Design and Implementation of Small Microphone Arrays

Transcription

1 Design and Implementation of Small Microphone Arrays for Acoustic and Speech Signal Processing Jingdong Chen and Jacob Benesty Northwestern Polytechnical University 127 Youyi West Road, Xi an, China Université du Québec, INRS-EMT Montréal, QC, Canada

2 Background Modern Tradition Voice Communication Network 2

3 Background M Noise Echo Reverberation Noise Interference Reverberation Echo 3

4 Why Multiple Microphones? M Source extraction Source 2 Source 1 Echo Noise, interference, reverberation, and echo suppression Reverberation Noise Source separation 4

5 Why Multiple Microphones? Source extraction Noise, interference, reverberation, and echo suppression Source separation DOA estimation Source localization 5

6 Multiple-Microphone Systems Organized arrays Disorganized systems Geometry is known Sensors are uniform in responses Sampled with the same clock Geometry is unknown or time varying Sensors may be different in responses Clock skew 6

7 Microphone Array and Beamforming Geometry Selection of sensors Calibration A/D Array Signal Processing Output Beamforming Multichannel NR Source Separation Source Localization 7

8 Beamforming Σ 8

9 Beamforming 9 The core problem of beamforming design is to the optimal beamforming filter

10 Performance Criterion Signal model: Beampattern: Describes the sensitivity of a beamformer to a plane wave impinging on the array from the direction ) 10

11 Beamforming DS Beampattern: Main lobe Nulls Beam width Side lobes Beampattern of a DS beamformer with a ten-sensor array when 11

12 Beamforming DS Beampattern: Main lobe Side lobes Grating lobe Grating lobe Beampattern of a DS beamformer with a ten-sensor array when 12

13 Performance Measures (Cont d) SNR Gain Signal model: Input SNR: BF output: Output SNR: 13

14 Performance Measures (Cont d) SNR Gain SNR Gain: SNR gain depends on the noise pseudo-coherence matrix White Noise Gain (SNR gain in white noise) White Noise: WNG: 14

15 Performance Measures (Cont d) SNR Gain SNR Gain: Directivity Index (SNR gain in diffuse noise) Diffuse Noise: Directivity Index: 15

16 Performance Measures (Cont d) SNR Gain SNR Gain: SNR gain in point-source noise Point Noise: SNR Gain: 16

17 Beamforming Microphone Array Beamforming Isotropic noise generally assumed Stationary, Known before the design Fixed Beamformers Noise Field? Delay-and-Sum Delay-and-Sum Simple Non-uniform directional responses over a wide spectrum of frequencies 17

18 Delay and Sum Σ 18

19 Delay and Sum (db) 19 Nonuniform beam width (spectral tilt, lowpass filtering the desired speech signal) Not very effective in reducing the reverberation effect.

20 Constant Beamwidth Beamforming Filter-and-Sum: Subband: Nested Array: G. W. Elko and Y. Meyer, Microphone Arrays, in Springer Handbook on Speech Processing and Speech Communication, J. Benesty, M. M. Sondhi, and Y. Huang, Eds., Berlin: Springer-Verlag,

21 Beamforming Microphone Array Beamformers Isotropic noise generally assumed Stationary, Known before the design Fixed Beamformers Noise Field? Delay-and-Sum Filter-and-Sum Delay-and-Sum Simple Non-uniform directional responses over a wide spectrum of frequencies Filter-and-Sum Uniform directional responses over a wide spectrum of frequencies: good for wideband signals, like speech 21

22 Beamforming Isotropic noise generally assumed Stationary, Known before the design Fixed Beamformers Microphone Array Beamformers Noise Field? Not Concerned Time Varying, Unknown Adaptive Beamformers Reverberation? Significant Delay-and-Sum Filter-and-Sum MVDR (Capon) LCMV (Frost)/GSC Delay-and-Sum Simple Non-uniform directional responses over a wide spectrum of frequencies Filter-and-Sum Super Gain MVDR (Capon) Complicated Only the TDOAs of the Uniform directional (assuming interested noise speech responses over a wide source need to be spectrum of Correlation matrix known is known) simple frequencies: good for requirements. wideband signals, like Reverberation causes speech the signal cancellation problem. Time-domain or frequency-domain LCMV (Frost)/GSC The impulse responses (IRs) from the source to the microphones have to be known or estimated. Errors in the IRs lead to the signal cancellation problem. 22

23 Performance consistency over frequencies Performance consistency in different environments Working with other Processors Working with modern devices 23

24 Small Microphone Arrays Differential Microphone Arrays 24

25 Additive Array vs Differential Array Both sensors and the array are responsive to the pressure field Size is large (spacing from a couple of centimeters to a few decimeters) Optimal gain is on the broadside Signal extraction is achieved by steering the main lobe to the signal direction 25

26 Additive Array vs Differential Array Sensors measure the pressure field; while the array is responsive to the spatial derivatives of the acoustic pressure field Size is small: the sensor spacing, δ, is much smaller than the acoustic wavelength, so that the true acoustic pressure differentials can be approximated by finite differences of the microphones outputs. Optimal gain is on the endfire direction 26

27 Traditional Design of DMA Zero-Order Outputs 1 θ r 1 r Sound source Zero-Order Outputs First-Order Outputs 1 θ r 1 r Sound source r 2 2 r 3 FODMA Output 2 SODMA Output 3 1 st -Order DMA 2 nd -Order DMA An Nth order DMA is formed by subtractively combining the outputs of two DMAs of order N-1 Not flexible to design different beampatterns Not flexible in dealing with white noise amplification 27

28 New Method of DMA Design The new paradigm is for processing nonstationary broadband signals like speech Analysis (STFT) DMA Processing Synthesis (ISTFT) 28

29 What is a DMA DMA Beampatterns: 29

30 What is a DMA 1 st -order DMA: 30

31 What is a DMA 2 nd -order DMA: 31

32 What is a DMA 3 rd -order DMA: 32

33 DMA Beamforming Ideal DMA Beampatterns: Beampattern with Given M, N, and the array geometry, finding coefficients in so that 33

34 DMA Beamforming for a 2 nd -Order Cardioid Beampattern: 34

35 DMA Beamforming for a 2 nd -Order Cardioid 2 nd -order Cardioid 35

36 DMA Beamforming for a 2 nd -Order Cardioid Is the design beampattern the same as the ideal beampattern? Is the method generalizable? 36

37 DMA Beamforming with Distinct Nulls N+1 Constraints: Linear system with N+1 equations 37

38 DMA Beamforming with Distinct Nulls: Examples DMA filter: 1 st -order DMA filter 38

39 1 st -order DMA filter: 39

40 2 nd -order DMA filter 40

41 3 rd -order DMA filter 41

42 DMA Beamforming with Distinct Nulls: Examples 3 rd -order DMA filter 42

43 DMA Beamforming with Nulls of Multiplicity More Than One st rd -order Cardioid

44 DMA Beamforming with Nulls of Multiplicity More Than One 44

45 DMA Beamforming with Nulls of Multiplicity More Than One Beampattern with 45

46 DMA Beamforming with Nulls of Multiplicity More Than One 46

47 DMA Beamforming with Nulls of Multiplicity More Than One (Examples) Cardioid Directivity one WNG null of multiplicity Factor 32 at 47

48 DMA Beamforming with Ideal Pattern Information N+1 Constraints: Linear system with N+1 equations 48

49 DMA Beamforming with Ideal Pattern Information Linear system with N+1 equations Fundamental constraints 49

50 Problem of White Noise Amplification 50

51 WNG Improvement Use more than N+1 microphones to design a DMA with order of less than N (i.e., M > N+1). 51

52 WNG Improvement Linear system with M ( N+1) equations 52

53 WNG Improvement Maximization of the WNG 53

54 Design and Implementation of Small Microphone Arrays WNG Improvement (Examples: a 5th-order DMA, ) 8 microphones microphones 54

55 References J. Benesty and J. Chen, Study and Design of Differential Microphone Arrays. Berlin: Springer-Verlag, 2013 J. Chen and J. Benesty, A general approach to the design and implementation of linear differential microphone arrays, in Proc. APSIPA Annual Summit and Conference, Oct J. Benesty, J. Chen, and Y. Huang, Microphone Array Processing. Berlin: Springer-Verlag,

56 Microphone arrays, particularly the ones with small aperture are more and more popularly used. Consistency in performance and flexibility in working with other processors are very important. A general approach to DMA Implementation is discussed, which converts the DMA design into a linear system solving problem. This method is very flexible and can design any desired beampattern. A robust method is discussed, that can use more microphones to design a given order DMA with less white noise amplification. 56