Sidelobe controllable beam forming method based on directional array element annular differential microphone array

Abstract

The invention discloses a sidelobe controllable beam forming method based on a directional array element annular differential microphone array. According to the method, first-order directional microphone units are distributed on a circular ring at equal azimuth angles; under the condition that the steering vector is based on circular harmonic decomposition, enabling the designed wave beam to approach a Chebyshev type ideal wave beam; the annular differential microphone array can effectively overcome the null problem in the beam forming of the omnidirectional array element annular differential microphone array, improves the low-frequency white noise amplification problem, and can keep the minimum main lobe width while controlling the beam side lobe.

Description

Technical Field

[0001] The present invention relates to the field of speech signal processing, and particularly to a sidelobe controllable beamforming method based on a directional element circular differential microphone array. Background Art

[0002] Applications of voice communication and interaction cover many fields such as remote video conferencing, intelligent cockpits, artificial intelligence, national defense and military. In different acoustic environments, the requirements for the sound pickup system are also different. In a complex acoustic environment with large noise interference, a single microphone is difficult to achieve an effective sound pickup effect. Microphone array technology can effectively enhance the target signal while suppressing the noise signal, and has become the development trend of the sound pickup system. The differential microphone array has the characteristics of small size, high gain and frequency-invariant spatial response, and has been widely used.

[0003] In the traditional cascaded differential array, the signals received by the microphones are subtracted pairwise to obtain the sound pressure gradient value, thereby forming a directional beam pattern. However, the cascaded differential array faces serious problems of low-frequency white noise amplification, poor beam robustness, and a fixed structure, making it difficult to be flexibly applied.

[0004] The linear differential microphone array based on the zero-point constraint method can improve the white noise gain and the white noise amplification problem by increasing the number of microphones, but its optimal beam direction is only in the end-fire direction. The frequency-invariant circular differential array based on the Jacobi expansion method can adjust the beam to any azimuth angle within the plane of the microphone array, and the designed beam has symmetry and frequency invariance. However, at some specific frequencies, due to the existence of zero values of the Bessel function, the filter coefficients approach infinity, resulting in a serious attenuation of the white noise gain and the directivity factor, leading to the problem of beam nulls. At these frequencies, the desired signal is significantly distorted, and the directivity pattern of the beam also undergoes serious distortion.

[0005] Using a first-order directional microphone to replace an omnidirectional microphone and designing a frequency-invariant circular differential microphone array based on the circular harmonic decomposition method avoids the problem of beam nulls in the array and greatly improves the white noise amplification problem of the array at low frequencies. However, this array cannot achieve a beam pattern with the minimum main lobe width while constraining the sidelobes. Summary of the Invention

[0006] The purpose of the present invention is to provide a sidelobe controllable beamforming method based on a directional element circular differential microphone array in view of the deficiencies of the above technologies. It realizes the control of the sidelobes of the beam pattern and maintains the minimum main lobe width under the condition that the sidelobes are determined. At the same time, the use of directional elements solves the problem of beam nulls in the circular array during beamforming based on the Jacobi expansion method and improves the low-frequency performance of the microphone array.

[0007] To achieve the above object, a sidelobe controllable beamforming method based on a directional element circular differential microphone array designed by the present invention includes the following steps:

[0008] S1: Set N the desired pointing angle and sidelobe control parameters of the

[0009] Chebyshev-type ideal beam pattern of M orders;

[0010] S3: Perform circular harmonic decomposition on the steering vector of the directional element circular differential microphone array and take the first N orders;

[0011] S4: Set N the Chebyshev-type ideal beam pattern of

[0012] orders to be the same as the beam pattern in S3, and the beam is distortionless in the desired pointing direction, to obtain the minimum norm solution vector of the designed beamforming filter coefficients;

[0013] S5: Multiply the minimum norm solution vector of the designed beamforming filter coefficients by the steering vector to obtain the desired frequency-invariant beam pattern of the directional element sidelobe controllable circular differential microphone array, and evaluate the performance of the beamformer.

[0013] Further, in the sidelobe controllable beamforming method based on a directional element circular differential microphone array, in step S1, the main lobe of the ideal beam pattern can point to any azimuth angle in the two-dimensional plane, has frequency invariance, and can obtain the minimum main lobe beam width under the given sidelobe control parameters. The desired pointing angle is θ s of the N order ideal beam pattern can be expressed as:

[0014]

[0015] where θ is the incident wave direction, is N the Chebyshev polynomial of a orders. The parameters b and ε are introduced to ensure that the ideal beam pattern has the maximum power pointing to the desired direction and the signal in the desired direction is distortionless; ε is the sidelobe control parameter used to satisfy the sidelobe constraint.

[0016]

[0017] Among them, the first equation is the sidelobe constraint, and the latter two equations are the ideal beam pattern constraints. By solving this system of equations, the relationship between a , b and ε can be obtained, expressed as . Substituting into the N -order ideal beam pattern expression and converting the cosine part in the expression into exponential form using Euler's formula, we get:

[0018]

[0019] where are the rearranged beamformer coefficients.

[0020] Further, in the sidelobe controllable beamforming method based on a directional element circular differential microphone array, it is characterized in that in step S2, the number of microphones M and the order N of the ideal beam pattern satisfy the relationship . The spacing between microphone array elements is much smaller than the minimum wavelength of sound waves. The microphones are evenly distributed on the ring, and the azimuth difference between adjacent microphones is 2 π / M . The pointing pattern m of the -th element is:

[0021]

[0022] where is the azimuth of the position where the m -th element is located, and is the weight factor. For , the microphone is omnidirectional; for , the microphone is directional and the shape of the directivity pattern is determined by .

[0023] Further, in the sidelobe controllable beamforming method based on a directional element circular differential microphone array, it is characterized in that in step S3, the steering vector of the directional element circular differential microphone array can be expressed as:

[0024]

[0025] where [•] T represents the transpose operation, and the circular harmonic decomposition expansion of the ω -th row element of d( θ , n ) can be expressed as:

[0026]

[0027] where j is the imaginary unit, , c is the speed of sound in air, ω is the angular frequency of the sound wave, r is the radius of the ring, denotes that the argument is of the n order Bessel function of the first kind, is the first-order derivative of.[[ID=()]] [[ID=()]]

[0028] Furthermore, for a sidelobe controllable beamforming method based on a directional element circular differential microphone array, it is characterized in that in step S4, the N order beam pattern of the directional element circular differential microphone array can be expressed as:

[0029]

[0030] where [•] * represents the conjugate operation, , the vector form of the beamforming filter coefficient can be expressed as:

[0031]

[0032] The designed beam is distortionless in the direction of the pointing angle , and the constraint condition is , where [•] H represents the conjugate transpose operation; the minimum norm solution vector of the designed beamforming filter coefficient can be expressed as:

[0033]

[0034] where:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Furthermore, for a sidelobe controllable beamforming method based on a directional element circular differential microphone array, it is characterized in that in step S5, when analyzing the performance of the beamformer, the white noise gain, directivity factor, and beam pattern are introduced.

[0041] The beneficial effects of the present invention are as follows: The sidelobe controllable beamforming method based on the directional element circular differential microphone array proposed by the present invention can achieve the control of the beam pattern sidelobes, maintain the minimum main lobe width under the condition of determined sidelobes, obtain better beam directivity, and at the same time solve the null problem and the low-frequency white noise amplification problem that occur in the beamforming of the circular microphone array based on the Jacobi expansion method. Description of the Drawings

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings required to be used in the embodiments of the present application. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0043] Figure 1 is a schematic structural diagram of a directional element circular differential microphone array;

[0044] Figure 2 is the beam directivity diagram of the first- and second-order circular differential microphone arrays when the sidelobe control parameter is 1 / 8;

[0045] Figure 3 is the beam directivity diagram of the first- and second-order circular differential microphone arrays when the sidelobe control parameter is 1 / 4;

[0046] Figure 4 is the beam directivity diagram of the first- and second-order circular differential microphone arrays when the sidelobe control parameter is 1 / 2;

[0047] Figure 5 is the diagram of the white noise gain and directivity factor varying with frequency of the first-order circular differential microphone array when the sidelobe control parameter is 1 / 8;

[0048] Figure 6 is the diagram of the white noise gain and directivity factor varying with frequency of the second-order circular differential microphone array when the sidelobe control parameter is 1 / 8. Detailed Embodiments

[0049] In order to enable those skilled in the art of the present technology to better understand the solutions of the embodiments of the present invention, the following will further elaborate on the embodiments of the present invention in conjunction with the drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0050] As Figure 1 shown, the present application provides a sidelobe controllable beamforming method based on a directional element circular differential microphone array, including the following steps:

[0051] S1: Set N The desired steering angle and sidelobe control parameters of the Chebyshev-type ideal beam pattern. The steering angle of the ideal beam pattern can point to any azimuth angle in the two-dimensional plane, has frequency invariance, and can obtain the minimum main lobe beam width under the given sidelobe control parameters. The desired steering angle is of N order ideal beam pattern can be expressed as:

[0052]

[0053] where θ is the incident wave direction, T N ( x ) is the N order Chebyshev polynomial. The parameters a and b are introduced to ensure that the maximum power of the ideal beam pattern points to the desired direction and the signal in the desired direction is distortion-free. ε is the sidelobe control parameter, which is used to meet the sidelobe constraint. ε Taking different values can form specific beam patterns. The specific constraint relationship is:

[0054]

[0055] The first formula is the sidelobe constraint, and the last two formulas are the ideal beam pattern constraints. By solving this system of equations, the relationship between a , b and ε can be obtained, expressed as , . Substituting it into the N order ideal beam pattern expression and converting the cosine part in the expression into exponential form using Euler's formula, we get:

[0056]

[0057] where is the rearranged beamformer coefficient.

[0058] S2: Construct a directional array of circular differential microphones. The array consists of M directional microphones evenly distributed on a circle. The number of microphones M and the order N of the ideal beam pattern satisfy the relationship . The spacing between microphone array elements is much smaller than the minimum wavelength of sound waves, and the azimuth difference between adjacent microphones is 2 π / M . The steering pattern m of the th element is:

[0059]

[0060] in For the m The azimuth angle of the position of the array element, is the weight factor, for , the microphone is omnidirectional; for , the microphone is directional and the directivity pattern is shaped by Assuming that all microphones have the same directivity pattern, the weighting factors are given by express.

[0061] S3: Decompose the steering vector of the directional element annular differential microphone array into circular harmonics and take the front N The steering vector of the directional element ring differential microphone array can be expressed as:

[0062]

[0063] in[•] T represents the transpose operation, d( ω , θ ) n The circular harmonic decomposition expansion of the row elements can be expressed as:

[0064]

[0065] in j is the imaginary unit, , c is the speed of sound in air, ω is the angular frequency of the sound wave, r is the ring radius. The quantity is of n Bessel function of the first kind, for The first derivative of .

[0066] S4: Settings N The ideal beam pattern of the Chebyshev type is the same as the beam pattern designed by the directional element annular differential microphone array, and the designed beam is distortion-free in the desired pointing angle direction, and the minimum norm solution vector of the designed beamforming filter coefficient is obtained. N The order beam pattern can be expressed as:

[0067]

[0068] in[•] * represents the conjugate operation, , the vector form of the beamforming filter coefficients Can be expressed as:

[0069]

[0070] The designed beam has no distortion in the pointing angle direction, and the constraint condition is , where [•] H represents the conjugate transpose operation. The minimum norm solution vector for designing the beamforming filter coefficients Can be expressed as:

[0071]

[0072] Where:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] S5: Multiply the minimum norm solution vector of the designed beamforming filter coefficients by the steering vector to obtain a frequency-invariant beam of the annular differential microphone array with controllable sidelobes, and evaluate the performance of the beamformer. When analyzing the performance of the beamformer, the white noise gain, directivity factor, and beam pattern are introduced. Among them, the mathematical form of the white noise gain is:

[0079]

[0080] The mathematical form of the directivity factor is:

[0081]

[0082] Where is the number of discrete points in the range of [0, 2 π .

[0083] Set the radius of the annular array r = 30mm, the speed of sound c = 340m / s, set the frequency range of the signal to 0 - 8 kHz, and the desired pointing angle = 0 o 。The schematic diagram of the array structure is as shown in Figure 1 , and all array elements use omnidirectional microphones with the same directivity, and are directed radially towards this point. The directivity array element pointing control parameter α= 1 / 2. For comparison, the conditions of the omnidirectional element circular array are the same as those of the directional element column, but the array element pointing control parameter α = 1.

[0084] Figures 2 to 4 are, respectively, the first-order and second-order beam directivity diagrams when the sidelobe control parameter is ε = 1 / 8, 1 / 4, 1 / 2 at 1 kHz. On the left side of each diagram is the comparison of the first-order ideal beam diagram, the first-order beam diagrams of the omnidirectional element and the directional element circular differential arrays; on the right side is the comparison of the second-order ideal beam diagram, the second-order beam diagrams of the omnidirectional element and the directional element circular differential arrays. The number of microphones in the first-order array M = 6, and the number of microphones in the second-order array M = 10. It can be seen that the first-order and second-order beam diagrams of the directional element circular array in the figure fit well with the ideal beam diagram, and the sidelobe amplitude of the beam can be adjusted by the sidelobe control parameter to keep the main lobe at the minimum width and obtain better beam directivity.

[0085] Figure 5 is M = 6, ε = 1 / 8, the white noise gain and directivity factor of the first-order sidelobe controllable circular differential array varying with frequency. From the white noise gain diagram, it can be seen that the omnidirectional element circular differential array has nulling phenomena near 4330 Hz and 7182 Hz. This is because the denominator of the filter coefficient of the circular array consists of zero-order and first-order Bessel functions. At these two frequency points, the Bessel function tends to zero, and the filter coefficient approaches infinity, resulting in serious signal distortion. However, since the denominator of the filter coefficient of the directional element circular array consists of an additive combination of the Bessel function and its first derivative, it overcomes the nulling problem that occurs in the circular array at specific frequencies and also improves the white noise amplification problem caused by the denominator of the filter coefficient tending to 0 at low frequencies. From the directivity factor diagram, it can be seen that the omnidirectional element first-order circular differential array has beam distortion starting from 4 kHz, while the directional element first-order circular differential array does not have beam distortion until above 6 kHz. The directional element first-order circular microphone array shows better robustness.

[0086] Figure 6 is M = 10, ε= Variation diagram of white noise gain and directivity factor of a second-order sidelobe controllable circular differential array at 1 / 8 wavelength. From the white noise gain diagram, it can be seen that null phenomena occur near 4340 Hz and 6916 Hz in the omnidirectional element circular differential array, while no null phenomena occur in the sidelobe controllable circular differential array composed of directional elements. From the directivity factor diagram, it can be seen that beam distortion occurs near 6900 Hz in the omnidirectional element second-order circular differential array, while no beam distortion occurs in the directional element second-order circular differential array within the entire research frequency band. The omnidirectional element second-order circular differential array has better robustness.

[0087] As described above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered within the protection scope of the present invention.

Claims

1. A sidelobe controllable beamforming method based on a directional array element circular differential microphone array, characterized in that, Including the following steps: S1: Set N The desired pointing angle and sidelobe control parameters of the stepped Chebyshev ideal beam pattern; S2: Construct a circular frequency-invariant differential microphone array, where the differential microphone array consists of M directional microphones evenly distributed on a ring; S3: Perform circular harmonic decomposition on the steering vector of the directional array element circular differential microphone array and take the first N order; S4: Setting N The ideal beam pattern of the Chebyshev type of order is the same as the beam pattern described in S3, and the beam is undistorted in the desired pointing direction, obtaining the minimum norm solution vector of the designed beamforming filter coefficients; S5: Multiply the minimum norm solution vector of the designed beamforming filter coefficients by the steering vector to obtain the desired frequency-invariant beam pattern of the directional element sidelobe controllable circular differential microphone array, and evaluate the performance of the beamformer.

2. The sidelobe controllable beamforming method based on a directional array element circular differential microphone array according to claim 1, characterized in that In the step S1, the main lobe of the ideal beam pattern can point to any azimuth angle in the two-dimensional plane, has frequency invariance, and can obtain the minimum main lobe beam width under the given sidelobe control parameters. The desired pointing angle is of N order ideal beam pattern can be expressed as: ， where θ is the incident wave direction, is N the N -order Chebyshev polynomial. The parameters a and b are introduced a and b to ensure that the maximum power of the ideal beam pattern points to the desired direction and the signal in the desired direction is undistorted; ε is the sidelobe control parameter, which is used to meet the sidelobe constraint, ε Taking different values, specific beam patterns can be formed. The specific constraint relationship is as follows: ， Among them, the first equation is the sidelobe constraint, and the last two equations are the ideal beam pattern constraints. Solving this system of equations can obtain a , b and ε The relationship between them is expressed as , Substitute into N The expression of the ideal beam pattern of order, and use Euler's formula to transform the cosine part in the expression into exponential form, we can get: ， Among them are the beamformer coefficients after arrangement.

3. A sidelobe controllable beamforming method based on a directional array element circular differential microphone array according to claim 1, characterized in that, In the step S2, the number of microphones M and the order of the ideal beam pattern N satisfy the relationship , the spacing between the microphone array elements is much smaller than the minimum wavelength of the sound wave, the microphones are evenly distributed on the ring, and the azimuth difference between adjacent microphones is 2 π / M ; the pointing pattern m of the th element is: ， wherein is the azimuth angle of the position where the m -th array element is located, is the weight factor. For , the microphone is omnidirectional; for , the microphone is directional and the shape of the directivity pattern is determined by .

4. A sidelobe controllable beamforming method based on a directional array element circular differential microphone array according to claim 1, characterized in that, In the step S3, the steering vector of the directional element circular differential microphone array can be expressed as: ， where [•] T represents the transpose operation, d( ω , θ )'s circular harmonic decomposition expansion of the n row elements can be expressed as: ， where j is the imaginary unit, , c is the speed of sound in air, ω is the angular frequency of the sound wave, r is the radius of the ring, denotes the -th n order Bessel function of the first kind, is the first derivative of.

5. A sidelobe controllable beamforming method based on a directional array element circular differential microphone array according to claim 1, characterized in that In the step S4, the N order beam pattern of the directional array element circular differential microphone array can be expressed as: ， where [•] * denotes the conjugate operation, , the vector form h( ω ) of the beamforming filter coefficients can be expressed as: ， The designed beam has no distortion in the pointing angle direction, and the constraint condition is , where [•] H represents the conjugate transpose operation; the minimum norm solution vector for designing the beamforming filter coefficients can be expressed as: ， Where: ， ， ， ， 。 6. A sidelobe controllable beamforming method based on a directional array element circular differential microphone array according to claim 1, characterized in that In the step S5, when analyzing the performance of the beamformer, the white noise gain, the directivity factor, and the beam pattern are introduced.

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