CN109493844A - Constant beam-width Beamforming Method based on FIR filter - Google Patents
Constant beam-width Beamforming Method based on FIR filter Download PDFInfo
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Abstract
The present invention discloses a kind of constant beam-width Beamforming Method based on FIR filter, reception signal f (t, x)=[f (t, x of microphone array0),…,f(t,xm),…,f(t,xM‑1)]TIt handles to obtain output signal by Beamforming Method:Wherein, f (t, x) indicates that t moment position is the sampled signal of microphone array at x, ()TRepresenting matrix transposition, m indicate microphone index, m=0,1 ..., M-1, and M indicates microphone array element number, xmIndicate the corresponding element position of m-th of microphone, x=[x0,…,xm,…,xM‑1]；N indicates the FIR filter order connect after each microphone,Indicate that m-th of microphone is followed by n rank FIR filter coefficient, subscript * expression takes conjugation, TsIndicate the delay between adjacent filter.Resignation method can make array in main lobe width to the input signal of different frequency roomage response having the same, using the symmetric properties of FIR filter array and microphone even linear array, design has approximately constant beamwidth and the Beam-former compared with low sidelobe array response.
Description
Technical field
The present invention relates to a kind of constant beam-width Beamforming Method based on FIR filter.
Background technique
The more horn of plenty compared with narrow band signal of information content entrained by communication system middle width strip signal carries out broadband signal
Processing is more advantageous to realization to the detection of target, parameter Estimation and extraction etc..Due to containing heterogeneity frequency in broadband signal
Component will lead to array output signal distortion according to traditional narrow beam-forming technology, and signal bandwidth is wider, and distortion is got over
Seriously.Therefore constant beam-width beam-forming technology is applied in broadband array signal processing, receive signal without distortions as far as possible,
Have become the research hotspot in broadband array signal processing and the neck such as be widely used in video conference, speech processes and subsurface communication
Domain.
Constant beam-width Wave beam forming refers to broadband signal by making the master of beam pattern after a certain specific sensor array
Valve width keeps relative constant in scope of design, efficiently solves the inconsistent problem of broad-band EDFA frequency.According to biography
Sensor array broadband signal model, the principal element for influencing beam pattern have the weighting coefficient of array element number and each array element.Various
In traditional beamforming algorithm, it is wide not to provide enough constant wave beams for Capon Wave beam forming, blocking matrix Wave beam forming etc.
It spends and parameter mismatch sensitivity is lower and robustness is poor；And undistorted response (the Minimum Variance of minimum variance
Distortionless Response, MVDR), linear constraint minimal variance (Linearly Constrained Minimum
Variance, LCMV), the robust ada- ptive beamformers algorithm such as weighted least-squares (Weighted Least Squares, WLS), though
The robustness of beamforming algorithm is so improved, but still does not have ideal constant beam angle.Utilize wave beam response and FIR
The beamformer with constant beamwidth of relational design between (Finite Impulse Response, FIR) filter array improves
The constant beam-width characteristic of Beam-former.
By analyzing above, array received is caused to be believed for increment difference corresponding to different frequency component in broadband signal
Number distortion is led to the problem of, thus this case generates.
Summary of the invention
The purpose of the present invention is to provide a kind of constant beam-width Beamforming Method based on FIR filter, can make battle array
It is listed in main lobe width to the input signal of different frequency roomage response having the same, utilizes FIR filter array and Mike
The symmetric properties of wind even linear array, design have approximately constant beamwidth and the Beam-former compared with low sidelobe array response.
In order to achieve the above objectives, solution of the invention is:
A kind of constant beam-width Beamforming Method based on FIR filter, the reception signal f (t, x) of microphone array=
[f(t,x0),…,f(t,xm),…,f(t,xM-1)]TIt handles to obtain output signal by Beamforming Method:Wherein, f (t, x) indicates that t moment position is the sampled signal of microphone array at x,
()TRepresenting matrix transposition, m indicate microphone index, m=0,1 ..., M-1, and M indicates microphone array element number, xmIt indicates m-th
The corresponding element position of microphone, x=[x0,…,xm,…,xM-1]；N indicates the FIR filter rank connect after each microphone
Number,Indicate that m-th of microphone is followed by n rank FIR filter coefficient, subscript * expression takes conjugation, TsIndicate adjacent filter it
Between delay
The best initial weights W of the microphone array responseoptAcquisition, steps are as follows:
Step (a): according to beam angle and array structure feature, determine that the corresponding frequency range of constant beam-width is [fl,
fmax]；It is known ideal beam angle beArray number is M, and array element spacing is d, then minimum frequency
Step (b): beam angle and array element number, array element spacing, acoustic wave propagation velocity, the relational expression between signal frequency
ForAccording to beam angle θ known to step (a)BW, then keep constant Mf, M is necessary
It can change with the variation of frequency f.Call effective microphone M the constant microphone of Mf is metp, with the increasing of frequency
Add, effective microphone M in arraypIt reduces, and MpIt is necessary for integer, MpRange be Mmin≤Mp≤M.Theoretically Mmin=1, but
Actually this value is infeasible, because single microphone is omnidirectional, cannot generate desired beam angle.To odd number
Battle array, the minimum value of effective microphone are Mmin=3；Dual numbers battle array, Mmin=2.By MminValue replace formula
In M, obtain maximum frequencyWhen frequency is greater than fmaxWhen, beam angle will narrow.In [fmin,
fmax] in range, with the increase of frequency, effective microphone MpQuantity with step-length be 2 reduce.Such as, M1=M-2, M2=M-4,
Keep symmetrical.Use MpInstead of formulaIn M, obtaining corresponding frequency is
Step (c): indicating the matrix of N × M dimension with W, and each corresponding m-th of channel n-th order FIR filter of column is
Number；
When M is odd number, W can be expressed as
The column of W indicate that each microphone corresponds to the amplitude response of FIR filter, and the row of W corresponds to frequency.Array element M is
Odd number, the centre three of W arrange corresponding Mmin=3.Frequency is (0, f1) when, M microphone is effective；When frequency is from f1Increase to f2, M1
=M-2 microphone is effective.When frequency is from f2Increase to f3, M2=M-4 microphone is effective.The rest may be inferred, until Mmin=3.
Step (d): as microphone M effective in step (b)pAlso it is 2 reductions with step-length, at this moment utilizes the value of W in step (c)
When calculating Beam-former array response, beam angle will lead in adjacent fpBetween will appear fluctuation；To reduce beam angle
It floats, in conjunction with the reference wave beam design method of the constant Beam-former of wideband frequency, if reference wave beam isWherein, θ is direction of arrival degree；Coefficient { h-3,h-2,…,h2,h3Occurrence be { hn}
=[0.0307,0.2028,0.1663,0.2004,0.1663,0.2028,0.0307] objective function is equivalent tosubject to|P(k,θSL) |≤ζ, in formula, ζ be sidelobe magnitudes about
Beam value, Wk,mIndicate wm,nFourier transformation；Regularization least square is solved the problems, such as using MATLAB, solves best initial weights Wk,m,
And to fk∈[fl,fu], k=0, the optimal solution in 1 ..., N-1 frequency range carries out amplitude normalization processing, to obtain uniform gain
Factor alphak.Use fkIndicate k-th of Frequency point (k=0,1 ..., N-1), then in fkThe frequency response at place is
Step (e): even linear array symmetry is utilized, to Wk,mAmplitude be normalized, solve linear equation with one unknown
(Wk,0+Wk,1+…+Wk,m-1)·αk=1, then
At this moment obtaining best initial weights is Wopt=αk·W1。
After adopting the above scheme, the present invention leads to battle array for gain difference corresponding to different frequency component in broadband signal
Column receive signal and lead to the problem of distortion, using the symmetric properties of FIR filter array structure and microphone uniform line array, really
Determine the frequency range of beamforming algorithm constant beam-width and obtains the array response of approximately constant beamwidth；For adjacent cutoff frequency
The larger problem of the fluctuation of beam angle between rate devises reference wave beam and obtains best initial weights using least square method；Finally
Best initial weights are normalized, uniform gain is obtained.It is finally reached the frequency invariant feature of beamforming algorithm.
Detailed description of the invention
Fig. 1 is conventional beamformer structural schematic diagram；
Fig. 2 is FIR broad-band EDFA device structural schematic diagram；
Fig. 3 is beam pattern；
Wherein, (a) is traditional Beam-former array response, (b) is rung for FIR beamformer with constant beamwidth array
It answers；
Fig. 4 is reference wave beam and array response schematic diagram；
Wherein, (a) is reference wave beam, (b) is beamformer with constant beamwidth array response；
Fig. 5 is that weighted value beam pattern is compared in the projection of yz plane and beam pattern；
Wherein, (a) is not normalized projection, is (b) projection after normalization, (c) compares for beam pattern；
Fig. 6 is 11 array element microphone even linear arrays；
Fig. 7 is experimental result schematic diagram；
Wherein, (a1), (a2), (a3) are the experimental result that signal that centre frequency is 2400Hz obtains respectively, (b1),
(b2), (b3) is the experimental result that centre frequency obtains for the signal of 3000Hz respectively, and (c1), (c2), (c3) are center respectively
Frequency is the experimental result that the signal of 3600Hz obtains.
Specific embodiment
Below with reference to attached drawing, technical solution of the present invention and beneficial effect are described in detail.
1. broad-band EDFA device structure
1.1 Conventional wide band Beam-formers
The classical broad-band EDFA device knot being made of microphone even linear array (Uniform Linear Array, ULA)
Structure, as shown in Figure 1.In ULA, microphone position is expressed as
xm=md (1)
In formula, m indicates microphone index, m=0,1 ..., M-1, xmIndicate the corresponding element position of m-th of microphone, d
Indicate array element spacing, M indicates microphone array element number.
In Fig. 1, θ is direction of arrival degree (Direction of Arrival, DOA),f(t,x0) table
Show that microphone position is x0, t moment microphone samples signal, wmIndicate the weighted value of m-th of microphone, () * expression takes multiple
Conjugation, y (t) indicate the output of Beam-former.
Space domain sampling is carried out to input signal by microphone array, then the sampled signal of t moment microphone array is
F (t, x)=[f (t, x0),…,f(t,xm),…,f(t,xM-1)]T (2)
In formula, ()TRepresenting matrix transposition, x=[x0,…,xm,…,xM-1], then the output of Beam-former is
If fω(t)=ejωtIt is the plane wave that angular frequency is ω, then the spatial sampling signal of microphone array is
fω(t, x)=[fω(t-τ0),fω(t-τ1)…,fω(t-τM-1)]T (4)
In formula,Indicate time delay of m-th of microphone received signal relative to reference point；C table
Show the aerial spread speed of sound；Indicate the wave number of plane wave；λ indicates wavelength.
IfFor the steering vector of array, P (ω, θ) is the frequency of Beam-former
Response, then
In formula, w=[w0,w1,…,wm,…,wM-1]T, ()HIndicate Hermitian transposition.
In order to measure the performance of Beam-former, the beam pattern of standing wave beamformer is represented to D (ω, θ), then
D (ω, θ)=20log10|P(ω,θ)| (6)
In formula, log10Indicate the common logarithm with 10 bottom of for.
Beam angle and array element number, array element spacing, acoustic wave propagation velocity, the relational expression between signal frequency are
Obtaining beam angle by formula (7) is
As it can be seen that θBWReduce with the increase of frequency f.
The 1.2 broad-band EDFA devices based on FIR filter
FIR broad-band EDFA device structure, as shown in Figure 2.Broadband signal is made of multi-frequency component, therefore broadband wave
The weighted value of beamformer can change with the change of frequency, and the weighting coefficient of array is
W (ω)=[w0(ω),…,wM-1(ω)]T (9)
Time-domain filtering is carried out with FIR broad-band EDFA device, to compensate the phase of the various frequency components of input broadband signal
The output of potential difference, FIR Beam-former is
In formula, N indicates the FIR filter order connect after each microphone,Indicate that m-th of microphone is followed by n rank
FIR filter coefficient, TsIndicate the delay between adjacent filter.Assuming that one plane wave signal of input is ejωt, then wave beam shape
The output grown up to be a useful person is
If using as(ω, θ) indicates that MN × 1 ties up array manifold vector, enables
In formula, each sub-vector is M dimension, represents the array manifold vector of a specific FIR filter.First son arrow
AmountSecond sub-vectorThe rest may be inferred.
Convolution (11) and (12), the response for obtaining Beam-former are
In formula, wsIt indicates to tie up compound accumulation weight vector by the MN × 1 of vector superposed generation.Wherein w0=[w0,0,w1,0,…,
wM-1,0]TFor first sub-vector, w1=[w0,1,w1,1,…,wM-1,1]TFor second sub-vector, and so on.It enables
In formula,It is wm,nFourier transformation, then formula (13) can transform to
Because the order of filter is N, therefore their frequency response can be expressed as the N point DFT of each filter, corresponding
SamplingK=0 ..., N-1.
1.3 beamformer with constant beamwidth based on FIR filter
Now utilize one beamformer with constant beamwidth of FIR filter Array Design.According to beam angle and array structure
Feature determines that the corresponding frequency range of constant beam-width is [fl,fmax].If known ideal beam angle isArray number is M, and array element spacing is d, minimum frequency fl, and
By formula (8) it is found that if known beam angle θBW, then keep constant Mf, M is allowed for frequency f
Variation and change.Call effective microphone M the constant microphone of Mf is metp, effective in array with the increase of frequency
Microphone MpIt reduces, and MpIt is necessary for integer, MpRange be Mmin≤Mp≤M.Theoretically Mmin=1, but actually this value
It is infeasible, because single microphone is omnidirectional, desired beam angle cannot be generated.To odd number battle array, effective microphone
Minimum value be Mmin=3；Dual numbers battle array, Mmin=2.
By MminValue substitute into formula (17) in, obtain maximum frequency fmax.When frequency is greater than fmaxWhen, beam angle will narrow.
Constant beam-width beamforming algorithm based on FIR filter will be in [fmin,fmax] an approximately constant beamwidth is obtained in range.
In [fmin,fmax] in range, with the increase of frequency, the quantity of effective microphone is 2 to reduce with step-length.Such as, M1=M-2, M2=
M-4 keeps symmetrical.Use MpInstead of the M in formula (17), acquiring corresponding frequency is fp.Effective microphone MpAlso subtracted with step-length for 2
It is few, cause beam angle in adjacent fpBetween will appear fluctuation, try that decrease will be fluctuated in subsequent Curve guide impeller method.
Formula (16) is to control the theoretical foundation of Beam-former frequency response.The matrix of N × M dimension is indicated with W, it is each
Arrange the coefficient of corresponding m-th of channel n-th order FIR filter.
When M is odd number, W can be expressed as
The column of W indicate that each microphone corresponds to the amplitude response of FIR filter, and the row of W corresponds to frequency.Formula (18)
In, array element M is odd number, and the centre three of W arranges corresponding Mmin=3.Frequency is (0, f1) when, M microphone is effective；When frequency is from f1Increase
F is arrived greatly2, M1=M-2 microphone is effective.When frequency is from f2Increase to f3, M2=M-4 microphone is effective.The rest may be inferred, until
Mmin=3.
1.4 embodiment
Known by formula (8), the beam angle θ of Conventional wide band Beam-formerBWIt reduces, is considered by 11 as frequency f increases
The uniform line array of a omnidirectional microphone composition, filter order 19, array element spacing are 0.05m, simulation result such as Fig. 3
(a) shown in.Beamformer with constant beamwidth based on FIR filter utilizes FIR filter array structure and microphone uniform line
The symmetric properties of array determine the frequency range of constant beam-width and obtain the array response of approximately constant beamwidth, and simulation result is such as
Shown in Fig. 3 (b).
2. the improvement beamformer with constant beamwidth based on FIR filter
2.1 improve beamformer with constant beamwidth
From Fig. 3 (b): the beam angle substantially constant of the constant beam-width beamforming algorithm based on FIR filter, but
The fluctuation of beam angle is larger between adjacent cutoff frequency.It floats to reduce beam angle, in conjunction with the constant wave beam of wideband frequency
The reference wave beam design method of shaper, and regularization least square thought is utilized, best initial weights are solved, and it is imitative to carry out algorithm
Very.
If reference wave beam is
In formula, coefficient { h-3,h-2,…,h2,h3Occurrence be
{hn}=[0.0307,0.2028,0.1663,0.2004,0.1663,0.2028,0.0307] (20)
Shown in reference wave beam figure such as Fig. 4 (a).
According to criterion of least squares, objective function can be written as
min||P(k,θ)-Pd(sinθ)||2 (21)
Convolution (15), objective function is equivalent to
Regularization least square is solved the problems, such as using MATLAB, solves best initial weights Wk,m, and to fk∈[fl,fu], k=0,
Optimal solution in 1 ..., N-1 frequency range carries out amplitude normalization processing, to obtain uniform gain factor alphak。
Use fkIndicate k-th of Frequency point (k=0,1 ..., N-1), then in fkThe frequency response at place is
Using even linear array symmetry, to WkmAmplitude be normalized, solve linear equation with one unknown
(Wk,0+Wk,1+…+Wk,m-1)·αk=1 (24)
3 embodiments
3.1 emulation examples
Consider the odd number uniform line array being made of 11 omnidirectional microphones, filter order 19, adjacent array element spacing is
0.05m, Fig. 4 (b) are the array response of the improvement beamformer with constant beamwidth based on FIR filter.The result shows that improving permanent
The beam angle for determining beam-width beam shaper is more constant, is effectively improved beam angle floating problem.Fig. 5 shows weighted value
Wk,mProjection and single frequency point algorithms of different and reference wave beam pair of the beam pattern in yz plane after not normalizing and normalizing
Than.
Fig. 5 (c) is the wave beam and reference wave beam comparison diagram of two kinds of algorithms of single frequency point.The chart is bright, is filtered based on FIR
The main lobe beamwidth of the beamformer with constant beamwidth of device is narrower than reference wave beam width, and wave beam broadband is non-constant；And it is based on
The improvement beamformer with constant beamwidth of FIR filter is to weighted value Wk,mAfter normalization, it is constant not only to realize beam angle,
And uniform gain can be obtained in entire frequency band.
3.2 experimental example
It tests and is carried out in October, 2017 in Nanjing Information engineering Univ's whole elimination room, anechoic room is having a size of 5.5m × 3.3m
×2.3m.Testing array used is 11 array element even linear arrays being made of omni-directional microphone, filter order 19, battle array
First spacing is 0.05m, as shown in fig. 6, DOA is 0 °, sets Far Left microphone as reference array element, acquires far field voice signal,
Data acquisition is carried out by ESU1808 Multi-channel data acquisition equipment, test signal is played by sound equipment.
Several narrow band signals in the constant range of frequency, center are extracted in signal firstly, receiving from microphone channel
Frequency fkRespectively 2400Hz, 3000Hz and 3600Hz；Secondly, utilizing the improvement constant beam-width wave beam shape based on FIR filter
It grows up to be a useful person and seeks output signal；It is separately added into -2dB and 5dB white noise finally, being added in original signal, using based on FIR filter
It improves beamformer with constant beamwidth and inhibits noise, experimental result is as shown in Figure 7.
Fig. 7 shows that in the constant range of frequency, the improvement beamformer with constant beamwidth based on FIR filter can nothing
Distorted reception voice signal；When signal contains white noise, the part electrical noise in acquisition voice signal can be eliminated, is remained
More high-frequency informations.
The above examples only illustrate the technical idea of the present invention, and this does not limit the scope of protection of the present invention, all
According to the technical idea provided by the invention, any changes made on the basis of the technical scheme each falls within the scope of the present invention
Within.
Claims (3)
1. a kind of constant beam-width Beamforming Method based on FIR filter, it is characterised in that: the reception signal of microphone array
F (t, x)=[f (t, x0),…,f(t,xm),…,f(t,xM-1)]TIt handles to obtain output signal by Beamforming Method:Wherein, f (t, x) indicates that t moment position is the sampled signal of microphone array at x,
() T representing matrix transposition, m indicate microphone index, m=0,1 ..., M-1, and M indicates microphone array element number, xmIt indicates m-th
The corresponding element position of microphone, x=[x0,…,xm,…,xM-1]；N indicates the FIR filter rank connect after each microphone
Number,Indicate that m-th of microphone is followed by n rank FIR filter coefficient, subscript * expression takes conjugation, TsIndicate adjacent filter it
Between delay.
2. the constant beam-width Beamforming Method based on FIR filter as described in claim 1, it is characterised in that: microphone
The best initial weights W of array responseopt, obtaining step is as follows:
Step 1, determine that the corresponding frequency range of constant beam-width is [fl,fmax]；It is known ideal beam angle beArray element number is M, and array element spacing is d, then minimum frequency
Step 2, beam angle θBWWith the relationship between array element number M, array element spacing d, acoustic wave propagation velocity ω, signal frequency f
Formula isCall effective microphone M the constant microphone of Mf is metp, with the increasing of frequency
Add, effective microphone M in arraypIt reduces, and MpIt is necessary for integer, MpRange be Mmin≤Mp≤M；For odd number battle array, effectively
The minimum value of microphone is Mmin=3, for even number battle array, the minimum value of effective microphone is Mmin=2；By MminValue replace formulaIn M, obtain maximum frequencyWhen frequency is greater than fmaxWhen, beam angle
It will narrow, in [fmin,fmax] in range, with the increase of frequency, effective microphone MpQuantity with step-length be 2 reduce；Use Mp
Instead of formulaIn M, obtaining corresponding frequency is
Step 3, the matrix of N × M dimension, each coefficient for arranging corresponding m-th of channel n-th order FIR filter are indicated with W；
When M is odd number, W is indicated are as follows:
The column of W indicate that each microphone corresponds to the amplitude response of FIR filter, and the row of W corresponds to frequency；Array element M is odd number,
The centre three of W arranges corresponding Mmin=3；Frequency is (0, f1) when, M microphone is effective；When frequency is from f1Increase to f2, M1=M-2
A microphone is effective, when frequency is from f2Increase to f3, M2=M-4 microphone is effective, and so on, until Mmin=3；
Step 4, as microphone M effective in step 2pAlso it is 2 reductions with step-length, at this moment calculates wave beam shape using the value of W in step 3
Grow up to be a useful person array response when, will lead to beam angle in adjacent fpBetween will appear fluctuation；It floats to reduce beam angle, in conjunction with width
Reference wave beam design method with the constant Beam-former of frequency, if reference wave beam isWherein,
θ is direction of arrival degree, { h-3,h-2,…,h2,h3It is coefficient, objective function is equivalent tosubject to|P(k,θSL) |≤ζ, in formula, ζ be sidelobe magnitudes about
Beam value, Wk,mIndicate wm,nFourier transformation；Regularization least square is solved the problems, such as using MATLAB, solves best initial weights Wk,m,
And to fk∈[fl,fu], k=0, the optimal solution in 1 ..., N-1 frequency range carries out amplitude normalization processing, is uniformly increased with obtaining
Beneficial factor alphak；Use fkIndicate k-th of Frequency point, k=0,1 ..., N-1, then in fkThe frequency response at place is
Step 5, using even linear array symmetry, to Wk,mAmplitude be normalized, solve linear equation with one unknown (Wk,0+Wk,1
+…+Wk,m-1)·αk=1, then
Obtaining best initial weights is Wopt=αk·W1。
3. the constant beam-width Beamforming Method based on FIR filter as claimed in claim 2, it is characterised in that: the step
In rapid 4, coefficient { h-3,h-2,…,h2,h3Occurrence be { hn}=[0.0307,0.2028,0.1663,0.2004,
0.1663,0.2028,0.0307]。
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| CN110099330A (en) * | 2019-06-03 | 2019-08-06 | 广州由我科技股份有限公司 | A kind of earphone, earphone system and earphone charging system |
| WO2022071812A1 (en) * | 2020-10-01 | 2022-04-07 | Dotterel Technologies Limited | Beamformed microphone array |
| CN114578289A (en) * | 2022-04-26 | 2022-06-03 | 浙江大学湖州研究院 | High-resolution spectrum estimation acoustic array imaging method |
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