Broadband high-gain beam pattern optimization method suitable for any array

Abstract

The invention is suitable for the technical field of acoustics, array signal processing and sonar, and provides a broadband high-gain beam pattern optimization method suitable for any array. S1, calculating a weight vector matrix of each order of eigen beams; s2, solving a broadband weighting matrix through CVX; s3, synthesizing a broadband high-gain beam pattern; according to the method, the optimal beam pattern is decomposed into characteristic beams with different robustness and directivity based on generalized characteristic decomposition, under the constraint of expected beam pattern performance, the joint weighting coefficient of each order of characteristic beams is optimized, the broadband weighting matrix of the characteristic beams is calculated, and the final broadband high-gain beam pattern is synthesized according to the weighting coefficient. According to the method, the broadband high-gain beam pattern can be obtained under the constraint condition, meanwhile, the effects of constant beam width, robustness and high gain are achieved, compared with a method disclosed in the prior art, the directivity of a beam former is higher, and the method is suitable for any array.

Description

Technical Field

[0001] This invention belongs to the fields of acoustics, array signal processing and sonar technology, and particularly relates to a broadband high-gain beammap optimization method applicable to arbitrary arrays. Background Technology

[0002] With the rapid development of fields such as sonar, wireless communication, and radar, beamforming technology for sensor arrays faces increasingly stringent performance requirements. In practical applications, broadband constant beamwidth response and high beam gain characteristics have become key to improving system performance.

[0003] However, traditional beam optimization methods (such as narrowband beamforming and fixed weight design) are difficult to achieve stable high gain and constant beamwidth response under broadband conditions, especially in arbitrary arrays with irregular or sparse element arrangements, where their performance is often limited. Reference 1, "An Arbitrary Order Supergain Beamforming Method Applicable to Arbitrary Arrays, Patent No. CN202210666523.4," discloses a robust high-gain beamforming method (EDAO method) applicable to arbitrary arrays. It obtains robust high-gain results using a near-closed solution method, but this method does not constrain the main lobe and side lobe performance of the beam pattern. Reference 2, "O. Peretz and I. Cohen, Constant Elevation-Beamwidth BeamformingWith Concentric Ring Arrays, in IEEE / ACM Transactions on Audio, Speech, and Language Processing, vol.32, pp.1662-1672, 2024," discloses a constant beamwidth beamforming method for multi-layer circular ring arrays based on Bessel function expansion. This method adjusts the array aperture by closing the receiving array elements from the outside to the inside physical layer, thereby achieving a constant beamwidth function. However, the array element utilization and beamformer directivity of this method still need to be improved, and it is only applicable to circular ring arrays. Therefore, a broadband high-gain beammap optimization method applicable to arbitrary arrays is needed to solve the above problems. Summary of the Invention

[0004] The purpose of this invention is to provide a broadband high-gain beammap optimization method applicable to arbitrary arrays, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A broadband high-gain beammap optimization method applicable to arbitrary arrays includes the following steps; S1. Calculate the weight vector matrix of each order of characteristic beam; S2. Solving the broadband weighting matrix using CVX ; S3. Synthesized broadband high-gain beammap.

[0006] This method optimizes the joint weighting coefficients of characteristic beams of each order to achieve good broadband high-gain performance for the desired broadband beam pattern requirements.

[0007] In a further technical solution, in "Step S1", the weight vector matrices of each order can be represented as: ; in, M The number of array elements is the order of the characteristic beam. Indicates signal frequency; Indicates the direction of the main lobe; and These are the azimuth and elevation angles of the main lobe, respectively. Indicates the first m The weight vector of order n is expressed as: ; in, Indicates conjugate transpose; and They are respectively No. m Each eigenvector and its corresponding eigenvalue. ; For the normalized noise covariance matrix, each element The expression is: ; in, For the first Array element and the first Distance between array elements Depend on The entire set of eigenvectors is composed of, It is an eigenvalue diagonal matrix, and These are the corresponding eigenvalues; For the direction received by the array The expression for an incident unit amplitude plane wave signal is: ; in, and These are the azimuth and elevation angles, respectively. , , , Indicates the speed of sound. For the first mThe position vector of the array element.

[0008] A further technical solution involves constructing the following multi-constraint optimization problem in "Step S2": ; in, It is an M×J dimensional matrix; J represents the number of discrete frequency points; express The j-th column; Regularization factors that represent directionality and robustness; C1, C2, C3, and C4 represent different constraints; Indicates the first The directivity factor corresponding to the broadband high-gain beam pattern at each frequency. directional index , This represents the error sensitivity function for the corresponding frequency. The This represents the 2-norm of a vector, and the error sensitivity index. ; in, Indicates the main lobe; G Indicates the number of discrete main lobe angles; Indicates the constraint value of the main lobe region; This represents the main lobe flatness constraint value; Indicates the main lobe; S Indicates the number of discrete sidelobe angles; Indicates the constraint value of the main lobe region; Indicates conjugate transpose; This indicates taking the maximum value.

[0009] A further technical solution involves adjusting the regularization factor. To balance the directivity and robustness of broadband high-gain beam patterns.

[0010] Further technical solutions include constraint values ​​for the main lobe region. Main lobe flatness constraint value and the constraint values ​​of the sidelobe region It is used to control the main lobe and side lobe performance of broadband high-gain beammaps.

[0011] A further technical solution, in "Step S3", is... Broadband high-gain beamform at each frequency Synthesized by the following formula: .

[0012] A further technical solution involves synthesizing a broadband high-gain beammap at J discrete frequency points to achieve high-gain performance.

[0013] In a further technical solution, the number of array elements M, the number of discrete frequency points J, the number of discrete main lobe angles G, and the number of discrete side lobe angles S are set according to the actual application scenario.

[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention decomposes the optimal beammap into characteristic beams with different robustness and directivity based on generalized eigenvalue decomposition. Under the constraint of desired beammap performance, it optimizes the joint weighting coefficients of each order of characteristic beams, calculates their broadband weighting matrix, and synthesizes the final broadband high-gain beammap according to the weighting coefficients. It can obtain a broadband high-gain beammap under constraints, and has the effects of constant beamwidth and robust high gain. Compared with the methods disclosed in the prior art, the beamformer has higher directivity and is applicable to arbitrary arrays. This invention achieves excellent broadband high-gain performance by optimizing the joint weighting coefficients of characteristic beams of each order, which is superior to the beammap performance obtained in Reference 1. Compared to the method disclosed in Document 2, the present invention can be applied to any array, and the beamformer of this invention has better directivity and robustness.

[0015] To more clearly illustrate the structural features and effects of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0016] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of an arbitrary irregular array used in the simulation of this invention; Figure 3 The weighting coefficient matrix and broadband beammap of the arbitrary irregular matrix EDJO method of this invention are shown below. Figure 4 For the DIs and WNGs of the arbitrary irregular matrix EDJO method of this invention, Figure 4 (a) is DIs. Figure 4 (b) are WNGs; Figure 5 This is a schematic diagram of the five-layer circular array used in the simulation of this invention; Figure 6 This is the broadband beammap of the five-layer circular array EDJO method and FIRCB of this invention. Figure 6 (a)-(d) are the broadband beam plots of the EDJO method when the regularization coefficients are 0, 0.3, 0.7, and 1, respectively. Figure 6(e)-(f) are the beam diagrams of the FIRCB method when the regularization coefficients are 0 and 1, respectively; Figure 7 The DIs and WNGs of the five-layer circular annular array EDJO method of this invention are as follows. Figure 7 (a) is DIs. Figure 7 (b) are WNGs. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0018] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0019] Example 1 like Figures 1-7 As shown, this embodiment of the invention provides a broadband high-gain beammap optimization method applicable to arbitrary arrays, including the following steps; S1. Calculate the weight vector matrix of each order of characteristic beam; The weight vector matrices of each order can be represented as: ; in, M The number of array elements is the order of the characteristic beam. Indicates signal frequency; Indicates the direction of the main lobe; and These are the azimuth and elevation angles of the main lobe, respectively. Indicates the first m The weight vector of order n is expressed as: ; in, Indicates conjugate transpose; and They are respectively No. m Each eigenvector and its corresponding eigenvalue. ; For the normalized noise covariance matrix, each element The expression is: ; in, For the first Array element and the first Distance between array elements Depend on The entire set of eigenvectors is composed of, It is an eigenvalue diagonal matrix, and These are the corresponding eigenvalues; For the direction received by the array The expression for an incident unit amplitude plane wave signal is: ; in, and These are the azimuth and elevation angles, respectively. , , , Indicates the speed of sound. For the first m The position vector of the array element.

[0020] S2. Solving the broadband weighting matrix using CVX ; Construct the following multi-constraint optimization problem: ; in, It is an M×J dimensional matrix; J represents the number of discrete frequency points; express The j-th column; Regularization factors that represent directionality and robustness; C1, C2, C3, and C4 represent different constraints; Indicates the first The directivity factor corresponding to the broadband high-gain beam pattern at each frequency. directional index , This represents the error sensitivity function for the corresponding frequency. The This represents the 2-norm of a vector, and the error sensitivity index. ; in, Indicates the main lobe; G Indicates the number of discrete main lobe angles; Indicates the constraint value of the main lobe region; This represents the main lobe flatness constraint value; Indicates the main lobe; S Indicates the number of discrete sidelobe angles; Indicates the constraint value of the main lobe region; Indicates conjugate transpose; This indicates taking the maximum value.

[0021] By adjusting the regularization factor To balance the directivity and robustness of broadband high-gain beammaps; Constraint values ​​of the main lobe region Main lobe flatness constraint value and the constraint values ​​of the sidelobe region It is used to control the main lobe and side lobe performance of broadband high-gain beammaps.

[0022] S3, Synthetic broadband high-gain beamform; In the Broadband high-gain beamform at each frequency Synthesized by the following formula: .

[0023] A broadband high-gain beammap is synthesized at J discrete frequency points to achieve high-gain performance. The number of array elements M, the number of discrete frequency points J, the number of discrete main lobe angles G, and the number of discrete side lobe angles S are set according to the actual application scenario.

[0024] Working principle and usage process of this invention: Simulation 1: Consider an arbitrary irregular matrix; like Figure 2 As shown, the number of array elements M =16, plane wave incident direction is The sound speed is 1500 m / s, and the frequency range is [200 Hz, 8000 Hz]. Constraints C1, C2, C3, and C4 are applied, and the main lobe width in the horizontal direction is set to 30°. Regularization parameters are... =0.7, main lobe constraint value Main lobe flatness constraint value =0.01, sidelobe constraint value ; For any array shown, the EDAO method selects the beamformer's DI as the sole focus by using a high-order truncation approach, retaining only low-order characteristic beams and directly discarding high-order characteristic beams. like Figure 3 As shown in b, as the frequency increases, the order of synthesis required by the EDAO method gradually increases. Due to the asymmetry of the array, the main lobe of the beam pattern obtained by the EDAO method is severely asymmetrical and the main lobe is relatively wide. At the same time, as the frequency increases, the width of the EDAO main lobe gradually narrows and the side lobes gradually increase. This indicates that the EDAO method cannot effectively control the performance of the main lobe and side lobe of the synthesized beam pattern. The EDJO method adjusts the contribution of each type of characteristic beam to the synthesized beammap by jointly optimizing the weighting coefficients of each type of characteristic beam, thus ensuring the main lobe and side lobe performance of the final synthesized beammap. like Figure 3As shown in c and 3e, the beam pattern of the EDJO method has its side lobes strictly controlled at -12dB, and has a main lobe of constant width with good consistency and strict symmetry with the target direction. like Figure 4 As shown, the DI of the two methods is as follows: the DI of the EDAO method remains constant at 9.5dB, while the WNG gradually increases with increasing frequency; the performance of the EDJO method is similar to that of EDAO, except that the WNG decreases slightly at high frequencies.

[0025] Simulation 2: Consider a five-layer circular array; like Figure 5 As shown, the total number of array elements M =72, plane wave incident direction is The sound speed is 340 m / s, and the frequency range is [1500 Hz, 8000 Hz]. Constraints C1, C2, and C3 are applied, and the main lobe width in the pitch direction is set to 30°. Regularization parameters are... The main lobe constraint values ​​are 0, 0.3, 0.7, and 1, respectively. Main lobe flatness constraint value =0.008; For the multi-layer circular array shown, this method can synthesize a constant beamwidth in the elevation direction under different regularization parameters; like Figure 6 Figures a, 6b, 6c, and 6d show constant-width beam patterns synthesized using the EDJO method. like Figure 6 As shown in e and 6f, constant-width beamforms synthesized by the FIRCB method involved in Reference 2; The -3dB beamwidth of these beammaps is 30°; however, the main difference between the two methods lies in the DI and SI of the beamformer. like Figure 7 As shown, the FIRCB method adjusts the array aperture by closing the receiving array elements from the outside to the inside physical layer, thereby achieving a constant beamwidth function, resulting in low array element utilization. In contrast, the EDJO method utilizes all array elements across the entire frequency band and synthesizes the desired constrained beam pattern through modal filtering. When maximizing directivity (i.e.) When = 1), the DI obtained by the EDJO method is much greater than that of the FIRCB method, but the robustness of the EDJO method is poor at this time; When maximizing robustness (i.e.) When the regularization parameter is 0, the DI and SI of the EDJO method are better than those of the FIRCB method. At the same time, the larger the regularization parameter is, the greater the directivity index of the EDJO method is, while the worse the WNG is. However, for regularization of 0.3 and 0.7, the performance of the EDJO method is better than the FIRCB method mentioned in reference 2 in most frequency bands. In addition, the EDJO method can be applied to any form of sensor array, while the FIR method is only for arrays with a ring structure.

[0026] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A broadband high-gain beammap optimization method applicable to arbitrary arrays, characterized in that, Includes the following steps; S1. Calculate the weight vector matrix of each order of characteristic beam; S2. Solving the broadband weighting matrix using CVX ; S3. Synthesized broadband high-gain beammap.

2. The broadband high-gain beammap optimization method applicable to arbitrary arrays according to claim 1, characterized in that, In "Step S1", the weight vector matrices of each order can be represented as: ； in, M The number of array elements is the order of the characteristic beam. Indicates signal frequency; Indicates the direction of the main lobe; and These are the azimuth and elevation angles of the main lobe, respectively. Indicates the first m The weight vector of order n is expressed as: ; in, Indicates conjugate transpose; and They are respectively No. m Each eigenvector and its corresponding eigenvalue. ; For the normalized noise covariance matrix, each element The expression is: ； in, For the first Array element and the first Distance between array elements Depend on The entire set of eigenvectors is composed of, It is an eigenvalue diagonal matrix, and These are the corresponding eigenvalues; For the direction received by the array The expression for an incident unit amplitude plane wave signal is: ; in, and These are the azimuth and elevation angles, respectively. , , , Indicates the speed of sound. For the first m The position vector of the array element.

3. The broadband high-gain beammap optimization method applicable to arbitrary arrays according to claim 1, characterized in that, In "Step S2", the following multi-constraint optimization problem is constructed: ； in, It is an M×J dimensional matrix; J represents the number of discrete frequency points; express The j-th column; Regularization factors that represent directionality and robustness; C1, C2, C3, and C4 represent different constraints; Indicates the first The directivity factor corresponding to the broadband high-gain beam pattern at each frequency. directional index , This represents the error sensitivity function for the corresponding frequency. The This represents the 2-norm of a vector, and the error sensitivity index. ; in, Indicates the main lobe; G Indicates the number of discrete main lobe angles; Indicates the constraint value of the main lobe region; This represents the main lobe flatness constraint value; Indicates the main lobe; S Indicates the number of discrete sidelobe angles; Indicates the constraint value of the main lobe region; Indicates conjugate transpose; This indicates taking the maximum value.

4. The broadband high-gain beammap optimization method applicable to arbitrary arrays according to claim 3, characterized in that, By adjusting the regularization factor To balance the directivity and robustness of broadband high-gain beam patterns.

5. The broadband high-gain beammap optimization method applicable to arbitrary arrays according to claim 3, characterized in that, Constraint values ​​of the main lobe region Main lobe flatness constraint value and the constraint values ​​of the sidelobe region It is used to control the main lobe and side lobe performance of broadband high-gain beammaps.

6. The broadband high-gain beammap optimization method applicable to arbitrary arrays according to claim 1, characterized in that, In "Step S3", at the... Broadband high-gain beamform at each frequency Synthesized by the following formula: .

7. The broadband high-gain beammap optimization method applicable to arbitrary arrays according to claim 6, characterized in that, A broadband high-gain beammap is synthesized at J discrete frequency points to achieve high-gain performance.

8. The broadband high-gain beammap optimization method applicable to arbitrary arrays according to claim 8, characterized in that, The number of array elements M, the number of discrete frequency points J, the number of discrete main lobe angles G, and the number of discrete side lobe angles S are set according to the actual application scenario.

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