Audio Beamforming

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Contents

Introduction Beamforming Adaptive LCMV Beamformer Wideband Constraints Source Tracking Results Conclusion

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Introduction

Beamforming - Spatial filtering Array of sensors Signal processing

Direct or block the radiation or the reception of signals in specified directions

Applications: Sonar radar siesmology radio astronomy

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Beamforming

Figure 1: Example of beamforming[14]

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Sensor arrays in Speech Processing

Comparatively newer area of research Use in hands free speech acquisition

hearing aids teleconferencing

Microphone arrays Set of microphones arranged in specific geometries

Beamformer Processes received signals to extract the desired signal

Based on the knowledge of location of the source Speech- Broadband signal

Narrowband techniques not useful in acoustic applications

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Beamforming

Data independent

Statistically optimum

Only the position of the desired source is known

Filter coefficients adjusted according to the array data

Desired signal strength is unknown

Difficult to estimate signal and noise covariance matrices

These limitations may overcome through application of linear

constraints

Linearly Constrained Minimum Variance Beamforming

Application of linear constraints to the weight

vector

Features

Constraint the response of beamformer

Minimizes output power

Preserves a unity gain at the look direction

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Adaptive LCMV Beamformer

Figure2: Adaptive LCMV Beamformer[6]

KknInsnr kkk ,...1),()()( Recorded signals represented as

= received signal

=desired signal

=interference SignalModelg.pptx

)(

)(

)(

nI

ns

nr

k

k

k

…..(1)

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C=constraint matrixf=constraint vector

)()( nXWny T

output

…..(2)

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fWCT

Under the constraint

WRWnyE XXT

WWminmin ])([ 2

…..(4)

…..(3)

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Find unit vector vTv ]cossinsincossin[

Steering delay calculation

Compute the delayCompute the delay

c

vmD

.

Constraint matrix formation

Weight computation

Filtering

LCMV Beamformer

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ArP.pptx

L

Ll cccC ....1 …..(5)

KL

Each weight =sum of weights in the corresponding vertical column

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Constraint matrix formation

Constraint matrix formation

Weight computation

Filtering

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1z 1z 1z 1z

1z 1z 1z 1z

1z 1z 1z 1z

y

Equivalence of array processor and tapped delay line

0f 1f 2f 3f Lf

Solution to the optimization problem

fCRCCRW xxT

xxopt111 ][

Assumes knowledge of Rxx

Rxx close to singular, matrix inverses may be incorrect

…..(6)

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Constraint matrix formation

Weight computationWeight computation

Filtering

TT

T

CCCCIP

fCCCF

FnX

nXnynWPnW

1

1

2

][

][

)(

)()()()1(

…..(7)

…..(8)

…..(10)

…..(9)

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FW )0(

Initial Weight vector

Weight update using NLMS Algorithm

NLMS.pptx

)()( nXWny T

output

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Constraint matrix formation

Weight computation

FilteringFiltering

…..(11)

Constraint modification

To provide some control over response locations To decrease the sensitivity to steering

inaccuracies To achieve constant bandwidth over the

frequency band of interest Additional constraints called Wideband

Constraints are added

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Wideband Constraints Pair of constraints

to fix the beamformer response in one particular direction at one frequency Fc

phaseshift

gaindesiredA

AAWsc TT

)]sin(),cos([],[ …..(12)

TKLKK

TKLKK

s

c

)sin(...)sin(......)sin(...)sin(

)cos(...)cos(......)cos(...)cos(

11

11

…..(13)

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Beamforming system

Bank of bandpass filters to split the input into frequency subbands

Each have its own adaptive beamformer

Constraints covering only its respective subband

A set of frequencies within the band of interest is chosen

A group of constraints at each of these frequency points is defined

Figure 3: Block diagram of beamforming system[6]

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Band Pass Filters Bank of bandpass filters to split the input into

frequency subbands (4 subbands, each1KHz wide) only one constraint frequency were chosen in the

lowest subband beamwidth at low frequencies is large

2 or 3 constraint frequency were chosen for the higher bands

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Source Tracking

Steering delays update

Wide band constraint

modification

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segment of the beamformer output output of the steering delay block

Compute cross correlation

the lag ( ) at which maxima

occurs

Compensation requiredsteering delays are correct

kpeakn

Lag=?

strg_up.pptx22

00

Steering delays update

=error in the kth steering delay Power varies between voiced and unvoiced

segments To determine whether given segment contains

strong desired signal

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k

Find the running maximum of peak value

Find the M-sample average value

Find the dynamic threshold value

)(max lp )(lpavg

)(lpTH

Contains desired signal Doesn’t contain desired signal

eqn.pptx

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)()( lplp TH )()( lplp TH?)( lp

Beamformer with tracking The lth segment contains desired signal if p(l)

is above the threshold value.

Figure 4:Beamformer with tracking[6]

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Constraint Modification for tracking

KLEUCJL

2

]|[

…..(14)

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constraint.pptx

Let the old set of steering delays used to generate one of the wideband constraints

the new delays are c’ and s’ are modified as

Kkk ,...,1,

kkk '

sccss

ssccc

'

'…..(15)

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Results: simulation using sine waveillustration of steering delay compensation

Figure 5: Before steering delay compensation

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Illustration of steering delay compensation

Figure 6: After steering delay compensation

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100 200 300 400 500 600 700-2

-1

0

1

no.of samples-->

ampl

itude

-->

microphone output

0 100 200 300 400 500 600 700 800

-1

0

1

no.of samples-->

ampl

itude

-->

beamformer output

Figure 7: time domain representation at various stages

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0 100 200 300 400 500 600 700

-1

0

1

no. of samples--->

ampl

itude

--->

desired signal

Figure 8: frequency response before beamforming

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0 2000 4000 6000 8000 10000 12000 14000 16000-20

-10

0

10

20

30

40

X: 1600Y: 35.83

frequency--->

mag

nitu

de--

>

frequency response

Figure 9: frequency response after beamforming

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0 2000 4000 6000 8000 10000 12000 14000 16000-20

-10

0

10

20

30

40

X: 1600Y: 17.74

mag

nitu

de--

->

frequency(Hz)-->

frequency response

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0 20 40 60 80 100 120 140 160 1800

100

200

300

400

500

600

700

800

900

1000Beamformer output vs look angle

Look angle(elevation)

Out

put

pow

er

Figure 10: Beamformer output vs look angle, with source at 900

Time domain plot of the desired speech signal at various stages

Figure 10:Time domain plot of the desired speech signal at various stages

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

-2

0

2

no.of samples-->

ampl

itude

-->

source

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

-2

0

2

no.of samples-->

ampl

itude

-->

microphone output

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

-2

0

2

no.of samples-->

ampl

itude

-->

beamformer output

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Desired signal𝜽=100,𝝓=20

Interfering signal𝜽=40,𝝓=20

Microphone output

Beamformer output

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Array of microphon

es

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

-2

0

2

no.of samples-->

ampl

itude

-->

source

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

-2

0

2

no.of samples-->

ampl

itude

-->

microphone output

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

-2

0

2

no.of samples-->

ampl

itude

-->

beamformer output

Figure 11:Time domain plot of the desired speech signal at various stages

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Desired signal𝜽=90,𝝓=30

Interfering signal𝜽=60,𝝓=40

Microphone output

Beamformer output

Array of microphon

es

Beamformer output vs look angle

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0 20 40 60 80 100 120 140 160 1800

10

20

30

40

50

60

70

80

90Beamformer output vs look angle

Look angle(elevation)

Out

put

pow

er

Figure 8: Beamformer output vs look angle, with source at 900

Conclusion

Beamformer forms the output signal as a weighted combination of data received at the array of sensors

Weights determine spatial filtering characteristics of the beamformer

Optimal improvement of speech quality in noisy environment can be achieved through spatial filtering

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Works completed Studied concepts of beamforming delay calculation of source and interference Calculation of steering delay for compensating

propagation delay Performed LCMV beamforming (without wideband

constraints) Works to be done LCMV beamforming with wideband constraints Source tracking

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Reference[1] Johnson , D H Dudgeon, “Array Signal Processing, Concepts and

Techniques”, Pentice Hall,1993[2] Otis Lamont Frost, “An Algorithm For Linearly ConstrainedAdaptive

Array Processing”, proceedings of the IEEE, Vol. 60, No. 8, August 1972

[3] K. M. Buckley, “Spatial/spectral filtering with linearly constrained minimum variance beamformers”, IEEE Transactions on Acoustics, Speech and SignalProcessing, vol. ASSP-35,No.3, pp. 249266, Mar. 1987.

[4] Barry D Van Veen, Kevin M Buckley, “Beamforming: A Versatile Approach to Spatial Filtering”, IEEE ASSP Magazine, April 1988

[5] Jacob Benesty, Jingdong Chen, Yiteng Huang and Jacck Dmochowski, “On Microphone Arrray Beamforming From a MIMO Acoustic Signal Processing Perspective”, IEEE Transactions on audio speech and language processing, vol.15, No.3, pp:1053-1065,March 2007

[6] Sergey Timofeev, Ahmad R. S. Bahai, and Pravin Varaiya, “Adaptive Acoustic Beamformer With Source Tracking Capabilities”, IEEE Transactions On Signal Processing, Vol. 56, No. 7, pp: 2812-2819, July 2008

[7]Olaf Jaeckel, “Strengths and weaknesses of calculating beamforming in the time domain”, Berlin beamforming Conference 2010

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Reference[8]Iain McCowen, "Robust Speech Recognition using Microphone

Arrays", PhD Thesis Queensland University of Technology, Australia 2001

[9]Athanassios Manikas and Christos Proukakis, "Modeling and Estimation ofAmbiguities in Linear Arrays, IEEE Transactions On Signal Processing, Vol.46, No. 8, August 1998

[10] D Ward, "Theory and Application of Broadband Frequency Invariant Beamforming", PhD thesis, Australian National University, July 1996

[11] R L Bouquin and G Faucon, "Using the coherence function for noise reduction", IEEE proceedings,vol.139, pp 276-280,June 1992

[12]S. Gazor, S. Aes, and Y. Grenier, "Robust adaptive beamforming via targettracking," IEEE Transactions on Acoustics, Speech, Signal Procesing., vol.44, pp. 15891593, Jun. 1996.

[13] Y. Kaneda and J. Ohga, "Adaptive microphone-array system for noise reduc-tion," IEEE Trans. Acoustics. Speech, Signal Processing,

vol. ASSP-34, no.6, pp. 13911400, Dec. 1986.[14] www.labbookpages.co.uk/audio/beamforming.html

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Thank You

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