Deflectable beam forming method and system based on transducer array
The deflectable beamforming method using the Jacobi series expansion method addresses inflexible beam deflection and narrowing lobe width issues, enabling precise sound control with a transducer array.
Patent Information
- Application Number
- CN202411233451.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-04
- Publication Date
- 2024-12-27
AI Technical Summary
Traditional beamforming algorithms using linear differential transducer arrays are limited by inflexible beam deflection and main lobe width narrowing with frequency increases, restricting their application in scenarios requiring precise sound control.
A deflectable beamforming method based on a transducer array using the Jacobi series expansion method to calculate weight coefficients, allowing flexible beam deflection while maintaining a constant main lobe width, achieved through target beam construction, distortion-free and extreme value constraints, and optimization problems.
Enables flexible beam deflection and maintains a consistent main lobe width across varying frequencies, enhancing sound control precision in large-scale settings.
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Figure CN119211807A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of beam deflection, and in particular to a deflectable beam forming method and system based on a transducer array. Background Art
[0002] In large-scale occasions such as concerts, school playgrounds, museums and stadiums, traditional single transducers can no longer meet the requirements of uniform sound distribution or coverage. Therefore, it is necessary to study the signal processing technology of transducer arrays to enhance the precise control of sound.
[0003] The main beam of the constant beamwidth beamforming algorithm implemented by the traditional linear differential transducer array can only be in the vertical direction of the array, and the main beam cannot change with the change of the target area, that is, there are problems such as difficulty in beam deflection, which restricts its application in practical scenarios.
[0004] The traditional delay-and-sum (DAS) method is implemented by delaying, weighting and summing the output signals of each transducer unit. Although this method can achieve beam deflection, its main lobe width will become narrower as the frequency increases.
[0005] Therefore, it is necessary to study a beamforming scheme that can achieve flexible beam deflection while keeping the main lobe width unchanged. Summary of the invention
[0006] The object of the present invention is to provide a deflectable beamforming method and system based on a transducer array.
[0007] To achieve the above object, on the one hand, the present invention proposes a deflectable beamforming method based on a transducer array, comprising:
[0008] S1, construct the desired target beam form according to the position of the target;
[0009] S2, using the target radiation pattern designed by the Jacobi series expansion method to approximate the target beam form to obtain the corresponding beam equation;
[0010] S3, calculating the beam equation, and solving it to obtain the weight coefficient of each transducer in the transducer array.
[0011] In a preferred embodiment, the S1 comprises:
[0012] S11, constructing the target beam form as a cumulative sum form of differential beam patterns;
[0013] S12, converting the cumulative sum form of the differential beam pattern into an exponential function form.
[0014] In a preferred embodiment, the S1 further comprises:
[0015] Adding a distortion-free constraint to the target beam so that the sound wave radiation direction is deflected to the target direction, and adding an extreme value constraint to constrain the extreme value in the target sound wave direction, and minimizing the sound energy in the sidelobe area;
[0016] An optimization problem is used to solve the real coefficient vector in the target beam.
[0017] In a preferred embodiment, in S11, the cumulative sum of the N-order differential beam patterns is expressed as:
[0018]
[0019] Among them, α N =[α N,0 α N,1 … α N,N ] T ;c N =[1 cosθ … cos N θ] T ;
[0020] And / or, the distortion-free constraint and the extreme value constraint are combined to form a linear equation system, and the linear equation system is expressed as:
[0021] A T α N = b;
[0022] in, θ s is the desired direction of the target beam, and N is the order of the target differential beam;
[0023] And / or, the optimization problem is expressed as:
[0024]
[0025] Among them, Θ SL ∈[0°,θ s -Δ / 2]∪[θ s +Δ / 2,180°],Δ≤2·min(θ s ,180°-θ s ), Δ is the main lobe area of the target beam, Θ SL is the sidelobe area of the target beam, It is the acoustic energy radiated from the target beam to the sidelobe area;
[0026] By solving the optimization problem, the real coefficient vector α is calculated. N .
[0027] In a preferred embodiment, the S12 includes: expanding the target beam form into a form of adding even-order terms and odd-order terms of a trigonometric function, and converting the even-order terms and odd-order terms of the trigonometric function into exponential forms and then adding them.
[0028] In a preferred embodiment, when N is an even number, let When N is an odd number, let Then the exponential function form of the target beam is expressed as:
[0029]
[0030] Among them, α N,-1 =0, t=0,±1,...,±n.;
[0031]
[0032] In a preferred embodiment, the S2 comprises:
[0033] S21, performing Jacobian series expansion on the transfer function of the target radiation pattern;
[0034] S22, substituting the expanded transfer function into the target radiation pattern to obtain the target radiation pattern designed using the Jacobi series expansion method.
[0035] In a preferred embodiment, the target radiation pattern after far-field normalization of the transducer array is expressed as:
[0036]
[0037] Among them, w l (k) is the weight coefficient of the lth loudspeaker unit to be determined, (·) * is the conjugate symbol, k is the wave number, L is the number of speakers, x l is the x-axis position coordinate of the lth speaker unit;
[0038] And / or, the transfer function of the target radiation pattern is expressed as follows after Jacobian series expansion:
[0039] Where i is the imaginary unit, function J n (kx) refers to the Bessel function of the first kind of order n;
[0040] And / or, the target radiation pattern designed using the Jacobi series expansion method is truncated in order N, and the truncated pattern is expressed as:
[0041]
[0042] And / or, the beam equation is expressed as:
[0043] n=0,±1,...,±N, where
[0044] In a preferred embodiment, the beam equation is written in matrix form, and the matrix is solved to obtain the minimum norm solution of the weight coefficients of each transducer.
[0045] In a preferred embodiment, the beam equation is written in matrix form as:
[0046] Φw=γ N ;in,
[0047]
[0048] The minimum norm solution of the weight coefficient is expressed as:
[0049] w=Φ H (ΦΦ H ) -1 γ N .
[0050] On the other hand, the present invention provides a deflectable beamforming system based on a transducer array, comprising:
[0051] A target beam construction module, used to construct a desired target beam form according to the position of the target object;
[0052] A beam equation acquisition module uses a target radiation pattern designed by a Jacobi series expansion method to approximate the target beam form and obtain a corresponding beam equation;
[0053] The weight coefficient solving module is used to calculate the beam equation and solve the weight coefficient of each transducer in the transducer array.
[0054] Compared with the prior art, the present invention has the following beneficial effects: the present invention proposes a deflectable beamforming scheme based on a transducer array, which calculates the weight vector by the Jacobi series expansion method, can realize flexible beam deflection, and can ensure that the main lobe width remains basically unchanged as the frequency increases. BRIEF DESCRIPTION OF THE DRAWINGS
[0055] Figure 1 It is a schematic diagram of the process of the present invention;
[0056] Figure 2 A schematic diagram of a model of a linear speaker array in a specific embodiment of the present invention;
[0057] Figure 3a and 3bThe beam patterns achieved by the method of the present invention at a frequency of 500 Hz with the beam deflected to different angles (corresponding to deflection angles of 60° and 120°, respectively) are compared with the expected beam pattern simulation;
[0058] Figure 4a and Figure 4b They are simulation comparison diagrams of the traditional delay-and-sum (DAS) method and the method proposed in the present invention with the beam deflected to a direction of 60° at different frequencies;
[0059] Figure 5 Schematic diagram of the modules of the system of the present invention. DETAILED DESCRIPTION
[0060] The specific embodiments of the present invention are described in detail below, but it should be understood that the protection scope of the present invention is not limited by the specific embodiments.
[0061] Unless explicitly stated otherwise, throughout the specification and claims, the term “comprise” or variations such as “include” or “comprising”, etc., will be understood to include the stated elements or components but not to exclude other elements or components.
[0062] like Figure 1 As shown, the present invention discloses a deflectable beamforming method based on a transducer array, which mainly includes the following steps:
[0063] S1, construct the desired target beam form according to the position of the target.
[0064] Specifically, in one embodiment, the S1 includes:
[0065] S11, construct the target beam form as the cumulative sum of differential beam patterns.
[0066] If the spacing of the transducer array is much smaller than the wavelength, an ideal (i.e., desired) N-order differential beam pattern can be written in the form of a cumulative sum. In this embodiment, the cumulative sum form of an ideal N-order differential beam pattern is:
[0067]
[0068] Among them, α N =[α N,0 α N,1 … α N,N ] T ;c N =[1 cosθ … cos N θ] T ;
[0069]
[0070]
[0071] Preferably, this step also includes:
[0072] A distortion-free constraint is added to the target beam so that the sound wave radiation direction is deflected to the target direction, and an extreme value constraint is added to constrain the extreme value in the target sound wave direction and minimize the sound energy in the sidelobe area.
[0073] Specifically, in order to deflect the sound wave radiation direction to the target direction, the corresponding direction must be set with a distortion-free constraint, and when the desired sound wave direction is not the target direction, there may be a local extreme value, that is, the amplitude of the beam response in the desired direction is not as large as in some other directions, so consider adding an extreme value constraint. The distortion-free constraint and the extreme value constraint are combined to form a linear equation group. In a specific embodiment, the linear equation group is expressed as:
[0074] A T α N =b.
[0075] in, θ s is the desired direction of the target beam, and N is the order of the target differential beam.
[0076] Solve the real coefficient vector α in the target beam through an optimization problem N .
[0077] In a specific embodiment, the optimization problem is expressed as:
[0078]
[0079] Among them, Θ SL ∈[0°,θ s -Δ / 2]∪[θ s +Δ / 2,180°],Δ≤2·min(θ s ,180°-θ s ), Δ is the main lobe area of the target beam, Θ SL is the sidelobe area of the target beam, It is the acoustic energy radiated from the target beam to the sidelobe area;
[0080] Then, by solving the above optimization problem, the real coefficient vector α N It can be obtained through calculation.
[0081] S12, converting the cumulative sum form of the differential beam pattern into an exponential function form.
[0082] This step specifically includes: writing the ideal target beam form as the sum of the odd and even terms of the trigonometric function, and then converting the odd and even terms of the trigonometric function into the corresponding exponential form of e and adding them. Specifically, the differential beam mode is divided into two cases of even order and odd order for discussion. First, the case where the differential beam is of even order is discussed:
[0083] In one embodiment, the differential beam is an even order The target beam form is:
[0084]
[0085] Let α N,-1 =0, it can be expanded into the form of the addition of even and odd terms of trigonometric functions as follows:
[0086]
[0087] Convert the 2nth power (i.e. even-order term) of the trigonometric function into exponential form and add them together. The specific expression is:
[0088] in,
[0089]
[0090] Convert the 2n-1th power (i.e. odd-order terms) of the trigonometric function into exponential form and add them together. The specific expression is:
[0091] in,
[0092]
[0093] The target beam can be expressed as the cumulative sum of exponential functions:
[0094]
[0095] Let's discuss the case where the differential beam is an odd order:
[0096] In one embodiment, the differential beam is an odd order The target beam form is:
[0097]
[0098] Then, it can be expanded into the form of adding the even and odd terms of trigonometric functions as follows:
[0099]
[0100] Then the exponential addition form of converting the odd-order differential beam to the even-order differential beam is expressed as:
[0101]
[0102] in,
[0103]
[0104] S2, use the target radiation pattern designed by the Jacobi series expansion method to approximate the above target beam form and obtain the corresponding beam equation.
[0105] Specifically, the S2 includes:
[0106] S21, performing Jacobian series expansion on the transfer function of the target radiation pattern.
[0107] In a specific embodiment, the target radiation pattern after far-field normalization of the transducer array is expressed as:
[0108]
[0109] Among them, w l (k) is the weight coefficient of the lth loudspeaker unit to be determined, (·) * is the conjugate symbol, k is the wave number, L is the number of speakers, x l is the x-axis position coordinate of the lth speaker unit.
[0110] The transfer function of the target radiation pattern is expressed as follows after Jacobi series expansion:
[0111] Where i is the imaginary unit, function J n (kx) refers to the Bessel function of the first kind of order n.
[0112] Substituting this transfer function into the above target radiation pattern yields:
[0113]
[0114] In order to obtain an N-order difference mode, the above infinite series is truncated to Nth order, and we get:
[0115]
[0116] S22, substituting the expanded transfer function into the target radiation pattern to obtain the target radiation pattern designed using the Jacobi series expansion method.
[0117] In order to approximate the target radiation pattern to the above target beam form, the corresponding beam equation is expressed as:
[0118]
[0119] S3, calculating the beam equation, and solving it to obtain the weight coefficient of each transducer in the transducer array.
[0120] The step S3 specifically includes: writing the above beam equation into a matrix form, and solving the matrix to obtain the minimum norm solution of the weight coefficient of each transducer.
[0121] Specifically, in one embodiment, when the differential beam is of order N, the matrix form of the beam equation is expressed as:
[0122] Φw=γ N .
[0123] in,
[0124] According to the symmetry properties of the Bessel function, the matrix form can be expressed as:
[0125]
[0126] in,
[0127] When the number of transducers used in the transducer array is L>N+1, the minimum norm solution of the weight coefficient is expressed as:
[0128]
[0129] The effect achieved by the method proposed in the present invention is described below in conjunction with a specific embodiment, and a simulation comparison is performed with a traditional DAS method.
[0130] The transducer array can be implemented as either a speaker array or a microphone array. Figure 2 As shown, in this embodiment, the number of loudspeakers L used in the linear loudspeaker array is 11, the array spacing δ is 3.8 cm, the target differential beam order N is 4, and the target direction θ s is 60°, and the main lobe area Δ is 50°. Figure 3a and 3b As shown in the figure, the beam pattern achieved by the method of the present invention at a frequency of 500 Hz with the beam deflected to different angles (corresponding to deflection angles of 60° and 120°) is compared with the expected beam pattern simulation. In the figure, the red beam represents the beam pattern achieved by the method of the present invention, and the blue beam represents the expected beam pattern. It can be seen from these simulation figures that the beam pattern formed by the present invention is almost overlapped with the expected beam pattern. Figure 4a and 4b As shown, they are simulation comparison diagrams of the DAS method and the method proposed in the present invention with the beam deflected to a direction of 60° at different frequencies (respectively 100 Hz, 500 Hz, 1000 Hz and 2000 Hz). Figure 4a 4b shows that, although the DAS method can also achieve beam deflection, its main lobe width will become narrower as the frequency increases. However, the method of the present invention can achieve flexible beam deflection while keeping the main lobe width unchanged.
[0131] like Figure 5 As shown, corresponding to the above-mentioned deflectable beamforming method based on a transducer array, the present invention also discloses a deflectable beamforming system based on a transducer array, which specifically includes the following modules:
[0132] The target beam construction module is used to construct a desired target beam form according to the position of the target object.
[0133] The beam equation acquisition module uses the target radiation pattern designed by the Jacobi series expansion method to approximate the target beam form and obtain the corresponding beam equation.
[0134] The weight coefficient solving module is used to calculate the beam equation and solve the weight coefficient of each transducer in the transducer array.
[0135] The implementation principle of each module may refer to the description in the above steps S1 to S3 respectively, and will not be elaborated here.
[0136] The advantage of the present invention is that it proposes a deflectable beamforming scheme based on a transducer array, calculates the weight vector by the Jacobi series expansion method, can realize flexible beam deflection, and can ensure that the main lobe width remains basically unchanged as the frequency increases.
[0137] The foregoing description of specific exemplary embodiments of the present invention is for the purpose of illustration and demonstration. These descriptions are not intended to limit the present invention to the precise form disclosed, and it is clear that many changes and variations can be made based on the above teachings. The purpose of selecting and describing the exemplary embodiments is to explain the specific principles of the present invention and its practical application, so that those skilled in the art can realize and utilize various different exemplary embodiments of the present invention and various different selections and changes. The scope of the present invention is intended to be limited by the claims and their equivalents.
Claims
1. A deflectable beamforming method based on a transducer array, characterized in that: include: S1, construct the desired target beam form according to the position of the target; S2, using the target radiation pattern designed by the Jacobi series expansion method to approximate the target beam form to obtain the corresponding beam equation; S3, calculating the beam equation, and solving it to obtain the weight coefficient of each transducer in the transducer array.
2. A deflectable beamforming method based on a transducer array as claimed in claim 1, characterized in that: The S1 includes: S11, constructing the target beam form as a cumulative sum form of differential beam patterns; S12, converting the cumulative sum form of the differential beam pattern into an exponential function form.
3. A deflectable beamforming method based on a transducer array as claimed in claim 2, characterized in that: The S1 further comprises: Adding a distortion-free constraint to the target beam so that the sound wave radiation direction is deflected to the target direction, and adding an extreme value constraint to constrain the extreme value in the target sound wave direction, and minimizing the sound energy in the sidelobe area; An optimization problem is used to solve the real coefficient vector in the target beam.
4. A deflectable beamforming method based on a transducer array as claimed in claim 3, characterized in that: In S11, the cumulative sum of the N-order differential beam patterns is expressed as: Among them, a N =[a N,0 a N,1 … a N,N ] T ;c N =[1 cosθ … cos N [i] T ; And / or, the distortion-free constraint and the extreme value constraint are combined to form a linear equation system, and the linear equation system is expressed as: A T a N =b; in, b=[1 0] T ,θ s is the desired direction of the target beam, and N is the order of the target differential beam; And / or, the optimization problem is expressed as: Among them, Θ SL ∈[0°,θ s -Δ / 2]∪[θ s +Δ / 2,180°],Δ≤2·min(θ s ,180°-θ s ), Δ is the main lobe area of the target beam, Θ SL is the sidelobe area of the target beam, It is the acoustic energy radiated from the target beam to the sidelobe area; By solving the optimization problem, the real coefficient vector α is calculated. N .
5. A deflectable beamforming method based on a transducer array as claimed in claim 2, characterized in that: The S12 includes: expanding the target beam form into a form of adding even-order terms and odd-order terms of a trigonometric function, and converting the even-order terms and odd-order terms of the trigonometric function into exponential forms and then adding them.
6. A deflectable beamforming method based on a transducer array as claimed in claim 5, characterized in that: When N is an even number, let When N is an odd number, let Then the exponential function form of the target beam is expressed as: in, 7. A deflectable beamforming method based on a transducer array as claimed in claim 1, characterized in that: The S2 includes: S21, performing Jacobian series expansion on the transfer function of the target radiation pattern; S22, substituting the expanded transfer function into the target radiation pattern to obtain the target radiation pattern designed using the Jacobi series expansion method.
8. A deflectable beamforming method based on a transducer array as claimed in claim 7, characterized in that: The target radiation pattern after far-field normalization of the transducer array is expressed as: Among them, w l (k) is the weight coefficient of the lth speaker unit to be determined, (·) * is the conjugate symbol, k is the wave number, L is the number of speakers, x l is the x-axis position coordinate of the lth speaker unit; And / or, the transfer function of the target radiation pattern is expressed as follows after Jacobian series expansion: Where i is the imaginary unit, function J n (kx) refers to the Bessel function of the first kind of order n; And / or, the target radiation pattern designed using the Jacobi series expansion method is truncated in order N, and the truncated pattern is expressed as: And / or, the beam equation is expressed as: in, 9. The method for forming a deflectable beam based on a transducer array according to claim 1, characterized in that: The S3 includes: writing the beam equation into a matrix form, and solving the matrix to obtain a minimum norm solution of the weight coefficients of each transducer.
10. A deflectable beamforming system based on a transducer array, characterized in that: include: A target beam construction module, used to construct a desired target beam form according to the position of the target object; A beam equation acquisition module uses a target radiation pattern designed by a Jacobi series expansion method to approximate the target beam form and obtain a corresponding beam equation; The weight coefficient solving module is used to calculate the beam equation and solve the weight coefficient of each transducer in the transducer array.