CN112491455A - Robust beam forming method based on array unit position correction - Google Patents

Robust beam forming method based on array unit position correction Download PDF

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CN112491455A
CN112491455A CN202110158869.9A CN202110158869A CN112491455A CN 112491455 A CN112491455 A CN 112491455A CN 202110158869 A CN202110158869 A CN 202110158869A CN 112491455 A CN112491455 A CN 112491455A
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array
vector
representing
array antenna
complex weighting
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CN112491455B (en
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田径
雷世文
林志鹏
胡皓全
陈波
杨伟
唐璞
何子远
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming

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Abstract

The invention discloses a robust beam forming method based on array unit position correction, and belongs to the technical field of beam forming of array antennas. In order to effectively solve the technical problem of side lobe deterioration caused by the position deviation of the array unit, the invention sets an estimation optimization model of the position of the array unit through the high-order Taylor description of the position deviation, and corrects the array position through the iterative operation processing of the invention, thereby providing better array position estimation information for the beam forming application of the array antenna, particularly the large-scale array antenna, and being beneficial to synthesizing low side lobe array beams.

Description

Robust beam forming method based on array unit position correction
Technical Field
The invention belongs to the technical field of beam forming of array antennas, and particularly relates to a robust beam forming method based on array unit position correction.
Background
Beamforming is a signal preprocessing technique based on an array antenna, and generates a directional beam by adjusting a complex weighting coefficient (also called excitation) of each array unit in the array antenna, so as to obtain an obvious array gain. That is, in order to perform signal transceiving processing based on a desired radiation waveform, first, the complex weighting coefficients (including amplitudes and phases) of each array element of the array antenna are optimally set through beamforming processing to obtain a desired radiation waveform, so as to implement configuration of the complex weighting coefficients of each array element, and then, transmission or reception of signals is performed based on the configured array antenna. The beamforming technology has great advantages in the aspects of expanding the coverage area, improving the edge throughput, suppressing the interference and the like.
In beamforming with array antennas, existing methods mostly assume that the location of the array elements is accurate and known. However, in practical engineering, especially in the application of large arrays, due to the influence of factors such as machining errors, deformation, and cell conformality, the actual positions of the array cells often do not coincide with the expected positions, i.e. there is a certain position error. When the array position error is large, the synthesized beam performance will drop sharply if the actual position change of the array elements is not taken into account, i.e. the side lobe level of the synthesized beam will be greatly increased and even worsen by more than 10 dB.
Taking a line array with N elements as an example, assume the ideal (desired) position of the array elements as
Figure 904957DEST_PATH_IMAGE001
And the corresponding real position is
Figure 617829DEST_PATH_IMAGE002
Far field radiation of array antenna
Figure 761103DEST_PATH_IMAGE003
Can be described as:
Figure 390668DEST_PATH_IMAGE004
wherein,
Figure 472281DEST_PATH_IMAGE005
and
Figure 46350DEST_PATH_IMAGE006
respectively the complex weighting coefficient, the real array factor and the far field pattern of the nth array unit, and
Figure 557097DEST_PATH_IMAGE007
，
Figure 711609DEST_PATH_IMAGE008
is the wavelength of the electromagnetic wave and is,
Figure 413723DEST_PATH_IMAGE009
is the distance that the nth array element deviates from its ideal position (i.e. the array element is offset in position),
Figure 84876DEST_PATH_IMAGE010
the number of the units of the imaginary number is expressed,
Figure 540259DEST_PATH_IMAGE011
representing the main lobe direction, i.e., the signal incident angle. I.e. based on the above expression
Figure 347678DEST_PATH_IMAGE003
Is the true composite far field radiation of the array antenna.
To pair
Figure 630149DEST_PATH_IMAGE003
The expression of (a) is vectorized to obtain:
Figure 523018DEST_PATH_IMAGE012
wherein the array complex weighting coefficients
Figure 31360DEST_PATH_IMAGE013
，
Figure 709597DEST_PATH_IMAGE014
True array factor vector
Figure 645192DEST_PATH_IMAGE015
Far field pattern of array antenna
Figure 540205DEST_PATH_IMAGE016
The superscript "H" denotes the Hermite transpose of the vector, the symbol "
Figure 852237DEST_PATH_IMAGE017
"denotes a dot Product, i.e., a Hadamard Product.
To obtain low sidelobe pencil beams, the following beam optimization model needs to be solved:
Figure 368669DEST_PATH_IMAGE018
wherein,
Figure 225898DEST_PATH_IMAGE019
and
Figure 93360DEST_PATH_IMAGE020
respectively showing a main lobe region and a side lobe region,
Figure 461281DEST_PATH_IMAGE021
is the array side lobe level to be optimized. Taking the array complex weighting coefficient obtained by the solution of the beam optimization model as the optimal array complex weighting coefficient to configure the complex addition of each array element of the array antenna during signal transmission or receptionA weight coefficient.
In the prior art, however, it is generally assumed that the above-mentioned optimization problem is solved
Figure 97798DEST_PATH_IMAGE022
I.e. the specific location of the array elements is known accurately, and the optimization problem is solved to obtain the pencil beam with the lowest side lobe.
The inventor of the present invention finds that, when implementing the technical solution of the present invention, for an application scenario with a large array position deviation, a better forming result can be obtained only by first correcting the actual position of the array unit and then performing beamforming.
Disclosure of Invention
The invention aims to: in order to effectively solve the technical problem of side lobe deterioration caused by position deviation of an array unit, the invention discloses a robust beam forming method based on array unit position correction, so that better array position estimation information is provided for array antennas, particularly beam forming application of large array antennas, and low side lobe array beams are synthesized.
The robust beam forming method based on array unit position correction comprises the following steps:
step 1: random initialization of array antenna position offset
Figure 657087DEST_PATH_IMAGE023
Wherein
Figure 11845DEST_PATH_IMAGE024
,
Figure 914948DEST_PATH_IMAGE025
The number of array elements of the array antenna is represented, and the superscript 'T' represents vector transposition;
step 2: according to the current array antenna position offset
Figure 405972DEST_PATH_IMAGE023
Calculating the parameters
Figure 119850DEST_PATH_IMAGE026
And
Figure 712636DEST_PATH_IMAGE027
；
wherein,
Figure 904583DEST_PATH_IMAGE028
parameter of
Figure 33470DEST_PATH_IMAGE029
The elements of (A) are:
Figure 652670DEST_PATH_IMAGE030
，
wherein,
Figure 716441DEST_PATH_IMAGE031
the order of the taylor expansion is represented,
Figure 462811DEST_PATH_IMAGE032
which represents the wavelength of the electromagnetic waves,
Figure 928427DEST_PATH_IMAGE033
which represents the direction of the main lobe or lobes,
Figure 233376DEST_PATH_IMAGE034
represents an imaginary unit;
parameter of
Figure 784443DEST_PATH_IMAGE035
Wherein
Figure 334504DEST_PATH_IMAGE027
The elements of (A) are:
Figure 654627DEST_PATH_IMAGE036
，
Figure 881209DEST_PATH_IMAGE037
representing complex weighting coefficients of an array, a vector of array factors
Figure 425630DEST_PATH_IMAGE038
，
Figure 497491DEST_PATH_IMAGE039
Representing the desired position, vector, of the nth array element
Figure 688432DEST_PATH_IMAGE040
，
Figure 820336DEST_PATH_IMAGE041
Represents the far field pattern of the nth array element, the superscript "H" represents the hermitian transpose of the vector;
and step 3: based on the current calculated parameters
Figure 611574DEST_PATH_IMAGE027
Calculating intermediate update parameters
Figure 736394DEST_PATH_IMAGE042
；
Wherein,
Figure 31109DEST_PATH_IMAGE043
the upper label "
Figure 615806DEST_PATH_IMAGE044
"represents the pseudo-inverse of the matrix;
far field radiation
Figure 363182DEST_PATH_IMAGE045
Representing the far-field radiation of the array antenna excited by the array complex weighting coefficients solved according to the expected array position;
matrix array
Figure 42425DEST_PATH_IMAGE046
，
Figure 709423DEST_PATH_IMAGE047
Angular region
Figure 448709DEST_PATH_IMAGE048
，
Figure 699693DEST_PATH_IMAGE049
And
Figure 917047DEST_PATH_IMAGE050
respectively showing a main lobe region and a side lobe region,
Figure 701201DEST_PATH_IMAGE051
a column vector representing elements all of which are a number 1;
and 4, step 4: intermediate update parameters based on current calculations
Figure 611389DEST_PATH_IMAGE042
For each array unit, shift in position
Figure 333357DEST_PATH_IMAGE009
Performing updating, after updating
Figure 105135DEST_PATH_IMAGE009
Comprises the following steps:
Figure 228949DEST_PATH_IMAGE052
；
wherein, the symbol "
Figure 562235DEST_PATH_IMAGE053
"representing the real part of a vector, a symbol"
Figure 37078DEST_PATH_IMAGE054
"denotes the nth element of the vector in parentheses,
Figure 612547DEST_PATH_IMAGE055
a complex weighting coefficient representing an nth array element;
and 5: determining whether a preset iteration convergence condition is met, if so, executing a step 6; otherwise, repeating the steps 2 to 5;
step 6: array antenna position offset based on last calculation
Figure 122026DEST_PATH_IMAGE023
Calculating the real array factor of each array unit
Figure 623283DEST_PATH_IMAGE056
To obtain the real array factor vector
Figure 585423DEST_PATH_IMAGE057
And calculating the parameters
Figure 964583DEST_PATH_IMAGE058
；
Then solving the beam optimization model, and obtaining the array complex weighting coefficient by solving
Figure 328568DEST_PATH_IMAGE037
The optimal array complex weighting coefficient is used for configuring the complex weighting coefficient of each array unit of the array antenna during signal transmission or signal reception;
the beam optimization model specifically comprises the following steps:
Figure 3657DEST_PATH_IMAGE018
wherein,
Figure 187513DEST_PATH_IMAGE021
representing the array side lobe levels to be optimized.
Further, in step 1, the array antenna is shifted in position
Figure 354052DEST_PATH_IMAGE023
Subject to a mean of 0 and a variance of
Figure 323276DEST_PATH_IMAGE059
The normal distribution of (a), wherein,
Figure 431916DEST_PATH_IMAGE060
。
further, in step 5, the iteration convergence condition is as follows: the iteration times reach the preset upper limit of the iteration times or the position deviation of the array antenna obtained by two adjacent calculations
Figure 837489DEST_PATH_IMAGE023
The difference satisfies a preset condition.
Further, in step 5, when it is determined whether the preset iterative convergence condition is satisfied, the array antenna position offset obtained by the last two times of calculation is calculated
Figure 89610DEST_PATH_IMAGE023
And determining whether the largest element value in the vector difference is less than or equal to
Figure 897029DEST_PATH_IMAGE061
If so, an iterative convergence condition is satisfied, wherein,
Figure 927302DEST_PATH_IMAGE062
。
in summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
according to the method, the estimation optimization model of the array unit position is set through high-order Taylor description of the position deviation, and the array position is corrected through iterative operation processing, so that better array position estimation information is provided for array antennas, particularly beam forming application of large array antennas, and low side lobe array beams are synthesized.
Drawings
Fig. 1 is a schematic layout diagram of an array antenna including 41 array elements in an embodiment;
FIG. 2 is a diagram comparing beams obtained by the present invention and the prior art when the main lobe direction is 0 degree in the embodiment;
FIG. 3 is a diagram showing a comparison between beams obtained by the present invention and a conventional method when the main lobe direction is 20 degrees in the example;
fig. 4 is a beam contrast diagram obtained by the present invention and the prior art method when the main lobe direction is 40 degrees in the embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings.
The existing beamforming method usually assumes that the positions of the array elements are accurately known, but in practical engineering, especially in large-scale array applications, such assumption is often inaccurate, i.e. the positions of the array elements often have large deviations. At this time, if the position of the array unit is not corrected, the beamforming result thereof tends to generate a higher side lobe. According to the method, the estimation optimization model of the array unit position is set through high-order Taylor description of the position deviation, and the array position is corrected through iterative operation processing, so that better array position estimation information is provided for array antennas, particularly beam forming application of large array antennas, and low side lobe array beams are synthesized.
The specific implementation process of the robust beamforming method based on array unit position correction of the invention is as follows:
first, the array unit position of the nth array unit is shifted
Figure 84088DEST_PATH_IMAGE009
And (6) estimating.
To simplify the description, parameters are defined
Figure 858009DEST_PATH_IMAGE063
Rewriting the real array factor:
Figure 270667DEST_PATH_IMAGE064
Figure 471841DEST_PATH_IMAGE065
when in use
Figure 366853DEST_PATH_IMAGE066
And performing high-order Taylor expansion on the expression of the real array factor to obtain:
Figure 678886DEST_PATH_IMAGE065
wherein,
Figure 477209DEST_PATH_IMAGE031
is the order of the taylor expansion,
Figure 849284DEST_PATH_IMAGE067
to relate to
Figure 234523DEST_PATH_IMAGE009
Of high order infinitesimal quantity, when
Figure 84667DEST_PATH_IMAGE031
Large enough (e.g., M =20, specific values for visual scene adjustments), this infinitesimal amount is negligible. Order to
Figure 721185DEST_PATH_IMAGE068
The far field radiation of the array antenna can be described as:
Figure 14894DEST_PATH_IMAGE069
therefore, the position is shifted for each array unit
Figure 104073DEST_PATH_IMAGE009
The estimation problem of (a) can be described as the following estimation model:
Figure 272755DEST_PATH_IMAGE070
wherein,
Figure 29358DEST_PATH_IMAGE071
array weighting coefficients solved by existing methods from ideal array position
Figure 493969DEST_PATH_IMAGE037
Far field radiation, sign, of excited array antenna "
Figure 336023DEST_PATH_IMAGE072
"denotes a two-norm.
Array unit position shift
Figure 45746DEST_PATH_IMAGE009
Is calculated in the estimation model
Figure 656856DEST_PATH_IMAGE073
The further transformations may be:
Figure 823526DEST_PATH_IMAGE074
wherein,
Figure 152876DEST_PATH_IMAGE075
wherein,
Figure 663361DEST_PATH_IMAGE076
in bold
Figure 128977DEST_PATH_IMAGE051
A column vector with elements of 1 is represented,
Figure 200970DEST_PATH_IMAGE048
，
Figure 17616DEST_PATH_IMAGE077
the superscript "T" denotes vector transposition.
Order to
Figure 69142DEST_PATH_IMAGE078
，
Figure 654844DEST_PATH_IMAGE079
And is and
Figure 632159DEST_PATH_IMAGE080
then the array unit is shifted in position
Figure 670522DEST_PATH_IMAGE009
The estimation model of (2) can be rewritten as:
Figure 522809DEST_PATH_IMAGE081
when solving the rewritten estimation model, assume
Figure 228597DEST_PATH_IMAGE082
The array antenna position can be offset by iterative operations for a known quantity
Figure 376813DEST_PATH_IMAGE083
An efficient estimation is performed.
In the present embodiment, the array antenna position offset is obtained by iterative operation processing
Figure 168051DEST_PATH_IMAGE083
The specific implementation process of beamforming is as follows:
step 1: initialization, number of iterations
Figure 549661DEST_PATH_IMAGE084
Randomly initializing the position offset of the array antenna to obtain
Figure 109955DEST_PATH_IMAGE085
I.e. by
Figure 147181DEST_PATH_IMAGE086
。
Further, obtained by random initialization
Figure 442028DEST_PATH_IMAGE085
Satisfy any
Figure 636117DEST_PATH_IMAGE087
Obeying a mean of 0 and a variance of
Figure 50918DEST_PATH_IMAGE088
Normal distribution of (a), wherein
Figure 790204DEST_PATH_IMAGE089
Is preferably taken as
Figure 41188DEST_PATH_IMAGE090
。
Step 2: according to the current array antenna position offset
Figure 258543DEST_PATH_IMAGE086
Calculating the parameters
Figure 311206DEST_PATH_IMAGE091
And
Figure 955814DEST_PATH_IMAGE092
；
namely, it is
Figure 694094DEST_PATH_IMAGE093
，
Figure 715139DEST_PATH_IMAGE094
；
And step 3: using a formula
Figure 353800DEST_PATH_IMAGE095
Calculating the parameter of the (k + 1) th time
Figure 434888DEST_PATH_IMAGE096
。
And 4, step 4: using a formula
Figure 660465DEST_PATH_IMAGE097
Updating the array unit position offset of the nth array unit to obtain the (k + 1) th array unit position offset
Figure 485201DEST_PATH_IMAGE098
Where N =1, 2, …, N, the symbol "real (x)" represents the real part of the vector x, the symbol "[ x ]]n"denotes the nth element of the vector x.
And 5: judging whether a preset iteration convergence condition is met, if so, executing the step; otherwise, increasing the iteration number k by 1, and repeatedly executing the step 2 to the step 5;
wherein the iteration convergence condition is that the iteration number reaches a preset upper limit of the iteration number (for example, 100 times), or the difference of the position offsets of the array antennas obtained by two adjacent calculations is small enough, for example
Figure 463521DEST_PATH_IMAGE099
Wherein
Figure 233288DEST_PATH_IMAGE100
representing a vector
Figure 195427DEST_PATH_IMAGE101
The value of the largest element in (a),
Figure 309008DEST_PATH_IMAGE102
and preferably takes on a value of
Figure 407414DEST_PATH_IMAGE103
。
Step 6: shifting the position of the array antenna obtained by the last calculation
Figure 345152DEST_PATH_IMAGE104
As an estimate of the optimum array bias, i.e. order
Figure 794588DEST_PATH_IMAGE105
(ii) a Then using the formula
Figure 446280DEST_PATH_IMAGE106
Computing true array factors
Figure 664772DEST_PATH_IMAGE107
To obtain the real array factor vector
Figure 307499DEST_PATH_IMAGE108
Thereby obtaining
Figure 713073DEST_PATH_IMAGE058
；
Then solving the beam optimization model, and obtaining the array complex weighting coefficient by solving
Figure 699615DEST_PATH_IMAGE037
As optimal array complex weighting coefficients (i.e., optimal array excitation)
Figure 772613DEST_PATH_IMAGE109
。
When the signal is transmitted and received, the feed network of the array antenna performs corresponding transmitting or receiving excitation configuration according to the optimal array excitation to obtain a desired waveform, thereby realizing the transmission or reception of the signal.
To verify the beamforming performance of the present invention, simulation experiments were performed on a uniform linear array containing 41 array elements. Ideally, the spacing between adjacent array elements is one-half wavelength (
Figure 52153DEST_PATH_IMAGE110
) The array units are uniformly arranged to obtain a uniform linear array, but due to the influence of various factors in practical application, such as arrangement precision, antenna unit deformation and the like, the actual positions of the array units are not the same as the ideal conditions, that is, the spacing between adjacent array units is not fixed by half wavelength in the real conditions, the arrangement schematic diagram of each array unit in the simulation experiment is shown in fig. 1, and the schematic diagram of the arrangement of each array unit is shown in fig. 1The middle numerals 1 to 41 are different array element numbers, and for convenience of describing the positions of the array elements, the position of the array element (array element number 21) located at the middle position is taken as the origin of coordinates, that is, the array element position of the array element number 21 is 0, and the positions of the array elements are labeled based on the origin of coordinates, and in the simulation experiment, a group of array elements symmetrical with respect to the origin of coordinates is taken as a signal transceiving group, for example, the array element numbers 1 and 41, 2 and 40, 3 and 39 respectively form a group of signal transceiving groups, taking the array element numbers 1 and 41 as examples, the positions (relative positions) of the array elements are respectively located at-10 wavelengths and +10 wavelengths, and the specific array element positions (relative positions) of other array elements are shown in table 1:
Figure 210602DEST_PATH_IMAGE111
as can be seen from table 1, the interval between adjacent array elements is not a fixed half wavelength, but a certain offset exists, that is, in the uniform linear array antenna, after the coordinate origin of the array element coordinate system is calibrated, the ideal (expected) position of each array element can be specifically calculated based on the step array rule that the interval between adjacent array elements is a half wavelength, and then the array element position offset of each array element is estimated based on the estimation method for the array antenna position offset provided by the present invention, so as to obtain the estimation value of the real array element position. And then, acquiring the optimal array excitation (optimal array complex weighting coefficient) of the array antenna based on the estimated value to perform transmission or reception excitation configuration, so that the array antenna performs signal transceiving processing based on the required radiation waveform.
And respectively carrying out waveform simulation based on the array unit positions (positions before correction, namely expected positions) determined by the half-wavelength intervals among the array units and the real array unit positions (positions after correction) estimated by the invention, wherein the array units are assumed to have omnidirectional radiation characteristics, the angle resolution of a directional diagram is set to be 0.5 degrees, a main lobe beam is set to be 10 degrees, an optimal array complex weighting coefficient is determined based on an adopted beam optimization model, the directional diagram simulation of the array antenna is carried out, and then the obtained directional diagram is compared with an expected directional diagram (the directional diagram corresponding to the optimal array complex weighting coefficient obtained by accurately knowing the position condition of the array units) in the simulation experiment, wherein the beam diagram contrast in three different main lobe directions (0, 20 and 40) is respectively shown in figures 2, 3 and 4, the results show that when there is a deviation of the true array element position from the actual array element position, the side lobe level will rise by more than 10dB (compare the "desired pattern" curve to the "pre-correction" curve). The method estimates the position of the array unit, then solves the optimal array complex weighting coefficient, and the performance of the method is basically consistent with the optimization result of accurately knowing the position of the array (comparing an expected directional diagram curve with a corrected curve), namely the method can effectively solve the technical problem of side lobe deterioration caused by the position deviation of the array unit.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.

Claims (4)

1. A robust beam forming method based on array unit position correction is characterized by comprising the following steps:
step 1: random initialization of array antenna position offset
Figure 885844DEST_PATH_IMAGE001
Wherein
Figure 124934DEST_PATH_IMAGE002
,
Figure 326108DEST_PATH_IMAGE003
Number of array elements representing array antenna, superscript "T"Representing a vector transpose;
step 2: according to the current array antenna position offset
Figure 457006DEST_PATH_IMAGE001
Calculating the parameters
Figure 349132DEST_PATH_IMAGE004
And
Figure 131143DEST_PATH_IMAGE005
；
wherein, the parameter
Figure 581847DEST_PATH_IMAGE006
Parameter of
Figure 370681DEST_PATH_IMAGE007
The elements of (A) are:
Figure 66498DEST_PATH_IMAGE008
，
wherein,
Figure 93228DEST_PATH_IMAGE009
the order of the taylor expansion is represented,
Figure 560506DEST_PATH_IMAGE010
which represents the wavelength of the electromagnetic waves,
Figure 728314DEST_PATH_IMAGE011
which represents the direction of the main lobe or lobes,
Figure 382149DEST_PATH_IMAGE012
represents an imaginary unit;
parameter of
Figure 653599DEST_PATH_IMAGE013
Wherein parameter of
Figure 367477DEST_PATH_IMAGE005
The elements of (A) are:
Figure 22580DEST_PATH_IMAGE014
，
Figure 595951DEST_PATH_IMAGE015
representing complex weighting coefficients, signs, of the array "
Figure 49804DEST_PATH_IMAGE016
"denotes a point-by-point, array factor vector
Figure 124464DEST_PATH_IMAGE017
Array factor of the nth array element
Figure 1284DEST_PATH_IMAGE018
，
Figure 996922DEST_PATH_IMAGE019
Indicating the desired position of the nth array element, the array antenna far field pattern
Figure 977385DEST_PATH_IMAGE020
，
Figure 564224DEST_PATH_IMAGE021
Represents the far field pattern of the nth array element, the superscript "H" represents the hermitian transpose of the vector;
and step 3: based on the current calculated parameters
Figure 866024DEST_PATH_IMAGE005
Calculating intermediate update parameters
Figure 134194DEST_PATH_IMAGE022
；
Wherein,
Figure 985475DEST_PATH_IMAGE023
the upper label "
Figure 464255DEST_PATH_IMAGE024
"represents the pseudo-inverse of the matrix;
far field radiation
Figure 971459DEST_PATH_IMAGE025
Representing the far-field radiation of the array antenna excited by the array complex weighting coefficients solved according to the expected array position;
matrix array
Figure 590791DEST_PATH_IMAGE026
，
Figure 234262DEST_PATH_IMAGE027
Angular region
Figure 162903DEST_PATH_IMAGE028
，
Figure 937830DEST_PATH_IMAGE029
And
Figure 813382DEST_PATH_IMAGE030
respectively showing a main lobe region and a side lobe region,
Figure 124409DEST_PATH_IMAGE031
a column vector representing elements all of which are a number 1;
and 4, step 4: intermediate update parameters based on current calculations
Figure 692794DEST_PATH_IMAGE022
For each array unit, shift in position
Figure 174591DEST_PATH_IMAGE032
Performing updating, after updating
Figure 637189DEST_PATH_IMAGE032
Comprises the following steps:
Figure 255253DEST_PATH_IMAGE033
；
wherein, the symbol "
Figure 10850DEST_PATH_IMAGE034
"representing the real part of a vector, a symbol"
Figure 511102DEST_PATH_IMAGE035
"denotes the nth element of the vector in parentheses,
Figure 728456DEST_PATH_IMAGE036
a complex weighting coefficient representing an nth array element;
and 5: determining whether a preset iteration convergence condition is met, if so, executing a step 6; otherwise, repeating the steps 2 to 5;
step 6: array antenna position offset based on last calculation
Figure 247031DEST_PATH_IMAGE001
Calculating the real array factor of each array unit
Figure 626060DEST_PATH_IMAGE037
To obtain the real array factor vector
Figure 161078DEST_PATH_IMAGE038
And calculating the parameters
Figure 650965DEST_PATH_IMAGE039
；
Then solving the beam optimization model, and obtaining the array complex weighting coefficient by solving
Figure 304274DEST_PATH_IMAGE015
The complex weighting coefficients are used as the optimal array complex weighting coefficients to configure the complex weighting coefficients of each array unit of the array antenna during signal transmission or signal reception;
the beam optimization model specifically comprises the following steps:
Figure 916521DEST_PATH_IMAGE040
wherein,
Figure 329048DEST_PATH_IMAGE041
representing the array side lobe levels to be optimized.
2. The robust beamforming method based on array element position correction according to claim 1 wherein in step 1, the array antenna position is shifted
Figure 435675DEST_PATH_IMAGE001
Subject to a mean of 0 and a variance of
Figure 882837DEST_PATH_IMAGE042
The normal distribution of (a), wherein,
Figure 649673DEST_PATH_IMAGE043
。
3. the robust beamforming method based on array element position correction according to claim 1, wherein in step 5, the iterative convergence condition is: the iteration times reach the preset upper limit of the iteration times or the position deviation of the array antenna obtained by two adjacent calculations
Figure 877392DEST_PATH_IMAGE001
The difference satisfies a preset condition.
4. As claimed inThe robust beamforming method based on array unit position correction of claim 1 is characterized in that when determining whether a preset iterative convergence condition is satisfied, the position offset of the array antenna obtained by the last two times of calculation is calculated
Figure 256552DEST_PATH_IMAGE001
And determining whether the largest element value in the vector difference is less than or equal to
Figure 558221DEST_PATH_IMAGE044
If so, an iterative convergence condition is satisfied, wherein,
Figure 295626DEST_PATH_IMAGE045
。
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