Broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization

Abstract

The invention discloses a broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization, which comprises the following steps of: firstly, optimizing broadband two-dimensional uniform array directional diagram representation based on a two-dimensional subarray optimization method, constructing an optimization model of a sparse two-dimensional array based on L0-norm, setting a two-dimensional subarray constraint condition meeting a beam forming requirement, and constructing a sparse two-dimensional array layout optimization model based on L0-norm; and generating a two-dimensional array coefficient by using the optimization model, carrying out sparsity check on the two-dimensional array coefficient, and finally determining an optimal coefficient according to the generated two-dimensional sparse array to obtain a finally determined two-dimensional sparse array. According to the scheme of the invention, the broadband two-dimensional sparse array arrangement optimization method based on compressed sensing and subarray optimization is provided, and a two-dimensional subarray optimization algorithm and an L0-norm compressed sensing algorithm are combined. According to the method, the array element number of the large-scale two-dimensional array can be efficiently compressed, the beam width, the main-to-auxiliary ratio and the broadband response characteristic of the main lobe of the two-dimensional array can be restrained at the same time, and hardware overhead can be remarkably saved.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing, specifically a broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization. Background Technology

[0002] A broadband two-dimensional sparse array layout method based on compressed sensing and subarray optimization combines two-dimensional subarray optimization with sparse array design, which can reduce the resource consumption of broadband two-dimensional large array layout. An existing invention includes a sparse linear array optimization method based on the L1 / 2 norm. This method transforms the L1 / 2 norm non-convex problem into a series of L1 norm convex optimization problems, resulting in a layout method with a lower number of array elements under the constraint of principal aspect ratio for one-dimensional linear arrays.

[0003] An existing invention provides an optimization method for sparse linear arrays based on the L1 / 2 norm. This method transforms the non-convex problem of the L1 / 2 norm into a series of convex optimization problems of the L1 norm, resulting in an array arrangement method with a lower number of array elements under the constraint of principal aspect ratio for 1D linear arrays. However, this method is only applicable to 1D narrowband arrays.

[0004] An existing invention provides a method for optimizing the layout of sparse subarray antennas. This method solves a sparse subarray antenna layout problem using a particle swarm optimization algorithm. However, this method is complex, has a slow convergence speed, and carries the risk of non-convergence, making it particularly unsuitable for large-scale arrays.

[0005] Existing inventions include a sparse array design method and apparatus based on frequency-domain broadband beamforming. This method constructs an objective function using a maximum output signal-to-noise ratio criterion, providing a sparse array design apparatus based on frequency-domain broadband beamforming. However, this method employs broadband coherent signals, thus requiring prior information; it utilizes a covariance matrix, which becomes enormous under large-scale array conditions, resulting in significant algorithmic resource consumption; furthermore, this method cannot constrain the broadband response characteristics of beamwidth, main-to-sublobe ratio, and main lobe.

[0006] Existing inventions include a method for optimizing the layout of sparse linear arrays under geographical constraints. This method establishes an objective function using the peak sidelobe level of the antenna pattern as the optimization criterion, and incorporates minimum antenna spacing constraints and geographical constraints. The P-system membrane algorithm used in this method requires continuous AC replacement, resulting in slow convergence speed, algorithm complexity, and poor robustness under large-scale array conditions.

[0007] It can be seen that there is a lack of patents in the existing technology that can efficiently compress the number of array elements of a large-scale two-dimensional array and simultaneously constrain the beamwidth, main-to-sub ratio and broadband response characteristics of the main lobe of the two-dimensional array. Summary of the Invention

[0008] To address the aforementioned problems, the present invention aims to provide a broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization. This method combines L0-norm-based compressed sensing and two-dimensional subarray optimization algorithms to optimize the broadband two-dimensional large-scale array layout method, which can significantly reduce hardware overhead and is suitable for practical signal processing applications.

[0009] The specific technical solution for achieving the objective of this invention is as follows:

[0010] A broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization includes the following steps:

[0011] Step 1: Optimize the pattern representation of a broadband two-dimensional uniform array based on the two-dimensional subarray optimization method;

[0012] Step 2: Construct an optimization model for a sparse two-dimensional array based on L0-norm, set two-dimensional subarray constraints that meet beamforming requirements, and use the optimization model to generate two-dimensional array coefficients.

[0013] Step 3: Perform a sparsity check on the two-dimensional array coefficients generated in Step 2 to determine whether the sparsity is stable. If it is, proceed to Step 4; otherwise, return to Step 2.

[0014] Step 4: Determine the optimal coefficients based on the generated two-dimensional sparse array to obtain the final determined two-dimensional sparse array.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0016] The present invention provides a broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization. It combines a two-dimensional subarray optimization algorithm and a compressed sensing algorithm based on L0-norm. This method can efficiently compress the number of array elements in a large-scale two-dimensional array and simultaneously constrain the beamwidth, main-to-sub ratio and broadband response characteristics of the main lobe of the two-dimensional array, which can significantly save hardware costs.

[0017] The present invention will be further described below with reference to specific embodiments. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization in this scheme.

[0019] Figure 2 This embodiment of the scheme shows the array element distribution of a 128-array with a main lobe width of 80 degrees and a peak sidelobe level of less than 0.0001.

[0020] Figure 3 yes Figure 2 Direction pattern under certain conditions.

[0021] Figure 4 This embodiment of the scheme shows the array element distribution of a 128-array with a main lobe width of 80 degrees and a peak sidelobe level of less than 0.001.

[0022] Figure 5 yes Figure 4 Direction pattern under certain conditions.

[0023] Figure 6 This embodiment of the scheme shows the array element distribution of a 128-array with a main lobe width of 40 degrees and a peak sidelobe level of less than 0.001.

[0024] Figure 7 yes Figure 6 Direction pattern under certain conditions. Detailed Implementation

[0025] Example

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0028] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0029] Combination Figure 1A broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization includes the following steps:

[0030] Step 1: Optimize the pattern representation of a broadband two-dimensional uniform array based on the two-dimensional subarray optimization method:

[0031] Step 1-1: Initialize the parameters of the two-dimensional array:

[0032] Set up an initial distribution of a large-scale two-dimensional array with uniformly arranged array elements, where N and L are the number of array elements and the filter order corresponding to the array elements, respectively.

[0033] The array element spacing is set to d based on the detected signal frequency range, and the signal frequency range is Ω=[0,αω]. max ], where α≤1 constrains the upper limit of the signal's frequency range; the sampling rate of each sub-filter is f. s =4πω max ;

[0034] Steps 1-2: Frequency-invariant beamforming generates the beam pattern through a filtering and summing beamforming architecture, where each sensor is connected to a digital filter that provides frequency-related weighting. Consider a linear array consisting of N isotropic elements located along the x-axis, each element connected to an FIR filter of length L, whose radiation pattern is represented as follows:

[0035]

[0036] Among them, h l,n Let a be the array coefficient variable. n (ω,θ) are the pattern weighting coefficients, θ is the beam direction, and T s τ is the sampling period of the FIR filter. n This is a time delay between array elements;

[0037] Steps 1-3: Optimize the radiation pattern using the two-dimensional subarray optimization method:

[0038]

[0039] Where T is the sparse transformation matrix; h is the FIR filter of length L for each element; γ is the difference in filter coefficient vectors between elements; and s t (ω) is the delay vector between the coefficients of each FIR filter element, and sτ(ω,θ) is the beam pointing vector;

[0040] Step 2: Construct an optimization model for a sparse two-dimensional array based on L0-norm, set constraints for the two-dimensional subarray that meet beamforming requirements, and use this optimization model to generate the two-dimensional array coefficients:

[0041]

[0042] Where r = [r1, r2, ..., r N [Auxiliary variables to constrain the filters of each array element;]

[0043] The two-dimensional subarray constraints that satisfy the beamforming requirements include:

[0044] Two-dimensional subarray constraints:

[0045] Primary / Secondary Ratio Constraint:

[0046] Spatial response variation constraints:

[0047] Beam pointing constraint:

[0048] Where, θ Look Let ω be the angle at which the signal is incident. ref For reference frequency, For the extent of the side lobe, Main lobe range, ε SL For the highest sidelobe level, ε ML The mean square error of the broadband response variation of the main lobe relative to the reference angular frequency value.

[0049] Since L0-norm is a non-convex function, while L1-norm is the closest convex function to L0-norm, the optimization model of the sparse two-dimensional array based on L0-norm is rewritten as a weighted L1-norm optimization model and solved:

[0050]

[0051] Solve the optimization problem to obtain the optimized two-dimensional array coefficients.

[0052] Step 3: Perform a sparsity check on the two-dimensional array coefficients generated in Step 2 to determine if the sparsity is stable. If it is, proceed to Step 4; otherwise, return to Step 2.

[0053] Based on the two-dimensional array coefficients obtained in step 2, determine whether the following formula can remain stable for several consecutive cycles, that is, whether the change in value is less than Delta for three consecutive cycles. If so, the value is determined to be stable and converged.

[0054]

[0055] Where k represents the iteration number, the initial value k = 0, and δ > 0 is a parameter used to provide numerical stability;

[0056] Step 4: Determine the optimal coefficients based on the generated two-dimensional sparse array to obtain the final determined two-dimensional sparse array.

[0057] Based on the final determined two-dimensional array coefficients, values ​​that are significantly smaller than other coefficients are assigned a value of 0. In this embodiment, this means assigning values ​​smaller than the maximum value among all coefficients multiplied by 10. -5 The coefficient is assigned a value of 0;

[0058] If all coefficients of a certain array element are 0, then that array element is removed.

[0059] The optimal two-dimensional sparse array layout is finally obtained.

[0060] Example 1 in this embodiment:

[0061] The main lobe width is set to 80 degrees, the peak sidelobe level is less than 0.0001, the specified (weighted) mean square error of the broadband response variation of the main lobe relative to the reference angular frequency value is 0.001, the number of array elements is 128, the filter order corresponding to the array elements is 10, the signal frequency range is 100MHz to 450MHz, and the broadband beam pointing is 0 degrees. Figure 2 Array element distribution and Figure 3 Direction map.

[0062] Example 2:

[0063] The main lobe width is set to 80 degrees, the peak sidelobe level is less than 0.001, the specified (weighted) mean square error of the broadband response variation of the main lobe relative to the reference angular frequency value is 0.001, the number of array elements is 128, the filter order corresponding to the array elements is 10, the signal frequency range is 100MHz to 450MHz, and the broadband beam pointing is 0 degrees. Figure 4 Array element distribution and Figure 5 Direction map.

[0064] Example 3:

[0065] The main lobe width is set to 40 degrees, the peak sidelobe level is less than 0.001, the specified (weighted) mean square error of the broadband response variation of the main lobe relative to the reference angular frequency value is 0.001, the number of array elements is 128, the filter order corresponding to the array elements is 10, the signal frequency range is 100MHz to 450MHz, and the broadband beam pointing is 0 degrees. Figure 6 Array element distribution and Figure 7 Direction map.

[0066] Comparing Examples 2 and 3 reveals that increasing the main lobe width improves array sparsity, meaning fewer non-zero array elements. Comparing Examples 1 and 2, increasing the sidelobe level further improves array sparsity, again resulting in fewer non-zero array elements. This demonstrates the effectiveness of the proposed broadband two-dimensional sparse array deployment method based on compressed sensing and subarray optimization.

[0067] This invention also provides a broadband two-dimensional sparse array layout optimization system based on compressed sensing and subarray optimization, comprising the following modules:

[0068] Broadband 2D Uniform Array Optimization Module: Used to optimize the radiation pattern representation of a broadband 2D uniform array based on the 2D subarray optimization method;

[0069] Two-dimensional array coefficient optimization module: used to construct an optimization model of a sparse two-dimensional array based on L0-norm, set two-dimensional subarray constraints that meet beamforming requirements, and use the optimization model to generate two-dimensional array coefficients.

[0070] Two-dimensional array coefficient sparsity checking module: used to check the sparsity of the generated two-dimensional array coefficients and determine whether the sparsity is stable;

[0071] Broadband 2D sparse array layout optimization module: used to determine the optimal coefficients based on the generated 2D sparse array, and obtain the final determined 2D sparse array.

[0072] 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 perform the following steps:

[0073] Step 1: Optimize the pattern representation of a broadband two-dimensional uniform array based on the two-dimensional subarray optimization method;

[0074] Step 2: Construct an optimization model for a sparse two-dimensional array based on L0-norm, set two-dimensional subarray constraints that meet beamforming requirements, and use the optimization model to generate two-dimensional array coefficients.

[0075] Step 3: Perform a sparsity check on the two-dimensional array coefficients generated in Step 2 to determine whether the sparsity is stable. If it is, proceed to Step 4; otherwise, return to Step 2.

[0076] Step 4: Determine the optimal coefficients based on the generated two-dimensional sparse array to obtain the final determined two-dimensional sparse array.

[0077] The present invention also provides a computer-storable medium having a computer program stored thereon, wherein the computer program, when executed by a processor, performs the following steps:

[0078] Step 1: Optimize the pattern representation of a broadband two-dimensional uniform array based on the two-dimensional subarray optimization method;

[0079] Step 2: Construct an optimization model for a sparse two-dimensional array based on L0-norm, set two-dimensional subarray constraints that meet beamforming requirements, and use the optimization model to generate two-dimensional array coefficients.

[0080] Step 3: Perform a sparsity check on the two-dimensional array coefficients generated in Step 2 to determine whether the sparsity is stable. If it is, proceed to Step 4; otherwise, return to Step 2.

[0081] Step 4: Determine the optimal coefficients based on the generated two-dimensional sparse array to obtain the final determined two-dimensional sparse array.

[0082] The embodiments described above are merely one implementation method of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization, characterized in that, Includes the following steps: Step 1: Optimize the pattern representation of a broadband two-dimensional uniform array based on the two-dimensional subarray optimization method; Step 2: Construct an optimization model for a sparse two-dimensional array based on L0-norm, set two-dimensional subarray constraints that meet beamforming requirements, and use the optimization model to generate two-dimensional array coefficients. Step 3: Perform a sparsity check on the two-dimensional array coefficients generated in Step 2 to determine whether the sparsity is stable. If it is, proceed to Step 4; otherwise, return to Step 2. Step 4: Determine the optimal coefficients based on the generated two-dimensional sparse array to obtain the final determined two-dimensional sparse array.

2. The broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization according to claim 1, characterized in that, The optimization of the broadband two-dimensional uniform array radiation pattern representation based on the two-dimensional subarray optimization method in step 1 is specifically as follows: Step 1-1: Initialize the parameters of the two-dimensional array: Set up an initial distribution of a large-scale two-dimensional array with uniformly arranged array elements, where N and L are the number of array elements and the filter order corresponding to the array elements, respectively. The array element spacing is set to d based on the detected signal frequency range, and the signal frequency range is Ω=[0,αω]. max ], where α≤1 is used to constrain the upper limit of the signal's frequency range, and the sampling rate of each sub-filter is f. s =4πω max ; Step 1-2: Consider a linear array consisting of N isotropic elements located along the x-axis. Each element is connected to an FIR filter of length L. Its radiation pattern is represented as follows: Among them, h l,n Let a be the array coefficient variable. n (ω,θ) are the pattern weighting coefficients, θ is the beam direction, and T s τ is the sampling period of the FIR filter. n This is a time delay between array elements; Steps 1-3: Optimize the radiation pattern using the two-dimensional subarray optimization method: Where T is the sparse transformation matrix; h is the FIR filter of length L for each element; γ is the difference in filter coefficient vectors between elements; and s t (ω) is the delay vector between the coefficients of each element FIR filter, s τ (ω,θ) is the beam pointing vector.

3. The broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization according to claim 2, characterized in that, The optimization model for the L0-norm-based sparse two-dimensional array in step 2 is as follows: Where r = [r1, r2, ..., r N [Auxiliary variables to constrain the filters of each array element;] The two-dimensional subarray constraints that satisfy the beamforming requirements include: Two-dimensional subarray constraints: Primary / Secondary Ratio Constraint: Spatial response variation constraints: Beam pointing constraint: Where, θ Look Let ω be the angle at which the signal is incident. ref For reference frequency, For the extent of the side lobe, Main lobe range, ε SL For the highest sidelobe level, ε ML The mean square error of the broadband response variation of the main lobe relative to the reference angular frequency value.

4. The broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization according to claim 3, characterized in that, The optimization model of the sparse two-dimensional array based on L0-norm is rewritten as a weighted L1-norm optimization model and solved: Solve the optimization problem to obtain the optimized two-dimensional array coefficients.

5. The broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization according to claim 2, characterized in that, The sparsity check of the two-dimensional array coefficients in step 3 is specifically as follows: Based on the two-dimensional array coefficients obtained in step 2, determine whether the following formula remains stable and converges if its change value is less than the set threshold over several consecutive cycles: Where k represents the iteration number, and δ>0 is a parameter used to provide numerical stability.

6. The broadband two-dimensional sparse array layout optimization method based on compressed sensing and subarray optimization according to claim 2, characterized in that, In step 4, obtaining the final determined two-dimensional sparse array specifically involves: Based on the final determined two-dimensional array coefficients, coefficients that are less than a certain maximum value among all coefficients are assigned the value 0; If all coefficients of a certain array element are 0, then that array element is removed. The optimal two-dimensional sparse array layout is finally obtained.

7. A broadband two-dimensional sparse array layout optimization system based on compressed sensing and subarray optimization, characterized in that, Includes the following modules: Broadband 2D Uniform Array Optimization Module: Used to optimize the radiation pattern representation of a broadband 2D uniform array based on the 2D subarray optimization method; Two-dimensional array coefficient optimization module: used to construct an optimization model of a sparse two-dimensional array based on L0-norm, set two-dimensional subarray constraints that meet beamforming requirements, and use the optimization model to generate two-dimensional array coefficients. Two-dimensional array coefficient sparsity checking module: used to check the sparsity of the generated two-dimensional array coefficients and determine whether the sparsity is stable; Broadband 2D sparse array layout optimization module: used to determine the optimal coefficients based on the generated 2D sparse array, and obtain the final determined 2D sparse array.

8. 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 steps of the method according to any one of claims 1-6.

9. A computer-storable medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

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