A method for constructing a reconfigurable sparse linear array

Abstract

The application provides a method for constructing a reconfigurable sparse linear array, which comprises the following steps: firstly, sampling a target beam to obtain a matrix constituted by sampling beams; secondly, obtaining a rank-minimum Toeplitz matrix by a weighted atom norm minimization method; thirdly, estimating the frequency and weight of the atom by using a Root-MUSIC algorithm; and finally, converting the frequency and weight into the element position and excitation of the reconfigurable sparse linear array through a mapping relationship. The RANM algorithm provided by the application has a performance advantage in the sparsity, can reduce the number of elements under the condition that the shape of the radiation beam pattern is almost unchanged, and thus reduces the complexity and power consumption of the system. The algorithm avoids the grid mismatch problem existing in the traditional sparse recovery algorithm, and thus is superior to the traditional reconfigurable sparse linear array algorithm in the matching accuracy of the reconstructed beam.

Description

Technical Field

[0001] This invention belongs to the field of reconfigurable linear arrays, and specifically relates to a method for constructing a reconfigurable sparse linear array. Background Technology

[0002] In the information age, data acquisition, transmission, and processing technologies have always been core issues in fields such as underwater exploration, mobile communication, autonomous driving, and satellite communication. Since antennas and transducers can radiate and receive signals, they are crucial mediums for information transmission. To improve the efficiency of information transmission in space, multiple antennas and transducers can be arranged into a linear array, and combined with beam pattern synthesis technology, the linear array system can radiate a specific shape of low-sidelobe, high-gain beam pattern, thereby suppressing interference and noise from other directions during information transmission. Therefore, beam pattern synthesis technology plays a vital role in the design of linear array systems.

[0003] In practical engineering, to reduce the main lobe width of the beam pattern and improve the angular resolution of the linear array, it is necessary to increase the array aperture and the number of elements. Therefore, for uniform linear array systems with element spacing no greater than half a wavelength, increasing the number of elements increases system complexity, power consumption, cost, and maintenance difficulty. To reduce system complexity and cost, beam pattern synthesis technology for sparse linear arrays has gained attention. This technology reduces the number of elements and optimizes their physical layout while maintaining a nearly constant array aperture (i.e., constant angular resolution), enabling the generation of a beam pattern that meets desired performance. Because most sparse linear arrays designed in this way have element spacing greater than half a wavelength, their inter-element coupling effect is weaker compared to uniform linear arrays, resulting in better performance in real-world environments.

[0004] In recent years, reconfigurable linear arrays have experienced rapid development. Unlike traditional linear arrays with a single operating mode, reconfigurable linear arrays, for linear array structures with fixed element positions, achieve operating mode switching by introducing switching devices to control the radiation characteristics of the elements. In other words, reconfigurable linear arrays can transmit beam patterns of different shapes by changing the excitation mode of each element. However, uniformly arranged reconfigurable linear arrays require a large number of elements and have complex back-end circuitry, resulting in high system complexity and high power consumption, making them difficult to use in systems with power consumption requirements. To address this issue, beam pattern synthesis techniques based on sparse reconfigurable linear arrays have received extensive research. For example, some researchers have proposed matrix beamforming (MPM) and unitary matrix beamforming (UMPM) methods based on parameter estimation. The linear array structures designed by these algorithms can reduce the number of elements while maintaining almost no change in the beam pattern shape, further reducing system complexity and cost. However, these two algorithms only design the element positions and excitations of the reconfigurable sparse linear array based on parameter estimation, and do not design the reconfigurable sparse linear array based on the sparsity of the elements in the position interval. Therefore, in terms of element sparsity performance, they are not as good as the algorithms that start from the sparsity perspective.

[0005] Although matrix beamforming (MPM) and unitary matrix beamforming (UMPM) algorithms can design reconfigurable sparse linear arrays, these two algorithms only design the element positions and excitations of reconfigurable sparse linear arrays from the perspective of parameter estimation. They do not consider the sparsity of the elements in the position interval when designing the beam of reconfigurable sparse linear arrays. Therefore, in terms of element sparsity performance, they are not as good as algorithms that start from the perspective of sparsity. Summary of the Invention

[0006] The purpose of this invention is to overcome the poor performance of existing reconfigurable sparse linear array algorithms.

[0007] To achieve the above objectives, this invention proposes a method for constructing a reconfigurable sparse linear array. The method involves first sampling the target beam to obtain a matrix composed of the sampled beams, then obtaining the rank-minimum Toplitz matrix through a weighted atom norm minimization method, then estimating the frequency and weight of the atoms using the Root-MUSIC algorithm, and finally converting the frequency and weight into the element positions and excitations of the reconfigurable sparse linear array through a mapping relationship.

[0008] As an improvement to the above method, the method specifically includes:

[0009] Step 1: Obtain data by uniformly sampling the M beammaps of the known reconfigurable uniform linear array. That is, for ,have:

[0010]

[0011] in, Indicates the comprehensive first When the beam pattern is in The corresponding reference beam pattern data; This is a hyperparameter representing the number of sampling points; For the first n The position of each array element; Indicates wave number; Indicates wavelength; Represents the imaginary unit; N The number of array elements; To comprehensively The corresponding beam pattern of the first beam The incentive of each array element; To comprehensively When the beam pattern is... Phase coefficients of the excitation of each array element To comprehensively When the beam pattern is... The amplitude coefficient of the excitation of each array element;

[0012] Set the maximum number of iterations in the reweighted atomic norm minimization model. q reweighted matrix The penalty term hyperparameter Optimize the error hyperparameters in the equation ;

[0013] Step 2: Initialize the weight parameters for the first time ;

[0014] in, The sign for conjugate transpose; It is the identity matrix;

[0015] Step 3: Solve the optimization equation

[0016]

[0017] Obtain the current iteration, i.e., the... j The optimal solution of the next iteration ;

[0018] in, This represents the computation of the trace of a matrix; Represents the Toeplitz mapping; Denotes the Frobenius norm; For the first j Weight parameters at the next iteration; , , All are complex optimization variables. , , Indicates the first j During the next iteration , , The optimal value, that is, the value that can be achieved in step 3. The solution with the smallest value; For complex numbers;

[0019] Step 4: Solve based on the results of the current iteration Update the weight matrix to be used in the next iteration:

[0020]

[0021] in, For the first j+1 Weight parameters at the next iteration;

[0022] Step 5: Set the current iteration number j +1, if j Greater than the maximum number of iterations q If so, proceed to step 6; otherwise, proceed to step 3.

[0023] Step 6: Optimize the result from the last iteration in Step 3. As the optimal solution ,right Using eigenvalue decomposition, i.e.:

[0024]

[0025] in, It is a monotonically decreasing diagonal matrix, and the eigenvalues ​​are located on the diagonal. The feature matrix is ​​composed of eigenvectors, and each column vector is linearly independent.

[0026] Estimating the number of elements in a sparse linear array based on the ratio of eigenvalues. ,Right now The following conditions must be met:

[0027]

[0028] in, This is the ratio threshold;

[0029] Step 7: Use the Root-MUSIC algorithm to pass estimate K A vector composed of frequencies Then, the weight matrix of the atoms is obtained using the least squares method. ;

[0030] in, A matrix composed of frequency vectors; This indicates a pseudo-inverse operation; The optimal variable after multiple iterations of optimization in step 3. ;

[0031] Step 8: Use the following formula to... and Transformation into element positions of a reconfigurable sparse linear array and incentives ,Right now:

[0032]

[0033] in, Wavelength; It represents the Hadamardi (or Hadama) stack.

[0034] As an improvement to the above method, the hyperparameter of the number of sampling points Values ​​range from 12 to 15; the maximum number of iterations in the reweighted atomic norm minimization model. q=6 Reweighted matrix The penalty term hyperparameter Values ​​range from 1 to 10; error hyperparameters in the optimization equation. Values ​​range from 0.001 to 0.01; the ratio threshold in eigenvalue decomposition. The value ranges from 0.01 to 0.03.

[0035] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method as described in any of the preceding claims.

[0036] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the method described in any of the preceding claims.

[0037] Compared with the prior art, the advantages of the present invention are:

[0038] 1. Compared with MPM and UMPM algorithms, the RANM algorithm proposed in this invention represents the design problem of reconfigurable sparse linear arrays as an optimization model based on the atomic norm. It directly optimizes the array element positions and excitations from the perspective of the sparsity of array elements. Therefore, the RANM algorithm has a performance advantage in sparsity and can reduce the number of array elements while keeping the shape of the radiation beam pattern almost unchanged, thereby reducing the complexity and power consumption of the system.

[0039] 2. This invention proposes a reweighted atom norm minimization algorithm (RANM) from the perspective of the sparsity of the array element position arrangement. This algorithm regards the design problem of reconfigurable sparse linear array as a sparse optimization problem on a continuous interval, constructs the corresponding convex optimization model, and then theoretically obtains the sparsest solution of reconfigurable sparse linear array.

[0040] 3. The algorithm used in this invention is an optimization algorithm based on continuous intervals. Therefore, it avoids the grid mismatch problem existing in traditional sparse recovery algorithms, and thus outperforms traditional reconfigurable sparse linear array design algorithms in terms of matching accuracy of reconstructed beams. Attached Figure Description

[0041] Figure 1 The diagram shown is a flowchart of the design of a reconfigurable sparse linear array based on the reweighted atomic norm.

[0042] Figure 2 The image shows the multi-mode beam pattern of the original uniform linear array in the experiment of reconfigurable linear array sparse design with two working modes.

[0043] Figure 3 The figure shown is a sparse design result diagram of the RANM algorithm for the sparse design experiment of reconfigurable linear array in two working modes;

[0044] Figure 4 The image shows the multi-mode beam pattern of the original uniform linear array in the experiment of reconfigurable linear array sparse design with three working modes.

[0045] Figure 5 The figure shows the sparse design results of the RANM algorithm in the sparse design experiment of reconfigurable linear arrays with three working modes. Detailed Implementation

[0046] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0047] This invention proposes a reweighted atom norm minimization algorithm (RANM) based on the sparsity of the array element arrangement. This algorithm treats the sparse linear array design problem as a sparse optimization problem over a continuous interval, constructs a corresponding convex optimization model, and theoretically obtains the sparsest solution for the reconfigurable sparse linear array design. Furthermore, since this algorithm is based on continuous interval optimization, it avoids the mesh mismatch problem present in traditional sparse recovery algorithms, thus outperforming traditional reconfigurable sparse linear array algorithms in terms of beam matching accuracy.

[0048] The RANM algorithm requires four steps to design a reconfigurable sparse linear array. First, the target beam is sampled to obtain the matrix formed by the sampled beams. Second, the Toeplitz matrix with the minimum rank is obtained through the weighted atom norm minimization method. Third, the Root-MUSIC algorithm is used to estimate the frequencies and weights of the atoms. Finally, the frequencies and weights are transformed into the element positions and excitations of the reconfigurable sparse linear array through a mapping relationship. The algorithm flow is as follows: Figure 1 As shown.

[0049] For the beam pattern model of a reconfigurable linear array, assuming the aperture length is... The number of array elements is The position of the array element is For a reconfigurable beam pattern of a half-wavelength uniform linear array, the element positions satisfy... Furthermore, changing the element excitation of each element can switch the array's [function / function]. This working state, that is, generating Different beam patterns can be represented by the following model:

[0050] (1)

[0051] in Indicates the first n The position of each array element; Indicates the comprehensive first The corresponding beam pattern of the first beam The incentive of each array element; Indicates wave number; ,in The angle between the beam direction and the linear array normal; It represents the imaginary unit.

[0052] In the design problem of reconfigurable sparse linear arrays, the main objective is to design a new linear array with the minimum number of elements, which can emit a beam pattern that is nearly identical to the target reference beam shape. This problem can be represented by the following mathematical model:

[0053] (2)

[0054] in Given a known reference beam pattern, the element positions of the sparse linear array. and array element incentive These are the variables that need to be solved. It can be seen that formula (2) is a sparse recovery model, so the sparse recovery algorithm can effectively design sparse linear arrays.

[0055] In this invention, a reweighted atomic norm method is used to design a reconfigurable sparse linear array. First, equation (1) is integrated into an atom-based polynomial summation form, considering the sampling of beam patterns for each mode at uniform intervals, i.e., defining... and Furthermore, the definition of the atom set in the line spectrum estimation problem is introduced, that is, the basis vector of frequency can be defined as the atom set. Then the set of atoms is represented as:

[0056] (3)

[0057] in Represents frequency parameters The interval in which it is located. Therefore, the beam pattern of formula (1) can be represented as a linear combination model of atoms:

[0058] (4)

[0059] in And atomic weight As can be seen from Equation (4), the beam pattern model of the reconfigurable array is consistent with the multi-observation vector model in the line spectrum estimation problem, that is, there is consistency between the array design problem and the sparse line spectrum estimation problem. Furthermore, Equation (4) shows that the array parameters and frequency parameters follow a linear relationship, i.e., the array element positions... ,excitation The frequency of atoms in the frequency estimation problem and weight The following relationships exist:

[0060] (5)

[0061] 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 meshless sparse parameter algorithm in the line spectrum estimation problem can be extended to the design of sparse reconfigurable linear arrays. In summary, in order to express the sparse reconfigurable linear array design model represented by formula (2) in the form of sparse parameter estimation, the definition of the atomic 0 norm in the meshless sparse estimation algorithm is first introduced. ,Right now:

[0062] (6)

[0063] As can be seen from the form of formula (6), the meaning of the atomic 0 norm is consistent with the objective function of formula (2). Therefore, formula (2) can be further expressed as a norm optimization model, namely:

[0064] (7)

[0065] in This represents the Frobenius norm. Equation (7) means that the sampling matrix of the observed beam... It conforms to model (1) and constrains its error with the target beam matrix to be less than Under the condition of minimizing the number of array elements K, that is, obtaining the sparsest solution through optimization. However, the atomic 0 norm as the objective function is non-convex, so the optimization problem of formula (7) cannot be solved by convex optimization algorithm. In order to estimate the array element positions and excitations of sparse array elements using convex optimization algorithm, it is necessary to perform convex relaxation on the objective function of formula (6), that is, to convexly relax the atomic 0 norm into the atomic norm. The atomic norm is defined as:

[0066] (8)

[0067] Then equation (6) can be relaxed into the following convex optimization problem:

[0068] (9)

[0069] Furthermore, this convex optimization problem is equivalent to the following positive semidefinite programming problem:

[0070] (10)

[0071] in This represents the computation of the trace of a matrix. , , All are variables, and the optimal solution of formula (10) can be directly obtained using the CVX package. It is important to note that here... The meaning of u is different from that in formulas (1)-(4), here... The variable that needs to be optimized is u in formulas (1)-(4), which represents the angle function of the beam in space, i.e., u=sinθ in formulas (1)-(4). This represents the Toeplitz mapping, i.e.:

[0072] (11)

[0073] For the sparse parameter optimization models of formulas (9) and (10), the atomic norm after convex relaxation is... While it can achieve a sparsity effect, its frequency sparsity is not comparable to that of the atomic zero norm. There will be a certain performance gap between them, that is, the accuracy and sparsity of the frequencies obtained by solving formula (10) may not be as good as the results of formula (7). In order to improve the performance of the optimization model (10), the idea of ​​reweighted iteration is introduced to transform the optimization problem of formula (10) into an iterative optimization form. This iterative optimization algorithm can break through the atomic norm. The sparsity and resolution performance limitations of the optimization model allow its performance to approach that of the atomic 0-norm. The performance of this iterative optimization model can be expressed in the following form:

[0074] (12)

[0075] in j As a subscript, it indicates the first... j iteration Represents a reweighted matrix. I Represents the identity matrix. It is an adjustable parameter, when When the objective function performance of formula (12) is close to the atomic 0 norm, when At that time, the performance of the objective function of formula (12) is close to the atomic norm. Setting appropriate parameters... This can appropriately improve the sparsity and accuracy of the estimated parameters. However, this optimization model requires recalculating the optimization weights in each iteration. Therefore, this model is also called the reweighted atomic norm minimization model (RANM). Furthermore, the optimal variable obtained through formula (12) is expressed as... .

[0076] For the meshless optimization algorithm, the optimal result obtained by formula (12) is... The corresponding Toeplitz matrix This is equivalent to the covariance matrix of the signal model, and this covariance matrix... It contains sparse frequency parameters The information can be used to estimate the sparse frequency using the subspace method. ,Right now It conforms to the following relationship:

[0077] (13)

[0078] in A matrix composed of frequency vectors. and In order to successfully obtain K optimal frequencies First, we need to use the covariance matrix. The eigenvalues ​​determine the number of atoms K, i.e., the Toeplitz matrix. By performing eigenvalue decomposition, we can obtain:

[0079] (14)

[0080] in K is a diagonal matrix, and its value is estimated by the energy ratio of the diagonal elements of the characteristic matrix. Specifically, K needs to satisfy the following formula:

[0081] (15)

[0082] Once K is determined, it can be used through subspace class methods. Estimate the corresponding K frequencies In this invention, the Root-MUSIC algorithm is used to estimate the frequency. When the optimal atomic frequency is obtained Then, the weights of the atoms in formula (4) are estimated using the least squares method. ,in This indicates a pseudo-inverse operation.

[0083] When the optimal frequency is obtained and weight Then, the atomic frequency and weight are converted into the element positions and excitations of the sparse array using formula (5), thereby completing the design of the sparse reconfigurable linear array.

[0084] Algorithm: A reconfigurable sparse linear array design method based on reweighted atomic norms:

[0085]

[0086]

[0087] In the experiments, the performance of the algorithm was verified through beam pattern experiments with two reconfigurable sparse linear arrays, and the sparsity and normalized mean square error were used to evaluate the algorithm's performance. First, the normalized mean square error between the reconfigured beam and the target beam was defined. for

[0088] (16)

[0089] In addition, the sparsity of a reconfigurable sparse linear array is defined. for .

[0090] In Experiment 1, for Figure 2 The reconfigurable linear array is designed with sparse density. For Figure 2 The original uniform linear array in the image has the following number of elements. Work mode The beam patterns corresponding to the two modes are pencil beam and flat-top beam, respectively, and the positions and excitations of each array element are shown in Table 1. The results of sparse design using the RANM algorithm are as follows: Figure 3 As shown in Table 2, the excitation and element positions of the sparse linear array and the original linear array are shown.

[0091] from Figure 2 As shown in Table 2, the reconfigurable sparse linear array designed using the RANM algorithm requires only 15 elements to emit a beam pattern similar to that of the original uniform linear array. Therefore, the sparsity is [missing information]. Furthermore, the normalized mean square error is This demonstrates that a reconfigurable sparse linear array designed using the RANM algorithm can still transmit multi-mode beammaps with the same shape while reducing the number of array elements.

[0092] Table 1. Figure 2 Corresponding uniformly arranged reconfigurable linear array element positions and element excitation table

[0093]

[0094] Table 2. Figure 3 The corresponding RANM design reconfigurable sparse linear array element positions and element excitation tables

[0095]

[0096] In Experiment 2, for Figure 4 The multi-beam antenna array is designed with a sparse distribution. Figure 4 A reconfigurable linear array with uniformly arranged elements, the number of its array elements Work mode The beam patterns corresponding to the three operating modes are pencil beam, flat-top beam, and cosecant square beam, respectively. The positions and excitations of each array element are shown in Table 3. The results of sparse design using the RANM algorithm are as follows: Figure 5 As shown in Table 4, the excitation and element positions of the sparse linear array and the original linear array are as follows.

[0097] from Figure 4 , 5 As shown in Table 4, the reconfigurable sparse linear array designed using the RANM algorithm requires only 16 elements to emit a beam pattern similar to that of the original uniform linear array. Based on the element positions and excitation values ​​of the sparse linear array in Table 4, the sparsity can be calculated to be... The normalized mean square error is .

[0098] Table 3. Figure 4 Corresponding uniformly arranged reconfigurable linear array element positions and element excitation table

[0099]

[0100] Table 4. Figure 5 The corresponding RANM design reconfigurable sparse linear array element positions and element excitation tables

[0101]

[0102] Compared with the MPM and UMPM algorithms, the RANM algorithm proposed in this invention represents the design problem of reconfigurable sparse linear arrays as an optimization model based on the atomic norm. It directly optimizes the array element positions and excitations from the perspective of the sparsity of the array elements. Therefore, the RANM algorithm has a performance advantage in sparsity and can reduce the number of array elements while keeping the shape of the radiation beam pattern almost unchanged, thereby reducing the complexity and power consumption of the system.

[0103] This invention proposes a reweighted atom norm minimization algorithm (RANM) based on the sparsity of the array element arrangement. This algorithm treats the design problem of reconfigurable sparse linear arrays as a sparse optimization problem over continuous intervals, constructs a corresponding convex optimization model, and theoretically obtains the sparsest solution for the reconfigurable sparse linear array. Furthermore, since this algorithm is based on continuous interval optimization, it avoids the grid mismatch problem present in traditional sparse recovery algorithms, thus outperforming traditional reconfigurable sparse linear array design algorithms in terms of beam matching accuracy.

[0104] The present invention also provides a computer device comprising: at least one processor, a memory, at least one network interface, and a user interface. The various components of this device are coupled together via a bus system. It is understood that the bus system is used to enable communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0105] The user interface may include a display, keyboard, or clicking device (e.g., mouse, trackball, touchpad, or touchscreen).

[0106] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0107] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0108] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0109] In the above embodiments, the processor can also invoke programs or instructions stored in memory, specifically programs or instructions stored in an application program, for the following purposes:

[0110] Follow the steps described above.

[0111] The above methods can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the disclosed methods, steps, and logic block diagrams. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the disclosed methods can be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0112] It is understood that the embodiments described in this invention can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0113] For software implementation, the technology of this invention can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this invention. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or externally.

[0114] The present invention may also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above method embodiments.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for constructing a reconfigurable sparse linear array, wherein the method first samples the target beam to obtain the matrix composed of the sampled beam, then obtains the rank-minimum Toplitz matrix by the weighted atom norm minimization method, then uses the Root-MUSIC algorithm to estimate the frequency and weight of the atom, and finally converts the frequency and weight into the element position and excitation of the reconfigurable sparse linear array through the mapping relationship. The method specifically includes: Step 1: Obtain data by uniformly sampling the M beammaps of the known reconfigurable uniform linear array. That is, for ,have: in, Indicates the comprehensive first When the beam pattern is in The corresponding reference beam pattern data; This is a hyperparameter representing the number of sampling points; For the first n The position of each array element; Indicates wave number; Indicates wavelength; Represents the imaginary unit; N The number of array elements; To comprehensively The corresponding beam pattern of the first beam The incentive of each array element; To comprehensively When the beam pattern is... Phase coefficients of the excitation of each array element To comprehensively When the beam pattern is... The amplitude coefficient of the excitation of each array element; Set the maximum number of iterations in the reweighted atomic norm minimization model. q reweighted matrix The penalty term hyperparameter Optimize the error hyperparameters in the equation ; Step 2: Initialize the weight parameters for the first time ; in, The sign for conjugate transpose; It is the identity matrix; Step 3: Solve the optimization equation Obtain the current iteration, i.e., the... j The optimal solution of the next iteration ; in, This represents the computation of the trace of a matrix; Represents the Toeplitz mapping; Denotes the Frobenius norm; For the first j Weight parameters at the next iteration; , , All are complex optimization variables. , , Indicates the first j During the next iteration , , The optimal value, that is, the value that can be achieved in step 3. The solution with the smallest value; For complex numbers; Step 4: Solve based on the results of the current iteration Update the weight matrix to be used in the next iteration: in, For the first j+1 Weight parameters at the next iteration; Step 5: Set the current iteration number j +1, if j Greater than the maximum number of iterations q If so, proceed to step 6; otherwise, proceed to step 3. Step 6: Optimize the result from the last iteration in Step 3. As the optimal solution ,right Using eigenvalue decomposition, i.e.: in, It is a monotonically decreasing diagonal matrix, and the eigenvalues ​​are located on the diagonal. The feature matrix is ​​composed of eigenvectors, and each column vector is linearly independent. Estimating the number of elements in a sparse linear array based on the ratio of eigenvalues. ,Right now The following conditions must be met: in, This is the ratio threshold; Step 7: Use the Root-MUSIC algorithm to pass estimate K A vector composed of frequencies Then, the weight matrix of the atoms is obtained using the least squares method. ; in, A matrix composed of frequency vectors; This indicates a pseudo-inverse operation; The optimal variable after multiple iterations of optimization in step 3. ; Step 8: Use the following formula to... and Transformation into element positions of a reconfigurable sparse linear array and incentives ,Right now: in, Wavelength; It represents the Hadamardi (or Hadama) stack.

2. The method for constructing a reconfigurable sparse linear array according to claim 1, characterized in that, The hyperparameter of the number of sampling points Values ​​range from 12 to 15; the maximum number of iterations in the reweighted atomic norm minimization model. q=6 Reweighted matrix The penalty term hyperparameter Values ​​range from 1 to 10; error hyperparameters in the optimization equation. Values ​​range from 0.001 to 0.01; the ratio threshold in eigenvalue decomposition. The value ranges from 0.01 to 0.

03.

3. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 2.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, causes the processor to perform the method as described in any one of claims 1 to 2.

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