A New Fast Double-Talk Detector Based on the Error Variance for Acoustic Echo Cancellation

2.1 Single-talk scenario

In communication systems, acoustic echo occurs when the loudspeakers are picked-up by the microphone in the terminal device. Acoustic echo cancellation is use to remove this undesirable feedback signal; this issue is classified as a system identification problem. The basic principle of AEC is to generate a replica $\hat{y}(n)$ of the actual echo signal y(n) and subtract it from the microphone signal d(n), as is illustrated in Figure 1. In another words, an adaptive filter is used to identify an unknown system, i.e., the acoustic echo path h which is modeled by the impulse response of the loudspeaker-enclosure-microphones (LEM). In the first case, we consider the single-talk scenario, when the near-end speaker is in the silence-state.

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Figure 1. Illustration of AEC system

The acoustic echo signal y(n) at the discrete-time index n is the filter resulting of the near-end signal x(n) through the room impulse response h as is modeled by the following equation:

$y(n)=\mathbf{x}^T(n) \mathbf{h}$              (1)

where, h=[h₀, h₁, …, h_L-1]^T is the echo path of the length L, the superscript (∙)^T denotes transpose of a vector, x(n)=[x(n), x(n-1), …, x(n-L+1)]^T is a vector containing the L most recent time samples of the received signal x(n), or the far-end signal.

The microphone signal d(n) includes the echo signal y(n) and the background noise signal b(n) as:

$d(n)=y(n)+b(n)$              (2)

The estimated echo signal $\hat{y}(n)$ generated by the adaptive filter, which is a linear combination of several inputs at time n. This copy version of echo is subtracted from the microphone signal and it is given by:

$\hat{y}(n)=\mathbf{x}^T(n) \mathbf{w}(n)$              (3)

where, $\mathbf{w}(n)=\left[w_0(n) w_1(n), \ldots, w_{L-1}(n)\right]^T$ is the weight vector of the adaptive filter. The length of the adaptive filter is generally equal to the length of the acoustic echo path h.

The error signal e(n) at time n is given by:

$e(n)=d(n)-\hat{y}(n)$              (4)

Several adaptive filtering algorithms are proposed to adapt the weights w(n) of the filter using the feedback of the estimation error. The ideal algorithms should have a speed convergence rate and good tracking capabilities but achieving low misalignment. One of the most used due to its stability and low complexity is the normalized least mean squares (NLMS) algorithm [20]. It is defined by the following update equation:

$\mathbf{w}(n+1)=\mathbf{w}(n)+\frac{\mu}{\mathbf{x}^T(n) \mathbf{x}(n)+\varepsilon} e(n) \mathbf{x}(n)$              (5)

where, w(n+1) is the next tap weight value and w(n) is the present tap weight value of the adaptive filter. μ is the step-size parameter used in the weight vector updating with 0<μ<2 for the stability considerations, and ε>0 is a regularization constant used to improve adaptation stability and to avoid division by zero.

2.2 Double-talk scenario

In this scenario, the near-end speaker is in the speech-state and the DT situation is occurred when the echo signal y(n) and the near-end signal s(n) appear simultaneously. This situation causes a quick divergence of the adaptive filter coefficients w(n) from their optimum values where the microphone signal d(n) in this case combines the echo y(n), the near-end s(n) and background noise b(n) signals. This combination affects the comparison with the estimated echo signal $\hat{y}(n)$ in the adaptive cancellation where a better process requires that the microphone observation contains only the echo signal y(n).

For this raison, DTD is use for controlling the update of the filter coefficients as is shown in Figure 2. In essence, the main goal of DTD is to detect the presence of the near-end speech and freeze the adaptation process in DT situations [21].

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Figure 2. Representation of AEC with conventional DTD

Typically, the DTD calculates a statistic decision ξ(n), and the DT is declared when ξ(n) is lower than the threshold value T. The optimum decision variable ξ(n) for DTD will behave as follows [19]:

$\left\{\begin{array}{l}\text { If } s(n)=0 \text { (double }- \text { talk is not present), } \xi(n) \geq T . \\ \text { If } s(n) \neq 0 \text { (double - talk is present), } \xi(n)<T .\end{array}\right.$

The control of the adaptive filter by DTD is defined as:

Control $=\left\{\begin{array}{l}\xi(n) \geq T, \quad \text { DTD }=0 \text { adaptation } \quad \mu \neq 0 \\ \xi(n)<T, \quad \text { DTD }=1 \text { no adaptation } \mu=0\end{array}\right\}$

where, the update of the adaptive filter coefficients will be stopped during DT situations (μ=0), that means w(n+1)=w(n) according to Eq. (5).

The well-known method of DTD is the Geigel algorithm [7], where the variable statistic decision ξ_G(n) of the latter is defined as follows:

$\begin{aligned} & \xi_G(n) =\frac{\max [|x(n)||x(n-1)|, \ldots,|x(n-L+1)|]}{|d(n)|}\end{aligned}$            (6)

where, $\max [.]$ and $|\cdot|$ denote the maximum and the absolute value, respectively.

This section presents the experimental tests with the evaluation to prove the effectiveness of our proposed DTD method. We used AEC based on NLMS algorithm controlled by the step-size μ=0.9 and ε=2.2204×10^-16 where the length of the adaptive filter is L=1024 equals to the length of the acoustic echo path (car cockpit impulse response sampled at $16 \mathrm{kHz}$) [22]. We use also speech signals for simulating the far-end and the near-end speakers which are sampled at 16 kHz. Furthermore, we adopted the proposed structure in [22] which investigates insignificant samples of the received far-end signal by creating a delay and adding a short period time of the AWGN. We take a period of delay t_d=125 ms with σ²=0.005 is the variance value of AWGN.

In order to further demonstrate the performance of the proposed DTD we compare it with Geigel [6], normalized cross-correlation (NCC) [9] methods and zero-crossing rate (ZCR) method based DTD proposed in the study [4].

The optimal threshold values are given by: T_G=1.5, T_NCC=0.92, T_ZCR=0.25 and T_V=0.96 of Geigel, NCC, ZCR and the proposed DTD, respectively. Also, we choice M=512 the length of the frame f contents 512 recent sample history of the signals in ZCR and the proposed DTD.

The real environment is modeled by a white Gaussian back-ground noise signal b(n) that is added to the echo signal y(n) at various signal-to-noise ratio (SNR) values, where the SNR value is defined by:

$\operatorname{SNR}(\mathrm{dB})=10 \log _{10}\left(\frac{E\left\{|y(n)|^2\right\}}{E\left\{|b(n)|^2\right\}}\right)$         (11)

We evaluated our method by calculating the different probabilities P_d, P_m and P_f of detection, miss and false alarm, respectively, where the output DTD signal is compared with the VAD of near-end signal s(n). Also, we have used three performances measures: the normalized mean square deviation (NMSD) (mismatch system), mean square error (MSE) and echo return loss enhancement (ERLE) which are calculated by:

$\operatorname{NMSD}(\mathrm{dB})=10 \log _{10}\left(\frac{\|\mathbf{w}(n)-\mathbf{h}\|^2}{\|\mathbf{h}\|^2}\right)$           (12)

where, $\|\mathbf{w}(n)-\mathbf{h}\|$ is the Euclidian distance between the adaptive coefficients vector and the true echo path vector.

$\operatorname{MSE}(\mathrm{dB})=10 \log _{10}\left(E\left\{|e(n)|^2\right\}\right)$          (13)

where, $E\{\cdot\}$ denotes the mathematical expectation.

$\operatorname{ERLE}(\mathrm{dB})=10 \log _{10}\left\{\frac{E\left[|y(n)|^2\right]}{E\left[|e(n)|^2\right]}\right\}$        (14)

Good performance of AEC system is indicated by the capability to minimize the misalignment, the MSE and maximize the ERLE values.

Figures 4 and 5 illustrate the decision variable and the DTD signal of the proposed method using echo with 2.5s duration and near-end speech signals pronounced in English and background noise modeled by SNR value equals to 60 dB.

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Figure 4. Decision variable of the proposed DTD

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Figure 5. Representation of the proposed DTD decision

In addition, temporal evolutions and spectrograms of the near-end and the output signals are depicted in Figures 6 and 7. The obtained results indicate a great similarity between the near-end and the output signals temporal evolution, also as well as in their spectrograms.

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Figure 6. Temporal evolution of speech signals, (blue) near-end, (red) output

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Figure 7. Spectrograms of speech signals, (a) microphone, (b) near-end, (c) output

To confirm effectiveness of the proposed DTD, we include long speech signals pronounced in French in DT scenario with duration of 30 seconds. The near-end speech (double-talk) appears between times 10 and 16.5 seconds.

Similarly to the previous tests, consider Figures 8, 9 and 10, which depict DTD signal and comparison of the near-end and the output (estimated near-end) signals, it is clear that the proposed method also has good performance in terms of echo cancellation for a long duration of speech conversation.

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Figure 8. Representation of the proposed DTD decision for long speech signals, SNR=60 dB

A comparison between the proposed DTD, Geigel, NCC and ZCR methods is shown in Figures 11 and 12 using NMSD curves for short and long speech signals. According to the obtained results, the proposed method outperforms the other methods in terms of minimizing the steady-state NMSD where the proposed DTD maintains the NMSD level during DT period and avoids NMSD divergence. In other words, the proposed DTD allows the NLMS algorithm to ignore the effect of the near-end signal on NMSD convergence, such as its NMSD curves bring closer to the single-talk (ST) curves i.e., absence of the near-end signal.

On the contrary, the presence of DT affects the Geigel, NCC and ZCR behaviours as well as an increase in the NMSD level.

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Figure 9. Temporal evolution for long speech signals, (blue) near-end, (red) output

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Figure 10. Spectrograms of long speech signals, (a) microphone, (b) near-end, (c) output

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Figure 11. NMSD curves for short speech signals, SNR=60 dB, the near-end speech (double-talk) appears between times 0.625 and 1.76 seconds

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Figure 12. NMSD curves for long speech signals, SNR=60 dB, the near-end speech (double-talk) appears between times 10 and 16.5 seconds

MSE curves are shown in Figure 13, which are evaluated for each 2048 iterations. It is observed that the proposed method of DTD yields better performance in terms of MSE minimizing compared to the others methods. This result indicates a reduction in the error signal (returned echo) energy during the ST periods.

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Figure 13. MSE evaluation for long speech signals, SNR=60 dB

According to the ERLE comparison of DTD methods in different SNR values (15 dB, 35 dB and 55 dB) given in Table 1, the obtained results confirm the superiority of the proposed method of DTD compared to the others methods which has large values of ERLE average that can reduce the effect of the acoustic echo.

Table 1. Evaluation of ERLE in function of SNR for different methods of DTD

Table 2. Evaluation of PESQ in function of SNR for different methods of DTD

A perceptual evaluation of speech quality (PESQ) [23] is also considered to evaluate the quality of the output speech signal of each method of DTD as is depicted in Table 2. The values of PESQ are ranging from 4.5 (the highest possible quality) to 0 (the worst quality) where the output signal i, e., the estimated near-end signal is compared with the original near-end signal.

From the obtained results, we can observe that the proposed method has better performance in terms of the speech intelligibility.

Table 3 presents the obtained probabilities (P_d, P_m and P_f) of the different DTD methods utilizing several tests of speech signals for near-end and far-end speakers, under three SNR levels (15, 35 and 55 dB). It is worth noting that, the goal is to maximize the detection probability P_d and minimize the miss probability P_m for better detection of DT. On the other side, for avoiding the update stopping during the convergence process the false alarm probability P_f should be minimized.

The obtained results evince that the proposed DTD yields lower values of P_m and P_f, also higher value of P_d for the three levels of SNR compared to the others methods. We indicate that the increasing on P_f value causes convergence halting of the NLMS algorithm. We can therefore conclude that the proposed DTD performs better in terms of probabilities evaluation.

Table 3. Comparison of probabilities in function of SNR for different methods of DTD