135DEST_PATH_IMAGE022
（8a）
Figure 430108DEST_PATH_IMAGE023
（8b）
step four: obtaining a final far-field directional diagram through a quasi-far-field mathematical absorption reflection suppression technology; the method comprises the following specific steps: converting the measured antenna back to the origin of the measurement coordinate system by applying the differential phase change and the formula (9), calculating the converted mode coefficient as the formula (11) so that the measured antenna is conceptually positioned at the center of the measurement coordinate system, applying a band-pass filter function, namely the formula (12), to suppress unnecessary high-order cylindrical mode coefficients, and calculating a directional diagram filtered by a mathematical absorption reflection suppression algorithm from the cylindrical mode coefficients by using the formula (13);
as described above, the far-field mathematical absorption reflection suppression technique is such that once the single tangential component of the far field is obtained by equation (2)
Figure 334610DEST_PATH_IMAGE004
Sum component
Figure 371837DEST_PATH_IMAGE005
The measured antenna is then converted back to the origin of the measurement coordinate system by phase transformation, i.e.:
Figure 994579DEST_PATH_IMAGE024
（9）
wherein
Figure 408243DEST_PATH_IMAGE025
Representing a distance offset vector between the measured coordinate system center and the measured antenna center,E t (r →∞, θ) In order to test the electric field,E 0 (r →∞, θ) Representing the electric field centered at the center of the antenna being measured, the offset distance makes the source phase from the receiver at different locations significantly different, which enables us to remove the scattered field from the field, the angular separation of the data points (by
Figure 167251DEST_PATH_IMAGE026
Expressed) should satisfy the following condition:
Figure 640958DEST_PATH_IMAGE027
（10）
wherein
Figure 485417DEST_PATH_IMAGE028
Is to bekρ 0 The function of rounding down is performed on the basis of the function,n 0 is generally set to 10, and is therefore derived fromE 0 (r →∞, θ) Is/are as follows
Figure 702772DEST_PATH_IMAGE005
And
Figure 316287DEST_PATH_IMAGE004
obtaining equivalent cylindrical mode coefficient from component
Figure 960895DEST_PATH_IMAGE029
And
Figure 292650DEST_PATH_IMAGE030
：
Figure 48117DEST_PATH_IMAGE031
（11a）
Figure 781717DEST_PATH_IMAGE032
（11b）
wherein
Figure 800489DEST_PATH_IMAGE033
Satisfy the requirement ofΛ 2 + h 2 = k 2 ；
It is noted that integers can be setnPolarization and Fourier variableshIs complex, and effectively obtains settable integers from the measured data by using a one-dimensional fast Fourier transformnSum polarization and Fourier variableshTherefore, the filter is stably eliminated by using the following filtering functionρ min Any cylindrical mode coefficient of the external field:
Figure 744174DEST_PATH_IMAGE034
（12）
where τ ∈ {1,2}, the far-field pattern is thus obtained using the filtered cylindrical mode coefficients, such as:
Figure 913119DEST_PATH_IMAGE035
（13a）
Figure 625860DEST_PATH_IMAGE036
（13b）
the technical effects of the present invention will be explained by simulation and data thereof;
simulation results and analysis
The method comprises the following steps that a spiral array antenna is selected, the circular polarization frequency is 2.2GHz, the spiral array antenna is used for measurement, the spiral array antenna consists of 8 antennas which are uniformly distributed, the overall size is 900mm multiplied by 230mm multiplied by 110mm, and the dynamic range of an experimental environment is better than 60dB;
the simulation is carried out in two steps: (1) Measuring the antenna array at a far-field distance, i.e. 12m, (2) measuring the antennas at 2m, using a fixed circular metal plate as a scattering source, to satisfy a quasi-far-field condition, in which case the distance offset of the measured antenna is 1m, the scattering source is placed approximately in the middle between the probe and the measured antenna, and the distance between the scattering source and the rotation center is 1.8m;
results of 45 ° linear polarization: analyzing the results of a 45 ° linearly polarized linear array antenna in the xoy plane, the nominal amplitude of which is-30 dB, in which case the far-field distance can be obtained using the far-field condition, i.e. 2D2/λ, with a value of 18.5m, it can be seen from fig. 3 that the quasi far-field results of 45 ° linear polarization at 2.8m (28 λ) show a pronounced near-field behavior, precisely the main lobe is very wide, the direction of which deviates from the nominal value due to the presence of the distance shift of the measured antenna, whereas, referring to fig. 4, it can be noted from the reconstruction results of the proposed quasi far-field-far-field transformation algorithm that the main lobe is identical to the theoretical far field.
It is worth mentioning that some of the unfiltered side lobes do not match perfectly due to the presence of interference, and the high lobe appearing at about 70 ° is its behavior, but the filtered far-field pattern is substantially identical to the theoretical result, and for the cross-polarization case, the theoretical far-field pattern and the filtered far-field pattern are as shown in fig. 5, while fig. 6 shows the difference between the theoretical far-field pattern and the filtered far-field pattern.
Therefore, it can be clear that when scattering sources exist in the quasi far-field area, the measured directional diagram is greatly different from a far-field directional diagram, however, the filtered directional diagram obtained by the quasi far-field-far-field transformation algorithm has good consistency with the directional diagram of a reference far field.
The method provided by the invention solves the problem that the conventional antenna quasi-far field measurement can only meet the measurement of a linear antenna array, cannot inhibit the influence of multipath interference and cannot accurately obtain the directional diagram of the antenna to be measured. Furthermore, the invention solves the technical problems that the multi-path interference cannot be inhibited in the quasi-far-field antenna measurement, and the far-field pattern of the linear antenna array cannot be accurately extrapolated in the interference environment.
The invention provides a single-section far-field directional diagram extrapolation measurement method based on a quasi-far-field mode filtering technology, which is suitable for a measuring line antenna array, and not only can improve the test efficiency of an antenna, but also can improve the measurement precision of the antenna.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.

Claims (3)

1. The method for measuring the directional diagram of the arbitrary polarized linear antenna array based on quasi-far field mode filtering is characterized by comprising the following technical steps of:
the method comprises the following steps: determining a quasi-far field measurement distance of an antenna to be measured;
step two: measuring the amplitude and phase on a surface at a quasi-far-field position of the antenna;
step three: correcting the measured directional diagram through a far field directional diagram reconstruction technology, wherein in the third step, one-dimensional quasi far field electric field measurement is carried out under the condition that the measured antenna deviates from the original point to obtain
Figure 739367DEST_PATH_IMAGE001
And
Figure 139256DEST_PATH_IMAGE002
wherein, in the process,
Figure 424743DEST_PATH_IMAGE003
andθall variables are variables in a standard coordinate system under a spherical coordinate, and the far field region of the antenna to be measured is obtained through the following formula (2 a) and formula (2 b)
Figure 833859DEST_PATH_IMAGE004
Component sum
Figure 888403DEST_PATH_IMAGE005
A component;
Figure 459193DEST_PATH_IMAGE006
（2a）
Figure 231977DEST_PATH_IMAGE007
（2b）
wherein, the first and the second end of the pipe are connected with each other,kas the number of free-space waves,kwhere = 2 pi/lambda is the wave number,jis the unit of an imaginary number,nin order to be able to set the integer number,eis the bottom of the index, and is,
Figure 179204DEST_PATH_IMAGE008
and
Figure 353833DEST_PATH_IMAGE009
is the coefficient of expansion of the cylindrical wave,
Figure 191182DEST_PATH_IMAGE008
and
Figure 185683DEST_PATH_IMAGE009
is defined by the following formula (3 a) and formula (3 b):
Figure 936601DEST_PATH_IMAGE010
（3a）
Figure 700158DEST_PATH_IMAGE011
（3b）
wherein the content of the first and second substances,
Figure 878329DEST_PATH_IMAGE001
and
Figure 563388DEST_PATH_IMAGE002
respectively electric field
Figure 977052DEST_PATH_IMAGE004
Component sum
Figure 736061DEST_PATH_IMAGE005
Component, and can be obtained from equation (4):
Figure 209767DEST_PATH_IMAGE012
（4）
wherein, the first and the second end of the pipe are connected with each other,
Figure 319806DEST_PATH_IMAGE013
and
Figure 537161DEST_PATH_IMAGE014
is defined as:
Figure 150676DEST_PATH_IMAGE015
（5）
Figure 795284DEST_PATH_IMAGE016
（6）
by using the above expression, if the linear polarization mode of the antenna to be measured is linear polarization, the main polarization of the antenna to be measured is
Figure 127039DEST_PATH_IMAGE017
And cross polarization
Figure 882505DEST_PATH_IMAGE018
Expressed as:
Figure 944002DEST_PATH_IMAGE019
（7a）
Figure 369299DEST_PATH_IMAGE020
（7b）
wherein
Figure 312984DEST_PATH_IMAGE021
Is that
Figure 747507DEST_PATH_IMAGE004
Direction main polarization
Figure 725828DEST_PATH_IMAGE017
And cross polarization
Figure 587604DEST_PATH_IMAGE022
And if the measured antenna polarization mode is circular polarization, the left-hand circular polarization and the right-hand circular polarization of the measured antenna can be expressed as:
Figure 753007DEST_PATH_IMAGE023
（8a）
Figure 725642DEST_PATH_IMAGE024
（8b）；
step four: obtaining a final far-field directional diagram by a quasi-far-field mathematical absorption reflection suppression technology, wherein in the fourth step, a measured antenna is converted back to an original point of a measurement coordinate system by applying differential phase change and a formula (9), the converted mode coefficients are calculated into a formula (11 a) and a formula (11 b), so that the measured antenna is conceptually positioned at the center of the measurement coordinate system, a band-pass filter function, namely a formula (12), is applied to suppress unnecessary high-order cylindrical mode coefficients, and a directional diagram filtered by a mathematical absorption reflection suppression algorithm is calculated from the cylindrical mode coefficients by using a formula (13 a) and a formula (13 b);
Figure 558469DEST_PATH_IMAGE025
（9）
wherein the content of the first and second substances,
Figure 591147DEST_PATH_IMAGE026
representing a distance offset vector between the measured coordinate system center and the measured antenna center,E t (r →∞, θ) In order to test the electric field,E 0 (r →∞, θ) Representing the electric field centered at the center of the antenna being measured, the offset distance makes the source phase from the receiver at different locations significantly different, which enables us to remove the scattered field from the field, the angular separation of the data points being used
Figure 243845DEST_PATH_IMAGE027
It means that the following conditions should be satisfied:
Figure 348067DEST_PATH_IMAGE028
（10）
wherein the content of the first and second substances,
Figure 910767DEST_PATH_IMAGE029
is to bekρ 0 The function of rounding down is performed on the basis of the function,n 0 is set to 10, thus, fromE 0 (r →∞, θ) Is/are as follows
Figure 238980DEST_PATH_IMAGE005
And
Figure 519919DEST_PATH_IMAGE004
obtaining equivalent cylindrical mode coefficient from component
Figure 958991DEST_PATH_IMAGE030
And
Figure 376197DEST_PATH_IMAGE031
：
Figure 875311DEST_PATH_IMAGE032
（11a）
Figure 377968DEST_PATH_IMAGE033
（11b）
wherein the content of the first and second substances,
Figure 823993DEST_PATH_IMAGE034
satisfy the requirement ofΛ 2 + h 2 = k 2 ；
And can set an integernPolarization and Fourier variableshIs complex, and effectively obtains settable integers from the measured data by using a one-dimensional fast Fourier transformnSum polarization and Fourier variableshTherefore, the filter is stably eliminated by using the following filtering functionρ min Any cylindrical mode coefficient of the external field:
Figure 220339DEST_PATH_IMAGE035
（12）
wherein τ ∈ {1,2}, therefore, a far-field directional pattern is obtained by using the filtered cylindrical mode coefficients, as follows:
Figure 759862DEST_PATH_IMAGE036
（13a）
Figure 874448DEST_PATH_IMAGE037
（13b）。
2. the quasi-far-field mode filtering based arbitrary polarized linear antenna array pattern measurement method of claim 1, wherein: in the first step, the distance between the antenna to be tested and the test probe is calculated, the quasi-far-field distance measurement meets the far-field distance of the antenna unit, and the antenna is placed on the turntable at the distance.
3. The quasi-far-field mode filtering based arbitrary polarization linear antenna array pattern measurement method of claim 1, wherein: and in the second step, according to the sampling interval of the antenna to be tested, the control computer is utilized to control a test probe which has the same working frequency and known characteristics with the antenna to be tested, and the amplitude and phase distribution on a certain surface at the quasi-far-field position of the antenna are measured.
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