A linear microphone array geometry optimization method and system for time-delay-sum beamforming

Abstract

A linear microphone array geometry optimization method and system for delay-and-sum beamforming, the method comprising: calculating a candidate microphone position vector based on global front parameters of a microphone array; constructing a first objective function with a minimum noise output energy of a delay-and-sum beamformer as a target, and constructing a second objective function with a minimum non-normalized beam pattern energy of the delay-and-sum beamformer as a target; establishing engineering constraints based on the global front parameters of the microphone array; solving a position selection optimization model constructed by the first objective function and the engineering constraints to obtain a binary selection vector, and establishing a mapping with the candidate microphone position vector to obtain an initial array layout; taking the initial array layout as an input, iteratively solving a position fine-tuning optimization model constructed by the second objective function and the engineering constraints, and outputting an optimized linear microphone array layout; the method solves the problem that a traditional uniform array is fixed and cannot be finely positioned by relying on candidate points only.

Description

Technical Field

[0001] This invention relates to the field of microphone array beamforming technology, and more specifically to a method and system for optimizing the geometry of a linear microphone array for delay summation beamforming. Background Technology

[0002] Microphone array beamforming technology is widely used in acoustic front-end processing systems such as voice acquisition, remote conferencing, intelligent interaction, and hearing aids. By processing signals from multiple microphones, it can enhance the target direction signal while suppressing environmental noise and interference, thereby improving the system's sound pickup quality.

[0003] Delay-and-Sum Beamformers (DSBs) are widely used in practical systems due to their simple structure, high computational efficiency, good stability, and the highest white noise gain. However, DSBs typically have low directivity factors in the low-frequency band and limited ability to suppress spatial noise in diffuse noise fields (i.e., noise environments with uniform incidence from all directions). For DSBs, array geometry is a crucial factor affecting their performance. Geometric parameters such as element placement, element spacing, and array aperture directly influence the array's directional performance. Therefore, optimizing the microphone array geometry is an important way to improve the performance of DSBs.

[0004] Existing methods for optimizing array geometry mainly include methods based on metaheuristic algorithms and methods based on... Methods for norm optimization.

[0005] Methods based on metaheuristic algorithms mainly include array geometry optimization methods based on genetic algorithms, simulated annealing algorithms, or evolutionary algorithms. These methods find optimal array layouts through random search, which can improve performance to some extent. However, these methods have the following drawbacks: First, they are prone to getting trapped in local optima and cannot guarantee convergence to the global optimum; second, they have low computational efficiency, and reducing the probability of getting trapped in local optima often requires extremely high computational costs; third, they are very sensitive to algorithm parameters, requiring extensive trial and error to adjust. The drawback of norm optimization is that microphone positions can only fall on pre-defined candidate grid points, and there is a lack of clear criteria to determine the final number of microphones selected.

[0006] Y. Konforti et al. (Konforti Y, Cohen I, Berdugo B. Array geometryoptimization for region-of-interest broadband beamforming[C] / / 2022 International Workshop on Acoustic Signal Enhancement (IWAENC). IEEE, 2022:1-5) proposed an array geometry optimization method for region-of-interest broadband beamforming. This method constructs a mixed integer convex optimization model to select microphone positions from pre-set discrete candidate positions to solve the optimization problem of microphone array geometry layout when the incident direction of the broadband sound source changes within the region of interest. It obtains a microphone array layout that satisfies constraints such as the number of microphones, minimum element spacing, and white noise gain, and improves broadband directivity under different target pointing angles within the region of interest. However, the microphone positions of this method can only be selected from the preset discrete candidate positions, and the resulting array layout is limited by the candidate position grid. It lacks the technical means to further fine-tune the microphone positions based on the initial position selection results. Summary of the Invention

[0007] In order to overcome the shortcomings of the existing technology, the present invention aims to provide a method and system for optimizing the geometry of a linear microphone array for delay summation beamforming. This method solves the problem that the microphone position is fixed in traditional uniform arrays and it is difficult to finely adjust the microphone position by selecting only candidate positions.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for optimizing the geometry of a linear microphone array for delay-summing beamforming includes the following steps: Step 1: Calculate the candidate microphone position vector based on the global pre-setting parameters of the microphone array; the global pre-setting parameters of the microphone array include array aperture, minimum element spacing, number of target microphones, and target frequency band range; Step 2: Within the target frequency band, construct a first objective function with the goal of minimizing the noise output energy of the delay summation beamformer, and construct a second objective function with the goal of minimizing the nonnormalized beam pattern energy of the delay summation beamformer; Step 3: Establish the first engineering constraint and the second engineering constraint based on the array aperture, minimum element spacing, and number of candidate microphones of the microphone array, respectively; Step 4: Construct a discrete candidate position selection optimization model based on the first objective function and the first engineering constraints; solve the discrete candidate position selection optimization model to obtain a binary selection vector, and establish a mapping relationship between the binary selection vector and the candidate microphone position vector to obtain the initial array layout; Step 5: Construct a discrete candidate position fine-tuning optimization model based on the second objective function and the second engineering constraints; use the initial array layout as the initial position vector, iteratively solve the discrete candidate position fine-tuning optimization model, and output the optimized linear microphone array layout.

[0009] Further, step 1 specifically includes: Step 1.1: Within the linear range defined by the array aperture of the microphone array. Within, it is generated according to the uniform discrete layout rule. There are 10 candidate microphone locations; among them... , For the target number of microphones, The aperture of the microphone array; Step 1.2: Calculate the interval between adjacent candidate microphone positions based on the array aperture of the microphone array and the number of candidate microphones; the relevant expression is: in, The interval between adjacent candidate microphone positions; Step 1.3: Construct candidate microphone position vectors based on the interval between adjacent candidate microphone positions; the relevant expression is: in, is the candidate microphone position vector.

[0010] Furthermore, in step 2, the first objective function is: in, Let the first objective function be... The lower limit angular frequency of the target frequency band. The upper limit angular frequency of the target frequency band. Choose a vector for binary values. For Hadamard product, The beamforming coefficient vector is calculated by summing the delays corresponding to all candidate microphone positions. This is the conjugate transpose. This is the pseudocoherence matrix corresponding to the isotropic noise field on the cylindrical surface. The noise output energy matrix within the target frequency band; Among them, if , indicating the first If one candidate position is selected; This indicates that the position is not selected; in, It is a zero-order Bessel function of the first kind. This is the position difference matrix between candidate microphone positions. Angular frequency, It is a diagonal matrix composed of the elements of the delay-sum beamforming coefficient vector. It is a diagonal matrix composed of vector elements.

[0011] Furthermore, in step 2, the second objective function is: in, The second objective function is... The lower limit angular frequency of the target frequency band. The upper limit angular frequency of the target frequency band. This is the nonnormalized beam pattern of the time-delay summation beamformer after the first-order Taylor expansion approximation. The angle of signal incidence. Angular frequency, For the first The microphone position vector obtained in the next iteration. For position increment, A dimensional vector of all 1s These are the expansion coefficients obtained when performing a first-order Taylor expansion on the microphone position increment. The guide vector is determined by the current microphone position. , , The frequency band integral matrix determined by the current array layout; in, The imaginary unit, In the direction of the target sound source, For the speed of sound, For the first During the nth iteration The location of each microphone For the first In the nth iteration Microphone position increment; in, For conjugate, , , The angular domain integral matrix corresponding to the frequency band integral matrix determined by the current array layout; in, For the first The difference matrix between the microphone positions in the array during the next iteration. It is a zero-order Bessel function of the first kind. It is a first-order Bessel function of the first kind. It is a second-order Bessel function of the first kind.

[0012] Furthermore, in step 3, the first engineering constraint includes the target microphone number constraint, the reference position point constraint, and the first minimum array element spacing constraint; the second engineering constraint includes the microphone array aperture constraint, the second minimum array element spacing constraint, and the maximum displacement constraint in a single iteration. The target microphone quantity constraint is from Select from candidate microphone positions N One target microphone must meet the following requirements: in, Choose a vector for binary values. for M A 1-dimensional vector; The reference position point constraint is to ensure that the first microphone of the microphone array is located at the origin of the coordinate system, and must satisfy the following: in, for The first column vector of the identity matrix; The first minimum array element spacing constraint, to ensure sufficient installation spacing between adjacent microphones, must satisfy: Where, matrix U∈ M×G , for A dimensional vector of all 1s Each corresponding element is less than or equal to; in, To minimize the element spacing, The interval between adjacent candidate microphone positions; The microphone array aperture constraint requires that all microphone positions be within the defined range of the microphone array, and must satisfy the following: in, For the first The microphone position vector obtained in the next iteration. This is the microphone position increment vector. For the array aperture of the microphone array Composition dimensional vector; The second minimum element spacing constraint requires that the spacing between adjacent microphones be greater than the minimum element spacing, and must satisfy the following: in, For each corresponding element, it must be greater than or equal to. For adjacent difference matrices, For the minimum element spacing Composition -1 dimensional vector; The maximum displacement constraint in a single iteration limits the magnitude of the microphone position increment during a single iteration and must satisfy the following: in, , This represents the maximum allowable positional change in a single iteration.

[0013] Furthermore, in step 4, the discrete candidate position selection optimization model is as follows: Further, in step 4, the binary selection vector is obtained by solving the discrete candidate position selection optimization model. A mapping relationship is then established between the binary selection vector and the candidate microphone position vector to obtain the initial array layout, specifically: The mixed integer convex optimization tool configured on the MATLAB platform is used to solve the discrete candidate position selection optimization model and output a binary selection vector. Following the order of the candidate microphone positions, each element in the binary selection vector is read sequentially. The candidate microphone position indices corresponding to the elements with a value of 1 are arranged in ascending order to obtain the set of selected position indices: in, For the selected location index set, the first Candidate microphone location index , The target number of microphones; Based on the selected position index set Extract the indices from the candidate microphone position vectors sequentially. The candidate microphone positions are determined to form the initial microphone array layout.

[0014] Furthermore, in step 5, the discrete candidate position fine-tuning optimization model is as follows: Further, in step 5, using the initial array layout as the initial position vector, the discrete candidate position fine-tuning optimization model is iteratively solved to output the optimized linear microphone array layout, specifically: a) Using the initial position vector as the starting point for the iteration of the discrete candidate position fine-tuning optimization model, preset the maximum number of iterations, and initialize the iteration rounds. =1; b) with the first The array position vector obtained from the first iteration is used as the current position vector and input into the discrete candidate position fine-tuning optimization model. The solution is obtained using MATLAB's CVX toolbox. The position increment vector for each iteration; c) The first The array position vector obtained from the first iteration and the first iteration The position increment vectors of each iteration are added together to obtain the position increment vector of the first iteration. The array position vector for each iteration; d) Determine if the current iteration count has reached the preset maximum iteration count; if so, stop iterating and start the next iteration. The array position vector from the first iteration is used as the optimized linear microphone array layout; if this is not achieved, the second iteration will... The array position vector of the first iteration is used as the current position vector for the next iteration, and the number of iterations is... Increment by 1 and return to the execution step bd).

[0015] A linear microphone array geometry optimization system for delay-summing beamforming includes: Candidate microphone position vector calculation module: calculates candidate microphone position vectors based on the global pre-parameters of the microphone array; the global pre-parameters of the microphone array include array aperture, minimum element spacing, number of target microphones, and target frequency band range; Objective function construction module: Within the target frequency band, a first objective function is constructed with the goal of minimizing the noise output energy of the delay summation beamformer, and a second objective function is constructed with the goal of minimizing the nonnormalized beam pattern energy of the delay summation beamformer. Engineering constraint construction module: First and second engineering constraints are established based on the array aperture of the microphone array, the minimum element spacing, and the number of candidate microphones, respectively; Initial array layout construction module: Based on the first objective function and the first engineering constraints, a discrete candidate position selection optimization model is constructed; the binary selection vector is obtained by solving the discrete candidate position selection optimization model; the binary selection vector is mapped to the candidate microphone position vector to obtain the initial array layout; Linear microphone array geometry optimization module: Based on the second objective function and the second engineering constraints, a discrete candidate position fine-tuning optimization model is constructed; using the initial array layout as the initial position vector, the discrete candidate position fine-tuning optimization model is iteratively solved, and the optimized linear microphone array layout is output.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention constructs a first objective function with the goal of minimizing the noise output energy of the delay-sum beamformer in a cylindrical isotropic noise field. Based on the first objective function and the first engineering constraints, a discrete candidate position selection optimization model is constructed. The binary selection vector is solved and mapped to the candidate microphone position vector. This solves the problem that the array element positions of traditional uniform arrays are fixed and it is difficult to further improve the directivity of the delay-sum beamformer for the target frequency band. An initial array layout that meets the requirements of the number of target microphones, reference position points and minimum array element spacing is obtained. This is beneficial to reduce the noise output energy of the delay-sum beamformer in the target frequency band and improve its directivity. It has the characteristics of clear optimization objectives and array layout that meets engineering constraints.

[0017] 2. This invention constructs a second objective function with the goal of minimizing the nonnormalized beammap energy of the delay-sum beamformer within the target frequency band. Based on the second objective function and the second engineering constraints, a discrete candidate position fine-tuning optimization model is constructed. The position increment vector is iteratively solved and the microphone position is updated. This solves the problem that the beammap of the delay-sum beamformer and the microphone position have a nonlinear relationship, making it difficult to directly perform position fine-tuning optimization. It obtains an optimized array layout that further improves the directivity of the delay-sum beamformer within the target frequency band based on the initial array layout. It has the characteristic of being able to transform the nonlinear array position optimization problem into an iteratively solvable position fine-tuning problem and further improve the directivity within the target frequency band.

[0018] 3. This invention solves the problems of microphone positions exceeding the set array aperture, adjacent microphone spacing not meeting installation requirements, and excessively large single-iteration displacement constraints during the position fine-tuning process by setting microphone array aperture constraints, second minimum array element spacing constraints, and single-iteration maximum displacement constraints during the position fine-tuning process. It also solves the discrete candidate position fine-tuning optimization model by iteratively solving the position increment vector, updating the current array position vector, and using the updated array position vector for the next iteration. This results in an optimized array layout that is within the set array aperture, meets the minimum array element spacing requirements, and has a single position increment that does not exceed a preset range. It features controllable position update amplitude and optimization results that meet engineering installation requirements.

[0019] 4. Through simulation experiments, compared with the traditional uniform array, the initial array obtained by selecting discrete candidate positions has higher directivity in the target frequency band. After fine-tuning the position based on the initial array layout, the directivity is further improved.

[0020] In summary, this invention optimizes the geometry of a linear microphone array through two stages: position selection and position fine-tuning. First, a discrete candidate position selection optimization model is constructed based on a first objective function and a first engineering constraint to obtain the initial array layout. Then, a discrete candidate position fine-tuning optimization model is constructed based on a second objective function and a second engineering constraint. Using the initial array layout as the starting point, the position increment vector is iteratively solved and the microphone positions are updated to obtain the optimized linear microphone array layout. This method solves the problem of fixed microphone positions in traditional uniform arrays, where it is difficult to further adjust microphone positions through candidate position selection alone. It obtains a linear microphone array layout that is located within a set array aperture and meets the minimum element spacing requirement. This improves the directivity factor of the delay-summing beamformer in the target frequency band, enhances the attenuation capability and spatial resolution capability in non-target directions, and features seamless integration of microphone position selection and position fine-tuning, improved array directivity, and optimization results that meet engineering constraints. This invention is applicable to microphone array design in voice acquisition, remote conferencing, hearing aids, and mobile terminals, and can also be used for array optimization in general acoustic signal acquisition systems. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the method for optimizing the geometry of a linear microphone array used in delay-summing beamforming according to the present invention.

[0022] Figure 2 This diagram illustrates a comparison of microphone position distributions between a traditional uniform array, an initial array obtained through discrete candidate position selection using this invention, and an optimized array obtained by fine-tuning the position of the initial array.

[0023] Figure 3 shows a performance comparison of a traditional uniform array, an initial array obtained by discrete candidate position selection according to the present invention, and an optimized array obtained by position fine-tuning the initial array. In particular, Figure 3(a) shows a comparison of the directivity factors of the traditional uniform array, the initial array obtained by discrete candidate position selection according to the present invention, and the optimized array obtained by position fine-tuning the initial array in the target frequency band from 10 Hz to 500 Hz. Figure 3(b) shows the beam diagrams of the traditional uniform array, the initial array obtained by discrete candidate position selection according to the present invention, and the optimized array obtained by position fine-tuning the initial array at 100 Hz. Figure 3(c) shows the beam diagrams of the traditional uniform array, the initial array obtained by discrete candidate position selection according to the present invention, and the optimized array obtained by position fine-tuning the initial array at 400 Hz. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments: See Figure 1A method for optimizing the geometry of a linear microphone array for delay-summing beamforming includes the following steps: Step 1: Calculate the candidate microphone position vector based on the global pre-setting parameters of the microphone array; the global pre-setting parameters of the microphone array include array aperture, minimum element spacing, number of target microphones, and target frequency band range; Step 1 specifically involves: Step 1.1: Within the linear range defined by the array aperture of the microphone array. Within, it is generated according to the uniform discrete layout rule. There are 10 candidate microphone locations; among them... , For the target number of microphones, The aperture of the microphone array; Step 1.2: Calculate the interval between adjacent candidate microphone positions based on the array aperture of the microphone array and the number of candidate microphones; the relevant expression is: in, The interval between adjacent candidate microphone positions; Step 1.3: Construct candidate microphone position vectors based on the interval between adjacent candidate microphone positions; the relevant expression is: in, is the candidate microphone position vector.

[0025] Step 2: Within the target frequency band, construct a first objective function with the goal of minimizing the noise output energy of the delay summation beamformer, and construct a second objective function with the goal of minimizing the nonnormalized beam pattern energy of the delay summation beamformer; In step 2, the first objective function is: in, Let the first objective function be... The lower limit angular frequency of the target frequency band. The upper limit angular frequency of the target frequency band. Choose a vector for binary values. For Hadamard product, The beamforming coefficient vector is calculated by summing the delays corresponding to all candidate microphone positions. This is the conjugate transpose. This is the pseudocoherence matrix corresponding to the isotropic noise field on the cylindrical surface. The noise output energy matrix within the target frequency band; For all candidate microphone positions, in the direction of the target sound source, At that time, the non-normalized delay summation beamforming coefficient vector corresponding to the delay summation beamformer is: in, , represents the guide vector corresponding to all candidate microphones. Represents angular frequency. Indicates frequency, The vector represents the speed of sound; the above vector reflects the phase relationship when the signal in the target direction propagates to the positions of each candidate microphone.

[0026] Among them, if , indicating the first If one candidate position is selected; This indicates that the position is not selected; binary selection vector. Beamforming coefficient vectors corresponding to all candidate microphone positions Performing the Hadamard product is equivalent to using a binary selection vector to retain or set the coefficients corresponding to each candidate microphone position to zero, so that the first objective function can represent the noise output energy corresponding to different combinations of candidate microphone positions in a unified matrix form.

[0027] in, It is a zero-order Bessel function of the first kind. Let be the position difference matrix between candidate microphone positions, and its i-th Each element can be represented as , For the first One candidate microphone position For the first One candidate microphone position It is a diagonal matrix composed of the elements of the delay-sum beamforming coefficient vector. It is a diagonal matrix composed of vector elements.

[0028] In this embodiment, the first objective function characterizes the target frequency band noise output energy of the selected microphone array in a cylindrical isotropic noise field. By minimizing this objective function, the combination of microphone positions with lower target frequency band noise output energy can be determined from all candidate microphone positions. For different array layouts using the same number of target microphones and delay-summing beamforming methods, the target sound source directional response remains consistent; the lower the noise output energy, the higher the corresponding directivity factor. Therefore, minimizing the first objective function is beneficial for improving the directivity performance of the resulting initial array layout within the target frequency band.

[0029] In step 2, the second objective function is: in, The second objective function is... The lower limit angular frequency of the target frequency band. The upper limit angular frequency of the target frequency band. This is the nonnormalized beam pattern of the time-delay summation beamformer after the first-order Taylor expansion approximation. The angle of signal incidence. Angular frequency, For the first The microphone position vector obtained in the next iteration. For position increment, A dimensional vector of all 1s These are the expansion coefficients obtained when performing a first-order Taylor expansion on the microphone position increment. The guide vector is determined by the current microphone position. , , The frequency band integral matrix determined by the current array layout; For a time-delay summation beamformer, its nonnormalized beam pattern can be represented as: in, , where is the position vector of each microphone in the current array. For the first The location of each microphone The imaginary unit, In the direction of the target sound source, The beam pattern reflects the strength of the microphone array's response to incident signals from different directions; the target sound source direction in this embodiment... It can be at any angle; in the simulation stage, the target sound source is generally arranged on the array. 0° is taken as the reference direction, and at this point, all subsequent formulas... It can be simplified to 1, thereby simplifying the calculation of the guidance vector and time delay and reducing the complexity of algorithm derivation. 0° is only the preferred reference orientation, not the only fixed angle. Furthermore, when the position increment is sufficiently small, the change in the array steering vector caused by a small change in the microphone position can be approximated using a first-order Taylor expansion. This allows the non-normalized beammap of the delay-summation beamformer to be approximated as a function of the position increment vector. The expression for this local approximation provides the foundation for constructing an iteratively solvable discrete candidate position fine-tuning optimization model.

[0030] in, For the first During the nth iteration The location of each microphone For the first In the nth iteration Microphone position increment; in, For conjugate, , , The angular domain integral matrix corresponding to the frequency band integral matrix determined by the current array layout; in, For the first The difference matrix between the microphone positions in the array during the next iteration. It is a zero-order Bessel function of the first kind. It is a first-order Bessel function of the first kind. This is a second-order Bessel function of the first kind. The angular domain integral summarizes the beam pattern responses corresponding to different incident directions into a matrix form at a given angular frequency, while the band integral further summarizes the beam pattern energy corresponding to each angular frequency within the target band. Thus, the double integral objective function with respect to the incident angle and angular frequency can be transformed into a function with respect to the position increment vector. It is a quadratic function, which makes it easier to solve using convex optimization tools.

[0031] in, For the first During the nth iteration The location of each microphone For the first During the nth iteration The location of the microphone.

[0032] Step 3: Establish the first engineering constraint and the second engineering constraint based on the array aperture, minimum element spacing, and number of candidate microphones of the microphone array, respectively; In step 3, the first engineering constraints include the target microphone number constraint, the reference position point constraint, and the first minimum array element spacing constraint; the second engineering constraints include the microphone array aperture constraint, the second minimum array element spacing constraint, and the maximum displacement constraint in a single iteration. The target microphone quantity constraint is from Select from candidate microphone positions N One target microphone must meet the following requirements: in, Choose a vector for binary values. for M A 1-dimensional vector; The reference position point constraint is to ensure that the first microphone of the microphone array is located at the origin of the coordinate system, and must satisfy the following: in, for The first column vector of the identity matrix, .

[0033] The first minimum array element spacing constraint, to ensure sufficient installation spacing between adjacent microphones, must satisfy: in, for A dimensional vector of all 1s For each corresponding element, it is less than or equal to, for example For vectors Each element is less than or equal to the vector The element at the corresponding position in the array, i.e., for any element index. All have ; matrix U∈ M×G ,matrix The A column can be represented as ,in, and Let each represent a vector of all zeros of the corresponding dimension. for A 1-dimensional vector; The purpose of the first minimum array element spacing constraint in this embodiment is to ensure that, within any local interval whose length is less than or equal to the minimum array element spacing, two microphone positions that are too close to each other will not be selected at the same time. in, To minimize the element spacing, The interval between adjacent candidate microphone positions; The microphone array aperture constraint requires that all microphone positions be within the defined range of the microphone array, and must satisfy the following: in, For the first The microphone position vector obtained in the next iteration. This is the microphone position increment vector. For the array aperture of the microphone array Composition dimensional vector; The second minimum element spacing constraint requires that the spacing between adjacent microphones be greater than the minimum element spacing, and must satisfy the following: in, For each corresponding element, it must be greater than or equal to, for example For vectors Each element is greater than or equal to the vector The element at the corresponding position in the array, i.e., for any element index. All have , For adjacent difference matrices, For the minimum element spacing Composition -1 dimensional vector; The second minimum element spacing constraint is equivalent to: The maximum displacement constraint in a single iteration limits the magnitude of the microphone position increment during a single iteration and must satisfy the following: in, , This represents the maximum allowable positional change in a single iteration.

[0034] In this embodiment, the microphone array aperture constraint is used to ensure that each microphone remains within the set linear arrangement range after the position update. The second minimum array element spacing constraint is used to prevent insufficient spacing between adjacent microphones after position fine-tuning, ensuring that the final array layout meets the installation requirements. The single iteration maximum displacement constraint is used to limit the position change amplitude in each iteration, keeping the position increment within a local range near the current array position, thereby ensuring the accuracy of the first-order Taylor expansion approximation and improving the stability of subsequent position fine-tuning iterations.

[0035] Step 4: Construct a discrete candidate position selection optimization model based on the first objective function and the first engineering constraints; solve the discrete candidate position selection optimization model to obtain a binary selection vector, and establish a mapping relationship between the binary selection vector and the candidate microphone position vector to obtain the initial array layout; In step 4, the discrete candidate location selection optimization model is as follows: In step 4, the binary selection vector is obtained by solving the discrete candidate position selection optimization model. The binary selection vector is then mapped to the candidate microphone position vectors to obtain the initial array layout, specifically: The mixed integer convex optimization tools configured on the MATLAB platform are used to solve the discrete candidate position selection optimization model and output a binary selection vector. The mixed integer convex optimization tools in this embodiment include YALMIP and MOSEK. YALMIP is responsible for modeling and MOSEK is responsible for numerical solution.

[0036] Following the order of the candidate microphone positions, each element in the binary selection vector is read sequentially. The candidate microphone position indices corresponding to the elements with a value of 1 are arranged in ascending order to obtain the set of selected position indices: in, For the selected location index set, the first Candidate microphone location index , The target number of microphones; Based on the selected position index set Extract the indices from the candidate microphone position vectors sequentially. The candidate microphone positions form the initial array position vector; This embodiment solves the discrete candidate position selection optimization model, thereby enabling the selection of all... Select the candidate positions that satisfy the first engineering constraint. N The microphone positions are determined to form the initial array layout.

[0037] Step 5: Construct a discrete candidate position fine-tuning optimization model based on the second objective function and the second engineering constraints; use the initial array layout as the initial position vector, iteratively solve the discrete candidate position fine-tuning optimization model, and output the optimized linear microphone array layout.

[0038] In step 5, the discrete candidate position fine-tuning optimization model is as follows: In step 5, using the initial array layout as the initial position vector, the discrete candidate position fine-tuning optimization model is iteratively solved, and the optimized linear microphone array layout is output as follows: a) Using the initial position vector as the starting point for the iteration of the discrete candidate position fine-tuning optimization model, preset the maximum number of iterations, and initialize the iteration rounds. =1; b) with the first The array position vector obtained from the first iteration is used as the current position vector and input into the discrete candidate position fine-tuning optimization model. The solution is obtained using MATLAB's CVX toolbox. The position increment vector for each iteration; c) The first The array position vector obtained from the first iteration and the first iteration The position increment vectors of each iteration are added together to obtain the position increment vector of the first iteration. The array position vector of the round iteration; in this embodiment, the first... A microphone passed by The position update relationship after rounds of iteration can be represented as: in, Indicates the first In the nth iteration Microphone position increment; d) Determine if the current iteration count has reached the preset maximum iteration count; if so, stop iterating and start the next iteration. The array position vector from the first iteration is used as the optimized linear microphone array layout; if this is not achieved, the second iteration will... The array position vector of the first iteration is used as the current position vector for the next iteration, and the number of iterations is... Increment by 1 and return to the execution step bd).

[0039] A linear microphone array geometry optimization system for delay-summing beamforming includes: Candidate microphone position vector calculation module: calculates candidate microphone position vectors based on the global pre-parameters of the microphone array; the global pre-parameters of the microphone array include array aperture, minimum element spacing, number of target microphones, and target frequency band range; Objective function construction module: Within the target frequency band, a first objective function is constructed with the goal of minimizing the noise output energy of the delay summation beamformer, and a second objective function is constructed with the goal of minimizing the nonnormalized beam pattern energy of the delay summation beamformer. Engineering constraint construction module: First and second engineering constraints are established based on the array aperture of the microphone array, the minimum element spacing, and the number of candidate microphones, respectively; Initial array layout construction module: Based on the first objective function and the first engineering constraints, a discrete candidate position selection optimization model is constructed; the binary selection vector is obtained by solving the discrete candidate position selection optimization model; the binary selection vector is mapped to the candidate microphone position vector to obtain the initial array layout; Linear microphone array geometry optimization module: Based on the second objective function and the second engineering constraints, a discrete candidate position fine-tuning optimization model is constructed; using the initial array layout as the initial position vector, the discrete candidate position fine-tuning optimization model is iteratively solved, and the optimized linear microphone array layout is output.

[0040] The application effects of this invention will be described in detail below with reference to simulation experiments: In the simulation, it is assumed that the candidate microphones are located within a straight line range defined by the array aperture. Uniformly distributed within m, i.e., the allowable array arrangement range is taken as... =1.2m, the total number of candidate microphones was set to 50, and finally 20 microphones were selected to form a delay summation array, that is , At the same time, the minimum spacing constraint of the array elements is taken as follows: m, the maximum displacement in a single iteration is taken m. To highlight the improvement effect of this invention on the low-frequency pointing performance of the delay summing array, the lower limit of the frequency of interest is set to 10Hz and the upper limit is set to 500Hz.

[0041] See Figure 2In this example, a uniform array is used as a comparison array, and the array layout result obtained by optimizing the geometry of the linear microphone array of the present invention is given. Here, a uniform array (UA) represents 20 microphones in the interval... Uniformly distributed within m, FS represents the initial microphone array layout obtained after position selection using the discrete candidate position selection optimization model based on this invention, and FS+SS represents the linear microphone array layout obtained after further position fine-tuning using the discrete candidate position fine-tuning optimization model based on the initial microphone array layout. Figure 2 As can be seen, under the conditions of satisfying the array aperture and minimum spacing of array elements, the present invention can rearrange the microphone positions to obtain an optimized layout that is different from the traditional uniform array.

[0042] Figure 3 shows the performance comparison results of different methods. In Figure 3(a), the subband directivity factor is represented, and in Figure 3(b) and (c), the beam patterns at frequencies of 100 Hz and 400 Hz are represented, respectively.

[0043] As can be seen from Figure 3(a), compared with a uniform array, the directivity factor of the initial array in the target frequency band is improved after position selection using the discrete candidate position selection optimization model based on the present invention. On this basis, after position fine-tuning by the discrete candidate position fine-tuning optimization model, the sub-band directivity factor is further improved. This indicates that, based on the initial microphone array layout, after position fine-tuning by the discrete candidate position fine-tuning optimization model, the sub-band directivity factor of the delay summation array can be further improved.

[0044] As can be seen from Figure 3(b), at a lower frequency of 100Hz, compared to a uniform array, the linear microphone array layout optimized by this invention exhibits lower beam response away from the target direction, especially at... The array exhibits a more pronounced interference suppression effect near the target direction, indicating that the optimized array has a stronger attenuation capability for acoustic signals from non-target directions.

[0045] As can be seen from Figure 3(c), at a higher frequency of 400Hz, the main lobe width of the optimized linear microphone array layout is relatively narrower than that of the uniform array, indicating that its target direction response is more concentrated and has higher spatial resolution.

[0046] Simulation results show that, without changing the basic structure of the delay summing beamformer, the two-stage (position selection optimization and position fine-tuning optimization) microphone array geometry optimization method proposed in this invention can effectively improve the pointing performance of the array in the target frequency band, especially its low-frequency pointing performance and spatial interference suppression capability, and therefore has good practical application value.

[0047] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions or improvements made by those skilled in the art within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing the geometry of a linear microphone array for delay-summing beamforming, characterized in that, Includes the following steps: Step 1: Calculate the candidate microphone position vector based on the global pre-parameters of the microphone array; The global pre-configuration parameters of the microphone array include array aperture, minimum element spacing, number of target microphones, and target frequency band range. Step 2: Within the target frequency band, construct a first objective function with the goal of minimizing the noise output energy of the delay summation beamformer, and construct a second objective function with the goal of minimizing the nonnormalized beam pattern energy of the delay summation beamformer; Step 3: Establish the first engineering constraint and the second engineering constraint based on the array aperture, minimum element spacing, and number of candidate microphones of the microphone array, respectively; Step 4: Construct a discrete candidate position selection optimization model based on the first objective function and the first engineering constraints; solve the discrete candidate position selection optimization model to obtain a binary selection vector, and establish a mapping relationship between the binary selection vector and the candidate microphone position vector to obtain the initial array layout; Step 5: Construct a discrete candidate position fine-tuning optimization model based on the second objective function and the second engineering constraints; use the initial array layout as the initial position vector, iteratively solve the discrete candidate position fine-tuning optimization model, and output the optimized linear microphone array layout.

2. The method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, characterized in that, Step 1 specifically involves: Step 1.1: Within the linear range defined by the array aperture of the microphone array. Within, it is generated according to the uniform discrete layout rule. There are 10 candidate microphone locations; among them... , For the target number of microphones, The aperture of the microphone array; Step 1.2: Calculate the interval between adjacent candidate microphone positions based on the array aperture of the microphone array and the number of candidate microphones; the relevant expression is: in, The interval between adjacent candidate microphone positions; Step 1.3: Construct candidate microphone position vectors based on the interval between adjacent candidate microphone positions; the relevant expression is: in, is the candidate microphone position vector.

3. The method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, characterized in that, In step 2, the first objective function is: in, Let the first objective function be... The lower limit angular frequency of the target frequency band. The upper limit angular frequency of the target frequency band. Choose a vector for binary values. For Hadamard product, The beamforming coefficient vector is calculated by summing the delays corresponding to all candidate microphone positions. It is the conjugate transpose. This is the pseudocoherence matrix corresponding to the isotropic noise field on the cylindrical surface. The noise output energy matrix within the target frequency band; Among them, if , indicating the first If one candidate position is selected; This indicates that the position is not selected; in, It is a zero-order Bessel function of the first kind. This is the position difference matrix between candidate microphone positions. Angular frequency, It is a diagonal matrix composed of the elements of the delay-sum beamforming coefficient vector. It is a diagonal matrix composed of vector elements.

4. The method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, characterized in that, In step 2, the second objective function is: in, The second objective function is... The lower limit angular frequency of the target frequency band. The upper limit angular frequency of the target frequency band. This is the nonnormalized beam pattern of the time-delay summation beamformer after the first-order Taylor expansion approximation. The angle of signal incidence. Angular frequency, For the first The microphone position vector obtained in the next iteration. For position increment, A dimensional vector of all 1s These are the expansion coefficients obtained when performing a first-order Taylor expansion on the microphone position increment. The guide vector is determined by the current microphone position. , , The frequency band integral matrix determined by the current array layout; in, The imaginary unit, In the direction of the target sound source, For the speed of sound, For the first During the nth iteration The location of each microphone For the first In the nth iteration The position increment of each microphone; in, For conjugate, , , The angular domain integral matrix corresponding to the frequency band integral matrix determined by the current array layout; in, For the first The difference matrix between the microphone positions in the array during the next iteration. It is a zero-order Bessel function of the first kind. It is a first-order Bessel function of the first kind. It is a second-order Bessel function of the first kind.

5. The method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, characterized in that, In step 3, the first engineering constraints include the target microphone number constraint, the reference position point constraint, and the first minimum array element spacing constraint; the second engineering constraints include the microphone array aperture constraint, the second minimum array element spacing constraint, and the maximum displacement constraint in a single iteration. The target microphone quantity constraint is from Select from candidate microphone positions N One target microphone must meet the following requirements: in, Choose a vector for binary values. for M A 1-dimensional vector; The reference position point constraint is to ensure that the first microphone of the microphone array is located at the origin of the coordinate system, and must satisfy the following: in, for The first column vector of the identity matrix; The first minimum array element spacing constraint, to ensure sufficient installation spacing between adjacent microphones, must satisfy: Where, matrix U∈ M×G , for A dimensional vector of all 1s Each corresponding element is less than or equal to; in, To minimize the element spacing, The interval between adjacent candidate microphone positions; The microphone array aperture constraint requires that all microphone positions be within the defined range of the microphone array, and must satisfy the following: in, For the first The microphone position vector obtained in the next iteration. This is the microphone position increment vector. For the array aperture of the microphone array Composition dimensional vector; The second minimum element spacing constraint requires that the spacing between adjacent microphones be greater than the minimum element spacing, and must satisfy the following: in, For each corresponding element, it must be greater than or equal to. For adjacent difference matrices, For the minimum element spacing Composition -1 dimensional vector; The maximum displacement constraint in a single iteration limits the magnitude of the microphone position increment during a single iteration and must satisfy the following: in, , This represents the maximum allowable positional change in a single iteration.

6. A method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, 3, or 5, characterized in that, In step 4, the discrete candidate location selection optimization model is as follows: 。 7. The method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, characterized in that, In step 4, the binary selection vector is obtained by solving the discrete candidate position selection optimization model. The binary selection vector is then mapped to the candidate microphone position vectors to obtain the initial array layout, specifically: The mixed integer convex optimization tool configured on the MATLAB platform is used to solve the discrete candidate position selection optimization model and output a binary selection vector. Following the order of the candidate microphone positions, each element in the binary selection vector is read sequentially. The candidate microphone position indices corresponding to the elements with a value of 1 are arranged in ascending order to obtain the set of selected position indices: in, For the selected location index set, the first Candidate microphone location index , The target number of microphones; Based on the selected position index set Extract the indices from the candidate microphone position vectors sequentially. The candidate microphone positions are determined to form the initial microphone array layout.

8. A method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, 4, or 5, characterized in that, In step 5, the discrete candidate position fine-tuning optimization model is as follows: 。 9. The method for optimizing the geometry of a linear microphone array for delay-summing beamforming according to claim 1, characterized in that, In step 5, using the initial array layout as the initial position vector, the discrete candidate position fine-tuning optimization model is iteratively solved to output the optimized linear microphone array layout, specifically: a) Using the initial position vector as the starting point for the iteration of the discrete candidate position fine-tuning optimization model, preset the maximum number of iterations, and initialize the iteration rounds. =1; b) with the The array position vector obtained from the first iteration is used as the current position vector and input into the discrete candidate position fine-tuning optimization model. The solution is obtained using MATLAB's CVX toolbox. The position increment vector for each iteration; c) The first The array position vector obtained from the first iteration and the first iteration The position increment vectors of each iteration are added together to obtain the position increment vector of the first iteration. The array position vector for each iteration; d) Determine if the current iteration count has reached the preset maximum iteration count; If the condition is met, stop iterating, and proceed to the next iteration. The array position vectors of the round iterations are used as the optimized linear microphone array layout; If not achieved, the next step will be... The array position vector of the first iteration is used as the current position vector for the next iteration, and the number of iterations is... Increment by 1 and return to the execution step bd).

10. A system for optimizing the geometry of a linear microphone array for delay-summing beamforming, characterized in that, include: Candidate microphone position vector calculation module: Calculates candidate microphone position vectors based on the global pre-parameters of the microphone array; The global pre-configuration parameters of the microphone array include array aperture, minimum element spacing, number of target microphones, and target frequency band range. Objective function construction module: Within the target frequency band, a first objective function is constructed with the goal of minimizing the noise output energy of the delay summation beamformer, and a second objective function is constructed with the goal of minimizing the nonnormalized beam pattern energy of the delay summation beamformer. Engineering constraint construction module: First and second engineering constraints are established based on the array aperture of the microphone array, the minimum element spacing, and the number of candidate microphones, respectively; Initial array layout construction module: Based on the first objective function and the first engineering constraints, a discrete candidate position selection optimization model is constructed; the binary selection vector is obtained by solving the discrete candidate position selection optimization model; the binary selection vector is mapped to the candidate microphone position vector to obtain the initial array layout; Linear microphone array geometry optimization module: Constructs a discrete candidate position fine-tuning optimization model based on the second objective function and the second engineering constraints; Using the initial array layout as the initial position vector, the discrete candidate position fine-tuning optimization model is iteratively solved to output the optimized linear microphone array layout.

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