acoustic echo cancellation (AEC) when there is a continuous dis- tortion to the acoustic echo signal. The algorithm presented here differs from others in that the ...
15th European Signal Processing Conference (EUSIPCO 2007), Poznan, Poland, September 3-7, 2007, copyright by EURASIP
ENHANCEMENT OF RESIDUAL ECHO FOR IMPROVED ACOUSTIC ECHO CANCELLATION Ted S. Wada, Biing-Hwang (Fred) Juang Center for Image and Signal Processing Georgia Institute of Technology Atlanta, GA 30332 (twada,juang)@ece.gatech.edu
ABSTRACT This paper investigates the use of a signal enhancement technique, namely a noise suppressing nonlinearity, on the adaptive filter error in order to increase the stability and the performance of acoustic echo cancellation (AEC) when there is a continuous distortion to the acoustic echo signal. The algorithm presented here differs from others in that the enhancement of signal is done in the adaptation loop, rather than as a post-processing technique for further reduction of residual echo in the signal, and that the resulting nonlinearity for the cancellation error is formulated as a solution to the signal enhancement problem. Combining the nonlinear error suppression method with NLMS and other adaptive step-size algorithms based on NLMS shows an improvement of between 5 to 15 dB in the average ERLE for additive white noise and around 2 dB for speech coding distortion when a simulated acoustic echo is used. The reduction of the misalignment of 5 dB or more for both noise cases can be expected. The technique is shown to be beneficial also with a real acoustic echo. The new method is seen as a viable technique for improving the existing AEC algorithms when the acoustic echo is corrupted by linear distortion in the form of additive noise or by nonlinear distortion in the form of speech coding. 1. INTRODUCTION Introducing nonlinearity to the adaptive filter error in order to improve its robustness to poorly matched conditions has been explored on several occasions in the past. Most notable is [1] in which the optimal error nonlinearity for the least-mean-squares (LMS) adaptive algorithm is derived in terms of stability and steady-state performance. As far as the additive noise and its effect on the acoustic echo cancellation (AEC) performance is concerned, we may take a different point of view and postulate that if an adaptive filter is capable of a nearly perfect estimation of the true impulse response, then the filter adaptation process can be assisted if the effects of disruption to the filter error are removed. In other words, by minimizing the distortion of the cancellation error with which the filter coefficients are adapted, the linear portion of the echo path can then be better estimated. In the case of AEC, the noise may be a double-talk or a background noise. Double-talk distortion can be considered an impulsive “noise” and is solved by robust algorithms using a combination of a double-talk detector, which switches off adaptation after the detection, and a compression nonlinearity, which is a sigmoid-like function that limits the outliers in the filter error during the initial stage of double-talk [2]. In contrast, background noise is usually ubiquitous and prevalent (e.g. car engine or computer fan noise). The best achievable echo return loss enhancement (ERLE) would not be much higher than the signal-to-noise ratio (SNR). Another source of pervasive interference that degrades the overall AEC performance are the speech codecs used in wireless and VoIP communications. Speech coding distortion is nonlinear, and even fastconverging algorithms like frequency-block LMS (FBLMS) and reThis work is supported in part by the National Science Foundation Award IIS-0534221.
©2007 EURASIP
cursive least squares (RLS) may not be able to provide an adequate AEC performace [3]. This paper investigates a new perspective of applying signal enhancement techniques to the cancellation error in order to improve the AEC performance in a continuously noisy environment. Specifically, we will show that the normalized LMS (NLMS) algorithm can be made more robust to the effects of additive white noise or speech coding distortion by processing the filter error with an error suppression nonlinearity (ESN), represented by f (·) in the standard NLMS filter update equation w(n + 1) = w(n) + µ f (e(n))
x(n) , kx(n)k2
(1)
where x(n) is the reference signal vector, w(n) the filter coefficients vector, µ the step-size, and e(n) the adaptive filter error (i.e. the cancellation error). Our approach here is different in that the filter error is enhanced before it is fed back into an adaptive filter rather than having the enhancement done out of the adaptation loop as commonly performed for further echo reduction. The perspective of signal enhancement, particularly with methods that are built upon analytical foundations [4–6], may help us understand better the issue of optimality in adaptive filter designs in the presence of interference. The paper is organized as follows. First, ESN will be derived from the signal enhancement point-of-view and their optimality when used on the NLMS estimation error is discussed in Sec. 2. Second, methods for testing the proposed ESN’s is outlined in Sec. 3, followed by experimental results in Sec. 4. Finally, conclusions are given in Sec. 5. 2. ERROR SUPPRESSION NONLINEARITIES 2.1 MMSE approach Given a noisy speech s = s˜ + v, if the original speech s˜ is zeromean Laplacian distributed with its probability density function (pdf) given by 1 −|s|˜ e α , (2) ps˜ (s) ˜ = 2α and if the noise v is zero-mean Gaussian distributed with its pdf given by −v2 1 pv (v) = √ e 2σ 2 , (3) 2πσ 2 then the minimum mean-square error (MMSE) estimate of s˜ is [5] fMMSE (s) = √+ξ − (ψ − ξ )e−ξ erfc ψ √−ξ (ψ + ξ )eξ erfc ψ 2ψ 2ψ , α √+ξ + e−ξ erfc ψ √−ξ eξ erfc ψ 2ψ 2ψ
(4)
where ξ = s/α , ψ = σ 2 /α 2 , and erfc(x) = √2π x∞ e−r dr is the complimentary error function. (4) is obtained from the conditional expectation E[˜s|s].
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15th European Signal Processing Conference (EUSIPCO 2007), Poznan, Poland, September 3-7, 2007, copyright by EURASIP
MMSE
ML
−2
0 −2
−2
0 s
2
2 f(s)
0
0 −2
−2
0 s
2
mean-square error (MSE) E{e(n)2 } is given by [1]
Center−Clipping
2 f(s)
2 f(s)
f(s)
2
Coring
fLMS (e) = −
0 −2
−2
0 s
2
−2
0 s
o fMMSE (e) =
−∞
Assuming the same signal distributions as in fMMSE , the maximumlikelihood (ML) estimate of s˜ is obtained as [5] s − sign(s) 0,
σ α
,
if |s| ≥ if |s|
