CN113268853B - Antenna directional pattern optimization method and device and readable storage medium - Google Patents

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

An antenna pattern optimization method, device and readable storage medium

technical field

The present invention relates to the field, in particular to an antenna pattern optimization method, device and readable storage medium.

Background technique

The comprehensive optimization of the antenna array pattern is based on the technical indicators of the antenna pattern. Under the given constraints, through a series of optimization methods, the distribution shape of the antenna array and the spatial distribution of the array elements and the adjustment of the antenna array elements are adjusted. excitation to produce a beam pattern that satisfies desired performance metrics. The array antenna has a wide range of applications, and the requirements for the array pattern are also various, such as peak side lobe level, main lobe width, main lobe gain, average side lobe level, and so on. To address these requirements, various optimization methods have been proposed for pattern synthesis optimization. From the perspective of adjusting the spatial distribution of array elements, the research and application of non-periodic arrays has a history of more than 50 years. As early as the 1960s, some people proposed the idea of non-uniform arrays. Early research Basically stay on simple methods such as numerical formula solution and exhaustive method. Since then, with the development of computer technology, dynamic programming method, simulated annealing algorithm and genetic algorithm have gradually been born. Among them, the genetic algorithm is applied to the optimized layout of the linear array and the area array, and the variable containing the position information is coded into a binary string to perform the genetic operation. After a limited number of iterative optimizations, the lowest Array distribution of the peak sidelobe level, but the whole process has the problem of slow convergence. In the past ten years, a large number of improved genetic algorithms and hybrid algorithms used in conjunction with multiple algorithms have been proposed to improve optimization performance. From the aspect of adjusting the array element excitation, there are convex optimization methods, precise response control methods and so on. But generally speaking, these methods are independently optimized for the array element position and array element excitation. For example, first use the genetic algorithm to optimize the array element position, and then try to use the excitation optimization method when the optimization effect is insufficient. Optimizing for the same pattern index does not establish the connection with the position of the array element and the excitation of the array element at the same time during these optimization processes, so the optimization effect cannot be optimal.

Contents of the invention

Embodiments of the present invention provide an antenna pattern optimization method, device, and readable storage medium, which are used to quickly reconstruct a target pattern, save the number of array elements, and improve the sparse effect.

An embodiment of the present invention provides a method for optimizing an antenna pattern, including:

Determine the initial array parameters according to the target antenna pattern;

Establishing a compressed sensing model optimized for the array pattern according to the initial array parameters and preset constraints;

Solving the compressed sensing model obtains an optimized array distribution and an optimized excitation.

In an example, the determining the initial array parameters according to the target antenna pattern includes:

Sampling the target antenna pattern according to a preset number of sampling points to determine a measurement vector of the compressed sensing model.

In an example, the determining the initial array parameters according to the target antenna pattern further includes:

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 the initial spatial distribution and the initial excitation according to the aperture includes:

According to the aperture, determine the initial array element spacing and the number of array elements of the antenna array;

The initial excitation is determined according to the initial inter-array spacing and the number of inter-array elements.

In an example, the establishment of a compressed sensing model optimized for an array pattern according to the initial array parameters and preset constraints includes:

Taking the sparsest optimized excitation as the target and the reconstruction of the target pattern as the constraint, a compressed sensing model optimized for the array pattern is established according to the initial array parameters.

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;

The ADMM form is solved iteratively to obtain an optimized array distribution and an optimized excitation.

An embodiment of the present invention also provides an antenna pattern optimization device, including:

a parameter calculation unit, configured to determine initial array parameters according to the target antenna pattern;

A modeling unit, configured to establish a compressed sensing model optimized for an array pattern according to the initial array parameters and preset constraints;

The data processing unit is used to solve the compressed sensing model to obtain optimized array distribution and optimized excitation.

An embodiment of the present invention also 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.

In the embodiment of the present invention, the initial array parameters are determined according to the target antenna pattern; the compressed sensing model optimized for the array pattern is established according to the initial array parameters and preset constraints; the optimized array distribution and the optimized excitation are obtained by solving the compressed sensing model, The optimized array distribution and optimized excitation thus obtained can reconstruct the target pattern with high precision with fewer array elements, thereby effectively saving the number of array elements and improving the sparse effect.

The above description is only an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention, it can be implemented according to the contents of the description, and in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable , the specific embodiments of the present invention are enumerated below.

Description of drawings

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 embodiment. The drawings are only for the purpose of illustrating a preferred embodiment and are not to be considered as limiting the invention. Also throughout the drawings, the same reference numerals are used to designate the same parts. In the attached picture:

Fig. 1 is the basic flowchart of the first embodiment of the present invention;

Fig. 2 is the flowchart of the second embodiment of the present invention;

Fig. 3 is the comparison diagram of Chebyshev etc. side lobe expected pattern and the reconstruction pattern of the present invention;

Fig. 4 is the comparison result of the optimized array utilizing the method of the present invention and the original array;

Fig. 5 is the contrast of cosecant square expected direction diagram and reconstruction direction diagram of the present invention method;

Fig. 6 is a comparison between the optimized array and the original array using the method of the present invention.

detailed description

Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although 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 by the embodiments set forth herein. Rather, these embodiments are provided for more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

Embodiment one

The first embodiment of the present invention provides a method for optimizing an antenna pattern, as shown in FIG. 1 , including:

S101. Determine initial array parameters according to the target antenna pattern;

S102. Establish a compressed sensing model optimized for an array pattern according to the initial array parameters and preset constraints;

S103. Solve the compressed sensing model to obtain an optimized array distribution and an optimized excitation.

In this embodiment, initial array parameters may first be determined according to the required target antenna pattern, where the initial array parameters include the array element spacing, the number of array elements, and the initial excitation. Then, according to the initial array parameters and preset constraints, a compressed sensing model optimized for the array pattern is established. For example, it is necessary to accurately reconstruct the direction map as the constraint and make the excitation vector the sparsest as the goal, so as to establish the compressed sensing model. Finally, the optimized array distribution and optimized excitation can be obtained by solving the compressed sensing model. Arrange the antenna elements according to the optimized array distribution and generate the corresponding optimized excitation. The optimized array distribution and optimized excitation obtained by the method of the invention can reconstruct the target pattern with high precision with fewer array elements, thereby effectively saving the array elements and improving the sparse effect.

In an example, the determining the initial array parameters according to the target antenna pattern includes:

Sampling the target antenna pattern according to a preset number of sampling points to determine a measurement vector of the compressed sensing model.

In this example, the uniform sampling data of the input target pattern can be set, for example, the number of sampling points is set to J, and the sampled target pattern is used as the measurement vector of the subsequent compressed sensing model.

In an example, the determining the initial array parameters according to the target antenna pattern further includes:

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 the initial spatial distribution and the initial excitation according to the aperture includes:

According to the aperture, determine the initial array element spacing and the number of array elements of the antenna array;

The initial excitation is determined according to the initial inter-array spacing and the number of inter-array elements.

In this example, the setting for the initial array can be a virtual array, that is, the parameters of the initial array can be predetermined, for example, if the array aperture of the antenna is set to L, the array element spacing d _f of the virtual array and the number of array elements N, get The spatial distribution of the initial array corresponds to the initial excitation vector w. Thus, the solution space as the final array element distribution is obtained, forming the initial space distribution vector D=[d ₁ ,d ₂ , . . . ,d _N ] of the virtual array, where d _n =(n-1)d _f . Generally speaking, the denser the number of elements in the virtual array, the better the reconstruction effect and the greater the amount of calculation, which needs to be considered comprehensively.

In an example, the establishment of a compressed sensing model optimized for an array pattern according to the initial array parameters and preset constraints includes:

Taking the sparsest optimized excitation as the target and accurately reconstructing the target pattern as the constraint, a compressed sensing model optimized for the array pattern is established according to the initial array parameters.

The purpose of the method of the invention is to aim at the sparsest excitation after optimization and to be able to accurately reconstruct the target pattern as a constraint, thereby constructing a compressed sensing model optimized for the array pattern. For example, based on the aforementioned initial array parameters, the compressed sensing model satisfies:

s.t.F = f

Among them, w is the excitation vector of the virtual array to be optimized, the optimization goal is the most sparse excitation vector, that is, the minimum number of array elements, F is the direction diagram generated by the virtual array at the sampling angle, and its specific calculation method is F =Aw, A is a complex matrix of J×N, and its (j,n)th element is

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;

The intermediate model is transcribed into the ADMM form of the alternating direction multiplier method;

The ADMM form is solved iteratively to obtain an optimized array distribution and an optimized excitation.

In this example, under a certain error, the l ₀ norm of the matrix can be replaced by the l ₁ norm, so the model conversion is:

s.t.F = f

Then apply base tracking denoising, the above model can be transformed into a quadratic programming problem:

Among them, λ is a parameter.

Then the above model is transcribed into ADMM form:

min f(w)+g(z)

s.t.w-z=0

g(z)＝λ||z||₁，w与z均为变量。则可以写出其增广拉格朗日函数：in,

g(z)=λ||z|| ₁ , both w and z are variables. Then you can write its augmented Lagrangian function:

The idea of ADMM is to fix the remaining two variables and update one of the variables, then the general form of its iterative solution is:

By iteratively solving the above formula for the excitation vector w, w that meets the requirements can be obtained. According to the position of the non-zero elements in w, the virtual array elements that are actually effective can be obtained. These virtual array elements that are actually effective constitute the optimized final Location distribution of sparse arrays.

In sum, the inventive method has the following advantages

The method of the invention revises and converts the compressed sensing model comprehensively optimized for the antenna array pattern, and converts it into a quadratic programming model by applying the basis tracking noise reduction theory.

The method of the invention uses the high-efficiency and fast calculation performance of the ADMM algorithm to solve the above-mentioned model, accelerates the rebuilding speed of the algorithm, and improves the sparse performance.

The invention adopts the joint optimization method of antenna array array element position and array element excitation, realizes the effect of reconstructing the pattern through a unified optimization model, and significantly reduces the complexity of the comprehensive optimization of the pattern.

Embodiment two

The second embodiment of the present invention provides an implementation case of an antenna pattern optimization method, as shown in FIG. 2 , including the following steps:

Step 1. Parameter initialization

First, set the target pattern to be reconstructed as F _goal , uniformly sample it in the airspace angle range (-90°, 90°), the number of sampling points is J, and the obtained target pattern sampling is used as the measurement vector f=[F _goal (θ ₁ ), F _goal (θ ₂ ),...,F _goal (θ _J )].

Set the array element spacing _df and the number of array elements N of the virtual array. Generally speaking, the denser the number of array elements in the virtual array, the better the reconstruction effect and the greater the calculation amount, which requires comprehensive consideration. It can be set as d _f =0.05λ, then the virtual array element distribution D=[d ₁ , d ₂ , . . . , d _N ] at this time. Let the excitation vector corresponding to this virtual array be w, and initialize its value to 1.

Step 2. Build a sparse reconstruction model

则虚拟阵列在采样角度上生成的方向图为F＝Aw，以w最稀疏为目标，以重建期望方向图为约束建立稀疏重建模型：Set the observation matrix A according to the compressive sensing theory, A is a J×N complex matrix, and its (j, n)th element is

Then the pattern generated by the virtual array at the sampling angle is F=Aw, with the sparsest w as the goal and the reconstruction of the expected pattern as the constraint to establish a sparse reconstruction model:

s.t.F = f

Step 3. Model conversion

Since the above-mentioned problem about the l ₀ norm of the matrix is an NP-hard problem, it has been proved in the literature that under a certain error, the l ₀ norm of the matrix can be replaced by the l ₁ norm and the two are equivalent after conversion, so we get The following model:

s.t.F = f

Then apply the basis tracking noise reduction theory to it, and transform it into a quadratic programming problem:

Among them, λ is a parameter.

Step 4. ADMM solution

Write the above model in ADMM form:

min f(w)+g(z)

s.t.w-z=0

g(z)＝λ||z||₁，w与z均为变量。则可以写出其增广拉格朗日函数：in,

g(z)=λ||z|| ₁ , both w and z are variables. Then you can write its augmented Lagrangian function:

The idea of ADMM is to fix the remaining two variables and update one of the variables, then the general form of its iterative solution is:

根据KKT条件，

对w求偏导并置零：solve first

According to the KKT condition,

Take the partial derivative with respect to w and set to zero:

Solutions have to:

w ^k+1 ＝(A ^T A+ρI) ^-1 (A ^T f+ρz ^k -μ ^k )

这类问题，可以利用次微分计算出其闭式解，如下：for

For this type of problem, the closed-form solution can be calculated by sub-differentiation, as follows:

易得到其迭代表达式为：for

It is easy to get its iterative expression as:

μ ^k+1 ＝μ ^k +w ^k+1 -z ^k+1

The iteration termination of the above ADMM algorithm can be set to be that the pattern reconstruction error is less than 10 ^-5 , and finally the optimal excitation vector w is obtained through iterative solution.

Step 5 Solve for the optimal array based on the result

According to the compressed sensing theory, the w obtained by solving the above model is sparse, that is, it contains a large number of zero elements, and because the spatial distribution of the virtual array element and the excitation vector are in one-to-one correspondence when the model is established, that is, only non- The array element corresponding to the zero element is excited, so the final optimal array element distribution can be determined according to the position of the non-zero element of w. So far, through the technical method of the present invention, the sparseness of the reconstructed expected pattern is finally obtained at the same time Array element distribution and excitation vector.

Step 6. Simulation Test

For the generation of the target pattern, set the wavelength to 0.3m, use a uniform array with an initial number of array elements of 20 and an element spacing of half a wavelength, add a Chebyshev window to generate a standard pattern of equal sidelobes, and set the average sidelobe The level is -20dB. Uniform sampling is carried out to the expected pattern, the number of sampling points J=37, the distance between the elements of the virtual array is set to 0.05λ, the method of the present invention is used to comprehensively optimize the pattern, and the reconstructed pattern and the distribution of elements are obtained as shown in Fig. 3 and Fig. 4.

In order to verify that the method of the present invention can meet the requirements of multiple different forms of pattern synthesis, the cosecant squared expected pattern is used for simulation verification. The results obtained are shown in Figures 5 and 6, and it can be seen that the reconstruction of the expected pattern can be realized. And the expected effect of reducing the number of array elements.

An embodiment of the present invention also provides an antenna pattern optimization device, including:

a parameter calculation unit, configured to determine initial array parameters according to the target antenna pattern;

A modeling unit, configured to establish a compressed sensing model optimized for an array pattern according to the initial array parameters and preset constraints;

The data processing unit is used to solve the compressed sensing model to obtain optimized array distribution and optimized excitation.

An embodiment of the present invention also 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 term "comprising", "comprising" or any other variation thereof is intended to cover a non-exclusive inclusion such that a process, method, article or apparatus comprising a set of elements includes not only those elements, It also includes other elements not expressly listed, or elements inherent in the process, method, article, or device. Without further limitations, an element defined by the phrase "comprising a ..." does not preclude the presence of additional identical elements in the process, method, article, or apparatus comprising that element.

The serial numbers of the above embodiments of the present invention are for description only, and do not represent the advantages and disadvantages of the embodiments.

Through the description of the above embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus a necessary general-purpose hardware platform, and of course also by hardware, but in many cases the former is better implementation. Based on such an understanding, the essence of the technical solution of the present invention or the part that contributes to the prior art can be embodied in the form of software products, and the computer software products are stored in a storage medium (such as ROM/RAM, disk, CD) contains several instructions to make a terminal (which may be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) execute the methods described in various embodiments of the present invention.

Embodiments of the present invention have been described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementations, and the above-mentioned specific implementations are only illustrative, rather than restrictive, and those of ordinary skill in the art will Under the enlightenment of the present invention, many forms can also be made without departing from the gist of the present invention and the protection scope of the claims, and these all belong to the protection of the present invention.

Claims (4)

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;

solving the compressed sensing model to obtain optimized array distribution and optimized excitation;

the determining initial array parameters according to the target antenna pattern comprises:

sampling the target antenna directional diagram according to the number of preset sampling points, and determining a measurement vector of the compressed sensing model;

the determining initial array parameters according to the target antenna pattern further comprises:

determining an aperture of the target antenna pattern;

determining an initial spatial distribution and an initial excitation from the aperture;

the establishing of the compressed sensing model for optimizing the array directional diagram according to the initial array parameters and the preset constraint conditions comprises the following steps:

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 antenna directional diagram as a constraint, wherein the compressed sensing model meets the following requirements:

s.t.F＝f

wherein, w is the excitation vector of the virtual array to be optimized, the optimization target is the most sparse excitation vector, that is, the number of array elements is the minimum, F is the directional diagram generated by the virtual array at the sampling angle, the specific calculation method is F = Aw, a is a complex matrix of jxn, and the (J, N) th element is

The solving the compressed sensing model to obtain the optimized array distribution and the optimized excitation comprises:

converting the compressed sensing model within a preset error range to obtain an intermediate model;

under a certain error, the matrix l is divided into ₀ Norm is replaced by l ₁ Norm, model converts to:

s.t.F＝f

and then, applying basis tracking to reduce noise, and converting the model into a quadratic programming problem:

wherein λ is a parameter;

converting the intermediate model into an Alternating Direction Multiplier Method (ADMM) form:

min f(w)+g(z)

s.t.w-z＝0

wherein,

g(z)＝λ||z|| ₁ w and z are both variables, and the augmented Lagrangian function is written:

and carrying out iterative solution on the ADMM form to obtain optimized array distribution and optimized excitation, wherein the idea of the ADMM is to fix the other two variables and update one variable, and the general form of the iterative solution is as follows:

and (3) iteratively solving the excitation vector w 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.

2. The antenna pattern optimization method of claim 1, 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.

3. An antenna pattern optimization apparatus, comprising:

the parameter calculation unit is used for determining initial array parameters according to a 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;

the data processing unit is used for solving the compressed sensing model to obtain optimized array distribution and optimized excitation;

the determining initial array parameters according to the target antenna pattern comprises:

sampling the target antenna directional diagram according to the number of preset sampling points, and determining a measurement vector of the compressed sensing model;

the determining initial array parameters from the target antenna pattern further comprises:

determining an aperture of the target antenna pattern;

determining an initial spatial distribution and an initial excitation according to the aperture;

the establishing of the compressed sensing model for optimizing the array directional diagram according to the initial array parameters and the preset constraint conditions comprises the following steps:

and establishing a compressed sensing model optimized by an array directional diagram according to the initial array parameters by taking the optimized excitation sparsest as a target and the reconstructed target antenna directional diagram as a constraint:

s.t.F＝f

wherein, w is the excitation vector of the virtual array to be optimized, the optimization target is the most sparse excitation vector, that is, the number of array elements is the minimum, F is the directional diagram generated by the virtual array at the sampling angle, the specific calculation method is F = Aw, a is a complex matrix of jxn, and the (J, N) th element is

The solving the compressed sensing model to obtain the optimized array distribution and the optimized excitation comprises:

converting the compressed sensing model within a preset error range to obtain an intermediate model;

under a certain error, the matrix l is divided into ₀ Norm is replaced by l ₁ Norm, model converts to:

s.t.F＝f

and then, applying basis tracking to reduce noise, and converting the model into a quadratic programming problem:

wherein λ is a parameter;

converting the intermediate model into an Alternating Direction Multiplier Method (ADMM) form:

min f(w)+g(z)

s.t.w-z＝0

wherein,

g(z)＝λ||z|| ₁ w and z are both variables, and the augmented Lagrangian function is written:

and carrying out iterative solution on the ADMM form to obtain optimized array distribution and optimized excitation, wherein the idea of the ADMM is to fix the other two variables and update one variable, and the general form of the iterative solution is as follows:

and iteratively solving the excitation vector w to obtain w meeting the requirement, and obtaining actually effective virtual array elements according to the positions of nonzero elements in the w, wherein the actually effective virtual array elements form the optimized position distribution of the sparsest array.

4.A computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, which computer program, when being executed by a processor, carries out the steps of the antenna pattern optimization method of any one of claims 1 or 2.

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