Dynamic scene-oriented beam former dimension reduction sparse design method
By constructing a dimensionality reduction sparsity theory and using the alternating direction multiplier method to decompose and optimize the problem, the high complexity of traditional beamformers in dynamic scenarios is solved, achieving efficient sparsity design and reducing computational and hardware costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JIANGSU COLLEGE OF INFORMATION TECH
- Filing Date
- 2026-01-19
- Publication Date
- 2026-05-01
AI Technical Summary
Traditional beamformers cannot dynamically adjust the main lobe pointing in dynamic scenarios, which increases system complexity and cost. Existing sparse design methods are computationally time-consuming and complex.
By constructing a dimension reduction sparsity theory, and utilizing the sparsity symmetry theory and the alternating direction multiplier method, the optimization problem of polynomial structure beamformers is decomposed into subproblems, and the positions of array elements and sparse weight coefficients are solved step by step to achieve dimension reduction sparsity design.
While maintaining beam performance and sparsity performance, it significantly improves optimization efficiency and structural implementation efficiency, and reduces computational complexity and hardware requirements.
Smart Images
Figure CN121959934A_ABST
Abstract
Description
A Dimensionality Reduction and Sparsity Design Method for Beamformers in Dynamic Scenarios Technical Field
[0001] This invention relates to the field of linear microphone array technology, specifically to a beamformer dimensionality reduction and sparsification design method for dynamic scenarios. Background Technology
[0002] Beamforming, as a key technology in microphone array signal processing, has wide applications in audio and speech signal processing. Traditional microphone array beamformer design methods typically assume a fixed main lobe direction; however, in many practical applications, the target sound source location is variable. In such cases, beamformers with a fixed main lobe direction are no longer suitable, and it is necessary to consider designing beamformers with dynamically adjustable main lobe directions. Current polynomial beamformer designs are mainly limited to uniform arrays. For uniform arrays, to avoid spatial aliasing, the element spacing needs to satisfy the spatial Nyquist theorem, i.e., it cannot exceed half the wavelength corresponding to the highest signal frequency. On the other hand, to avoid signal distortion, the frequency invariance of the beam is usually considered in the design. For uniform arrays, achieving good frequency invariance requires a larger aperture array, leading to a significant increase in the number of elements, thus increasing system complexity and cost. Therefore, array sparsity design for polynomial beamformers is of significant research importance.
[0003] Compared to traditional broadband beamformers, polynomial beamformers differ in that each microphone is connected to a filter bank, not a single filter. Therefore, the weighting coefficients of polynomial beamformers have a higher dimensionality than those of traditional broadband beamformers. This is precisely why the dimensionality of the sparsity design problem for polynomial beamformer arrays is significantly higher. To address this issue, the literature (Wang CZ, Chen HW, Li Y W. Sparse design of polynomial beamformers by jointly sparsifying sensorlocations and Farrow structures. IEEE Sensors J, 2024; 24(16): 26044-26057) proposes an array sparsity optimization method based on the alternating direction multiplier method (see literature, Boyd S, Parikh N, Chu E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn, 2010; 3(1): 1-126). This method effectively solves the high-dimensional optimization problem faced by the sparsification of polynomial structure beamformer arrays. However, it should be noted that although this method effectively improves the sparsification design efficiency of polynomial structure frequency-invariant beamformers, the dimension of the optimization problem remains unchanged, the computation time is still long, and the system implementation complexity is high. Summary of the Invention
[0004] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.
[0005] Therefore, the purpose of this invention is to provide a beamformer dimensionality reduction and sparsity design method for dynamic scenarios, so as to solve the problems mentioned in the background art.
[0006] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:
[0007] A method for dimensionality reduction and sparsity reduction design of beamformers for dynamic scenarios, comprising the following steps:
[0008] S1. Construct a dimension reduction sparsity theory and analyze the weight coefficient symmetry of a sparse polynomial structure broadband beamformer.
[0009] S2. Using the sparse symmetry theory in step S1, construct a dimension-reduced sparse model for a polynomial structure broadband beamformer.
[0010] S3. Based on the alternating direction multiplier method, the optimization problem in step S2 is decomposed into multiple sub-problems, which are solved and updated separately to obtain the initial array element positions and sparse weight coefficients.
[0011] S4. Substitute the initial sparse positions of the array elements and the corresponding weight coefficients back into step S3, and repeat step S3 to obtain the final array element positions and weight coefficients, thereby realizing the dimensionality reduction and sparsification design of the polynomial structure beamformer.
[0012] As a preferred embodiment of the beamformer dimensionality reduction and sparsity design method for dynamic scenarios described in this invention, the specific steps in step S1, which involve constructing a dimensionality reduction and sparsity theory and analyzing the symmetry of the weight coefficients of the sparse polynomial structure broadband beamformer, are as follows:
[0013] For a uniform linear array, in the joint sparsification design optimization problem of a polynomial structure beamformer, if the weight vector of the h-th iteration is... If it is the optimal solution, then the weight coefficients have the following symmetric property:
[0014]
[0015] in, Represents the Kronecker product. Represents the identity matrix. and They are represented as follows:
[0016]
[0017]
[0018] That is, the weighting coefficients of a polynomial beamformer have the following symmetric relationship:
[0019]
[0020] in, Indicates the first Beamformer weighting coefficients.
[0021] As a preferred embodiment of the beamformer dimensionality reduction and sparsity design method for dynamic scenarios described in this invention, the specific steps in step S2, which utilize the sparse symmetry theory in step S1 to construct the dimensionality reduction and sparsity model of the polynomial structure broadband beamformer, are as follows:
[0022] Using the symmetry relation in step S1, the dimension-reduced beam response can be expressed as:
[0023]
[0024] in, Indicates transpose. The weight coefficient vector after dimensionality reduction:
[0025]
[0026] The directional vector after dimensionality reduction:
[0027]
[0028] In the formula, , , Represented as:
[0029]
[0030] The dimension reduction and sparsification problem of polynomial structure beamformers is constructed as follows:
[0031]
[0032] in, This represents the nth discrete angle within the beam pointing range. It is the p-th discrete frequency within the operating frequency range. Main petal The first Discrete angles Side lobe The first Discrete angles The reference frequency is represented by ε, the constraint threshold is Γ, and the sidelobe level is Г. This represents the lower bound of the white noise gain. Describing the L1 norm, This represents the weight vector after the h-th iteration following dimensionality reduction. Represents the weighting coefficients in the h-th iteration after dimensionality reduction. This represents the transformation matrix after dimensionality reduction, when M is even:
[0033]
[0034] When M is odd:
[0035]
[0036] in, This represents an L-row, M-column matrix of all zeros.
[0037] As a preferred embodiment of the beamformer dimensionality reduction and sparsity design method for dynamic scenarios described in this invention, in step S3, based on the alternating direction multiplier method, the optimization problem in step S2 is decomposed into multiple sub-problems, which are solved and updated separately to obtain the initial array element positions and sparse weight coefficients. The specific steps are as follows:
[0038] By introducing auxiliary variables and The augmented Lagrangian function of the dimension reduction sparse design problem in step S2 is constructed as follows:
[0039]
[0040] In the formula, , , The directional vector matrix after dimensionality reduction. express The i-th element, , , and For Lagrange multipliers, for Update iteration step size, Represents the real part of a complex number. This represents the conjugate transpose. During iterative updates of the variables, only one variable is updated at a time, while the others are treated as constants. Its subproblem is minimizing the augmented Lagrangian function, as shown below:
[0041] (1) Subproblem 1 is an auxiliary variable and The Next iteration update optimization problem:
[0042]
[0043] (2) Subproblem 2 is the original variable The Next iteration update optimization problem:
[0044]
[0045] Closed-form solutions to the two subproblems are derived separately, and the initial sparse array positions and their corresponding weight coefficients are obtained after iterative updates.
[0046] As a preferred embodiment of the beamformer dimensionality reduction and sparsity design method for dynamic scenarios described in this invention, in step S4, the initial sparse positions of the array elements and the corresponding weight coefficients are substituted back into step S3, and step S3 is repeated to obtain the final array element positions and weight coefficients, thereby realizing the dimensionality reduction and sparsity design of the polynomial structure beamformer. The specific steps are as follows:
[0047] The initial sparse array element positions and corresponding tap weights are iteratively weighted, and the auxiliary variables, original variables and Lagrange multipliers of the augmented Lagrange function in step S3 are updated until the maximum number of iterations is reached, at which point the iteration stops, and the final sparse array element positions and weight coefficients are obtained.
[0048] Compared with existing technologies, the advantages of this invention are: while maintaining essentially the same beam performance and sparsity performance, both optimization efficiency and structural implementation efficiency are significantly improved. The dimensionality reduction sparse method only needs to calculate nearly half of the weight coefficients during the optimization process; in terms of implementation complexity, the number of multipliers and adders in the dimensionality reduction sparse design is reduced by nearly half compared to the original sparse design. Attached Figure Description
[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:
[0050] Figure 1 is a structural diagram of the polynomial structure frequency-invariant beamformer in the embodiment;
[0051] Figure 2 shows the microphone position distribution before and after dimensionality reduction for the two sparse design methods.
[0052] Figure 3 shows the polynomial structure beamformer before and after dimensionality reduction. 3D view of the beam;
[0053] Figure 4 shows the polynomial structure beamformer before and after dimensionality reduction. Comparison of directional indices;
[0054] Figure 5 shows the average white noise gain and average directivity index of the two beamformers before and after the descent of different directional angles.
[0055] Figure 6 shows the k-th filtering and summing unit of the dimension-reduced polynomial structure beamformer when the number of array elements is even.
[0056] Figure 7 shows the k-th filtering and summing unit of the dimensionality-reduced polynomial beamformer when the number of array elements is odd. Detailed Implementation
[0057] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0058] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.
[0059] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.
[0060] This invention proposes a dimensionality reduction and sparse design method for polynomial structure beamformers in dynamic scenarios. It employs the polynomial structure shown in Figure 1, and performs dimensionality reduction and sparsification design based on this structure. The specific steps include:
[0061] Step 1: For a uniform linear array, when the beam response directions are respectively and When the continuous angles are uniformly discretized, the discretized angles are... and The following relationship exists:
[0062]
[0063]
[0064] From this, we can deduce that:
[0065]
[0066] in, This indicates the beam pointing corresponding to the k-th order. The adjustable parameters. The adjustable parameter vector... Represented as:
[0067]
[0068] in,
[0069]
[0070] Similarly, the array transfer function vector can be used. Represented as:
[0071]
[0072] in,
[0073]
[0074] Therefore, for the joint sparsification design optimization problem of polynomial structure beamformers, if the weight vector of the h-th iteration is... If it is the optimal solution, then the weight coefficients have the following symmetric property:
[0075]
[0076] in, Represents the Kronecker product. Represents the identity matrix.
[0077] Step 2: Using the symmetry relationship from Step 1, when the number of array elements M is even, for an input signal with frequency f and incident angle θ, the beam response of the polynomial structure beamformer can be rewritten as:
[0078]
[0079] Where K represents the order of the polynomial beamformer, and L represents the tap length of the filter. Where is the sampling frequency, and d is the spacing between adjacent array elements. denoted by , where represents the weighting coefficients of the polynomial beamformer, and c is the sound propagation speed.
[0080] When the number of array elements M is odd, the beam response is rewritten as:
[0081]
[0082] Therefore, the reduced beam response can be represented in vector form:
[0083]
[0084] in, The weight coefficient vector after dimensionality reduction:
[0085]
[0086] The directional vector after dimensionality reduction:
[0087]
[0088] In the formula, , , Represented as:
[0089]
[0090] At the same time,
[0091]
[0092] In summary, the dimension reduction and sparsification problem of polynomial structure beamformers can be constructed as follows:
[0093]
[0094] in, This represents the nth discrete angle within the beam pointing range. It is the p-th discrete frequency within the operating frequency range. Main petal The first Discrete angles Side lobe The first Discrete angles The reference frequency is represented by ε, the constraint threshold is Γ, and the sidelobe level is Г. This represents the lower bound of the white noise gain. Describing the L1 norm, This represents the weight vector after dimensionality reduction. Represents the weighting coefficients in the h-th iteration after dimensionality reduction. This represents the transformation matrix after dimensionality reduction, when M is even:
[0095]
[0096] When M is odd:
[0097]
[0098] in, This represents an L-row, M-column matrix of all zeros.
[0099] Step 3: The dimensionality reduction and sparsity design problem in Step 2 is equivalently transformed into:
[0100]
[0101] In the formula, Represents the L2 norm. This represents the i-th element in the vector. Represents a vector consisting entirely of 1s, oriented vector matrix , , , and They are represented as follows:
[0102]
[0103] in, , Represented as:
[0104]
[0105] By introducing auxiliary variables and We can obtain:
[0106]
[0107] Then let , Then its augmented Lagrangian function can be constructed as:
[0108]
[0109] In the formula, , , , and For Lagrange multipliers, for Update iteration step size, Let represent the real part of the complex number. When iterating through the variables, only one variable is updated at a time, and the rest are treated as constants. The subproblem is minimizing the augmented Lagrangian function. Subproblem one can be expressed as:
[0110]
[0111] Its Lagrangian function can be constructed as:
[0112]
[0113] in, and These are Lagrange multipliers constrained by inequality. Minimize those containing... Based on the KKT conditions of this optimization problem, we can know that... To reach the minimum value, the following conditions must be met:
[0114]
[0115] because yes A monotonically decreasing function, from which can be derived When the minimum value is reached, the Lagrange multipliers The value is Therefore, we can obtain The updated solution is:
[0116]
[0117] Similarly, by minimizing the content Update the solution using the terms. According to its KKT conditions, we can obtain The updated solution is:
[0118]
[0119] in, .
[0120] Subproblem two can be represented as:
[0121]
[0122] Among them, matrix sum vector They are represented as follows:
[0123]
[0124]
[0125] Next, its Lagrange function is constructed as follows:
[0126]
[0127] in, These are Lagrange multipliers. By introducing auxiliary variables... and We can obtain:
[0128]
[0129] Then its augmented Lagrange function is constructed as follows:
[0130]
[0131] in, and These correspond to the constraints. and Lagrange multipliers, It is its iterative update step size.
[0132] Update auxiliary variables : Based on the given original variables of the g-th iteration and Lagrange multipliers Auxiliary variables By minimizing the content The item obtained is:
[0133]
[0134] Its updated solution is:
[0135]
[0136] Update auxiliary variables : Based on the given original variables of the g-th iteration and Lagrange multipliers Auxiliary variables By minimizing the content The item obtained is:
[0137]
[0138] Next, we examine the cost function in the equation. Taking the derivative and setting it equal to zero, we get:
[0139]
[0140] in,
[0141]
[0142] Update the original variable : Based on the given Lagrange multipliers and And what was obtained and , original variables By minimizing the content The item obtained is:
[0143]
[0144] For the cost function in the formula Taking the derivative and setting it equal to zero, we get:
[0145]
[0146] Among them, matrix sum vector They are represented as follows:
[0147]
[0148]
[0149] Update Lagrange multipliers and Update the Lagrange multipliers using the gradient ascent method. and Its update formula is expressed as:
[0150]
[0151] Repeat the update steps above until... Reaching the specified maximum number of iterations .
[0152] Finally, the Lagrange multipliers are updated using the gradient ascent method. :
[0153]
[0154] Step 4: Iteratively weight the initial sparse array positions and their corresponding weight coefficients, and continue to update the auxiliary variables, original variables, and Lagrange multipliers of subproblems one and two in step 3 until h reaches the set maximum number of iterations H, at which point the iteration stops, and the final sparse array positions and their corresponding weight coefficients are obtained.
[0155] The technical effects of the present invention will be described in detail below with reference to some specific embodiments and comparison with existing design methods.
[0156] Example
[0157] Regarding the dimensionality reduction and sparsification design method for polynomial structure beamformers proposed in this invention, consider an aperture of... The linear array, the number of candidate array element positions Array element spacing order of polynomial structure Set the sampling rate to 0. The operating frequency range is Reference frequency for The main lobe range is The range of the side lobes is The adjustable beam range is Frequency points , number of angle points Number of discrete points for adjustable direction angle SRV constraint threshold Side lobe level The lower bound of the WNG constraint .
[0158] Comparison 1
[0159] First, the sparsity performance and beamforming performance of the design method of this invention (dimensionality reduction sparse design) are compared with those of the existing design method (original sparse design).
[0160] Figure 2 shows the element position distribution of the two polynomial beamformer joint sparsification designs before and after dimensionality reduction. From the perspective of element sparsity performance, the two design methods have the same sparsity capability. The number of elements after sparsification is 23, and the element distribution is the same, indicating that dimensionality reduction does not affect the array sparsity performance of the polynomial beamformer.
[0161] Table 1 compares the tap sparsity of the two sparse design methods before and after dimensionality reduction. As can be seen from the table, the number of taps that need optimization in the dimensionality-reduced sparse design is only 52.17% of that in the original design, and the tap sparsity is not significantly different between the two. Therefore, dimensionality reduction does not sacrifice the tap sparsity performance of the polynomial beamformer.
[0162] Table 1
[0163] Design Method | Total Number of Taps | Number of Non-zero Taps | Number of Zero-value Taps | Sparsity (%) | Original Sparsity | 3450 | 2072 | 1378 | 39.94 | Dimensionality Reduction Sparsity | 1800 | 10697 | 314 | 0.61 surface
[0164] Figures 3 and 4 show the beam patterns and directivity indices of the polynomial beamformers before and after dimensionality reduction at a pointing angle of 90°. As can be seen from the figures, the beam patterns and directivity indices remain essentially consistent before and after dimensionality reduction. Figure 5 shows the comparison of the average white noise gain and average directivity indices of the two beamformers before and after dimensionality reduction at different pointing angles. The maximum differences in average white noise gain and average directivity indices before and after dimensionality reduction are 0.078 dB and 0.012 dB, respectively. Simulation results indicate that dimensionality reduction has almost no impact on the beam performance of the sparse polynomial beamformer.
[0165] Comparison 2
[0166] The optimization efficiency and implementation complexity of the design method of this invention are compared with those of existing design methods. The computation time of different optimization solution methods before and after dimensionality reduction is shown in Table 2.
[0167] Table 2
[0168] Design Methodology CVXADMM: Original Sparsity 212.88 hours 5.52 hours; Dimensionality Reduction Sparsity 40.26 hours 0.72 hours surface
[0169] The computer used was configured with an Intel Xeon CPU E5-2680v4@2.4GHz and 96GB of RAM. Since both the original sparse and dimensionality-reduced sparse optimization problems are convex problems, they can also be solved using the CVX toolbox. Therefore, we compared the CPU time of the two design methods under CVX and ADMM algorithms. The table shows that the dimensionality-reduced design is more efficient, with a significantly shorter computation time than the original design. Through the dimensionality reduction processing proposed in this paper, the computation time of the optimized design can be reduced by 81.09% when using CVX optimization, and by 86.96% when using ADMM optimization. Compared to the original CVX optimization design, the computation time of the proposed original ADMM optimization algorithm is only 2.59% of its time; compared to the dimensionality-reduced CVX optimization design, the computation time of the proposed dimensionality-reduced ADMM optimization algorithm is only 1.78% of its time.
[0170] Next, we analyze the dimensionality reduction implementation structure using symmetry optimization, and then compare the implementation complexity of the proposed dimensionality reduction sparse design with the original sparse design in terms of the number of multipliers and adders. The simulation conditions are the same as in the previous example. First, we consider the case where M is even. We simplify the structure of the k-th filter summing unit in the dimensionality reduction design of the sparse polynomial beamformer based on the parity of k, as shown in Figures 6(a) and 6(b), respectively. In Figure 6(a), for the m-th and M-1-m-th array elements, where ,because This means that the filter after each pair of elements is the same. Therefore, the outputs of each pair of elements can be summed and then share a single filter. In Figure 6(b), for the m-th and M-1-m-th elements, where ,because That is, the filter coefficients connected to the m-th array element are exactly the opposite of those connected to the (M-1-m)-th array element. Therefore, the implementation structure of the dimensionality reduction design is simplified by subtracting the output of the m-th array element from the output of the (M-1-m)-th array element and sharing a single filter.
[0171] Considering the case where M is odd, Figure 7(a) shows the simplified structure of the k-th filter summing unit in the polynomial beamformer when k is even. It can be seen from the figure that the filter coefficients following the m-th and M-1-m-th array elements are the same, where... Therefore, the outputs of each array element can be summed and share a common filter. Figure 7(b) shows the simplified structure of the k-th filter summing unit in the polynomial beamformer when k is odd. It can be seen that the filter coefficients following the m-th and M-1-m-th array elements are opposite, where Therefore, the outputs of each pair of elements can be subtracted and share a common filter.
[0172] Therefore, the number of multipliers and adders used in the original design and the dimensionality reduction design when implementing the sparse linear array polynomial structure beamformer is shown in Table 3.
[0173] Table 3
[0174] Design Method: Number of Multipliers / Number of Adders: Original Sparsity: 2075 / 2011; Dimensionality Reduction Sparsity: 1072 / 1071 surface
[0175] As can be seen from the table, by utilizing symmetry, the number of multipliers and adders in the sparse polynomial beamformer is significantly reduced. Compared to the original sparse design, the number of multipliers in the dimensionality-reduced sparse design is reduced by 48.34%. Regarding the number of adders, the reduction rate is 46.74%.
[0176] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.
Claims
1. A method for dimensionality reduction and sparsity reduction design of beamformers for dynamic scenarios, characterized in that, The steps are as follows: S1. Construct a dimension reduction sparsity theory and analyze the symmetry of the weight coefficients of the sparse polynomial structure broadband beamformer; S2. Using the sparsity symmetry theory in step S1, construct a dimension reduction sparsity model for the polynomial structure broadband beamformer; S3. Based on the alternating direction multiplier method, decompose the optimization problem in step S2 into multiple sub-problems and solve and update them separately to obtain the initial array element positions and sparse weight coefficients. S4. Substitute the initial sparse positions of the array elements and the corresponding weight coefficients back into step S3, and repeat step S3 to obtain the final array element positions and weight coefficients, thereby realizing the dimensionality reduction and sparsification design of the polynomial structure beamformer.
2. The beamformer dimensionality reduction and sparsity design method for dynamic scenarios according to claim 1, characterized in that, In step S1, the dimensionality reduction sparsity theory is constructed, and the symmetry of the weight coefficients of the sparse polynomial structure broadband beamformer is analyzed. The specific steps are as follows: For a uniform linear array, in the joint sparsity design optimization problem of the polynomial structure beamformer, if the weight vector of the h-th iteration... If it is the optimal solution, then the weight coefficients have the following symmetric property: in, Represents the Kronecker product. Represents the identity matrix. and They are represented as follows: That is, the weighting coefficients of a polynomial beamformer have the following symmetric relationship: in, Indicates the first Beamformer weighting coefficients.
3. The beamformer dimensionality reduction and sparsity design method for dynamic scenarios according to claim 2, characterized in that, In step S2, the specific steps for constructing the dimension-reduced sparse model of the polynomial structure broadband beamformer using the sparse symmetry theory in step S1 are as follows: Using the symmetry relation in step S1, the dimension-reduced beam response is expressed as: in, Indicates transpose. The weight coefficient vector after dimensionality reduction: The directional vector after dimensionality reduction: In the formula, ， ， Represented as: The dimension reduction and sparsification problem of polynomial structure beamformers is constructed as follows: in, This represents the nth discrete angle within the beam pointing range. It is the p-th discrete frequency within the operating frequency range. Main petal The first Discrete angles Side lobe The first Discrete angles The reference frequency is represented by ε, the constraint threshold is Γ, and the sidelobe level is Г. This represents the lower bound of the white noise gain. Describing the L1 norm, This represents the weight vector after the h-th iteration following dimensionality reduction. Represents the weighting coefficients in the h-th iteration after dimensionality reduction. This represents the transformation matrix after dimensionality reduction, when M is even: When M is odd: in, This represents an L-row, M-column matrix of all zeros.
4. The beamformer dimensionality reduction and sparsity design method for dynamic scenarios according to claim 3, characterized in that, In step S3, based on the alternating direction multiplier method, the optimization problem in step S2 is decomposed into multiple subproblems, which are solved and updated separately to obtain the initial array element positions and sparse weight coefficients. The specific steps are as follows: by introducing auxiliary variables... and The augmented Lagrangian function of the dimension reduction sparse design problem in step S2 is constructed as follows: In the formula, ， ， The directional vector matrix after dimensionality reduction. express The i-th element, ， ， and For Lagrange multipliers, for Update iteration step size, Represents the real part of a complex number. The conjugate transpose is represented. When iterating through each variable, only one variable is updated each time, and the remaining variables are treated as constants. Its subproblem is minimizing the augmented Lagrangian function, as follows: (1) Subproblem one is the auxiliary variable and The Next iteration update optimization problem: (2) Subproblem 2 is the original variable The Next iteration update optimization problem: Closed-form solutions to the two subproblems are derived separately, and the initial sparse array positions and their corresponding weight coefficients are obtained after iterative updates.
5. The beamformer dimensionality reduction and sparsity design method for dynamic scenarios according to claim 4, characterized in that, In step S4, the initial sparse positions of the array elements and the corresponding weight coefficients are substituted back into step S3. Step S3 is repeated to obtain the final array element positions and weight coefficients. The specific steps for realizing the dimensionality reduction and sparsity design of the polynomial structure beamformer are as follows: Iteratively weight the initial sparse positions of the array elements and the corresponding tap weights, and continue to update the auxiliary variables, original variables and Lagrange multipliers of the augmented Lagrangian function in step S3 until the maximum number of iterations is reached and the iteration stops, thus obtaining the final sparse array element positions and weight coefficients.