Design, implementation, and evaluation of a robust multi-microphone noise reduction algorithm

Adaptive beamforming (GSC) : not robust against signal model errors Robust generalised multi-microphone noise reduction scheme

Efficient implementation using stochastic gradient algorithms

• Robustness: small deviations from assumed microphone characteristics (gain, phase, position)  large deviations from desired spatial directivity pattern

- measurement or calibration procedure: expensive, not effective against drift

- incorporate random deviations into design: consider all feasible microphone characteristics and optimise average performance using probability as weight

• Simulations :

N=3, [-0.01 0 0.015] m, L=20, end-fire beamformer (passband: 0^o-60^o)

• Spatial directivity patterns for non-robust and robust beamformer in case of no position errors and small position errors:

[0.002 –0.002 0.002] m

Design, implementation, and evaluation of a robust

multi-microphone noise reduction algorithm

Simon Doclo

¹⁾

, Ann Spriet

^1-2)

, Jan Wouters

²⁾

and Marc Moonen

¹⁾

1)

ESAT-SCD, KULeuven, Kasteelpark Arenberg 10, 3001 Leuven, Belgium

2)

Lab. Experimental ORL, KULeuven, Kapucijnenvoer 33, 3000 Leuven, Belgium

1. Multi-microphone noise reduction techniques

• reduction of noise wrt useful speech signal in different acoustic environments

• exploit spatial + spectral information of speech and noise sources

• small-size microphone arrays  increased sensitivity to signal model errors (e.g. microphone mismatch)

2. Spatially pre-processed SDW-MWF

Spatial pre-processing

u0

u1

1

uN_

Fixed

beamformer Speech

reference

0 0 0

y  x v

Blocking matrix

Noise references

1 1 1

y  x v

2 2 2

y  x v

1 1 1

N N N

y _  x _  v _

Multi-channel Wiener Filter (SDW-MWF)

]

0[k w

 

] [k

z

]

1[k w

]

2[k w

]

1[k w_N

( ) A z

( ) B z

• Structure of SP-SDW-MWF resembles Generalised Sidelobe Canceller (GSC):

- spatial pre-processor  speech reference and noise references

- adaptive stage : adaptive estimation of noise component in speech reference

v

₀

[k-  ]

• Standard GSC minimises output noise power :

• Fixed + adaptive stage rely on assumptions (e.g. no mismatch, no reverberation), but in practice these assumptions are not satisfied  speech distortion

- distortion of speech component in speech reference - speech leakage into noise references

• Design of robust noise reduction algorithm :

- robust fixed beamformer 

limit distortion in x

₀

[k] and limit speech leakage

- robust adaptive stage  limit effect of (remaining) speech leakage

] [ ] [ ]

[ ]

[ k x

₀

k k k

z

_x

    w

^T

x

 



^{0 2}



]

[

[ ] [ ] [ ]

min

E v k ^T k k

k w v

w

  

3. Robust spatial pre-processor

4. Robust adaptive stage: SDW-MWF

4.1. Cost function

4.2. Implementation: stochastic gradient algorithms

• Robustness: limit effect of speech leakage w

^T

[k]x[k] by controlling filter w[k]

- Quadratic inequality constraint (QIC-GSC):  conservative approach - Take speech distortion into account in optimisation criterion (SDW-MWF)

o 1/ trades off noise reduction and speech distortion (1/=0  GSC) o regularisation term ~ amount of speech leakage

• Wiener solution (using )

• Generalised scheme  different algorithms, depending on

^{1/ and}

w

₀

- Without w₀ : Speech Distortion Regularised GSC (SDR-GSC), i.e. standard ANC criterion is supplemented with regularisation term

- With w₀ : Spatially pre-processed SDW-MWF (SP-SDW-MWF)



^{[k] [k]}

 

^{E [k] [k]}

 

^{E [k] [k]}



E x x^T  y y^T  v v^T



 ]

[k w

Algorithm Complexity (MAC) MIPS

QIC-GSC (3N-1)FFT + 16N - 9 2.16

SDW-MWF (3M+2)FFT + 10M

²

+ 15M + 4 2.71

^(a)

, 4.31

^(b)

• Set-up:

3-microphone BTE (d=1cm,1.5cm) mounted on dummy head - speech (0^o) + 5 speech-like noise sources (75^o,120^o,180^o,240^o,285^o) - microphone gain mismatch ₂=4 dB at second microphone

• Performance measures: Intelligibility-weighted signal to noise ratio SNR

_intellig

and spectral distortion SD

_intellig

• Performance of SP-SDW-MWF:

- GSC (1/ = 0, no w₀): degraded performance if significant leakage

- SDR-GSC: 1/ > 0 increases robustness (speech distortion  noise reduction) - SP-SD-MWF (w₀ ) : performance not degraded by mismatch

• Comparison with QIC-GSC: QIC increases robustness of GSC, but QIC  f (amount of speech leakage)

4.3. Experimental validation

SP-SDW-MWF achieves better noise reduction than

QIC-GSC, for a given maximum speech distortion level

noise reduction speech distortion

 



^{0 2}

  ^{ }

²



[ ]

min [ ]

^T

[ ] [ ] 1

^T

[ ] [ ]

k

E v k k k E k k

    

w

w v w x

• Stochastic gradient algorithm in time-domain: LMS-based updating formula

- allows transition to classical LMS-based GSC by tuning parameters (1/, w₀) - approximation of regularisation term in time-domain using data buffers

• Complexity reduction in frequency-domain:

block-based implementation (FFT) - approximation of regularisation term  replace buffers by correlation matrices

• Computational complexity

(N = 3 (mics), M = 2 ^(a), M = 3 ^(b), L = 32, f_s = 16kHz)

Complexity comparable to FD implementation of QIC-GSC

regularisation term Classical GSC



⁰



[ 1] [ ] [ ] 1

[ ] [ ]

[ ]

^T

[ ] [ ]

^T

[ ]

k k  k v k k k k k k



 

      

  

w w  v v w x x w

speech-and-noise periods noise-only periods

 ^[   ^{[ ] [ ]} 

¹

^{ [ ] [}

⁰

^

1 1

[ k ] E k ]

^T

[ k ] 1 E k

^T

k E k v k ]

 

   



      

 

 v v  v  

w y y

0 1

0 1 0 1 0 1

( , , ) ( ) ( )

N

mean N N N

A A

J J A A f A f A dA dA



    

   ^{   }

Non-robust design Robust design