Matrix completion based non-uniform differential microphone array beamforming method

Abstract

The application relates to a non-uniform differential microphone array beam forming method based on matrix completion, which comprises the following steps: designing a uniform microphone array with consistent adjacent element spacing; setting a damaged microphone so that the uniform differential microphone array becomes a non-uniform differential microphone array; collecting a voice signal by using the non-uniform differential microphone array; obtaining a steering vector under the uniform array, and designing a corresponding beam former by using a uniform differential microphone array beam forming method; performing filtering processing on an array output signal; obtaining an output signal processed by the beam former, and evaluating the performance of the beam former; and the non-uniform differential microphone array beam forming method based on matrix completion recovers the signal matrix loss problem caused by microphone loss through matrix completion, thereby improving the performance of the microphone array beam forming algorithm.

Description

Technical Field

[0001] This application belongs to the field of microphone array speech enhancement, and more specifically, relates to a method for beamforming of a non-uniform differential microphone array based on matrix completion. Background Technology

[0002] Microphone array signal processing is a field that focuses on speech signals, building upon traditional array signal processing. Initially, research on microphone arrays primarily concentrated on additive microphone arrays (AMAs). It wasn't until the 1930s, with the invention of directional microphones, that the concept of differential microphone arrays was proposed, and research on differential microphone arrays gradually began thereafter. The first literature on differential microphone arrays appeared in the 1940s.

[0003] Differential beamforming is one of many beamforming algorithms. When designing beamformers using differential beamforming algorithms, the spacing between adjacent microphones in the microphone array is typically small, allowing the difference between the outputs of each microphone to approximate the differential of the sound pressure field. Generally, a first-order differential beamformer is formed by combining the differential outputs of two adjacent omnidirectional microphones, a second-order differential beamformer by combining the differential outputs of two adjacent first-order differential beamformers, and an N+1-order differential beamformer by combining the differential outputs of two adjacent N (N≥2)-order differential beamformers. Generally, a higher order of differential beamformer indicates a higher directivity factor (DF) and lower white noise gain (WNG). For an N (N≤M-1)-order beamformer composed of M omnidirectional microphones, its beam pattern typically forms N nulls between 0 and π. The beamformer forms the main beam in the desired direction and creates nulls in the direction of interference and noise, thereby enhancing the desired signal and suppressing noise and interference.

[0004] While differential beamforming offers numerous advantages over other beamforming algorithms, it suffers from issues such as increased white noise at higher orders and decreased directivity at lower orders. Furthermore, most current differential microphone array beamforming methods are based on uniform linear microphone arrays. However, considering potential microphone damage in practical applications, uniform linear microphone arrays will become non-uniform linear arrays. Therefore, designing a method to complement differential beamforming methods based on non-uniform microphone arrays is essential. Summary of the Invention

[0005] The purpose of this application is to provide a non-uniform differential microphone array beamforming method based on matrix completion, which enhances the adaptability of the differential array beamforming method when the uniform array becomes a non-uniform array due to the damage of one or more array elements in a uniform linear array.

[0006] To achieve the above objectives, this application provides the following technical solution:

[0007] This application provides a method for beamforming a non-uniform differential microphone array based on matrix completion, including the following steps:

[0008] S1: Design a uniform microphone array with consistent spacing between adjacent array elements;

[0009] S2: Set the damaged microphone to change the uniform differential microphone array into a non-uniform differential microphone array;

[0010] S3: Acquisition of speech signals using a non-uniform differential microphone array;

[0011] S4: Based on the acquired signal matrix, calculate the corresponding signal covariance matrix and noise variance matrix, and perform rank minimization matrix completion on the obtained covariance matrix.

[0012] S5: Based on the element spacing between uniform differential microphones and the initial value of the set variables, the guide vector under uniform array is obtained, and the corresponding beamformer is designed using the uniform differential microphone array beamforming method.

[0013] S6: The beamformer designed using the uniform microphone array beamforming method is applied to the signal output after matrix completion, and the array output signal is filtered.

[0014] S7: Obtain the output signal processed by the beamformer and evaluate the performance of the beamformer.

[0015] In step S1, a certain number of omnidirectional microphones are arranged in a linear geometric structure, with equal spacing between adjacent omnidirectional microphones, forming a uniform linear microphone array model under the far-field model. The omnidirectional microphones are array elements, and the spacing between adjacent array elements is δ. The array element spacing δ is set to be much smaller than λ, i.e., δ << λ. After equation transformation, we have:

[0016]

[0017] The time delay τ = δ / c, and the signal wavelength λ = c / f.

[0018] Specifically, S3 is:

[0019] In the frequency domain, when the number of microphone array elements is M, the distance between adjacent array elements is set to δ, and the incident angle of the source signal is θ, the signal received by the array, combined with the array's steering vector, can be expressed as:

[0020] y(ω)=[Y1(ω) Y2(ω) … Y M (ω)] T

[0021] =x(ω)+v(ω)

[0022] =d(ω)X(ω)+v(ω)

[0023] Among them, Y i (ω), i=1,2,...,M represents the signal collected by the i-th microphone, ω represents the frequency, x(ω) represents the desired signal vector collected by the microphone array, v(ω) represents the noise signal vector collected by the microphone array, d(ω) represents the steering vector of the linear array, and X(ω) represents the desired signal in space.

[0024]

[0025] M is the number of microphone elements, f represents the frequency, δ represents the distance between adjacent elements, c is the speed of sound in air, usually satisfying c = 340 m / s, X(ω) represents the desired signal in space, and V m (ω) represents the noise signal collected by the m-th microphone.

[0026] Step S5 specifically involves:

[0027] Solve for the covariance matrix of the received signal from the non-uniform microphone array:

[0028] R=E{y(ω)y H (ω)}=X+N

[0029] Where ω represents frequency, E{·} represents mathematical expectation, y(ω) is the signal acquired by the array, X represents the expected signal covariance matrix, N represents the noise covariance matrix, and the superscript H denotes matrix conjugate transpose. The minimum rank optimization formula for X is constructed using matrix completion theory to reconstruct the matrix elements.

[0030] Under different far-field models, there is a spatial phase difference between the sound wave propagation path and the microphone. This spatial phase difference is reflected by the difference in the path length of the signal propagation. This spatial information is usually represented by a steering vector in array signals. The steering vector is defined as follows:

[0031]

[0032] in, Let ω represent the imaginary part of the complex number, ω = 2πf represent the angular frequency, M be the number of microphone elements, f represent the frequency, c be the speed of sound in air (usually c = 340 m / s), the superscript T denotes matrix transpose, δ represent the spacing between adjacent elements, θ represent the angle of incidence of the desired signal, and h(ω) represent the beamformer, which is a complex vector of length M, defined mathematically as follows:

[0033] h(ω)=[H1(ω) H2(ω) … H M (ω)] T ,

[0034] Where ω represents the angular frequency, H i (ω), i = 1, 2, ..., M represents the data of the i-th element of the beamformer vector, with the superscript indicating the element's position. T This indicates the matrix transpose.

[0035] Specifically, S6 refers to the mathematical calculation process for beamforming, which can be described as follows:

[0036]

[0037] Among them, H i (ω), i = 1, 2, ..., M represents the data of the i-th element of the beamformer vector, ω represents the angular frequency, and Y... i (ω), i = 1, 2, ..., M represents the signal collected by the i-th microphone, with the superscript indicating the signal. * The superscript indicates the conjugate operation, h(ω) represents the beamformer weight coefficient vector, y(ω) represents the spatial signal vector acquired by the array, d(ω) represents the steering vector of the linear array, X(ω) represents the desired signal, and v(ω) represents the noise signal vector acquired by the array. H Z(ω) represents the conjugate transpose of the matrix, and Z(ω) is the array weighted result after beamforming, which is a scalar.

[0038] Specifically, S7 is...

[0039] When testing the performance of the beamformer, array response, white noise gain, directivity factor, and front-to-back ratio are introduced.

[0040] Compared with the prior art, the beneficial effects of the present invention are: the beamforming method for non-uniform differential microphone arrays based on matrix completion improves the beamforming algorithm for enhancing the desired signal of non-uniform arrays in the case of microphone damage, suppresses the attenuation of noise signal performance, and restores the filtering performance of the beamformer by completing the signal covariance matrix. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a flowchart illustrating the method of an embodiment of this application. Detailed Implementation

[0043] The technical solutions of the embodiments of this application will now be described with reference to the accompanying drawings. It should be noted that similar reference numerals and letters in the following drawings indicate similar items; therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0044] The terms “comprising,” “including,” or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0045] The terms “first,” “second,” etc., are used only to distinguish one entity or operation from another, and should not be construed as indicating or implying relative importance, nor as requiring or implying any such actual relationship or order between these entities or operations.

[0046] Please see Figure 1 This application provides a method for beamforming a non-uniform differential microphone array based on matrix completion, comprising the following steps:

[0047] S1: Design a uniform microphone array with consistent spacing between adjacent array elements;

[0048] S2: Set the damaged microphone to change the uniform differential microphone array into a non-uniform differential microphone array;

[0049] S3: Acquisition of speech signals using a non-uniform differential microphone array;

[0050] S4: Based on the acquired signal matrix, calculate the corresponding signal covariance matrix and noise variance matrix, and perform rank minimization matrix completion on the obtained covariance matrix.

[0051] S5: Based on the element spacing between uniform differential microphones and the initial value of the set variables, the guide vector under uniform array is obtained, and the corresponding beamformer is designed using the uniform differential microphone array beamforming method.

[0052] S6: The beamformer designed using the uniform microphone array beamforming method is applied to the signal output after matrix completion, and the array output signal is filtered.

[0053] S7: Obtain the output signal processed by the beamformer and evaluate the performance of the beamformer.

[0054] The diagram shows a uniform linear microphone array model in the far-field model, with the spacing between adjacent elements being δ. The steering vector of the array is defined using formula (2-2). Here, the time delay τ = δ / c, and the signal wavelength λ = c / f. In differential microphone arrays, it is usually necessary to set the element spacing δ to be much smaller than λ, i.e., δ << λ. After equation transformation, we have:

[0055]

[0056] Differential microphone arrays typically have a smaller spacing δ compared to additive microphone arrays, which avoids spatial aliasing. Furthermore, differential microphone arrays are essentially implemented using the sound pressure difference between adjacent elements. When the element spacing δ is sufficiently small, the actual sound pressure difference between elements can be approximated by the finite difference between the microphone outputs. Therefore, compared to the wavelength of sound waves, the spacing between adjacent elements in a differential microphone array is always very small, i.e., δ << λ. Consequently, differential microphone arrays are often embedded in small electronic devices such as mobile phones and headphones as receivers and locators for voice signals.

[0057] Specifically, S2 is:

[0058] Using the leftmost microphone of the array as the first element, in a uniform linear array model, the spacing between all elements is equal and δ = 1 cm. In a non-uniform linear array structure model, several scenarios of single microphone failure are simulated: failure of the first element, failure of the second element, failure of the third element, and failure of the fourth element. Several scenarios of more than one microphone failure are also simulated: failure of the second element, failure of the second and third elements simultaneously, failure of the second, third, and fourth elements simultaneously, and failure of the second, third, fourth, and fifth elements simultaneously.

[0059] Specifically, S3 is:

[0060] In the frequency domain, when the number of microphone array elements is M, the distance between adjacent array elements is set to δ, and the incident angle of the source signal is θ, the signal received by the array, combined with the array's steering vector, can be expressed as:

[0061] y(ω)=[Y1(ω) Y2(ω) … Y M (ω)] T

[0062] =x(ω)+v(ω)

[0063] =d(ω)X(ω)+v(ω)

[0064] in,

[0065]

[0066] M is the number of microphone elements, f represents the frequency, δ represents the distance between adjacent elements, c is the speed of sound in air, usually satisfying c = 340 m / s, X(ω) represents the desired signal in space, and V m (ω) represents the noise signal collected by the m-th microphone.

[0067] Specifically, S5 is:

[0068] Solve for the covariance matrix of the received signal from the non-uniform microphone array:

[0069] R=E{y(ω)y H (ω)}=X+N

[0070] The matrix elements are reconstructed by constructing a minimum rank optimization formula for X using matrix completion theory.

[0071] In the far-field model, the propagation trajectory of sound waves is considered as a plane wave. Although the incident angle of the source signal to each microphone on the array is the same, there is a spatial phase difference between different microphones. This spatial phase difference is represented by the path difference of the signal propagation. This spatial information is usually represented by a steering vector in the array signal. The steering vector is defined as follows:

[0072]

[0073] in, Let ω represent the imaginary part of the complex number, ω = 2πf represent the angular frequency, M be the number of microphone array elements, f represent the frequency, and c be the speed of sound in air, typically satisfying c = 340 m / s. The superscript T indicates matrix transpose. Let h(ω) represent the beamformer, which is a complex vector of length M (the number of microphone array elements), mathematically defined as follows:

[0074] h(ω)=[H1(ω) H2(ω) … HM (ω)] T

[0075] Specifically, S6 is:

[0076] Beamforming is a spatial filtering process for recovering a desired signal from a reverberant noise environment. Its purpose is to enhance the desired signal and suppress noise interference. Therefore, designing a beamformer is essentially designing a spatial filter that acts on each microphone element of a microphone array. The signal output of each element is weighted and summed to obtain the microphone array output signal processed by the beamformer. When the microphone array receives a signal in space (containing the desired signal and noise), it often utilizes the filtering characteristics of the beamformer to enhance the desired signal and reduce noise. Typically, the signal-to-noise ratio (SNR) of the signal processed by the beamformer is improved to some extent compared to the signal before processing. The mathematical calculation process of beamforming can be described as follows:

[0077]

[0078] Z(ω) is the array weighting result after beamforming, and is a scalar.

[0079] Specifically, S7 is:

[0080] When testing the performance of beamformers, several common performance measurement methods are typically used, including: array response, white noise gain, directivity factor, and front-to-back ratio. Their mathematical forms are as follows:

[0081] Array response:

[0082]

[0083] White noise gain:

[0084]

[0085] Directional factor:

[0086]

[0087] Before and after comparison:

[0088]

[0089] The array model is set as a uniform linear array, and the desired source signal direction is set at the end-fire direction of the linear array, i.e., the incident direction θ of the source signal. s=0°, number of microphone array elements M=4, speed of sound in air c=340m / s, spacing between adjacent microphone array elements δ=1cm; the frequency range f of this experiment is set between 200Hz and 4200Hz, and the null directions are set at 60°, 120°, and 150° respectively.

[0090] At the same frequency, the maximum array response is obtained when the incident angle θ = 0°, at which point the array response is close to 1. In other directions, the array response is less than or equal to 1. Furthermore, the array response reaches its minimum at 60°, 120°, and 150°, which is consistent with setting the null directions in these three directions in the simulation experiments. When the incident angle θ is fixed, the array response changes only slightly as the frequency gradually increases; this change is extremely small. Therefore, it can be approximated that the array response of differential microphone beamforming does not change with frequency. This is a characteristic of differential arrays, and it has a unique advantage in processing signals with a wide frequency range (wideband signals) such as speech signals.

[0091] As mentioned earlier, conventional uniform microphone array beamforming algorithms can improve white noise gain by increasing the number of microphone elements. Furthermore, the white noise gain gradually decreases as the order of the differential beamforming filter increases. The element spacing δ = 1 cm, and the null directions are set to 97°, 122°, and 153°. The initial settings for the four beam patterns are: (a) M = 6 elements, frequency 1000 Hz; (b) M = 6 elements, frequency 3000 Hz; (c) M = 12 elements, frequency 1000 Hz; (d) M = 12 elements, frequency 3000 Hz. Experiments show that the number of elements and frequency have relatively little impact on the array response. Additionally, a characteristic of the array's directional response is observed: the beam pattern is symmetrical about the epipolar line connecting 0° and 180°. This aligns with the previously described characteristic that the array response function is related to cosθ; that is, the array response is an even function of cosθ, symmetrical about the 0° direction.

[0092] The element spacing δ = 1 cm, and the null directions were set to 97°, 122°, and 153°, respectively. The corresponding initial conditions were: (a) M = 4 elements; (b) M = 8 elements; (c) M = 12 elements; and (d) M = 16 elements. When designing the beamformer using the minimum norm beamforming algorithm, the white noise gain increased with the increase of the number of microphone array elements. Furthermore, it can be observed that the white noise gain initially increases gradually with increasing frequency, then slowly levels off. This indicates that the microphone array suffers from significant white noise (array self-noise) amplification at low frequencies.

[0093] First, the performance of beamformers under uniform array and non-uniform array after matrix completion is compared. The number of array elements in the linear array is set to M=8. (1) Taking the leftmost microphone of the array as the first array element, the spacing between array elements in the uniform linear array model is equal and δ=1cm. In the non-uniform linear array structure model, two scenarios are simulated. (2) The second array element fails and cannot work. The spacing between adjacent array elements is δ1=2cm, δ2=1cm, δ3=1cm, δ4=1cm, δ5=1cm, δ6=1cm. (3) The second and third array elements fail and cannot work. The spacing between adjacent array elements is δ1=3cm, δ2=1cm, δ3=1cm, δ4=1cm, δ5=1cm. After solving the covariance matrix of the array signal collected under the non-uniform array, the low-rank matrix is ​​obtained by element completion. Let the beamformers designed using the beamforming algorithm in these three cases be represented as h1, h2, and h3, respectively.

[0094] Where h1 corresponds to the beamformer for a uniform linear microphone array design; h2 corresponds to the beamformer for a non-uniform linear microphone array where the second microphone element malfunctions; and h3 corresponds to the beamformer for a non-uniform linear microphone array where the second and third microphones malfunction. As can be seen from the beam direction, the beam responses of the three beamformers are quite similar in each direction, but the specific array response magnitudes differ somewhat. For example, at a directional angle of 60°, the array response relationship for the three beamformers is as follows: A comparison of the white noise gain results shows that the white noise gains of the three beamformers are basically the same at low frequencies, but there are slight differences at high frequencies. Magnifying the white noise gain curves in the frequency range of 4200Hz to 5400Hz reveals the following relationship: It can be concluded that when the array elements in the Kerf array malfunction, the performance of the beamforming algorithm is slightly reduced compared to the undamaged beamforming algorithm when the covariance matrix is ​​completed using matrix completion technology. However, this performance reduction is small.

[0095] In practical applications of linear arrays, microphones at different locations may malfunction. Next, we will compare different cases of non-uniform arrays. This experiment still takes the first microphone on the left side of the linear array as the reference array element and assumes the following four cases: (1) The first array element malfunctions, and the uniform linear microphone array becomes a non-uniform linear microphone array; (2) The second array element malfunctions, and the uniform linear microphone array becomes a non-uniform linear microphone array; (3) The third array element malfunctions, and the uniform linear microphone array becomes a non-uniform linear microphone array; (4) The fourth array element malfunctions, and the uniform linear microphone array becomes a non-uniform linear microphone array. The beamformers corresponding to them are h1, h2, h3, and h4, respectively. From the comparison results of the array response and white noise gain corresponding to the non-uniform linear beamformer, it can be found that when the direction angle is 60°, by performing matrix completion on the covariance matrix of the missing signal received by the array, the array response relationship satisfies: After amplification, the white noise gain relationship of each beamformer in the frequency range of 4950Hz to 5050Hz can be expressed as: Experimental comparisons also revealed that, assuming the number of array elements corresponding to the uniform linear array is M=8, when the damaged array element is symmetrical about the array center (for example, the damaged array element is the 1st or 8th, the 2nd or 7th, the 3rd or 6th), the beam pattern and white noise gain corresponding to the beamformer are exactly the same.

[0096] Assuming another scenario, in practical applications of uniform linear microphone arrays, there may be a situation where one microphone fails or multiple microphones fail simultaneously. Taking the first microphone of the microphone array as the reference element, consider the following four scenarios: (1) the second element fails; (2) the second and third elements fail simultaneously; (3) the second, third, and fourth elements fail simultaneously; (4) the second, third, fourth, and fifth elements fail simultaneously. The corresponding beamformers are represented as h1, h2, h3, and h4, respectively. From the array response results corresponding to the beamformers, it can be seen that the array responses of the beamformers in these four cases are basically the same, while from the comparison of the white noise gain results, it can be seen that there are differences in the white noise gain corresponding to these four beamformers, satisfying This shows that the more faulty elements there are, the worse the white noise gain of the array, but the decrease is relatively gradual. Furthermore, when the frequency is set to 5000Hz, the white noise gain of all four beamformers simultaneously reaches its minimum value.

[0097] This invention enhances the adaptability of differential array beamforming methods when the damage of one or more array elements in a uniform linear array causes the array to become non-uniform. After matrix completion, the array response and white noise gain will slightly differ depending on the location of the microphone failure. Furthermore, the more array elements that fail, the lower the performance of the corresponding beamforming algorithm, but the decrease is relatively gradual. In summary, although processing the covariance matrix of the signal acquired by the non-uniform microphone array using matrix completion may result in a slight performance reduction compared to an array without failures, it remains feasible if array elements fail.

[0098] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for beamforming a non-uniform differential microphone array based on matrix completion, characterized in that, Includes the following steps: S1: Design a uniform differential microphone array with consistent spacing between adjacent array elements; S2: Set the damaged microphone to change the uniform differential microphone array into a non-uniform differential microphone array; S3: Acquisition of speech signals using a non-uniform differential microphone array; S4: Based on the acquired signal matrix, calculate the corresponding signal covariance matrix and noise covariance matrix, and perform rank minimization matrix completion on the obtained covariance matrix; S5: Based on the element spacing between uniform differential microphones and the initial value of the set variables, the guide vector under uniform array is obtained, and the corresponding beamformer is designed using the uniform differential microphone array beamforming method. S6: The beamformer designed using the uniform differential microphone array beamforming method is applied to the signal output after matrix completion, and the array output signal is filtered. S7: Obtain the output signal processed by the beamformer and evaluate the performance of the beamformer; In step S1, a certain number of omnidirectional microphones are arranged in a linear geometric structure, with equal spacing between adjacent omnidirectional microphones, forming a uniform differential microphone array model under the far-field model. The omnidirectional microphones are array elements, and the spacing between adjacent array elements is [missing information]. Set the spacing between array elements Much smaller ,Right now After equation transformation, we have: ， Delay signal wavelength ; Specifically, S3 is: In the frequency domain, when the number of microphone array elements is The distance between adjacent array elements is set to The incident angle of the source signal is When combined with the array's steering vector, the signal received by the array can be expressed as: ， in, Indicates the first Signals collected by each microphone Indicates frequency, This represents the desired signal vector acquired by the non-uniform differential microphone array. This represents the noise signal vector acquired by the non-uniform differential microphone array. This represents the steering vector of a non-uniform differential microphone array. Represents the desired signal in space. ； It refers to the number of microphone array elements. Indicates frequency, Indicates the distance between adjacent array elements. For the speed at which sound travels through the air, satisfying m / s, Represents the desired signal in space. Indicates the first Noise signals collected by one microphone; Step S4 specifically involves: Solve for the covariance matrix of the received signal from the non-uniform differential microphone array: ， in, Indicates frequency, Represents the mathematical expectation. This represents the signal acquired by a non-uniform differential microphone array. Represents the covariance matrix of the desired signal. The noise covariance matrix is ​​represented by the superscript H, which denotes the matrix conjugate transpose. It is constructed using matrix completion theory. The minimum rank optimization formula is used to reconstruct the matrix elements. Under different far-field models, there is a spatial phase difference between the sound wave propagation trajectories and the microphone. This spatial phase difference is reflected by the path difference of the signal propagation. This spatial information is represented by a steering vector in the array signal. The steering vector is defined as follows: ， in, , represents the imaginary part of a complex number. Represents angular frequency. It refers to the number of microphone array elements. Indicates frequency, For the speed at which sound travels through the air, satisfying m / s, superscript Indicates matrix transpose. Indicates the spacing between adjacent array elements. Representing the angle of incidence of the desired signal, using This refers to a beamformer, which is a device with a length of... A complex vector is defined mathematically as follows: ， in, Represents angular frequency. Represents the beamformer vector. The data of each element, superscript This indicates the matrix transpose.

2. The non-uniform differential microphone array beamforming method based on matrix completion according to claim 1, characterized in that, Specifically, S7 is... When testing the performance of the beamformer, array response, white noise gain, directivity factor, and front-to-back ratio are introduced.

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