A SPARSENESS CONTROLLED PROPORTIONATE ALGORITHM FOR ACOUSTIC ECHO CANCELLATION

Transcription

1 A SPARSENESS CONTROLLED PROPORTIONATE ALGORITHM FOR ACOUSTIC ECHO CANCELLATION Pradeep Loganathan, Andy W.H. Khong, Patrick A. Naylor 1

2 Contents Introduction Review of NLMS & PNLMS The SC-PNLMS algorithm Simulation Results Complexity Conclusion 2

3 Introduction Acoustic echo appeared due to the coupling between the loudspeaker and microphone. Acoustic echo cancellation (AEC) applications: Hands-free car phone systems Standard speakerphone Teleconferencing systems Adaptive filters employed in AEC Two signals are available input signal to LRMS x( n) output signal from LRMS y( n) Predict h ( n) so that en ( ) is minimised at each iteration. 3

4 Motivation Loudspeaker-Room-Microphone system (LRMS) room dimension of loudspeaker fixed at microphone positioned at a) m b) m 8103 m m Sparse reduces with increasing separation between loudspeaker and microphone. Algorithms for AEC are required to be robust to the variations in the sparseness of the impulse response. 4

5 Adaptive filtering framework (NLMS) General formulation ( ) ( ) ˆ T en yn h ( n1) x( n) ˆ ˆ Q( n1) x( n) e( n) h( n) h( n1) T x ( n) Q( n1) x( n) Q( n1) diag q ( n1), q ( n1),..., q ( n1) 0 1 L1 NLMS: Q( n) I, LL NLMS 2 x straight forward implementation, low complexity slow convergence for sparse impulse response 5

6 Adaptive filtering framework (PNLMS) General formulation ( ) ( ) ˆ T en yn h ( n1) x( n) ˆ ˆ Q( n1) x( n) e( n) h( n) h( n1) T x ( n) Q( n1) x( n) PNLMS: Q( n1) diag q ( n1), q ( n1),..., q ( n1) 0 1 L1 l ( n) ql ( n) L1, l 0,1,..., L1 ( n) i0 i ˆ ˆ ˆ l( n) max max, h0( n),..., hl 1( n), hl 1( n) 0.01, 5/ L faster convergence for sparse impulse response slower convergence for dispersive impulse response 6

7 Sparseness measure Qualitative measure: ranging from strongly dispersive to strongly sparse Quantitative measure: L h( n) 1 ( n) = 1 L- L L h( n) Magnitude Magnitude Magnitude Magnitude Coefficient Index ( h) Coefficient Index Coefficient Index ( h ) ( h) Coefficient Index ( h) 1 More dispersive More sparse 7

8 Improving the performance of PNLMS PNLMS: l ( n) ql ( n) L1, l 0,1,..., L1 ( n) i i0 ˆ ˆ ˆ l 0 L1 L1 ( n) max max, h ( n),..., h ( n), h ( n) Sparse low value of Dispersive high value of Normalized misalignment: ( n) ˆ( n) ( n) h h 2 h( n)

9 The SC-PNLMS formulation low value of step-size magnitude of coefficient good for sparse high value of step-size = constant good for dispersive 9

10 The SC-PNLMS formulation Desired: low for high high for low ˆ( n) ˆ( ) n Exponential function allows SC-PNLMS to inherit proportionality step-size control over large range of ˆ( n) 10

11 The SC-PNLMS formulation ( ) ( ) ˆ T en yn h ( n1) x( n) ˆ ˆ Q( n1) x( n) e( n) h( n) h( n1) T x ( n) Q( n1) x( n) Q( n1) diag q ( n1), q ( n1),..., q ( n1) i0 0 1 L1 l ( n) ql ( n) L1, l 0,1,..., L1 ( n) i ˆ ˆ ˆ l( n) max max, h0( n),..., hl 1( n), hl 1( n), 0.01, standard PNLMS For n L, ( n) 5/ L For n L, ( ˆ n) ( n) e, 6 L hˆ ( n) 1 ˆ( n ) 1 L L L ˆ h( n) 2 modification 11

12 Simulation set-up x( n) White Gaussian Noise (WGN) Male speech signal ( n) h L 1024 Sparse sparseness measure, ( n) 0.83 Dispersive sparseness measure, ( n) 0.59 wn ( ) Step-sizes: WGN to give an SNR = 20dB NLMS = PNLMS = SC-PNLMS =

13 Simulation results of SC-PNLMS for different large inherit more PNLMS small inherit more NLMS ˆ( n) 0.83 ˆ( n )

14 Simulation results using WGN ˆ( n) 0.83 ˆ( n )

15 Simulation results using speech signal ˆ( n) 0.83 ˆ( n )

16 Complexity L hˆ ˆ( n ) 1 L L L ˆ 1 h 2 Compute offline Complexity for the case of L=1024 Algorithms (+) (x) (/) NLMS PNLMS SC-PNLMS

17 Conclusion Algorithms developed for mobile hands-free terminals are required to be robust to the variations in the sparseness of the acoustic path. SC-PNLMS: Sparseness measure has been incorporated into PNLMS. o Sparseness measured using estimated impulse response. o Modest increase in computational complexity o Outperformed across all sparseness levels. 17

18 Additional slide 1 Sparseness measure Vs. Distance between loudspeaker and microphone room dimensions of 8x10x3 m 18

19 Additional slide 2 Sensitivity of in(n) 19

20 Additional slide 3 Linear function for (n) 20