Clustered Blind Beamforming From Ad-Hoc …...Clustered Blind Beamforming From Ad-Hoc Microphone...

Clustered Blind Beamforming From Ad-Hoc Microphone Arrays

Clustered Blind Beamforming From Ad-HocMicrophone Arrays

I. Himawan, I. McCowan and S. Sridharan

Presented by Yaron Doweck

Digital Speech Processing in Noisy Environments - 049035, Spring 2012Technion - Israel Institute of Technology

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Outline

1 Background

2 Ad-Hoc Arrays

3 Clustering

4 Clustered Beamforming

5 Experimental Results

6 Proposed Extension

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Clustered Blind Beamforming From Ad-Hoc Microphone ArraysBackground

BackgroundBeamformer

Beamforming is an effective method of spatial filtering,differentiating desired signals from noise and interferencebased on their locations.Spatial filtering is possible due to the fact that the source andinterference signals reach each sensor at a different time.This difference is referred to as Time Difference of Arrival(TDOA).

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BackgroundDelay-and-Sum Beamformer

Each sensor is delayed according to the source’s location.Delayed sensors are averaged.Mathematically:

In the time domain: y(t) = 1N

N�i=1

xi (t + τi ), where xi (t) - Input

signal from sensor i .

In the frequency domain: y(f ) =N�

i=1w∗

i(f )xi (f ), where

wi (f ) = 1N

e−j2πf τi .In matrix form: y(f ) = wd(f )HX (f ), where

X (f ) = [x1(f ), ..., xN(f )]T ,

wd(f ) =1

N�e−j2πf τ1 , ..., e−j2πf τN

�T

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BackgroundMVDR Beamformer

Minimum Variance Distortionless Response.Minimizes the power at the array output subject to undistortedsignal response.The optimal weights vector is given by:

wMVDR(f ) =Γ−1

xx wd (f )

wd (f )HΓ−1xx wd (f )

Where (Γxx(f ))ij =Φxi xj (f )�

Φxi xi (f )Φxj xj (f ), and Φxx(f ) is the

cross-spectral density, and is estimated using exponential mean

Φtxixj

(f ) = αΦt−1xixj

(f ) + (1 − α)xi (f )x∗j (f )

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Clustered Blind Beamforming From Ad-Hoc Microphone ArraysAd-Hoc Arrays

Ad-Hoc Arrays

The calculation of weights vector for most beamformingmethods is dependent on the sensor geometry and the sourcelocation.In ad-hoc situations, however, when the microphones have notbeen systematically positioned, this information is not availableand beamforming must be achieved blindly.

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Clustered Blind Beamforming From Ad-Hoc Microphone ArraysAd-Hoc Arrays

Ad-Hoc Arrays

There are two general approaches to blindly estimate the weightsvector for beamforming:

1 Direct estimation of TDOA without regard to the microphoneand source locations.

2 Determine the unknown microphone positions through arraycalibration methods.

In this work, the first approach is examined.

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Clustered Blind Beamforming From Ad-Hoc Microphone ArraysClustering

ClusteringMotivation

TDOA corresponds to the peak in the generalized cross correlation(GCC) function [Knapp and Carter(1976)]. A PHAT-weighted crosscorrelation between microphones was used to estimate TDOA :

TDOAij = argmaxτ

�R̂

ijGCC−PHAT (τ)

�

Where

R̂ijGCC−PHAT (τ) � IDFT

xi (f )x∗

j (f )��xi (f )x∗j (f )

��

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ClusteringMotivation

However, large inter-microphone spacing may lead to erroneousTDOA computation, effectively causing delay inaccuracies in thesteering vector of the beamformer.

Box Plot of TDOA Values Rel-

ative to Microphone 1. Micro-

phones 1-4 are closely located

(within 20cm distance). The

others are about 2m from mi-

crophone 1.

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ClusteringInter-Microphone Proximity Measure

Microphones proximity is measured using the magnitude squaredcoherence (MSC) defined as the following:

Cij(f ) =

��Φxixj (f )��2

Φxi (f )Φxj (f )

The proximity measure is calculated by integrating the MSC acrossfrequencies

TijMSC =

fmax�

0

Cij(f )

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ClusteringClustering Methods

Two clustering methods for forming clusters were examined:1 Rule-Based Clustering.2 Spectral Clustering.

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ClusteringRule-Based Clustering

TijMSC is compared to some threshold, T�.

Pairs that satisfy the criteria are grouped in the same cluster.Single element clusters are merged to the nearest cluster.

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ClusteringSpectral Clustering

[Shi and Malik(2000)].The similarity matrix S is defined as

Sij = exp

�−α

�T ij

MSCN − 1

�2�

Define the matrix D as Dij =

�k

Skj i = j

0 else

Solve the generalized eigenvalues problem: (D − S)v = λDv

Perform k-means on the eigenvector with the second smallesteigenvalue.

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Clustered Blind Beamforming From Ad-Hoc Microphone ArraysClustered Beamforming

Clustered Beamforming

Following clustering of microphones, blind beamforming maybe performed for speech enhancement.Two methods are presented for beamforming using theclustering information:

1 Closest Cluster (CC) Beamforming

2 Weighted Cluster Combination (WCC) Beamforming

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Clustered BeamformingClosest Cluster (CC) Beamforming

Clusters are ranked according to the estimated distance fromthe speaker.

1 In each cluster, the closest microphone to the speaker is

selected as reference microphone. Define τk,ref as the TDOA

between cluster k and some reference cluster.

2 A measure of cluster spread, δ, is defined as the maximal

TDOA between the reference microphone and the other

microphones.

3 The cluster ranking is defined as

Dk = τk,ref + δk − Dmin, Dmin = min {τk,ref + δk}

MVDR beamforming is applied blindly for the closest cluster(Dk = 0) using the GCC TDOA estimation.

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Clustered BeamformingWeighted Cluster Combination (WCC) Beamforming

MVDR beamforming is applied blindly for each cluster usingthe GCC TDOA estimation.Delay-and-sum beamforming is applied blindly on the clusters’beams:

yout(t) =C�

k=1

αkyMVDR,k (t + τk)

WhereC�

k=1

αk = 1

Automatically determining cluster weights for combination hasnot been dealt with.

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Clustered Blind Beamforming From Ad-Hoc Microphone ArraysExperimental Results

Experimental ResultsMicrophone Clustering Evaluation

(A) Clustering based on true geometry, (B) Rule-based clustering,(C) Spectral clustering. 17 / 28


Experimental ResultsMicrophone Clustering Evaluation

(A) Clustering based on true geometry, (B) Rule-based clustering,(C) Spectral clustering. 18 / 28


Experimental ResultsSpeech Enhancement Evaluation - Configuration

Source: Single stationary speakerNoise: Babble noiseMicrophones signals were simulatedwith Habets’s RIR generator[Habets(2006)]SNR was measured by applyingbeamformer to clean signal and tonoise only signal separately

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Experimental ResultsSpeech Enhancement Evaluation

(A) - Speaker position 1(B) - Speaker position 2(C) - Speaker position 3

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Clustered Blind Beamforming From Ad-Hoc Microphone ArraysProposed Extension

Proposed ExtensionNull Steering Beamformer

In null steering, the array weights are selected so that the beampattern has a null in a given direction.

(A) - Initial beam pattern.(B) - Null steered beam pattern.

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Proposed ExtensionGoal

Apply a null steering beamformer blindly for ad-hoc array, that willimprove the SNR without a noticeable distortion.

Analyze and compare various null steering methods fordelay-and-sum and for MVDR beamformers.Examine the effect of clustering when applying null steering.

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Proposed Extension

In addition to the direction of the speaker, null steeringrequires the knowledge of the direction to the interference.Blind null steering will use TDOA measurements only for bothspeaker and interference.The use of VAD is required in order to measure TDOA forspeaker and interference.

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Proposed ExtensionInitial Results

Speaker position 1 - Speaker and interference are well separated.Delay-and-sum beamformer.

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Proposed ExtensionInitial Results

Speaker position 3 - Speaker and interference are close, speaker’ssignal is distorted in the lower frequencies. Delay-and-sumbeamformer.

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Proposed ExtensionFuture Work

1 MVDR blind null steering.2 Compare the performance of different null steering methods.3 Minimize signal distortion by modifying the null constraint.4 Evaluate the effect of errors in the TDOA measurements.5 Examine the effect of clustering when applying null steering.

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References

� I. Himawan, I. McCowan, and S. Sridharan, “Clustered blind beamforming fromad-hoc microphone arrays,” IEEE Transactions On Audio Speech And LanguageProcessing, vol. 19, no. 4, pp. 661–676, 2011.

� C. Knapp and G. Carter, “The generalized correlation method for estimation oftime delay,” IEEE Transactions on Acoustics, Speech and Signal Processing,vol. 24, no. 4, pp. 320–327, 1976.

� J. Shi and J. Malik, “Normalized cuts and image segmentation,” IEEE Transactionson Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp. 888–905, 2000.

� G. Lathoud, J. marc Odobez, and D. Gatica-perez, “Av16.3: an audio-visual corpusfor speaker localization and tracking,” in in Proceedings of the 2004 MLMIWorkshop, S. Bengio and H. Bourlard Eds. Springer Verlag, 2005.

� A. P. Habets, “Room impulse response generator,” Technical Report, pp. 1–21,2006.

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Questions?

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