A Comparison of the Convolutive Model and Real Recording for Using in Acoustic Echo Cancellation

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1 A Comparison of the Convolutive Model and Real Recording for Using in Acoustic Echo Cancellation SEPTIMIU MISCHIE Faculty of Electronics and Telecommunications Politehnica University of Timisoara Vasile Parvan, nr. 2 ROMANIA septimiu.mischie@etc.upt.ro Abstract: - The paper investigates the convolutive model, which models the interaction between a loudspeaker and a microphone. First, the impulse response of the channel from the loudspeaker to the microphone is experimentally measured. Then, a speech signal is played on the loudspeaker and the corresponding microphone response is recorded. This signal is compared with that obtained by convolution between the speech signal and the impulse response which was previously measured. To give a more weight to this comparison, an acoustic echo cancellation (AEC) is implemented, where the echo signal is either computed (using the convolutive model) or recorded. It follows a degradation of the quality of the AEC when the echo is recorded. Some methods to improve the result are proposed. Key-Words: - convolutive model, channel impulse response, acoustic echo cancellation. 1 Introduction Speech processing is a very challenging domain today. To implement a speech processing system, at least one loudspeaker and a microphone together with the hardware to control these devices are needed. For instance, this hardware must play a previous recorded signal on the loudspeaker and record in the same time the microphone response. Some processing operations must be performed by this hardware too. Another solution is to use some prerecorded speech waveforms and synthetically compute the microphone outputs by using the loudspeaker to microphone path. This path is called channel impulse response and can be computed by source-image method [1] depending on the room dimensions, absorption coefficient of the walls, relative positions of the loudspeaker and microphone and so on. Channel impulse response can also be experimentally measured using sine sweep method [2] and maximum length sequence method [3]. If it is denoted by h(n), n = 0,1,,L 1, L being the length of the path, the recorded speech can be modeled by [4]-[6] L 1 x( n) = s( n i) h( i) = s( n)* h( n) (1) i= 0 where s(n) is the speech signal played on the loudspeaker and the symbol * means convolution. The speech signal s(n) must be recorded in an anechoic room. Sometimes a noise η(n) is added to the right hand in (1). In most speech processing fields like speech separation [6] or acoustic echo cancellation (AEC) [7] the expression (1) is used to model the signal recorded by the microphone. However, this approach is good in simulations but the algorithms must be verified in real conditions. For instance, the AEC within a hands-free phone must consider the real recordings instead of the computed ones. Taking into account these remarks, in this paper we investigate how good the convolutive model is. For this purpose, we simple compare two signals. The first is recorded by a microphone excited by a loudspeaker. The second is the computed output of the system having the impulse response equal with the measured path of the loudspeakermicrophone used to recording the first signal. Both systems have the same speech signal on their inputs. Then we implement an AEC using each of the two signals and we study how these signals influence the functionality of the AEC. The paper is organized as follows. Section 2 presents basics about channel impulse response. Section 3 presents the structure and the main characteristics of an AEC, while section 4 presents the experimental results. Conclusions are drawn in section 5. ISBN:

2 2 Channel Impulse Response Measurement Methods As in previous section was presented, the main methods for channel impulse response measurement are the source-image method, the sine sweep method and respectively the maximum length sequence (MLS) method. The ideal impulse (Dirac function) will be presented in this section too. The sine sweep method implies generation of a sine sweep excitation which is emitted to the loudspeaker. The signal recorded by the microphone is then convolved with the inverse sweep signal to obtain the channel impulse response. The inverse sweep signal is a signal which gives an unit pulse when is convolved by the sine sweep signal. The MLS method uses a periodic pseudo-random signal to drive the loudspeaker. This signal has the same properties like a pure white noise. One period of this signal has 2 m 1 samples. The usual values of m are 13, 14, 15. The channel impulse response is obtained by the crosscorelation between the periodic pseudo-random signal and the recorded output. The ideal impulse method implies generation the signal 1, if n = 0 s( n) = (2) 0, otherwise which is emitted to the loudspeaker. In this case the recorded output is just the room impulse response. However this method is considered having only a theoretical importance [9]. 3 The Structure of an Acoustic Echo Cancellation System The block diagram of the AEC is presented in Fig. 1. AEC is used to enhance the quality of a conversation by hands free-phones. The main problem which appears in such a system is the acoustic echo. Thus, when the far-end speaker talks, his (her) voice, denoted s(n), is played on the loudspeaker of near-end talker to be heard by this. If the near-end speaker does not talk, that is v(n)=0, the signal which is captured by his (her) microphone is d(n)=x(n), a filtered version of s(n). The impulse response of the loudspeaker-microphone path is denoted h(n). In the absence of another processing operation, x(n) will be sent back to the far-end speaker as an echo. The task of the AEC is to process the signal x(n) such a very weak (zero if it is possible) signal to be sent to the far-end speaker. This task is performed by the adaptive filter. In this case we have a system identification problem. The adaptive filter must compute h ˆ( n), the estimate of h(n), such as its output xˆ( n) equals the echo signal x(n). In this way, the error signal e( n) = d( n) xˆ ( n) will be minimized. When also the near-end speaker talks (this case is known as double-talk), the output of the microphone is d(n)=x(n)+v(n). In this case, the adaptive filter will work such the signal error e(n) will be an estimate of the near-end signal, v(n). Another important problem of AEC is the background noise. This is present as a separate term in d(n) regardless the near-end speaker talks or does not. The most used form of the adaptive filter is the normalized least mean square (NLMS) filter. The equation which updates the coefficients of NLMS filter is [8]: ˆ ˆ e( n) s( n) h( n + 1) = h ( n) + µ (3) P( n) where h ˆ( n + 1) and h ˆ( n) are vectors containing the L filter coefficients at the time n+1, and n respectively, s(n) is a vector containing the most recent L samples of the far-end signal, s(n)=[s(n) s(n 1) s(n L+1)] and P(n) is the power of the most recent L samples in s(n), L 1 2 ( ) = [ ( )]. i= 0 P n s n i (4) The coefficient µ in (3) is the step size which controls the stability and the convergence of the adaptation algorithm. Two of the most important parameters which reflect the quality of the AEC are normalized projection misalignment (NPM) and echo return loss enhancement (ERLE). Thus, NPM [10], in db, represents how good the estimate h ˆ( n ) of h(n) is, and is given by [10] ε ( n) NPM( n) = 20log10 (5) h where h is the vector containing the L coefficients of the filter which models the loudspeakermicrophone path, represents the l 1 norm and ε(n) is given by T ˆ( n ) ε ( n) = h h h hˆ ( n) (6) ˆT h ( n) hˆ ( n) where superscript T means vector transposition. ISBN:

3 Fig. 1. The block diagram of the AEC ERLE [11] is a measure of the amount, in db, that the echo has been attenuated and is given by 2 [ d( n)] ERLE( n) = 10log 10. (7) 2 [ e( n)] 4 Experimental Results 4.1 Measurement System All the experiments were performed in a common room (our office) in order to be as close as possible to a real environment. The structure of the measurement system is presented in Fig. 2. We have used the sound card of a PC to generate and record audio signals. Thus, we connected one microphone at the Mic Input and one loudspeaker at the Line Out of the sound card. We used an usual Trust headset (one of the two headphones and the microphone), and, in some experiments, a Star SP 1601 loudspeaker instead the headphone. The distance between the loudspeaker and the microphone, denoted dist, was in the range cm. The programs were written in MATLAB. The sampling rate was 8000 Hz for both recording and playing. The most important part of the MATLAB code which is able to record and play back digital signals simultaneously is presented in the following. ai = analoginput('winsound'); addchannel(ai,1); ao = analogoutput('winsound'); addchannel(ao,1); putdata(ao,out); start(ai); start(ao); inp=getdata(ai); The variable out is a vector containing the signal to be played and variable inp is a vector where the recording signal will be loaded. Fig. 2. The measurement system. 4.2 Evaluation of the Convolutive Model in Comparison with a Real Recording In order to evaluate how good the convolutive model (1) is, first we measured the impulse response of the loudspeaker-microphone path. We used the sine sweep method. The distance between the two sound devices was 20 cm. Fig. 3 presents the measured impulse response. We have recorded 8000 samples but only the first 300 were kept because the amplitude of the next samples was insignificant. The delay of about 130 samples represents the execution time of the instruction start(ao). To make an experiment in the same conditions as impulse response measurement, a sequence of 8 sec. of clean (anechoic) speech called source was immediately played on the loudspeaker and the microphone response was recorded in the same time. The locations of loudspeaker and microphone were unchanged. The recorded waveform is called recorded. Then, the convolution between the source and the previous measured impulse response was computed, and the resulting waveform is called convolved. Fig. 4 presents the three speech waveforms. It can be seen that the second and the third waveforms have the amplitude with about one order smaller than the amplitude of the first waveform. This was expected because the amplitude of the impulse response is about To do a better comparison between the recorded and the convolved waveforms, Fig. 5 presents a detail of the three waveforms and Fig. 6 presents the difference between the last two waveforms, called error. By looking at Fig.5 it follows that there is a delay of about 130 samples between the source on the one hand and the recorded or convolved waveforms on the other hand. This delay corresponds to the positions of the main pulses in impulse response. Also it can be seen ISBN:

4 that the oscillations of recorded and convolved waveforms are very similar. However, both of them are different enough to source, as expected. Fig. 3. The measured impulse response Fig. 4. The original source, recorded and convolved waveforms. Fig. 5. A detail of waveforms from Fig. 4. By looking at Fig. 6 it can be seen that the difference between the recording and computed waveforms has the amplitude with about one order smaller than each of them (fig. 4). The SNR computed by 10log 10 ( Precorded / Perror ) is 10.3 db, where P means power. We will see in the next subsection if this value large enough. Fig. 6. The difference between the recorded and convolved waveforms 4.3 Evaluation of the AEC In this subsection we implement the AEC whose structure has been presented in section 3. We consider that the near- end speaker is absent, v(n)=0. The signal s(n) has the length of 8 sec. and is the source waveform used in subsection 4.2. The echo signal x(n) has mainly two forms, the convolved and recorded waveforms which also were previously used. The step size µ in (3) was chosen to 0.9. The length L of the h(n) was set to 300. The results when the echo signal x(n) is computed using the convolution are presented first. There are three cases. a) the noise-free case (unrealistic in practice), x(n)=s(n)*h(n), where h(n) is measured for dist=20 cm (see Fig. 3); b) x(n)= s(n) * h(n) + η(n); h(n) is the same as in a); the value of SNR was 22.1 db c) x(n)= s(n) * h(n)+ η(n); h(n) is measured for dist=10 cm and has higher amplitude than that of Fig. 3; the value of SNR was 31 db. The noise η(n) was recorded in the same room where all the experiments were achieved. Thus, Fig. 7 presents the signal x(n) and the corresponding e(n) in noise-free case, and for a comparison, e(n) when noise is present (SNR=22.1 db). Fig. 8 presents NPM and Fig. 9 presents ERLE, both of them when SNR=22.1 db. The gapes in ERLE curve correspond to time intervals when x(n) is very low. It can be seen that AEC performs very good in noise-free case and good when the noise is present. After about 1.5 sec. the echo signal is attenuated (e(n) in Fig.7) and therefore ERLE has large values. In the same time, NPM exceeds the value of 6 db. Table I presents the average value of ERLE for the three experiments. It can be seen that the noise implies a serious decreasing of ERLE. ISBN:

5 Fig. 7. The signal x(n) obtained by convolution (the top panel) and corresponding e(n) in noise-free case (the middle panel); e(n) when SNR is 22.1 db (the bottom panel). Fig. 8. NPM when SNR is 22.1 db. the noise of additive type (the way of combining between the convolved signal and the noise could be more complicated). To improve the value of ERLE, we used the fact that the convergence rate of an adaptive system increases when the length of the h(n) decreases. Thus we delayed the x(n) by 120 samples. That means that position of the maximum positive pulse in estimation of h(n) will be about 12. The length of h(n) in AEC algorithm was set to 50 (in this way the most important part of impulse response was considered). The average value of ERLE was increased to 23.8 db as in Table II can be seen. A shorter delay between the s(n) and x(n) can be obtained in practice by using a Digital Signal Processor (DSP). Thus, the delay can be of only few samples and in this way the length of the h(n) could be reduced, and the average value of ERLE will increase. However these improvements are not sufficient for a high quality AEC. The main reasons for these results are the nonlinear distortions of the loudspeaker-microphone path. To model these nonlinearities, Voltera series could be used. Thus, in the right hand of (1), a set of impulse responses h i (t), each of them convolved by a different power of the speech signal s(n) must be added. Then, nonlinear AEC based on Voltera filters [12] can be used. Table 2 Values of ERLE when echo was recorded ERLE [db] Conditions 21.9 L= L=50 Fig. 9. ERLE when SNR is 22.1 db. Table 1 Values of ERLE when echo was computed ERLE [db] Conditions 56.1 Noise-free 26.2 SNR=22 db 29.8 SNR=31 db Fig.10 presents the recorded form of x(n) and the corresponding e(n). In can be seen that e(n) is attenuated in comparison with x(n) as expected. However this attenuation is smaller in comparison with that in Fig. 7, when the echo x(n) is computed. This is also quantified by a smaller value of the average of ERLE, 21.9 db in comparison with 26.2 db. The reason for this decreasing of the quality could be the nonlinearities of the real system in comparison to the convolutive model or considering Fig. 10. The signal x(n) recorded and the corresponding e(n) 5. Conclusion The paper investigates using the recorded signals ISBN:

6 instead those computed by convolutive model. It follows that convolutive model is good enough to approximate a recorded signal. However, if an AEC performs well when convolutive model is used for echo signal, the AEC performance (ERLE) is not sufficiently high when a recorded signal is used for echo. Using DSP instead MATLAB environment to play and record in the same time could improve the performance of AEC. Furthermore, Voltera-based nonlinear AEC could be use to obtain a system which work good on recording signals. References: [1] J. B. Allen and D.A. Berkley, Image method for Efficiently Simulating Small-Room Acoustics J. Acoust. Soc. Amer., vol. 65, pp [2] S. Guy-Bart, E. Jean Jacques and A. Dominique, Comparison of different impulse response measurement techniques, Journal of the Audio Engineering Society, vol. 50. no.4, pp , Dec [3] J. Daigle and N. Xiang, A specialized fast cross-corelation for acoustical measurements using coded sequences, Journal Acoust. Soc. Am., vol.119, no.1, pp , Jan [4] M. Ikram and D. Morgan, Permutation Inconsistency in Blind Speech Separation: Investigation and Solutions, IEEE Trans. on Speech and Audio Processing, vol. 13, no.1, pp.1-13, Jan [5] S. Douglas, H. Sawada and S. Makino, Natural Gradient Multichannel Blind Deconvolution and Speech Separation Using Causal FIR Filters, IEEE Trans. on Speech and Audio Processing vol. 13, no.1, pp , Jan [6] H. Buchner, R. Aichner and W. Kellermann, A Generalization of Blind Source Separation Algorithms for Convolutive Mixtures Based on Second-Order Statistics, IEEE Trans. on Speech and Audio Processing, vol. 13, no.1, pp , Jan [7] R. M. Udrea, C. Paleologu, J. Benesty and S. Ciochină, Estimation of the noise Power in the NPVSS-NLMS Algorithm, Proceedings of the th International Symposium on Electronics and Telecommunications, Timisoara, Romania, 2010, pp [8] J. M. Valin, On adjusting the learninf rate in frequency domain echo cancelation with double-talk,, IEEE Trans. on Audio, Speech and Language Processing, vol. 15, no.3, pp , March [9] Measuring impulses responses using Dirac, Acoustical Engeneering, August 2007, [10] Y. Huang, J. Benesty and J. Chen, Optimal Step Size of the Adaptive Multichannel LMS Algorithm for Blind SIMO Identification, IEEE Signal Processing Letters, vol. 12, no.3, pp , March [11] I. Homana, M. Topa, B. Kirei and C. Contan, Adaptive Algorithms for Double-Talk Echo Cancelling, Proceedings of the th International Symposium on Electronics and Telecommunications, Timisoara, Romania, 2010, pp [12] J. B. Seo, K. J. Kim, and S. W. Nam, Nonlinear Acoustic Echo Cancelation using Voltera Filtering with a Variable Step-Size GSPAR algorithm, World Academy of Science, Engineering and Technology, 2009, pp ISBN: