A sparse linear array design method and device

Abstract

The embodiment of the present application provides a sparse linear array design method and device. The method includes: first, determining multiple performance indicators of the sparse linear array to be designed, the multiple performance indicators including the upper limit of aperture, the lower limit of aperture, etc.; then, based on the multiple performance indicators, establishing a gridless sparse optimization model based on sidelobe control, and determining the optimized constant diagonal matrix through the gridless sparse optimization model; then, based on the constant diagonal matrix, using the root-finding multi-signal classification Root‑MUSIC algorithm to estimate the frequency of the atoms, and processing the frequency by the least squares method to obtain the weight of the atoms; then, based on a pre-established mapping relationship, converting the frequency and weight into the array element position and excitation of the designed sparse linear array. In this way, the grid mismatch problem existing in the traditional method is overcome by introducing the gridless sparse optimization method, and the constraint term of the array aperture is added, so that the array element position of the sparse linear array falls within the aperture.

Description

Technical Field

[0001] The present application relates to the technical field of array antenna design, and in particular to a sparse linear array design method and device. Background Art

[0002] In the information age, data collection, transmission, and processing technologies have always been core issues in fields such as underwater exploration, mobile communications, unmanned driving, and satellite communications. Since antennas and transducers can radiate and receive signals, they are important media for information transmission. To improve the efficiency of information transmission in space, multiple antennas and transducers can be arranged to form a linear array. Combined with beamforming technology, the linear array system can synthesize a beam pattern with a specific low sidelobe level, thereby suppressing interference and noise from other directions during information transmission. Such array structures have been widely used in radar, sonar, and satellite communication systems. Among them, uniform linear arrays with an element spacing of half a wavelength have been studied by many scholars due to their simple arrangement.

[0003] In practical engineering, increasing the angular resolution of uniform linear arrays and reducing the mainlobe width requires expanding the array aperture. However, large-aperture arrays require a greater number of elements for filling and arranging, increasing system power consumption, cost, and maintenance. To reduce array system cost and equipment complexity, the optimization design of sparse arrays has attracted widespread attention. This involves designing an array structure with low sidelobe levels using a relatively small number of antenna elements while maintaining a nearly constant array size. For example, some researchers have used randomized optimization algorithms such as the ant colony algorithm and the particle swarm algorithm, using the sidelobe level as an objective function to implement element placement and corresponding element excitation solutions for sparse arrays on a position grid. However, such algorithms suffer from the problem of grid mismatch: they require constructing a manifold matrix corresponding to an evenly spaced grid, and the size of the grid affects the algorithm's performance. Furthermore, the optimization process of randomized optimization algorithms such as the ant colony algorithm and the particle swarm algorithm is inherently random, and optimality of the optimization results cannot be guaranteed. Summary of the Invention

[0004] The embodiments of the present application provide a sparse linear array design method and device. For the low-sidelobe sparse linear array optimization model, a reweighted gridless sparse optimization method is introduced to overcome the grid mismatch problem existing in the traditional method, so that the optimization result is a local optimal solution. The optimization model is further modified by adding a constraint term for the array aperture, so that the array element position of the sparse linear array falls within the aperture. The simulation results demonstrate the effectiveness of the algorithm.

[0005] According to a first aspect, a sparse linear array design method is provided. The method comprises: determining multiple performance indicators of a sparse linear array to be designed, the multiple performance indicators including an upper aperture limit, a lower aperture limit, a sidelobe interval, and a constraint upper limit of a peak sidelobe level; establishing a gridless sparse optimization model based on sidelobe control based on the multiple performance indicators, and determining an optimized constant diagonal matrix through the gridless sparse optimization model; estimating the frequency of atoms based on the constant diagonal matrix using a root-multiple signal classification Root-MUSIC algorithm, and processing the frequency using a least squares method to obtain the weight of the atoms; and converting the frequency and weight into element positions and excitations of the designed sparse linear array based on a pre-established mapping relationship.

[0006] In one embodiment, the model formula corresponding to the gridless sparse optimization model is:

[0007] min Tr(T(x))+t

[0008]

[0009]

[0010]

[0011]

[0012] Where T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized.

[0013] In one embodiment, the model formula corresponding to the gridless sparse optimization model is:

[0014] min Tr(WT(x))+t

[0015]

[0016]

[0017]

[0018]

[0019] Where W represents the weight parameter matrix to be optimized, T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized.

[0020] In one embodiment, the frequency constraint is the conjugate complex number of r1, and the calculation formula of r1 is:

[0021]

[0022] Among them, f H represents the upper frequency limit, which is determined based on the upper aperture limit; f L represents the lower frequency limit, which is determined based on the lower aperture limit.

[0023] In one embodiment, the frequency of the atom is estimated based on the constant diagonal matrix using a root-multi-signal classification Root-MUSIC algorithm, including: performing eigendecomposition on the constant diagonal matrix; based on the diagonal matrix included in the eigendecomposition result, estimating the number of arrays K by the energy ratio of the diagonal elements in the diagonal matrix; using the Root-MUSIC algorithm, estimating K frequencies corresponding to the constant diagonal matrix, where each frequency is the frequency of the atom.

[0024] According to a second aspect, a sparse linear array design device is provided, which includes: a performance index determination module for determining multiple performance indexes of a sparse linear array to be designed, the multiple performance indexes including an upper limit of aperture, a lower limit of aperture, a sidelobe interval, and a constraint upper limit of a peak sidelobe level; a model establishment module for establishing a gridless sparse optimization model based on sidelobe control based on the multiple performance indexes, and determining an optimized constant diagonal matrix through the gridless sparse optimization model; an atomic frequency determination module for estimating the frequency of atoms based on the constant diagonal matrix using a root-finding multiple signal classification Root-MUSIC algorithm; an atomic weight determination module for processing the frequency of the atoms by a least squares method to obtain the weight of the atoms; and an atomic data conversion module for converting the frequency and weight into the array element position and excitation of the designed sparse linear array based on a pre-established mapping relationship.

[0025] In one embodiment, the model formula corresponding to the gridless sparse optimization model is:

[0026] min Tr(T(x))+t

[0027]

[0028]

[0029]

[0030]

[0031] Where T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized.

[0032] In one embodiment, the model formula corresponding to the gridless sparse optimization model is:

[0033] min Tr(WT(x))+t

[0034]

[0035]

[0036]

[0037]

[0038] Where W represents the weight parameter matrix to be optimized, T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized.

[0039] In a specific embodiment, the frequency constraint condition is the conjugate complex number of r1, and the calculation formula of r1 is:

[0040]

[0041] Among them, f H represents the upper frequency limit, which is determined based on the upper aperture limit; f L represents the lower frequency limit, which is determined based on the lower aperture limit.

[0042] In one embodiment, the atomic frequency determination module is specifically configured as follows: performing eigendecomposition on the constant diagonal matrix; estimating the number of arrays K by the energy ratio of the diagonal clouds in the diagonal matrix based on the diagonal matrix included in the eigendecomposition result; and using the Root-MUSIC algorithm to estimate K frequencies corresponding to the constant diagonal matrix, where each frequency is the frequency of an atom.

[0043] A sparse linear array design method and device disclosed in an embodiment of this specification is used. First, multiple performance indicators of the sparse linear array to be designed are determined, and the multiple performance indicators include the upper limit of the aperture, the lower limit of the aperture, etc. Based on the multiple performance indicators, a gridless sparse optimization model based on sidelobe control is established, and the optimized constant diagonal matrix is determined through the gridless sparse optimization model; then, based on the constant diagonal matrix, the root-multi-signal classification Root-MUSIC algorithm is used to estimate the frequency of the atoms, and the frequency is processed by the least squares method to obtain the weight of the atoms; then, based on a pre-established mapping relationship, the frequency and weight are converted into the array element position and excitation of the designed sparse linear array. In this way, by introducing the gridless sparse optimization method, the grid mismatch problem existing in the traditional method is overcome, and the constraint term of the array aperture is added, so that the array element position of the sparse linear array falls within the aperture. The simulation results illustrate the effectiveness of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of a sparse linear array design method provided in an embodiment of the present application;

[0045] Figure 2 The beam pattern of the sparse linear array in the sparse linear array design result based on the sidelobe control of formula (9) is shown;

[0046] Figure 3 The amplitude distribution of the sparse linear array in the sparse linear array design result based on the sidelobe control of formula (9) is shown;

[0047] Figure 4 The beam pattern of the sparse linear array design results based on sidelobe control and aperture constraint of formula (18) is shown;

[0048] Figure 5 The amplitude distribution of the sparse linear array design results based on sidelobe control and aperture constraint of formula (18) is shown;

[0049] Figure 6It is a structural schematic diagram of a sparse linear array design device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below with reference to the accompanying drawings.

[0051] In the description of the embodiments of the present application, words such as "exemplary," "for example," or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary," "for example," or "for example" in the embodiments of the present application should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary," "for example," or "for example" is intended to present the relevant concepts in a concrete manner.

[0052] In the description of the embodiments of the present application, the term "and / or" is merely a description of the association relationship between associated objects, indicating that three relationships may exist. For example, A and / or B can represent: A exists alone, B exists alone, and A and B exist at the same time. In addition, unless otherwise specified, the term "plurality" means two or more. For example, "multiple systems" refers to two or more systems, and "multiple screen terminals" refers to two or more screen terminals.

[0053] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly identifying the technical features being referred to. Thus, features specified as "first" or "second" may explicitly or implicitly include one or more of such features. The terms "include," "comprising," "having," and their variations all mean "including but not limited to," unless otherwise specifically emphasized.

[0054] An embodiment of the present application provides a sparse linear array design method. For a low-sidelobe sparse linear array optimization model, a reweighted gridless sparse optimization method is introduced to overcome the grid mismatch problem existing in traditional methods, so that the optimization result is a local optimal solution. The optimization model is further modified by adding a constraint term for the array aperture, so that the array element position of the sparse linear array falls within the aperture.

[0055] Next, we will first describe the conception and derivation process of the algorithm structure corresponding to the above design method.

[0056] 1. The beam pattern model of the linear array is represented as a linear model based on an atomic set.

[0057] For the beam pattern model of a linear array, for the above aperture length L, the number of array elements N, the corresponding array element positions are [d1, d2, …, dN ], then the beam pattern model can be expressed as:

[0058]

[0059] where d n Indicates the position of the nth array element; represents the excitation of the nth array element corresponding to the integrated mth beam pattern; k0 represents the wave number, and k0 = 2π / λ, where λ is the wavelength; u represents the direction of the lobe, and u = sinθ, where θ is the angle between the beam direction and the normal of the linear array; Represents an imaginary unit.

[0060] The sparse linear array is designed using the reweighted gridless sparse optimization method provided by the embodiment of the present invention. First, formula (1) can be integrated into an atom-based polynomial addition form, considering the beam pattern of each mode sampled at a uniform interval, that is, defining Δ = 1 / (J-1) and In addition, the definition of atomic set is introduced, that is, for atoms with frequency f The corresponding atomic set can be expressed as:

[0061]

[0062] in represents the interval where the frequency parameter f is located. Formula (1) can then be expressed as a linear model based on an atomic set, namely:

[0063]

[0064] in, And the atomic weight

[0065] Second, the sparse linear array design problem is transformed into an optimization form through gridless optimization theory.

[0066] In some embodiments, it can be seen from formula (3) that the beam pattern model of the linear array is consistent with the multi-observation vector model in the line spectrum estimation problem. In other words, there is consistency between the array design problem and the sparse line spectrum estimation problem. In addition, the array parameters and the frequency parameters obey a linear relationship, that is, the array element position excitation Frequency of atoms with frequency estimation problem and weights There are the following relationships:

[0067]

[0068] in, is the array position, To motivate, is the frequency of the atom, is the weight.

[0069] The atomic zero norm based on formula (3) is defined as:

[0070]

[0071] According to formulas (4) and (5), due to the consistency between the array design problem and the line spectrum estimation problem, from the perspective of parameter sparsity, the gridless sparse parameter algorithm in the line spectrum estimation problem can be introduced into the sparse linear array design. In summary, in order to transform the sparse linear array design problem into an optimization form, we introduce the gridless sparse optimization algorithm.

[0072] Considering the peak sidelobe level suppression model, we can express the sparse linear array design problem as follows using meshless optimization theory:

[0073]

[0074] Where u0 = sin(θ0) represents the main lobe direction of the beam, u∈S represents the sidelobe area, and ρ(u) represents the upper limit of the sidelobe level, which is generally calculated using the peak side-lobe level (PSLL). For example, if we want to generate a pencil beam with a sidelobe level of PSLL, then

[0075] However, for formula (6), the atomic 0 norm is a non-convex function, and the optimization problem is NP-hard, and it is difficult to obtain the optimal solution. In order to use the convex optimization algorithm to obtain a better solution that approximates the performance of the optimization formula (6), the atomic 0 norm can be convexly relaxed to the atomic norm. Right now:

[0076]

[0077] Therefore, formula (6) is relaxed to the following optimized form:

[0078]

[0079] For formula (8), it is a standard convex optimization problem. However, the atomic norm is a norm expressed on a continuous parameter domain. Its norm form is much more complicated than the 1-norm, and it is difficult to directly solve the optimal solution through the optimization algorithm.

[0080] 3. Convert the optimization form into an equivalent semi-positive definite programming form.

[0081] The applicant proposed that the above formula (8) can be transformed into an equivalent semi-positive programming form, namely:

[0082]

[0083] Where T() represents the Toeplitz map, that is:

[0084]

[0085] However, if the optimization is performed according to formula (9), the optimized array element position will often exceed the preset aperture, causing the optimization result to lose physical meaning. Therefore, the frequency constraint condition is introduced, that is, the definition formula is:

[0086]

[0087] It should be noted that g(z) is equivalent to the following form, namely:

[0088]

[0089] in,

[0090]

[0091]

[0092] For formula (11), the frequency position corresponding to the variable z is located at [f L ,f H ] if and only if g(z)≥0, we can use the above conclusion to solve the problem of array aperture constraint that needs to be solved by the present invention. Assuming that the aperture of the sparse array is L, that is, the spacing between the array elements is within [0,L], then f L and f H It needs to be set as follows:

[0093]

[0094] For the variable to be optimized x=[x0,x1,x2,…,x N-1 ],definition

[0095]

[0096] x0=[x0,x1,x2,…,x N-2 ]

[0097] x1=[x2,x3,…,x N ] (15)

[0098] Then for T(x) in formula (9), the elements of the sparse array are located in [0, L] if and only if

[0099]

[0100] Then the optimization is transformed into

[0101]

[0102] Obviously, compared with formula (9), there is only one more aperture constraint term, but this term can ensure that the array element falls within the array aperture.

[0103] 4. Introducing the idea of reweighted iteration

[0104] Optionally, in order to increase the sparsity of the optimization results, the idea of reweighted iteration can be introduced and the optimization equation can be expressed as follows:

[0105]

[0106] Among them, W is the weighted term of the optimization iteration, which is obtained by calculating the results of each optimization, that is, W = T(x) + ∈ I) -1 , where ∈ represents the penalty term parameter and I represents the identity matrix.

[0107] Such weighted iterations often require two or three times to obtain the sparsest solution.

[0108] 5. Determine the array elements and excitation of the sparse array and complete the sparse array reconstruction

[0109] After obtaining the sparsest solution, the specific number of sparse array elements is determined by judging the eigenvalues of the covariance matrix. First, the Toeplitz matrix (or constant diagonal matrix) is decomposed to obtain

[0110] T(x)=EΛE H (19)

[0111] Where Λ is a diagonal matrix, K can be estimated by the energy ratio of the diagonal elements, that is, satisfying the following formula

[0112]

[0113] The above results in the number of array elements K.

[0114] When K is determined, the K frequencies corresponding to T(x) can be estimated by the subspace method. In this paper, we use the Root-MUSIC algorithm to estimate the frequency When the optimal atomic frequency is obtained Then, the weights of atoms are estimated using the least squares method, i.e. in Indicates the inverse operation. When the optimal frequency is obtained and weights After that, we can use formula (4) to convert the atomic frequency and weight into the array element position and excitation of the sparse array, thereby completing the design of the sparse reconfigurable linear array.

[0115] The above mainly describes the conception and derivation process of the algorithm structure corresponding to the above design method.

[0116] Figure 1 This is a flow chart of a sparse linear array design method provided in an embodiment of the present application. Figure 1 As shown, the method includes the following steps S10-S40:

[0117] Step S10, determining multiple performance indicators of the sparse linear array to be designed, the multiple performance indicators including the aperture upper limit L, the aperture lower limit (such as 0), the sidelobe interval S and the constrained upper limit ρ(u) of the peak sidelobe level.

[0118] Step S20: Based on the aforementioned multiple performance indicators, a gridless sparse optimization model based on sidelobe control is established, and the optimized constant diagonal matrix is determined by the gridless sparse optimization model. The model formula corresponding to the gridless sparse optimization model can be the aforementioned formula (17) or formula (18). Multiple iterations are performed based on the model formula to obtain the optimized (or optimized) constant diagonal matrix T(x).

[0119] Step S30: Based on the optimized constant diagonal matrix, the root-multi-signal classification Root-MUSIC algorithm is used to estimate the frequency of the atom. The frequency is processed by the least square method to obtain the weight of the atom

[0120] Step S40: Based on a pre-established mapping relationship, the frequency and weight are converted into the element position and excitation of the designed sparse linear array. For example, the above formula (4) can be used to achieve the conversion.

[0121] Next, an application example of the algorithm flow of the present invention is introduced.

[0122] Table 1 Algorithm flow chart

[0123]

[0124] In summary, the technical solution of the present invention, starting from gridless sparse optimization, proposes a sparse linear array design method based on sidelobe control and reweighted atomic norm minimization, thus avoiding the problem of grid mismatch. Furthermore, the present invention derives a constraint on the array aperture, which ensures that the array elements are arranged within the array aperture and ensures the effectiveness of the designed sparse linear array.

[0125] Furthermore, the effects of the embodiments of the present application are illustrated by conducting a sidelobe level experimental analysis.

[0126] Specifically, the experiment uses a sparse linear array with an aperture of 10.6λ. The resulting pencil beam has a peak sidelobe level no higher than -20.63dB, and a mainlobe width no wider than 11°. This means that any region with |u| greater than 0.0965 is considered a sidelobe region. The following experiments demonstrate the effectiveness of aperture constraints.

[0127] First, if we use formula (9) to optimize, the experimental results are as follows Figure 2 shown.

[0128] Obviously, the experiment shows that the beam pattern of the sparse linear array designed directly by formula (9) with the sidelobe level as the constraint cannot meet the requirements. According to analysis, the main problem of such a result is that the position of the array elements is not arranged within the aperture. Figure 3 As shown in , the position of the array element falls outside the aperture 10.6λ, resulting in the design result not meeting the expected settings.

[0129] If we use formula (18) to optimize, the experimental results are as follows: Figure 4 and Figure 5 shown.

[0130] from Figure 4 From the beam pattern of the sparse linear array, we can see that a pencil beam with low sidelobe level can be synthesized in the visible area, and its sidelobe level is -20.63dB, which is consistent with the performance of the sparse linear array we expect. Figure 5 From the position of the elements in the sparse linear array, it can be seen that the aperture of the array is 10.6λ, and the number of elements is 12, which is much smaller than the number of elements in the uniform linear array with equal intervals of half wavelength. This shows that the aperture constraint term in formula (18) plays the role of sparse design.

[0131] Corresponding to the above method, an embodiment of this specification also discloses a sparse linear array design device. Figure 6 This is a schematic structural diagram of a sparse linear array design device provided in an embodiment of the present application. Figure 6 As shown, the apparatus 600 includes the following modules:

[0132] The performance index determination module 610 is used to determine multiple performance indicators of the sparse linear array to be designed, and the multiple performance indicators include the upper limit of aperture, the lower limit of aperture, the sidelobe range and the upper limit of the peak sidelobe level constraint; the model establishment module 620 is used to establish a gridless sparse optimization model based on sidelobe control based on multiple performance indicators, and determine the optimized constant diagonal matrix through the gridless sparse optimization model; the atomic frequency determination module 630 is used to estimate the frequency of the atom based on the constant diagonal matrix using the root-finding multiple signal classification Root-MUSIC algorithm; the atomic weight determination module 640 is used to process the frequency by the least squares method to obtain the weight of the atom; the atomic data conversion module 650 is used to convert the frequency and weight into the array element position and excitation of the designed sparse linear array based on a pre-established mapping relationship.

[0133] In one embodiment, the model formula corresponding to the gridless sparse optimization model is the above formula (17).

[0134] In another embodiment, the model formula corresponding to the gridless sparse optimization model is the above formula (18).

[0135] In a specific embodiment, in the frequency constraint condition included in formula (17) or (18), is the conjugate complex number of r1, and the calculation formula of r1 is:

[0136]

[0137] Among them, f H Represents the upper frequency limit, which is determined based on the upper aperture limit; f L Represents the lower frequency limit, which is determined based on the lower aperture limit.

[0138] In one embodiment, the atomic frequency determination module is specifically configured as follows: performing eigendecomposition on a constant diagonal matrix; estimating the number of arrays K by the energy ratio of the diagonal clouds in the diagonal matrix based on the diagonal matrix included in the eigendecomposition result; and using the Root-MUSIC algorithm to estimate K frequencies corresponding to the constant diagonal matrix, where each frequency is the frequency of an atom.

[0139] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware or any combination thereof. When software is used for implementation, all or part of the embodiments can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions according to the embodiments of the present application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center via a wired connection, such as a coaxial cable, optical fiber, digital subscriber line (DSL), or wireless, such as infrared, wireless, microwave, etc. The computer-readable storage medium can be any available medium that a computer can access or a data storage computing device such as a server or data center that includes one or more available media. The available medium can be a magnetic medium (such as a floppy disk, hard disk, tape, etc.), an optical medium (such as a DVD, etc.), or a semiconductor medium, such as a solid state drive (SSD), etc.

[0140] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

Claims

1. A sparse linear array design method, characterized in that: include: Determining multiple performance indicators of a sparse linear array to be designed, the multiple performance indicators including an upper limit of aperture, a lower limit of aperture, a sidelobe interval, and a constraint upper limit of a peak sidelobe level; Based on the multiple performance indicators, a gridless sparse optimization model based on sidelobe control is established, and the optimized constant diagonal matrix is determined by the gridless sparse optimization model; the model formula corresponding to the gridless sparse optimization model is: min Tr(T(x))+t Where T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized; Based on the constant diagonal matrix, the frequencies of the atoms are estimated using the root-multiple signal classification (Root-MUSIC) algorithm, and the frequencies are processed by the least squares method to obtain the weights of the atoms; Based on a pre-established mapping relationship, the frequencies and weights are converted into element positions and excitations of the designed sparse linear array.

2. The method according to claim 1, characterized in that The model formula corresponding to the gridless sparse optimization model is: min Tr(WT(x))+t Where W represents the weight parameter matrix to be optimized, T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized.

3. The method according to claim 1 or 2, characterized in that The frequency constraint is the conjugate complex number of r1, and the calculation formula of r1 is: Among them, f H represents the upper frequency limit, which is determined based on the upper aperture limit; f L represents the lower frequency limit, which is determined based on the lower aperture limit.

4. The method according to claim 1, wherein The method of estimating the frequency of the atom using a root-multi-signal classification (RMSIC) algorithm based on the constant diagonal matrix includes: Performing eigendecomposition on the constant diagonal matrix; Based on the diagonal matrix included in the eigendecomposition result, the number of arrays K is estimated by the energy ratio of the diagonal elements in the diagonal matrix; Using the Root-MUSIC algorithm, K frequencies corresponding to the constant diagonal matrix are estimated, where each frequency is the frequency of an atom.

5. A sparse linear array design device, characterized in that: include: A performance index determination module is used to determine multiple performance indicators of the sparse linear array to be designed, wherein the multiple performance indicators include an upper limit of aperture, a lower limit of aperture, a sidelobe interval, and a constraint upper limit of a peak sidelobe level; A model building module is used to establish a gridless sparse optimization model based on sidelobe control based on the multiple performance indicators, and determine the optimized constant diagonal matrix through the gridless sparse optimization model; the model formula corresponding to the gridless sparse optimization model is: min Tr(T(x))+t Where T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized. an atomic frequency determination module, configured to estimate the frequency of the atom using a root-multi-signal classification (RMSIC) algorithm based on the constant diagonal matrix; an atom weight determination module, configured to process the frequencies of the atoms by a least square method to obtain the weights of the atoms; The atomic data conversion module is used to convert the frequency and weight into the array element position and excitation of the designed sparse linear array based on a pre-established mapping relationship.

6. The device according to claim 5, characterized in that The model formula corresponding to the gridless sparse optimization model is: min Tr(WT(x))+t Where W represents the weight parameter matrix to be optimized, T(x) represents the constant diagonal matrix to be optimized, represents the frequency constraint, represents the linear model based on the atomic set corresponding to the beam pattern model, Tr() represents the trace of the matrix, H represents the transpose of the matrix, represents the beam sample space, u0 represents the main lobe direction of the beam, u represents the side lobe direction of the beam, S represents the side lobe interval, ρ(u) represents the upper limit of the peak side lobe level, and t represents the intermediate parameter to be optimized.

7. The device according to claim 5 or 6, characterized in that The frequency constraint is the conjugate complex number of r1, and the calculation formula of r1 is: Among them, f H represents the upper frequency limit, which is determined based on the upper aperture limit; f L represents the lower frequency limit, which is determined based on the lower aperture limit.

8. The device according to claim 5, characterized in that The atomic frequency determination module is specifically configured as follows: Performing eigendecomposition on the constant diagonal matrix; Based on the diagonal matrix included in the eigendecomposition result, the array number K is estimated by the energy ratio of the diagonal clouds in the diagonal matrix; Using the Root-MUSIC algorithm, K frequencies corresponding to the constant diagonal matrix are estimated, where each frequency is the frequency of an atom.

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