Echo path identification for stereophonic acoustic echo cancellation without pre-processing

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1 Echo path identification for stereophonic acoustic echo cancellation without pre-processing Yuusuke MIZUNO Takuya NUNOME Akihiro HIRANO Kenji NAKAYAMA Division of Electronics and Computer Science Graduate School of Natural Science and Technology, Kanazawa Univ. y mizuno@leo.ec.t.kanazawa-u.ac.jp hirano@t.kanazawa-u.ac.jp nakayama@t.kanazawa-u.ac.jp () Abstract This paper proposes a novel technique in the stereo echo canceller for identifying the echo paths without using the preprocessing. It is assumed that two speakers (SEC) [1 SEC SEC or more alternately utter. The optimal value is estimated from the distribution of irregular solutions in the frequency domain for two speakers. The optimal value is estimated by specifying the distribution of irregular solutions by using two adaptive filters with different initial value, and solving the simultaneous equations for two speakers. Because the estimation accuracy depends on the selection of an initial value, a technique for setting an initial value again according to the convergence situation is shown. TV [2[3[4[5 ( )

2 [2 2.2 rooma 2 [6 X(z) rooma G L (z) G R (z) H LL (z) [7 H RL (z) LL (z) RL (z) LL (z) H LL (z) RL (z) 2 H RL (z) X L(z) = G L(z)X(z) (1) X 2 R(z) = G R(z)X(z) (2) SEC [1 D L(z) = H LL(z)X L(z) + H RL(z)X R(z) (3) 1 (room B) 2 (room A) rooma N A roomb N B SEC (room B) H LL (z) H LR (z) = {[H LL(z) LL(z)G L(z) + [H RL(z) RL(z)G R(z)}X(z) (5) H RL (z), H RR (z) 4 L,R {[H LL (z) LL (z)g L (z)+[h RL (z) RL (z)g R (z)}x(z) = (6) Left Right (6) E L (z)= LL (z) RL (z) room A room B H N A XL(z) Echo Canceller N LL (z) = LL (z) B H RL (z) = RL (z) G X(z) G L(z) R(z) X R(z) + LR E L(z) + RR + LL RL + D L(z) YL(z) H H LL(z) RL(z) 1: Y L(z) = LL(z)X L(z) + RL(z)X R(z) (4) E L(z) = D L(z) Y L(z) = [H LL(z) LL(z)X L(z) + [H RL(z) RL(z)X R(z) LL (z) RL (z) ( ) SEC [2[3[4[ α β (6)

3 [H LL(z) LL(z)G L(z)+[H RL(z) RL(z)G R(z) = (7) G αr (z) = a G αi (z) = b H LLr (z) + G Lα (z) (7) G Lα (z) G αr (z)h RLr (z) G αi (z)h RLi (z) = c H LLi (z) + (8) G αr (z)h RLi (z) + G αi (z)h RLr (z) = d (16) (17) H LL(z) LL(z) + [H RL(z) GRα(z) RL(z) G = (8) Lα(z) LLr(z) + a RLr(z) b RLi(z) = c (16) GRα(z) G Lα(z) = G α(z) = G αr (z) + jg αi (z) (9) r i = [H LLr(z) + jh LLi(z) LLr(z) j LLi(z) +[H RLr(z) + jh RLi(z) RLr(z) j RLi(z) [G αr(z) + jg αi(z) (9) (1) = H LLr(z) + jh LLi(z) LLr(z) j LLi(z) +G αr(z)h RLr(z) + jg αr(z)h RLi(z) G αr(z) RLr(z) jg αr(z) RLi(z) +jg αi(z)h RLr(z) G αi(z)h RLi(z) jg αi(z) RLr(z) + G αi(z) RLi(z) (1) LLr, LLi, RLr, RLi (11) 4 = H LLr(z) LLr(z) + G αr(z)h RLr(z) G αr(z) RLr(z) G αi(z)h RLi(z) + G αi(z) RLi(z) +j(h LLi(z) LLi(z) + G αr(z)h RLi(z) G αr(z) RLi(z) + G αi(z)h RLr(z) G αi(z) RLr(z)) (11) LLi(z) + a RLi(z) + b RLr(z) = d (17) (16) (17) 2 2 a,b,c,d 4 (18) 1 2 [ a b c d [ RLr1(z) RLi1(z) 1 RLi1(z) RLr1(z) 1 RLr2(z) RLi2(z) 1 RLi2(z) RLr2(z) 1 [ a b c d = [ LLr1(z) LLi1(z) LLr2(z) LLi2(z) (18) a,b,c,d (19) [ RLr1(z) RLi1(z) 1 RLi1(z) RLr1(z) 1 RLr2(z) RLi2(z) 1 RLi2(z) RLr2(z) 1 (18) 1 [ LLr1(z) = LLi1(z) LLr2(z) (19) LLi2(z) (19) a,b,c,d (16) (17) 2 (2) 1 a α b α 1 b α a α 1 a β b β 1 b β a β LLr(z) LLi(z) RLr(z) RLi(z) c α d α c β d β (2) (11) (12) (13) = H LLr (z) LLr (z) + G αr(z)h RLr (z) G αr(z) RLr (z) G αi (z)h RLi (z) + G αi (z) RLi (z) (12) = H LLi (z) LLi (z) + G αr(z)h RLi (z) G αr(z) RLi (z) +G αi (z)h RLr (z) G αi (z) RLr (z) (13) (12) (13) (14) (15) LLr(z) + G αr(z) RLr(z) G αi(z) RLi(z) = H LLr(z) + G αr(z)h RLr(z) G αi(z)h RLi(z) (14) LLi(z) + G αr(z) RLi(z) + G αi(z) RLr(z) = H LLi(z) + G αr(z)h RLi(z) + G αi(z)h RLr(z) (15) (19) (21) LLr(z) LLi(z) RLr(z) RLi(z) 1 a α b α 1 b α a α 1 a β b β 1 b β a β 1 c α d α c β d β (21) (21) LLr (z), LLi (z), RLr (z), RLi (z) (22) (23) w LL(n) = F 1 [ LLr(z) + j LLi(z) (22) w RL(n) = F 1 [ RLr(z) + j LRi(z) (23) j!

4 3.2 (16) (17) (19) 1 2 LL(Z) : RL(Z) 2 A V 1 = V 2 = LLr1(z) RLr1(z) LLi1(z) RLi1(z) LLr2(z) RLr2(z) LLi2(z) RLi2(z) v 1 v 2 v 3 v 4 (24) (25) 3 2 V 1 3 V = V = + + (27) (28) 2 1 V 2 V 1, V 2 2 V 3 V A α β x L x R m r m(n) = 1 N1 x L(n k m)x R(n k) (29) N k= m m max α β E[r m(n) = γ r m(n 1) + (1 γ) r m(n) (3) V = + (26) α β m max 3 1

5 α β m max α β LL optimum value initial value fixed 15 m max amplitude LL m max frequency (Hz) iteration x 1 5 4: 3: m max LL optimum value proposed α β 1 2 amplitude LL frequency (Hz) 5: 1: F IR N A, N B 128, 256 N µ.1 s(n) NLMS ( ) Hz 6 NCEV(Normalized Coefficient Error Vector) NCEV h w(n) 2 NCEV (n) = 1 log 1 (31) h 2 6 NCEV 4 2dB (19) 7 (Echo Return Loss Enhancement) ERLE e L d L M = 256 ERLE M1 dl(n i)2 i= ERLE(n) = 1 log 1 M1 el(n (32) i= i)2

6 5 initial value fixed proposed [1 26.Mar NCEV[dB [2 A. Hirano and A. Sugiyama, Convergence characteristics of a multi-channel echo canceller with strongly cross-correlated input signals Analytical Results, Proc. of 6th DSP Symposium, pp , November iteration x 1 5 6: [3 A. Hirano and A. Sugiyama, A compact multichannel echo canceller with a single adaptive filter per channel, Proc. of ISCAS 92, pp , [4 M. M. Sondhi and D. R. Morgan, Acoustic echo cancellation for stereophonic teleconferencing, presented at the 1991 IEEE ASSP orkshop Appls. Singal Processing Audio Acoustics, News Paltz, NY, Oct. 4 8, ERLE [db initial value fixed proposed iteration x 1 5 [5, 15 pp.1-8, 21.Nov [6 A. Sugiyama, Y. Joncour, and A. Hirano, A stereo echo canceller with correct echo-path identification based on an input sliding technique, IEEE Trans. Signal Process., vol. 49, no. 11, pp , Nov : [7 A. Hirano, K. Nakayama, D. Someda, M. Tanaka, Alternative Learning Algorithm for Stereophonic Acoustic Echo Canceller without Pre-Processing, IEICE Trans. Fundamentals, Vol. E87-A, No.8, pp , Aug

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