Speech processing in the watermarked domain: application in adaptive acoustic echo cancellation

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1 Speech processing in the watermared domain: application in adaptive acoustic echo cancellation Imen Mezghani-Marrachi, Monia Turi-Hadj-Allouane, Sonia Djaziri-Larbi, Meriem Jaïdane-Saïdane, Gaël Mahé To cite this version: Imen Mezghani-Marrachi, Monia Turi-Hadj-Allouane, Sonia Djaziri-Larbi, Meriem Jaïdane-Saïdane, Gaël Mahé. Speech processing in the watermared domain: application in adaptive acoustic echo cancellation. EURASIP. Sep 2006, EURASIP, pp , <hal > HAL Id: hal Submitted on 17 Nov 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 SPEECH PROCESSING IN THE WATERMARKED DOMAIN: APPLICATION IN ADAPTIVE ACOUSTIC ECHO CANCELLATION I. Marrachi (1), M. Turi-Hadj Alouane (1), S. Djaziri-Larbi (1), M. Jaïdane-Saïdane (1), G. Mahé (2) (1) Unité Signaux et Systèmes, Ecole Nationale d Ingénieurs de Tunis, Tunisia mezghani imen@yahoo.fr, {m.turi, sonia.larbi, meriem.jaidane}@enit.rnu.tn (2) UFR Mathématique et Informatique, Université René Descartes, Paris V, France gael.mahe@.math-info.univ-paris5.fr ABSTRACT Audio watermaring, or embedding information in a host signal was originally used for digital copyright protection purposes. As audio coding, watermaring is progressively brought in audio processing applications. In this paper, we investigate some benefits of watermaring in signal processing. We focus here on a generic application : adaptive Acoustic Echo Cancellation (). The proposed Watermared (W) is based on a coupling of two adaptive filters. The first one extracts a rough estimation of the echo response to the nown stationary watermar embedded in the speech signal. This extracted estimation constitutes the reference signal for the second adaptive filter. Driven by the nown watermar, the second adaptive filter estimates then the actual echo path. The goal here is to drive the estimation of the echo path by the watermar itself, in order to tae advantage of the its optimal properties (whiteness and stationarity). As expected, the proposed W exhibits better transient and steady state performance than the classical one. These results of some interest follow from the fact that the second adaptive filter deals with much more stationary signals that the first one. 1. INTRODUCTION Recently, watermaring, or embedding information in a host signal, originally used for digital copyright protection purposes has arisen the interest of researchers in many other application fields. In particular, watermaring was used to enhance the performance of audio processing systems. Indeed, in [1] watermaring aimed to stationarize the audio signal. The performance of a classical was then improved [2]. In [3], the ill-conditioning of the input covariance matrix in a stereophonic system, was reduced. In [4], Iapatov and Huffman sequences were embedded in speech signal, through perceptual masing, to improve the performance. Note that classical adaptive filters exhibit low performance when dealing with non stationary data. This paper investigates the benefits of classical signal processing in the watermared domain, where operating in the watermared domain refers to processing of watermared signals. Here, the watermaring is associated to an system according to an original way. Whereas the was driven by the watermared audio signal in the latter references, the goal here is to drive the estimation of the echo path by the watermar itself, in order to tae advantage of the optimal properties of the watermar (whiteness and stationarity). The paper is organized as follows : section 2 introduces a basic version of the W. To meet the inaudibility constraint the basic version is modified. The retained version of W is then presented in section 3. Performance analysis of the proposed W are discussed in section 4. Simulation results, presented in section 5, demonstrate the benefits of the proposed approach. Comparison with classical is performed. 2. WATERMARKED The proposed W aims at exploiting the good transient and steady state performance of adaptive filters in presence of an uncorrelated stationary input. Therefore, the structure of a classical is modified in such a way that the actual echo is adaptively estimated using a reference echo signal that includes the convolution between the actual echo path and a nown white stationary signal. As a matter of fact, the stationary white sequence, embedded in the received speech, is the carrier of the acoustic impulse response to be identified. The proposed W is depicted on Fig.1. Note that in this basic version, the watermaring process corresponds to a simple addition of the white signal and the received speech. x w + copy of H w - + x w F n H TW y + e + + H e t H w - + e w FIG. 1 Preliminary version of the watermared. Fig.1 shows two coupled adaptive filters. The first one H is driven by the non stationary watermared input x w = x + w, where x is the received speech signal and w the stationary and white watermar. The generic delimited by a dashed box on Fig.1 provides an estimation of the reference

3 echo signal y used by the second adaptive filter H w. The latter is driven by the watermar w only. The estimation of the watermar echo is e t = e + (H ) T W = F T W + n + (V ) T X, (1) }{{} n where V = F H denotes the deviation vector that describes the behaviour of H ( T denotes the transpose operator). According to (1), the echo is a sum of the useful information F T W and the non stationary noise n. That is equivalent to a situation where e t is the new reference signal and the echo path F is driven by w. Since H w performs in a more stationary context, it provides a better estimation of the acoustic echo path F than H. Consequently, H w is the filter used to compute the echo estimate ŷ n = (H w )T X w, where X w = (x w,..,xw p+1 )T is the watermared non stationary tap input vector. Therefore, the transmitted residual echo is given by e tr = y ŷ, where y = F T X w +n corresponds to the actual echo corrupted by a noise n assumed to be white. Note that an NLMS adaptation is used to adjust the two adaptive filters of length p assumed to be equal to that of the impulse response F. The update equations related to H are given by e = y (H ) T X w (2) H +1 = H + µ e X w (3) where µ = µ is the normalized step size. X w 2 The second adaptive filter, H w, is updated as follows e w = et (Hw )T W (4) H+1 w = Hw + µ w ew W, (5) where W = (w,..,w p+1 ) T is the stationary tap input vector and µ w = µw the normalized step size. X w 2 By substituting in (4) the echo e t given in (1), one can write e w = FT W (H w )T W + n = (V w )T W + n. (6) V w = F Hw denotes the deviation vector related to Hw. The analysis of (1) and (6) shows that the steady state performance of the adaptive filter H W and consequently that of the proposed depends on the Signal to Noise Ratio SNR w = P x P w. The lower the SNR w is, the better performance of the watermared can be achieved. But for low values of SNR w, the watermar w becomes audible whereas the inaudibility constraint must be satisfied in practice. Thus, in order to ensure the watermar masing, modifications of this basic version of the W are made. 3. THE PROPOSED WATERMARKED In general, speech watermaring is performed using a perceptual weighting filter [7, 9]. In our case, the watermar masing is based on a spectral shaping filter derived from the speech spectral envelope. Moreover, the intensity of the spectral shaped output is reduced by about 13 db in order to ensure an inaudibility quality equivalent to that obtained by a perceptual weighting filter. The spectral shaping filter coefficients are deduced from the speech predictor. The speech predictor is used here to achieve 1. the masing of the white sequence, 2. the whitening of the watermared input sequence which aims to enhance the convergence speed of the first NLMS adaptive filter. Indeed, in the previous W, the watermared input is correlated and consequently the convergence speed of H is slow. Note that the whitening is already used for system identification purposes [5]. The bloc diagram of the modified W is presented in Fig.2 and detailed in the following. w λσ e x() - + etr copy of H S w (z) n copy of t x x w y + F + E (z) e + copy of E (z) H - w H w FIG. 2 The proposed W scheme. 3.1 The whitening filter H T W + e t e w + - The speech is assumed to be an AutoRegressive process of order M (AR (M)). So, x = (P ) T X 1 + e x, where e x is the prediction error of variance σ 2 e (), P = (p 1,..., pm )T the predictor coefficients vector and X 1 = (x 1,...,x M ) T the input vector. A NLMS adaptation is used to update the predictor coefficients : P = P 1 + η e x X 1, (7) where η = η is the normalized step size. The whitening X 2 filter transfer function is E (z) = 1 P (z), where P (z) denotes the predictor transfer function.

4 3.2 The spectral shaping filter 8 The transfer function S (z) of the all-pole spectral shaping filter is then expressed by S (z) = λ σ e() E (z). The attenuation factor λ is chosen so that 20log 10 (λ) = 13 db. Thus, the watermared signal is obtained according to x w = x +t, as shown on Fig.2, where t refers to the spectral shaped watermar signal. log10 (Condition number) W 3.3 The echo estimation Let e x, exw and e n be the through E (z) filtered signals x, x w and n respectively. By applying the whitening filter to y, we obtain the reference echo for H e y = FT E x + FT W + en, where E x = (ex,...,ex p+1 )T and W = λσ e()w. The error signal e controlling the update of H is e = e y (H ) T (E x +W ), and the reference echo signal for the second adaptive filter H w becomes e t = e + (H ) T W = F T W + en + (V ) T E xw, (8) }{{} where E xw = (e xw,...,exw p+1 )T. The error e t expressed by (8) points out that the useful information for the filter H w is F T W. Therefore, and as shown on Fig.1, the filter Hw is driven by w, and its coefficients are adapted according to where the error e w e n H w +1 = Hw + µw ew W, (9) is given by e w = (V w )T W + en. (10) In this section, we have detailed the structure of the W. In the following, we focus on the performance analysis of the proposed system. 4. PERFORMANCE ANALYSIS OF THE PROPOSED W The transient and steady state performances of the proposed W are analysed in comparison with those of the generic, delimited by a dashed box on Fig.1. For this comparison, the generic must be driven by the watermared signal x w, because the available reference echo is generated by the watermared speech. Indeed, it has been proved in [2] that watermared audio is more stationary than the host signal. Furthermore, in [1] the authors have already shown that Frame number FIG. 3 Condition number of R w () (W, in blue) and of R x w() (classical with watermared inputin blac). a classical presents higher performance when driven by the watermared speech instead of the original. The transient and steady state behaviour of the classical and the W are studied through the time variation of the deviation vectors V and V w respectively. Using (1), (4) and (5) it is easy to show that V +1 = (I µ X w (X w )T ) V + µ n X w, (11) }{{}}{{} A C where I refers to the identity matrix of ran p. Besides, by combining (8), (9), and (10), it follows that V w +1 = (I µw W (W )T ) }{{} B V w + µw en W } {{ } D. (12) X w 2 We remind that the mean convergence depends on the conditioning of the matrices A and B [8]. Taing the expectation value of both sides of (11) one obtains E[V +1 ] = (I µr w x ())E[V ], (13) [ ] X where R w x () = E w (X w ) T. This result is obtained assuming the classical hypothesis of statistical independence between V and X w. Similarly, assuming that en is of zero mean and statistically independent from w, it follows from (12) that E[V+1 w ] = (I µ wr w ())E[V w ] (14) ] where R w () = E [ W ( W ) T W 2. From equations (13) and (14) we can notice that in the classical case, the transient behaviour is governed by the matrix R x w(), whereas in the case of the proposed W, the transient behaviour depends on the matrix R w (). The eigenvalue spread of R w () is expected to be small compared to that of R x w() since w is much more uncorrelated than the watermared speech x w. This is illustrated by Fig.3, where we compare the condition numbers of the covariance matrices R x w() and R w (), computed

5 over sample frames of length 20 ms. Knowing that the covariance matrix of a white signal has a logarithmic condition number equal to zero, we conclude from Fig.3 that R w () is better conditioned than R x w(). Hence, we may confirm that the convergence rate of the W will be higher than that of the classical. The analytical study of the mean square convergence is difficult to carry out as the signals are correlated and non stationary. However, one can see from equations (13) and (14) that the steady state performance of the and the W adaptive filters [ depends ] crucially on[ the instantaneous ] values of P C = E (C ) T C and P D = E (D ) T D respectively. As H w performs in a more stationary context, PD is expected to have smoother variations and lower values than P C. This aspect will improve the W performance in the steady state. 5. SIMULATION RESULTS The parameter settings chosen for all reported simulations are : a speech signal sampled at 8 Hz and a car acoustic impulse response truncated to 100 taps, SNR = 40 db, η = , M = 4 and p = 100. For the transient behaviour analysis, the same step size value 0.01 is used for the two coupled adaptive filters of the proposed W. For the classical with watermared input, the step size is also fixed to To demonstrate the enhancement of the convergence rate achieved by the proposed W, we plot on Fig.4 the time variations of the MSD related to the W ( H w ) and the MSD obtained by the classical with a watermared input (H ). The MSD measure is defined here for a deviation vector V as ( [ ]) MSD db = 10log 10 E V T V As expected theoretically, since the watermar is much more white than the watermared signal, the convergence rate of the proposed W is much higher than that of the classical. To have comparative results in steady state, the choice of the step size values must ensure the same convergence rate for both systems (the classical and the proposed one). To meet this condition, the same step size value 0.01 is used for both coupled adaptive filters of the proposed W, whereas, for the classical with watermared input, the step size is fixed to 0.1. The measure of the effect of an echo cancellation filter is the so-called Error Return Loss Enhancement (ERLE) : ( E[y 2 ) ERLE() = 10log ] 10 E[e 2 ], where y is the echo signal (it is the same in both cases) and e is the residual error in the generic case. The equivalent residual error in the W case is denoted e tr on Fig.2. To confirm the steady state analysis presented in Section 4, we depict on Fig.5 the time variation of P C and PD. As expected, this figure shows that the variations of P D are much more smoother than those of P C. In particular, PC taes very MSD(dB) W samples x 10 4 FIG. 4 MSD time variation in the W case (in blue) and in the classical case with watermared input (in blac). db W samples FIG. 5 Time variation of P D (W, in blue) and PC (classical with watermared input, in blac). large values during the low dynamics of the watermared speech. This results in considerable disturbance of the MSD time evolution as shown on Fig.6. Consequently, the ERLE related to the generic is impaired as displayed by Fig.7. Indeed, we notice that the W achieved a 10 db gain in the ERLE. The reported results presented on Fig.4 and Fig.7 show that both the transient and the steady state performances are considerably improved by the W. 6. CONCLUSION This paper investigated the advantages of speech processing in watermared domain. We have presented an original way to exploit watermaring for the improvement of a generic performance. The new proposed W benefits from the fact that white and stationary signals are the ideal inputs for classical adaptive filters. Compared to the classical, the proposed W exhibits much higher convergence rate and lower MSD. Moreover, an ERLE enhancement of up to 10 db was achieved. These reported re-

6 W MSD(dB) 40 ERLE (db) W samples x samples FIG. 6 MSD time variation in the steady state and in both cases : W (in blue) and classical with watermared input (in blac). sults are very promising and the slightly higher complexity of the W is not a serious drawbac considering the actual high-performance digital signal processors (DSP). However, a deeper theoretical and experimental analysis needs to be carried out to further improve the W system. REFERENCES [1] S. Larbi, M. Jaïdane, M.Turi and M. Bonnet, Réflexion sur un annuleur d écho robuste aux non stationarités de la parole, in CORESA, Compression et représentation des signaux audio visuels, Dijon, France, [2] S. Larbi and M. Jaïdane, Audio watermaring : a way to modify audio statistics, IEEE Trans. on Signal Processing, vol. 53(2), [3] A. Gilloire, V. Turbin, Using auditory properties to improve the behaviour of stereophonic acoustic echo cancellers, in ICASSP, Seattle, USA, FIG. 7 ERLE evolution for the W (in blue) and the classical with watermared input (in blac). [4] M. Peters, Psychoacoustical excitation of the (N)LMS algorithm for acoustical system identification, in ISSPA (fifth Int. Symp. on Signal Processing and its Applications), Brisbane, Australia, [5] M. Mboup, M. Bonnet and N. Bershad, LMS coupled adaptive prediction and system identification : A statistical model and transient mean analysis, IEEE Trans. on Signal Processing, vol. 42(10), [6] P. Scalart, F. Bouteille, On integrating speech coding functions into echo cancelling filters with decorrelating propeerties, in ICASSP, Orlando, USA, [7] B. Paillard, P. Mabilleau, S. Morisette, PERCEVAL : perceptual evaluation of the quality audio signals, JASA, Vol. 40(12), [8] S. Hayin, Adaptive Filter Theory, Prentice-Hall, [9] Wai C. Chu, Speech coding algorithms, Wiley, 2003.