A TRADE-OFF BETWEEN CONVERGENCE SPEED AND MISADJUSTMENT FOR FILTERING DISCONTINUOUS SPEECH SIGNALS J.M. G´ orriz, J. Ram´ ırez, C.G. Puntonet S. Cruces- ´ Alvarez, D. Erdogmus and E.W. Lang Dpt. Signal Theory and Communications, ETSIIT, University of Granada, Spain email: gorriz@ugr.es Dpt. Signal Theory and Communications, University of Seville, Spain email: sergio@us.es Dpts. of CSEE and BME Ore- gon Health and Science Univer- sity, USA. email: derdogmus@ieee.org Ins. Biophysik und physikalische Biochemie, University of Regensburg, Germany. email: elmar.lang@biologie.uni- regensburg.de. ABSTRACT In this paper we propose a novel LMS algorithm in com- bination with a voice activity detector (VAD) for filtering speech sounds in the Adaptive Noise Cancelation (ANC) problem. The filtering stage is based on the minimization of the squared Euclidean norm of the difference weight vector under a stability constraint over the a posteriori estimation error. To this purpose, the Lagrangian methodology has been used in order to propose a non-linear adaptation defined in terms of the product of differential inputs and errors. This approach yields better tracking ability under conditions held in Discontinuous Transmission (DTX) systems than previous approaches. In addition the use of a precise VAD provides two operation modes in order to obtain the best trade-off be- tween misadjustment and convergence speed in speech/non- speech frames. The experimental analysis carried out on the AURORA 3 speech databases provides an extensive per- formance evaluation together with an exhaustive comparison to standard LMS algorithms including the normalized (N)- LMS, and other recently reported LMS algorithms such as the Modified (M)-NLMS or the Normalized Data Nonlinear- ity (NDN)-LMS Adaptation. 1. INTRODUCTION The widely used least-mean-square (LMS) algorithm has been successfully applied to many filtering applications in- cluding modeling, equalization, control, echo cancelation biomedicine or beamforming [1]. The typical noise cance- lation scheme is shown in Figure 1. Two distant microphones                    -   Fig. 1. Adaptive Noise Canceler. are needed for such application to capture the nature of the noise and the speech sound simultaneously. The correlation between the additive noise that corrupts the clean speech (pri- mary signal) and the random noise in the reference input (adaptive filter input) is necessary to adaptively cancel the noise of the primary signal. The adjustable weights are typi- cally determined by the least mean squares (LMS) algorithm [1] because of its simplicity, ease of implementation and low computational complexity. The weight update equation for the adaptive noise canceler (ANC) is: w(n + 1)= w(n)+ μ e ∗ (n)x(n) (1) where μ is a step-size parameter, e ∗ (n) denotes the complex conjugate of output signal e(n), and x(n)=(ν 2 (n),..., ν 2 (n − L − 1)) T is the data vector containing L samples of the refer- ence signal ν 2 (n). Many ANCs [1, 2, 3] have been proposed in the past years using modified least mean-squares (LMS) algorithms in order to simultaneously improve the tracking ability and speed of convergence. Bershad studied the performance of the Normalized LMS (NLMS) with an adaptive step size in [5] showing advantages in convergence time and steady state. Later, Douglas and Meng [3] proposed the optimum nonlin- earity for any input probability density of the independent in- put data samples, obtaining the Normalized Data Nonlinear- ity adaptation (NDN-LMS). Although the latter algorithm is designed to improve steady-state performance, its derivation did not consider the ANC in case of a strong target signal in the primary input [2]. Greenberg’s Modified-LMS (M-LMS) extended the latter approach to the case of the ANC with the nonlinearity applied to the data vector and the target signal itself, obtaining substantial improvements in the performance of the canceler. The disadvantage of this method is that it requires a priori information about the processes which is generally unknown. This paper shows a novel adaptation for filtering speech signals in discontinuous speech transmission (DTX) systems, which are characterized by sudden changes of the signal statistics. The method is derived assuming stabil- ity in the sequence of a posteriori errors instead of the more restrictive hypothesis used in previous approaches [6], that is, enforcing it to vanish. The result of the Lagrange minimiza- tion is the application of the NLMS algorithm to a new set of difference signals that is more suitable for ANC of speech signals in DTX systems. The combination of the proposed method with an effective VAD [9]-[15] allows to change the operation of the algorithm over speech/non-speech segments 16th European Signal Processing Conference (EUSIPCO 2008), Lausanne, Switzerland, August 25-29, 2008, copyright by EURASIP