A method for spatial domain filtering and spectrum correction of broadband signals in the modal domain of a circular array

Abstract

This invention discloses a method for spatial domain filtering and spectrum correction of broadband signals in the mode domain of a circular array. The method involves performing a Discrete Fourier Transform (DFT) on the received time-domain data to obtain the array element frequency domain data. The broadband signal frequency band data is then extracted and subjected to a Circular Fourier Transform (CFT) to obtain the sub-band data in the mode domain. The distance between frequency points and the zeros of the Bessel function within the broadband signal frequency band is calculated, and a zero-point correction method is used to replace the frequency points. Sub-band frequency points in the mode domain are selected according to the correction results. The sub-band weighting vectors for mode domain beamforming are obtained according to the minimum variance and distortion-free criterion for data independence, and the beamformer is calculated. The sub-band data in the mode domain are weighted and summed based on the weighting vectors of each sub-band to obtain the beam output frequency domain data. Zeros are padded at all frequency points except for the broadband signal frequency domain data. An Inverse Fourier Transform is then performed on the beam output frequency domain data to obtain the beamforming output data sequence. This invention effectively preserves the original spectral components of the broadband signal while improving the signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing and relates to a method for spatial domain filtering spectrum correction of broadband signals in the mode domain of a circular array. Background Technology

[0002] Beamforming theory is widely used in fields such as microphone arrays, sonar arrays, radar, and radio communications. The most common beamforming process involves using a spatially distributed array of sensors to collect data, then weighting and integrating the data using a certain method to output a time-domain signal. Filters that can achieve the above function are called spatial filters, and their purpose is to improve the signal-to-noise ratio.

[0003] Because of their special array structure, circular arrays have significant advantages in design, deployment, and isotropic array gain, and are therefore widely used. In addition, modal domain beamformers based on circular arrays have become one of the research hotspots in recent years.

[0004] In the invention patent (Yan Shefeng et al., Modal Domain Beamformer for Circular Array and Frequency Domain Broadband Implementation Method), the modal domain beamforming of a broadband signal circular array was analyzed and studied. This patent uses multiple optimization criteria to perform modal domain beamforming, and the beamforming effect is consistent with the theory. At the same time, the relationship between the weighting vector and the array gain and robustness is analyzed and verified by simulation.

[0005] However, due to the inherent zero-point defect of the Bessel function in the modal domain of the circular array, spikes appear in the spectral components of the output signal. To address this phenomenon, the paper "Sound source localization using multiple circular microphone arrays based on harmonic analysis" utilizes multiple sub-arrays of circular arrays to provide different resolutions in different frequency ranges, avoiding performance degradation caused by the Bessel function; the paper "Design of robust concentric circular differential microphone arrays" uses a combination of circular arrays with different radii to form a differential array to improve the defect of deep zeros in the Bessel function, however, it increases the number of array elements. Summary of the Invention

[0006] In view of the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a method for spatial domain filtering and spectrum correction of broadband signals in the mode domain of a circular array. Without increasing the number of array elements, the method improves the frequency domain data spectrum abrupt changes that occur in the filtering of the circular array mode domain beamforming method, so as to smooth the in-band spectrum of the output signal of the broadband signal after the spatial domain filtering of the circular array mode domain, that is, to effectively maintain the original spectrum components of the broadband signal while improving the signal-to-noise ratio.

[0007] To solve the above-mentioned technical problems, the present invention provides a method for spatial domain filtering spectrum correction of a circular array mode-domain broadband signal, comprising:

[0008] Step 1: Perform Discrete Fourier Transform on the time-domain data received by the uniform circular array elements to obtain the array element frequency domain data. Extract the frequency domain data corresponding to the broadband signal frequency band and perform Circular Fourier Transform to obtain the circular array mode domain sub-band data.

[0009] Step 2: In the circular array mode transformation, calculate the distance between each frequency point and the zero of the Bessel function in the broadband signal frequency band. When a frequency point falls within the set threshold range near the zero, use the zero correction algorithm to replace the selected frequency point.

[0010] Step 3: Select the modal domain sub-band frequency points according to the corrected results in Step 2. Under white noise background, obtain the modal domain beamforming sub-band weighting vector according to the minimum variance distortion-free criterion of data independence, and calculate the corresponding beamformer.

[0011] Step 4: Perform weighted summation on the modal domain subband data from Step 1 based on the subband weighting vectors obtained in Step 3 to obtain the beam output frequency domain data.

[0012] Step 5: In addition to the frequency domain data of the broadband signal obtained in Step 4, zeros are padded at other frequency points. Then, inverse Fourier transform is performed on the frequency domain data of the beam output to obtain the beam synthesis output data sequence.

[0013] Furthermore, step 2, which describes using a zero-point correction algorithm to replace a frequency point when it falls within a set threshold range near the zero point, includes:

[0014] When the i-th frequency point kr i When the value falls within a set threshold range near the zero of the Bessel function:

[0015] When kr i When the value is less than the zero point value at that location, the value at the previous frequency point is taken instead, and it is represented as: J n (kr i→zero ) = J n (kr i-1 );

[0016] When kr i When the value is greater than the zero point value at that location, the next frequency point is used to replace the value at that frequency point, represented as: J n (kr i→zero ) = J n (kr i+1 ).

[0017] Furthermore, in step 3, the modal domain sub-band frequency points are selected according to the corrected results in step 2. Under white noise background, the modal domain beamforming sub-band weighting vector is obtained according to the minimum variance distortion-free criterion for data independence, and the corresponding beamformer is calculated, including:

[0018] The modal domain beamforming sub-band weighting vector obtained according to the data-independent minimum variance distortionless response criterion is:

[0019]

[0020] in:

[0021] The minimum variance undistorted response criterion for independent data is:

[0022]

[0023]

[0024] Where, ρ h (kr) represents the theoretical noise covariance matrix of the modal domain white noise background:

[0025] ρ h (kr)=diag[|C -N (kr)| 2 ,…,|C0(kr)| 2 ,…,|C N (kr)| 2 ]

[0026] Represents the desired direction steering vector of the (2N+1)th order in the circular modal domain:

[0027]

[0028]

[0029] in, C represents the desired direction of the nth mode. n (kr) represents the modal responses of the circular array model to the annular array:

[0030]

[0031] in, The unit is the imaginary number, and r is the radius of the annulus. The wave number is represented by c, the speed of sound in the ocean is represented by f, and the frequency is represented by J. n Represents the nth-order spherical Bessel function;

[0032] Then the corresponding beamformer is calculated.

[0033]

[0034] in, The guide vector for the (2N+1)th order scan direction in the circular modal domain:

[0035]

[0036]

[0037] in, Represents the h-th order scan guide vector of the circular modal domain and the n-th order mode.

[0038] Furthermore, the beam output frequency domain data mentioned in step 4 is as follows:

[0039]

[0040] Among them, X h (kr) represents the modal domain subband data:

[0041] X h (kr)=F H X e (kr)

[0042] In the formula, the circular matrix mode transformation matrix F = [F -N ,…,F n ,…,F N ] T Frequency domain subband data X e (kr) is the Fourier transform of x;

[0043] F n Let n be the nth order transformation matrix in the circular matrix mode transformation matrix:

[0044]

[0045] Where M represents the number of elements in the circular array.

[0046] Furthermore, the beamforming output data sequence described in step 5 is as follows:

[0047]

[0048] Where f l f h represents the lower and upper cutoff frequencies of the broadband signal, respectively; snaps represents the number of time-domain snapshots of the signal; ifft represents the inverse Fourier transform; and zeros represents the all-zero vector.

[0049] The beneficial effects of this invention are:

[0050] For the background of circular array receiving signals under broadband signals, this invention adopts a data-independent mode-domain MVDR beamforming method. At the same time, this invention uses the Bessel zero-point correction method to effectively overcome the peak phenomenon of the output data spectrum, significantly improving the spatial filtering effect. While improving the signal-to-noise ratio of the signal, it effectively preserves the original spectral components of the broadband signal. Attached Figure Description

[0051] Figure 1 This is a diagram of the overall structure of a circular array mode domain beamformer;

[0052] Figure 2 This is a schematic diagram of the spatial structure of a circular array;

[0053] Figure 3 It is an array gain diagram;

[0054] Figure 4 It is the output signal spectrum;

[0055] Figure 5 It is a correction array gain diagram;

[0056] Figure 6 It corrects the output signal spectrum. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] The purpose of this invention is to improve the data spectrum spikes that occur in the filtering of the circular array mode domain beamforming method without increasing the number of array elements. This results in a smoother in-band spectrum of the output signal of the broadband signal circular array mode domain spatial filtering, which better reflects the data characteristics and provides more accurate time-domain data for target identification and detection.

[0059] Combination Figure 1 This invention provides a circular array mode-domain beamformer for far-field broadband signals, mainly comprising a broadband signal narrowband quantization unit, a mode conversion unit, and a beamformer design unit. The broadband signal narrowband quantization unit extracts and narrowbands the received signals from the M array elements; the mode conversion unit comprises (2N+1) sub-units, each connected to the preceding K frequency domain data; the beamforming unit comprises multiple sub-band beamformers and an inverse discrete Fourier transform; the number of sub-units in the mode conversion unit and the number of sub-bands in the beamforming unit are both related to the number of sub-bands in the operating frequency band of the mode beamforming.

[0060] The broadband signal narrowband quantization unit performs frequency domain digital filtering on the linear frequency modulated signal received by the M-channel array, filtering out the broadband signal frequency band portion; each sub-unit of the mode conversion processes the M-channel sub-band data to obtain mode domain data; the mode domain data is input to the beamforming unit at each discrete frequency point for weighted summation to obtain the beam output frequency domain data; finally, the time domain data is output by the discrete inverse Fourier transform.

[0061] In the implementation of this invention, a schematic diagram of the circular array sensor is shown below. Figure 2 The array has M=16 sensors uniformly distributed on a circular ring with a spatial array radius of 0.5m and no obstructions. A broadband signal with an operating frequency band of [600, 2500] Hz is incident on the array from a horizontal 0° direction, satisfying the far-field assumption, corresponding to a spatial frequency range of [0.3, 5.5]. The signals received by each array element are as follows: Figure 2 The variable x(t) in the text.

[0062] Step 1) Perform Discrete Fourier Transform on the time-domain data received by the transparent circular array to obtain frequency-domain data. Extract the frequency-domain data corresponding to the broadband signal frequency band and perform Circular Fourier Transform on the data to obtain the sub-band data of the circular array mode domain.

[0063] Step 2) In the circular array mode transformation, due to the inherent zeros of the Bessel function, the distance between each frequency point and the zero of the Bessel function is calculated in the broadband signal frequency band; when a frequency point falls within 0.01 of the zero point in the above formula, the zero point correction algorithm is used to replace the selected frequency point.

[0064] Step 3) Select the sub-band frequency points in the modal domain according to step 2. Under the background of white noise, obtain the sub-band weighting vector of modal domain beamforming according to the minimum variance and distortion-free criterion of data independence, and calculate the corresponding beamformer.

[0065] Step 4) Based on the sub-band weighting vectors obtained in Step 3), perform weighted summation on the modal domain sub-band data obtained in Step 1) to obtain the beam output frequency domain data.

[0066] Step 5) Perform inverse Fourier transform on the beam output frequency domain data to obtain the beam synthesized output data sequence.

[0067] The broadband signal beamforming spectrum correction method of this invention involves the following conversion of circular array element domain data and mode data:

[0068] The data received by the element field of the circular array is represented as follows:

[0069] x| M×snaps =p e (Ω s ) H s0+Noise

[0070] Where x e The dimension is M×snaps, indicating that the data snapshots received by the M-element circular array are called snaps;

[0071] Modal domain subband data is represented as follows:

[0072] X h (kr)=F H X e (kr)

[0073] In the formula, the circular matrix mode transformation matrix F = [F -N ,…,F n ,…,F N ] T Frequency domain subband data X e (kr) is the Fourier transform of ;

[0074] The nth-order transformation matrix in the circular matrix mode transformation matrix is:

[0075]

[0076] in Represents the imaginary unit.

[0077] From the sound field decomposition, the distribution of the intrinsic zeros of the Bessel function is as follows:

[0078] bessel_zero=[2.41, 3.83, 5.14, 5.52, 6.38,…]

[0079] Determine the i-th frequency point kr i The threshold for falling near the zero of the Bessel function is set to 0.01, and the distance between them and the judgment condition are expressed as follows:

[0080] |kr i -bessel_zero|<0.01

[0081] When kr falls near a certain zero point i When the value is less than the zero point value at that location, the value at the previous frequency point is taken instead, and it is represented as: J n (kr i→zero ) = J n (kr i-1 );

[0082] When kr falls near a certain zero point i When the value is greater than the zero point value at that location, the next frequency point is used to replace the value at that frequency point, represented as: J n (kr i→zero ) = J n (kr i+1 );

[0083] The modal domain subband weighting vector designed in this invention is W. h , represented as:

[0084]

[0085] in,[·] T W represents transpose. N This represents the modal beamforming weighting coefficient.

[0086] The design criterion for beamformers is the data-independent minimum variance distortion-free response criterion, expressed as:

[0087]

[0088]

[0089] The desired direction guidance vector and the nth element are represented as follows:

[0090]

[0091]

[0092] After derivation, the result of the above formula is:

[0093]

[0094] Where ρ h (kr) represents the theoretical noise covariance matrix of the modal domain white noise background, expressed as:

[0095]

[0096] in The modal domain scan guide vector and the nth element are represented as follows:

[0097]

[0098]

[0099] The noise covariance matrix is ​​simplified to:

[0100] ρ h (kr)=diag[|C -N (kr)| 2 ,…,|C0(kr)| 2 ,…,|C N (kr)| 2 ]

[0101] The modal domain weighting coefficients at a certain frequency are designed as follows:

[0102] Based on the circular array model, the modal responses C of the circular array are obtained. n (kr)

[0103]

[0104] in The unit is the imaginary number, and r is the radius of the annulus. Let f represent the wave number, c represent the speed of sound in the ocean, and f represent the frequency. n This represents the Bessel function of an nth-order sphere.

[0105] Construct the desired direction steering vector of the modal domain based on the modal response of the circular array. Obtain the modal domain beamforming sub-band weighting vector The corresponding beamforming is represented as follows:

[0106]

[0107]

[0108] Wherein, the circular modal domain scanning guide vector and its nth element are represented as:

[0109]

[0110] The weighted spatial domain filter output is expressed as follows:

[0111] Using weighted vectors Spatial filtering is performed on the modal domain subband data, and the output data spectrum is represented as follows:

[0112]

[0113] Solving the above equation yields the frequency domain portion of the broadband signal output from the broadband beamforming output signal. Zeros are padded at other frequency points, and then an inverse Fourier transform is performed to obtain the time domain signal of the beamout, expressed as:

[0114]

[0115] Where f l f h represents the lower and upper cutoff frequencies of the broadband signal, respectively; snaps represents the number of time-domain snapshots of the signal; ifft represents the inverse Fourier transform; and zeros represents the all-zero vector.

[0116] This invention aims to eliminate X out The spectral abruptness caused by the zeros of the Bessel function in (kr) is effectively suppressed by the Bessel function zero correction process, ensuring the stability of the signal spectrum while filtering out noise within the broadband signal band.

[0117] The invention will be further illustrated below with simulation examples.

[0118] The simulation conditions and results analysis are as follows.

[0119] A uniform circular array of M=16, such as Figure 2 The array receives signals from the far-field horizontal direction at 0°. The far-field signal is a broadband signal with a frequency band of [600, 2500] Hz, a sampling frequency of 7000, a snapshot number of 1024, and the spatial frequency kr corresponding to the circular array is [1.25, 5.23].

[0120] For the unobstructed circular array Then construct Directional guidance vector

[0121]

[0122]

[0123] According to the MVDR criterion under data independence, the weighted vector is obtained from the following expression.

[0124]

[0125] The array gain is calculated using the weighted values ​​mentioned above. like Figure 3 .

[0126] Similarly, calculate the array gain output data spectrum. like Figure 4 .

[0127] Using the Bessel function zero-point correction method from step 2, the array gain and output data spectrum are simulated and calculated again following the above procedure, and are shown below. Figure 5 and Figure 6 .

[0128] Comparing the array gain before and after the correction, it can be seen that the null trap at the zero of the Bessel function becomes shallower.

[0129] Comparing the output broadband signal spectrum before and after correction, it can be seen that the peaks in the broadband signal spectrum have been smoothed out.

Claims

1. A method for spatial domain filtering and spectrum correction of a broadband signal in the modal domain of a circular array, characterized in that, include: Step 1: Perform Discrete Fourier Transform on the time-domain data received by the uniform circular array elements to obtain the array element frequency domain data. Extract the frequency domain data corresponding to the broadband signal frequency band and perform Circular Fourier Transform to obtain the circular array mode domain sub-band data. Step 2: In the circular array mode transformation, calculate the distance between each frequency point and the zero of the Bessel function in the broadband signal frequency band. When a frequency point falls within the set threshold range near the zero, use the zero correction algorithm to replace the selected frequency point. Step 3: Select the modal domain sub-band frequency points according to the corrected results in Step 2. Under white noise background, obtain the modal domain beamforming sub-band weighting vector according to the minimum variance distortion-free criterion of data independence, and calculate the corresponding beamformer. The modal domain beamforming sub-band weighting vector obtained according to the data-independent minimum variance distortionless response criterion is: in: The minimum variance undistorted response criterion for independent data is: in, The theoretical noise covariance matrix representing the modal domain white noise background: Represents the desired direction steering vector of the (2N+1)th order in the circular modal domain: in, This represents the nth mode in the desired direction. The modal responses of the circular array model to the annular array are represented as follows: in, Represents the imaginary unit. It is the radius of the annulus. Indicates wave number, Indicates the speed of sound in the ocean. Indicates frequency, Represents the nth-order spherical Bessel function; Then the corresponding beamformer is calculated. : in, The guide vector for the (2N+1)th order scan direction in the circular modal domain: in, This represents the h-th order scan guide vector and the n-th order mode in the circular modal domain. Step 4: Perform weighted summation on the modal domain subband data from Step 1 based on the subband weighting vectors obtained in Step 3 to obtain the beam output frequency domain data. Step 5: In addition to the frequency domain data of the broadband signal obtained in Step 4, zeros are padded at other frequency points. Then, inverse Fourier transform is performed on the frequency domain data of the beam output to obtain the beam synthesis output data sequence.

2. The method for spatial domain filtering and spectrum correction of a circular array modal domain broadband signal according to claim 1, characterized in that: Step 2, which describes the process of using a zero-point correction algorithm to replace a frequency point when it falls within a set threshold range near the zero point, includes: When the i-th frequency point When the value falls within a set threshold range near the zero of the Bessel function: when When the value is less than the zero point value at that location, the value at the previous frequency point is taken instead, and it is represented as: ; when When the value is greater than the zero point value at that location, the next frequency point is used to replace the value at that frequency point, which is represented as: .

3. The method for spatial domain filtering and spectrum correction of a circular array modal domain broadband signal according to claim 1, characterized in that: The beam output frequency domain data mentioned in step 4 is as follows: in, For modal domain subband data: In the formula, the circular matrix mode transformation matrix Frequency domain subband data Let x be the Fourier transform of x; Let n be the nth order transformation matrix in the circular matrix mode transformation matrix: in, This represents the number of elements in the circular array.

4. The method for spatial domain filtering and spectrum correction of a circular array modal domain broadband signal according to claim 3, characterized in that: The beamforming output data sequence described in step 5 is as follows: in These represent the lower and upper cutoff frequencies for broadband signals, respectively. denoted by the number of time-domain snapshots of the signal, ifft represents the inverse Fourier transform, and zeros represents an all-zero vector.

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