CN113268853A - Antenna directional pattern optimization method and device and readable storage medium - Google Patents

Antenna directional pattern optimization method and device and readable storage medium Download PDF

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CN113268853A
CN113268853A CN202110401827.3A CN202110401827A CN113268853A CN 113268853 A CN113268853 A CN 113268853A CN 202110401827 A CN202110401827 A CN 202110401827A CN 113268853 A CN113268853 A CN 113268853A
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CN113268853B (en
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胡瑞贤
陈竹梅
谢菊兰
雷川
徐宏宇
匡云连
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University of Electronic Science and Technology of China
Electronic Science Research Institute of CTEC
Qiantang Science and Technology Innovation Center
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Abstract

The invention discloses an antenna directional pattern optimization method, an antenna directional pattern optimization device and a readable storage medium, wherein the optimization method comprises the following steps: determining initial array parameters according to a target antenna directional diagram; establishing an array directional diagram optimized compressed sensing model according to the initial array parameters and preset constraint conditions; and solving the compressed sensing model to obtain optimized array distribution and optimized excitation. The optimized array distribution and optimized excitation obtained by the method can reconstruct a target directional diagram to the maximum extent by using less array element number, thereby effectively saving the array element number and improving the sparse effect.

Description

Antenna directional pattern optimization method and device and readable storage medium
Technical Field
The present invention relates to the field, and in particular, to an antenna pattern optimization method, apparatus, and readable storage medium.
Background
The antenna array directional diagram comprehensive optimization is based on antenna directional diagram technical indexes, and under the given constraint condition, the distribution shape of the antenna array and the array element space distribution condition in the antenna array are adjusted and the excitation of the antenna array elements is adjusted through a series of optimization methods to generate a beam directional diagram meeting the expected performance indexes. The array antenna has a wide application range, and has various index requirements on an array directional diagram, such as peak side lobe level, main lobe width, main lobe gain, average side lobe level and the like. To address these needs, various optimization methods have been proposed for pattern synthesis optimization. Starting from the aspect of adjusting the spatial distribution of array elements, the idea of non-uniform array arrangement is proposed for the research and application of non-periodic arrays which have been fifty years ago and in the sixties of the last century, the early research basically stays on simple methods such as numerical formula solution and exhaustion method, and then a dynamic programming method, a simulated annealing algorithm, a genetic algorithm and the like are gradually born along with the development of computer technology. The genetic algorithm is applied to the optimization arrangement of linear arrays and area arrays, genetic operation is carried out by encoding variables containing position information into binary strings, and after finite iteration optimization, array distribution with the lowest peak side lobe level in two array scenes is obtained, but the problem of low convergence speed exists in the whole process. In recent decades, a number of improved genetic algorithms and hybrid algorithms with which a variety of algorithms can be used have been proposed to improve optimization performance. And from the aspect of adjusting array element excitation, a convex optimization method, an accurate response control method and the like are provided. However, generally, the methods are independent for optimizing the array element position and the array element excitation, for example, the genetic algorithm and the like are firstly utilized to optimize the array element position, and then the excitation optimization method is tried under the condition of insufficient optimization effect, so that although the optimization is performed on the same directional diagram index, the connection between the optimization and the array element position and the array element excitation is not established at the same time in the optimization processes, and the optimization effect cannot be optimal.
Disclosure of Invention
The embodiment of the invention provides an antenna directional pattern optimization method, an antenna directional pattern optimization device and a readable storage medium, which are used for quickly reconstructing a target directional pattern, saving the number of array elements and improving the sparse effect.
The embodiment of the invention provides an antenna directional pattern optimization method, which comprises the following steps:
determining initial array parameters according to a target antenna directional diagram;
establishing an array directional diagram optimized compressed sensing model according to the initial array parameters and preset constraint conditions;
and solving the compressed sensing model to obtain optimized array distribution and optimized excitation.
In one example, the determining initial array parameters from the target antenna pattern comprises:
and sampling the target antenna directional diagram according to the number of preset sampling points, and determining a measurement vector of the compressed sensing model.
In one example, the determining initial array parameters from the target antenna pattern further comprises:
determining an aperture of the target antenna pattern;
an initial spatial distribution and an initial excitation are determined from the aperture.
In an example, the determining an initial spatial distribution and an initial excitation from the aperture comprises:
determining the initial array element spacing and the array element number of the antenna array according to the aperture;
and determining initial excitation according to the initial array element interval and the array element number.
In an example, the establishing of the array pattern optimized compressed sensing model according to the initial array parameters and preset constraints includes:
and establishing an array directional diagram optimized compressed sensing model according to the initial array parameters by taking the optimized excitation sparsest as a target and the target directional diagram reconstruction as a constraint.
In an example, the solving the compressed sensing model to obtain an optimized array distribution and an optimized excitation includes:
converting the compressed sensing model within a preset error range to obtain an intermediate model;
converting the intermediate model into an Alternating Direction Multiplier Method (ADMM) form;
and carrying out iterative solution on the ADMM form to obtain optimized array distribution and optimized excitation.
An embodiment of the present invention further provides an antenna pattern optimization apparatus, including:
the parameter calculation unit is used for determining initial array parameters according to the target antenna directional diagram;
the modeling unit is used for establishing a compressed sensing model for optimizing an array directional diagram according to the initial array parameters and preset constraint conditions;
and the data processing unit is used for solving the compressed sensing model to obtain optimized array distribution and optimized excitation.
An embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the foregoing antenna pattern optimization method are implemented.
According to the embodiment of the invention, the initial array parameters are determined according to the target antenna directional diagram; establishing an array directional diagram optimized compressed sensing model according to the initial array parameters and preset constraint conditions; and solving the compressed sensing model to obtain optimized array distribution and optimized excitation, wherein the obtained optimized array distribution and optimized excitation can be used for reconstructing a target directional diagram with less array element number and high precision, so that the array element number is effectively saved, and the sparse effect is improved.
The foregoing description is only an overview of the technical solutions of the present invention, and the embodiments of the present invention are described below in order to make the technical means of the present invention more clearly understood and to make the above and other objects, features, and advantages of the present invention more clearly understandable.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
FIG. 1 is a basic flow diagram of a first embodiment of the present invention;
FIG. 2 is a flow chart of a second embodiment of the present invention;
FIG. 3 is a comparison graph of a Chebyshev equal side lobe expected directional diagram and a reconstructed directional diagram by the method of the present invention;
FIG. 4 is a comparison of an optimized array using the method of the present invention with an original array;
FIG. 5 is a comparison of the cosecant squared desired pattern with the reconstructed pattern of the method of the present invention;
FIG. 6 is a comparison of an optimized array using the method of the present invention with an original array.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
Example one
A first embodiment of the present invention provides an antenna pattern optimization method, as shown in fig. 1, including:
s101, determining initial array parameters according to a target antenna directional diagram;
s102, establishing a compressed sensing model for optimizing an array directional diagram according to the initial array parameters and preset constraint conditions;
s103, solving the compressed sensing model to obtain optimized array distribution and optimized excitation.
In this embodiment, first, initial array parameters may be determined according to a desired target antenna pattern, where the initial array parameters include an array element pitch, an array element number, and initial excitation. And then establishing a compressed sensing model for optimizing an array directional diagram according to the initial array parameters and preset constraint conditions. For example, a compressed sensing model is built by taking a precise reconstruction directional diagram as a constraint and aiming at the sparsest excitation vector. And finally, obtaining the optimized array distribution and the optimized excitation by solving the compressed sensing model. And arranging antenna array elements according to the optimized array distribution and generating corresponding optimized excitation. The optimized array distribution and the optimized excitation obtained by the method can reconstruct a target directional diagram with less array element number and high precision, thereby effectively saving the array element number and improving the sparse effect.
In one example, the determining initial array parameters from the target antenna pattern comprises:
and sampling the target antenna directional diagram according to the number of preset sampling points, and determining a measurement vector of the compressed sensing model.
In this example, the target directional diagram obtained by sampling may be sampled as a measurement vector of a subsequent compressed sensing model for uniform sampling data of the input target directional diagram, for example, the number of sampling points is set to J.
In one example, the determining initial array parameters from the target antenna pattern further comprises:
determining an aperture of the target antenna pattern;
an initial spatial distribution and an initial excitation are determined from the aperture.
In an example, the determining an initial spatial distribution and an initial excitation from the aperture comprises:
determining the initial array element spacing and the array element number of the antenna array according to the aperture;
and determining initial excitation according to the initial array element interval and the array element number.
In this example, the initial array may be set as a virtual array, that is, the parameters of the initial array may be predetermined, for example, the array aperture of the antenna is set to L, and the array element spacing d of the virtual array is set tofAnd the number N of the array elements is obtained to obtain the initial excitation vector w corresponding to the spatial distribution of the initial array. Thus, a solution space is obtained as a final array element distribution, and an initial space distribution vector D ═ D is formed for the virtual array1,d2,…,dN]Wherein d isn＝(n-1)df. Generally, the denser the number of virtual array elements is, the better the reconstruction effect is, the larger the calculation amount is, and comprehensive consideration is required.
In an example, the establishing of the array pattern optimized compressed sensing model according to the initial array parameters and preset constraints includes:
and establishing an array directional diagram optimized compressed sensing model according to the initial array parameters by taking the optimized excitation sparsest as a target and accurately reconstructing the target directional diagram as a constraint.
The method aims to aim at the most sparse excitation after optimization and can accurately reconstruct a target directional diagram as constraint, so that an array directional diagram optimized compressed sensing model is constructed. For example, on the basis of the initial array parameters, the compressed sensing model satisfies:
Figure BDA0003020609780000061
s.t.F＝f
wherein w is a virtual array excitation vector to be optimized, an optimization target is that the most excitation vector is most sparse, that is, the number of array elements is the minimum, F is a directional diagram generated by the virtual array at a sampling angle, a specific calculation method is that F is Aw, a is a J × N complex matrix, and the (J, N) th element is
Figure BDA0003020609780000062
Figure BDA0003020609780000063
In an example, the solving the compressed sensing model to obtain an optimized array distribution and an optimized excitation includes:
converting the compressed sensing model within a preset error range to obtain an intermediate model;
transferring the intermediate model into an Alternating Direction Multiplier Method (ADMM) form;
and carrying out iterative solution on the ADMM form to obtain optimized array distribution and optimized excitation.
In this example, the matrix l can be set with some error0The norm can be replaced by l1Norm, so the model transforms to:
Figure BDA0003020609780000064
s.t.F＝f
and then applying basis tracking to reduce noise, wherein the model can be converted into a quadratic programming problem:
Figure BDA0003020609780000065
wherein λ is a parameter.
The model was then transcribed as ADMM:
min f(w)+g(z)
s.t.w-z＝0
wherein the content of the first and second substances,
Figure BDA0003020609780000066
g(z)＝λ||z||1w and z are both variables. Its augmented lagrangian function can be written:
Figure BDA0003020609780000067
the idea of ADMM is to fix the other two variables, and update one of them, then the general form of its iterative solution is:
Figure BDA0003020609780000071
Figure BDA0003020609780000072
Figure BDA0003020609780000073
and (3) iteratively solving the excitation vector w according to the formula to obtain the w meeting the requirement, and obtaining the virtual array elements which actually take effect according to the positions of the nonzero elements in the w, wherein the virtual array elements which actually take effect form the optimized position distribution of the sparsest array.
In summary, the method of the present invention has the following advantages
The method of the invention carries out revision conversion on the compressed sensing model comprehensively optimized by the antenna array directional diagram and converts the compressed sensing model into a quadratic programming model by applying a basis tracking noise reduction theory.
The method solves the model by utilizing the efficient and rapid calculation performance of the ADMM algorithm, accelerates the reconstruction speed of the algorithm and improves the sparsity.
The invention adopts the method of antenna array element position and array element excitation combined optimization, realizes the effect of reconstructing the directional diagram through a unified optimization model, and obviously reduces the complexity of comprehensive optimization of the directional diagram.
Example two
A second embodiment of the present invention provides an implementation of an antenna pattern optimization method, as shown in fig. 2, including the following steps:
step one, parameter initialization
Firstly, setting the target directional diagram needing to be reconstructed as FgoalUniformly sampling the space domain angle range (-90 degrees and 90 degrees), wherein the number of sampling points is J, and obtainingAs a measurement vector F ═ Fgoal(θ1),Fgoal(θ2),...,Fgoal(θJ)]。
Setting array element spacing d of virtual arrayfAnd the number of the array elements N, generally speaking, the denser the number of the array elements of the virtual array is, the better the reconstruction effect is, the larger the calculation amount is, and the comprehensive consideration is needed. It can be set to dfWhen the value is 0.05 lambda, the virtual array element distribution D at this time is [ D ═ D1,d2,…,dN]. Let the excitation vector for this virtual array be w, and initialize its value to 1.
Step two, establishing a sparse reconstruction model
Setting an observation matrix A according to a compressed sensing theory, wherein A is a J multiplied by N complex matrix, and the (J, N) th element of the observation matrix is
Figure BDA0003020609780000081
And then the directional diagram generated by the virtual array at the sampling angle is F ═ Aw, w is used as the target, and the reconstruction expected directional diagram is used as the constraint to establish a sparse reconstruction model:
Figure BDA0003020609780000082
s.t.F＝f
step 3. model conversion
Due to the above description with respect to matrix l0The problem of norm is the NP-hard problem, and it has been proven in literature that under certain error, l of matrix can be used0Norm is replaced by l1Norm and after transformation both are equivalent, so the following model is obtained:
Figure BDA0003020609780000083
s.t.F＝f
and then applying a basis tracking noise reduction theory to the data to convert the data into a quadratic programming problem:
Figure BDA0003020609780000084
wherein λ is a parameter.
Step 4.ADMM solving
The above model was written in the form of ADMM:
min f(w)+g(z)
s.t.w-z＝0
wherein the content of the first and second substances,
Figure BDA0003020609780000085
g(z)＝λ||z||1w and z are both variables. Its augmented lagrangian function can be written:
Figure BDA0003020609780000086
the idea of ADMM is to fix the other two variables, and update one of them, then the general form of its iterative solution is:
Figure BDA0003020609780000087
Figure BDA0003020609780000091
Figure BDA0003020609780000092
first, solve for
Figure BDA0003020609780000093
According to the conditions of the KKT,
Figure BDA0003020609780000094
bias and zero for w:
Figure BDA0003020609780000095
obtaining by solution:
wk+1＝(ATA+ρI)-1(ATf+ρzk-μk)
for the
Figure BDA0003020609780000096
Such a problem can be solved by using the second derivative to calculate its closed form solution as follows:
Figure BDA0003020609780000097
for the
Figure BDA0003020609780000098
The iterative expression is easy to obtain:
μk+1＝μk+wk+1-zk+1
the iteration of the above ADMM algorithm may be set to terminate with a pattern reconstruction error of less than 10-5And finally, obtaining an optimized excitation vector w through iterative solution.
Step 5, solving the optimal array according to the result
According to the compressive sensing theory, w obtained by solving the model has sparsity, namely, a large number of zero elements are contained, and because the spatial distribution and the excitation vectors of the virtual array elements are in one-to-one correspondence when the model is established, namely only the array elements corresponding to the non-zero elements are excited, the finally obtained optimal array element distribution can be determined according to the positions of the non-zero elements of w, so that the array element distribution and the excitation vectors of the sparse array for reconstructing the expected directional diagram are finally obtained simultaneously through the technical method provided by the invention.
Step 6, simulation test
And (3) generating a target direction diagram, setting the wavelength to be 0.3m, adopting a uniform array with the initial array element number of 20 and the array element spacing of half wavelength, adding a standard directional diagram of equal side lobes generated by a Chebyshev window, and setting the average side lobe level to be-20 dB. The expected directional diagram is uniformly sampled, the number of sampling points J is 37, the virtual array element interval is set to be 0.05 lambda, the directional diagram is comprehensively optimized by adopting the method, and the obtained reconstructed directional diagram and the array element distribution are respectively shown in fig. 3 and fig. 4.
In order to verify that the method can meet the comprehensive requirements of the directional diagrams in different forms, the cosecant square expected directional diagram is adopted for simulation verification, and the obtained results are shown in fig. 5 and 6, so that the expected effects of reconstructing the expected directional diagram and reducing the number of array elements can be realized.
An embodiment of the present invention further provides an antenna pattern optimization apparatus, including:
the parameter calculation unit is used for determining initial array parameters according to the target antenna directional diagram;
the modeling unit is used for establishing a compressed sensing model for optimizing an array directional diagram according to the initial array parameters and preset constraint conditions;
and the data processing unit is used for solving the compressed sensing model to obtain optimized array distribution and optimized excitation.
An embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the foregoing antenna pattern optimization method are implemented.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal (such as a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present invention.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (8)

1. A method for antenna pattern optimization, comprising:
determining initial array parameters according to a target antenna directional diagram;
establishing an array directional diagram optimized compressed sensing model according to the initial array parameters and preset constraint conditions;
and solving the compressed sensing model to obtain optimized array distribution and optimized excitation.
2. The antenna pattern optimization method of claim 1, wherein said determining initial array parameters from a target antenna pattern comprises:
and sampling the target antenna directional diagram according to the number of preset sampling points, and determining a measurement vector of the compressed sensing model.
3. The antenna pattern optimization method of claim 2, wherein said determining initial array parameters from a target antenna pattern further comprises:
determining an aperture of the target antenna pattern;
an initial spatial distribution and an initial excitation are determined from the aperture.
4. The antenna pattern optimization method of claim 3, wherein said determining an initial spatial distribution and an initial excitation based on said aperture comprises:
determining the initial array element spacing and the array element number of the antenna array according to the aperture;
and determining initial excitation according to the initial array element interval and the array element number.
5. The antenna pattern optimization method of claim 3, wherein said building a compressed sensing model for array pattern optimization based on said initial array parameters and pre-set constraints comprises:
and establishing an array directional diagram optimized compressed sensing model according to the initial array parameters by taking the optimized excitation sparsest as a target and the target directional diagram reconstruction as a constraint.
6. The antenna pattern optimization method of any one of claims 1-5, wherein solving the compressed sensing model to obtain an optimized array distribution and optimized excitation comprises:
converting the compressed sensing model within a preset error range to obtain an intermediate model;
converting the intermediate model into an Alternating Direction Multiplier Method (ADMM) form;
and carrying out iterative solution on the ADMM form to obtain optimized array distribution and optimized excitation.
7. An antenna pattern optimization apparatus, comprising:
the parameter calculation unit is used for determining initial array parameters according to the target antenna directional diagram;
the modeling unit is used for establishing a compressed sensing model for optimizing an array directional diagram according to the initial array parameters and preset constraint conditions;
and the data processing unit is used for solving the compressed sensing model to obtain optimized array distribution and optimized excitation.
8. A computer-readable storage medium, characterized in that a computer program is stored thereon, which computer program, when being executed by a processor, carries out the steps of the antenna pattern optimization method according to one of the claims 1 to 6.
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