The synoptic representation of the acquisition of the signal is represented in Figure 16.1. The speech signal was emitted by the front loudspeaker (0°), and the noise was presented from a loudspeaker (LS) array. The LSs were situated at angles θ ranging from − 90° to 90°. The acoustic signal is captured by the microphones (m₁ and m₂).

In addition, a percentage (α) of the input signal was reinjected after the noise reduction algorithms (Van den Bogaert et al., 2008). The values of α were fixed to 0.0, 0.2, and 0.4 (0%, 20% and 40%).

The basic reinjection formula used in this work was

$s\prime \left(t\right)=\left(1-\alpha \right).s\left(t\right)+\alpha .e\left(t\right)\text{,}$

where e(t) is the input signal, s(t) is the signal leaving the noise reduction processor, s′(t) is the signal output, (entering the vocoder), α is the reinjection (0%, 20%, 40%), and s″(t) is the output signal presented to the listeners.

2.1.2 Beamformer

The schematic representation of the Beamformer is presented on Figure 16.2.

The signal emitted by the sound source is captured by two microphones, m₁ and m₂ (right and left), situated on the ears of a Knowles Electronics Manikin for Acoustical Research (KEMAR) head. The classical Beamformer (BF) response is a cardioid centered on the front loudspeaker, LS3 (Bouchard et al., 2009). The BF algorithm is presented next, and it favors the front target (0° azimuth); the experiment was in the horizontal plane.

The input signal reaching the two ears e(t) can be represented (complex plane) in the case of a sine wave by

$e\left(t\right)=A.e^{j\omega \left(t-\tau \right)}=A.e^{j\omega \left(t-\frac{x}{c}\right)}=A.e^{j\left(\omega t-\frac{2\pi .x}{cT}\right)}=A.e^{j\left(\omega t^{\text{\_}}\frac{2\pi .x}{\lambda }\right)}=A.e^{j\left(\omega t-\mathrm{\Phi }\right)}$

where A is the signal magnitude, x is the distance between the source and the microphones (x₁ and x₂), c is the sound velocity in air (340 m/s), λ is the wavelength, τ is the propagation time between the source and the microphones, d is the distance between the two ears (20 cm), Φ is the phase delay between the source and the microphones, and θ is the orientation angle of the sound source.

The phase difference between the signals reaching the two ears is

$\mathrm{\Delta }\mathrm{\Phi }=\frac{2\pi }{\lambda }\left(x_1-x_2\right)\approx \frac{2\pi .d}{\lambda }sin\left(\theta \right)$

The beamformer algorithm (based on the phase information) is mainly helpful when

$\mathrm{\Delta }\mathrm{\Phi }=\frac{2\pi .d}{\lambda }\le \pi \text{,}$

leading to fc ≤ 850 Hz (850 Hz is obtained for θ = π/2). The maximum delay between the two ears represents about 10 samples at the sampling frequency fs = 16 kHz.

In the Beamformer strategy, the low-frequency part of the signal (below 850 Hz) is processed and the signals coming from the two microphones are added. Then the high-frequency components of the signal are restored for further treatment.

2.1.3 Doerbecker’s processing

Doerbecker’s processing is a noise reduction procedure enhancing the sound coming from the front; it is based on a spectral subtraction followed by an adaptive Wiener filtering (Figure 16.3). It begins by the estimation of the noise. Doerbecker’s strategy is mostly based on spectrum consideration.

In Doerbecker’s processing, the noise estimation follows one of two methods. The first is referred to as the Ephraim and Malah correction (Ephraim and Malah, 1984), which is a binaural process reducing the musical noise introduced by the spectral subtraction. The second is Scalart’s correction (Scalart and Filho, 1996), which selects, on each channel, the best SNR, which is similar to Wiener’s algorithm (Van den Bogaert et al., 2009).

The steps of Doerbecker’s processing are as follows:

1. A short-term fast Fourier transform (FFT) is applied to the signal captured by the two microphones m₁ and m₂, leading to two processing lines, one on each side:

$\begin{array}{l}{E}_1\left(f\right)=FFT\left(e_1\left(t\right)\right)\\ E_2\left(f\right)=FFT\left(e_2\left(t\right)\right)\end{array}$

where E₁(f) and E₂(f) are the spectrum components at a frequency f (amplitude and phase) in the complex plane.

2. The estimation of the noise spectrum is obtained by subtracting the cross-power spectrum to the power spectra as follows:
Power spectra:

$\begin{array}{l}{\mathrm{\Phi }}_{x_1{x}_1}\left(f\right)={\left|E_1\left(f\right)\right|}^2\\ {\mathrm{\Phi }}_{x_2{x}_2}\left(f\right)={\left|E_2\left(f\right)\right|}^2\cdot \end{array}$

Cross-power spectrum (scalar product):

${\mathrm{\Phi }}_{x_1{x}_2}\left(f\right)=\left|E_1\left(f\right).E_2\left(f\right)\right|\text{.}$

3. Noise estimation (on line 1) is given by

${{\mathrm{\Phi }}_{nn}}_1\left(f\right)={\mathrm{\Phi }}_{x_1{x}_1}\left(f\right)-{\mathrm{\Phi }}_{x_1{x}_2}\left(f\right)$

If Φ_nn(f) is negative, Φ_nn(f) is set to zero; this action is called the musical noise.
A similar formula is used on line 2.
It can be seen that if X₁(f) = X₂(f), then Φ_nn(f) = 0 (no noise) for the frequency f.

4. Ephraim and Malah correction
The Ephraim and Malah formula (Ephraim and Malah, 1984) introduces a spectrum amplitude correction for the speech signal in order to minimize the mean-square error of the log spectra. It attenuates the musical noise and represents a smoothing between the time frames:

$G=\frac{\sqrt{\pi }}{2}\sqrt{\left(\frac{1}{1+R_{\mathit{post}}}\right)\left(\frac{R_{\mathit{prio}}}{1+R_{\mathit{prio}}}\right)}*M\left[\left(1+R_{\mathit{post}}\right)\left(\frac{R_{\mathit{prio}}}{1+R_{\mathit{prio}}}\right)\right]$

where G is the gain that is applied to each short time spectrum; R_post is the a posteriori SNR, which is the local estimate of the SNR computed from the current data in the current short time frame; R_prio is the a priori SNR, which corresponds to the information on the spectrum magnitude gathered from previous frames (this value defines the attenuation of the musical noise and is widely discussed in Cappe, 1994); and M represents the Bessel functions of zero and first order.

5. Scalart correction
The Scalart formula was developed to improve the SNR in the frequency domain (Scalart and Filho, 1996):

$G\left(f\right)=\sqrt{\frac{SNR\left(f\right)-1}{SNR\left(f\right)}}=\sqrt{1-\frac{1}{SNR\left(f\right)}}$

G(f) weights the frequencies of the signal and is set to zero if SNR(f) < 1. Thus, frequencies with a low SNR are disadvantaged.

6. Spectral subtraction
In the next step, a spectral subtraction is performed (Yang and Fu, 2005):

$\mathrm{Right}\mathrm{side}\left(\mathrm{ear}\right):\stackrel{\neg }{X_1}\left(f\right)=\sqrt{{\mathrm{\Phi }}_{x_1{x}_1}\left(f\right)-{\mathrm{\Phi }}_{nn}\left(f\right)}$

$\mathrm{Left}\mathrm{side}\left(\mathrm{ear}\right):\stackrel{\neg }{X_2}\left(f\right)=\sqrt{{\mathrm{\Phi }}_{x_2{x}_2}\left(f\right)-{\mathrm{\Phi }}_{nn}\left(f\right)}$

This strategy disadvantages the frequencies where X₁(f) is different from X₂(f).

7. Wiener filtering
A general Wiener coefficient W_s(f) is calculated (Van den Bogaert et al., 2009; Doerbecker and Ernst, 1996), indicating the percentage of noise, for each frequency (Figure 16.3):

$Ws\left(f\right)=\frac{4{\left|{\mathrm{\Phi }}_{X_1{X}_2}\left(f\right)\right|}^2}{{\left(\left|{\mathrm{\Phi }}_{X_1{X}_1}\left(f\right)\right|+\left|{\mathrm{\Phi }}_{X_2{X}_2}\left(f\right)\right|\right)}^2}\text{,}$

with W_s(f) = 1 if X₁(f) = X₂(f).
Then, each frequency f of the input signal is corrected by W_s, on each way, as follows:

$\begin{array}{l}\left|S_1\left(f\right)\right|=\sqrt{\left|{\mathrm{\Phi }}_{X_1{X}_1}\left(f\right)\right|⁎W_s\left(f\right)}\\ \left|S_2\left(f\right)\right|=\sqrt{\left|{\mathrm{\Phi }}_{X_2{X}_2}\left(f\right)\right|⁎W_s\left(f\right)}\end{array}$

Finally, the processed signal is reconstructed using an inverse fast Fourier transform (IFFT).

2.1.3 Vocoder

CI coding was represented by a classical vocoder (Figure 16.4) (also see Loizou, 2006) performing the channel simulation.

For this application, the Neurelec BCI parameters have been taken:

1. Sampling frequency (fs): 16 kHz

2. Frame length: 8 ms (128 time samples); a 75% overlap between the frames was used, leading to the signal refreshing every 2 ms. Spectral bins (spectral lines) were calculated using a FFT; then the 64 bins were grouped according to the bark scale in order to build up the channels (Table 16.1). The bark scale follows the cochlea lin-log properties of the cochlea.

3. The spectrum was parted into 12 frequency bands, (12 channels, corresponding to the 12 electrodes) on each ear. According to the short-term FFT theory, bin spacing was 125 Hz.

4. The eight highest energy channels were selected Dorman and Loizou, 1997; Friesen et al., 2001). For each channel, a sine wave, taken at the center frequency of each band, was multiplied by the energy of the frequency band. The four remaining (nonselected) channels were eliminated.

The noise was obtained from a speech signal analyzed by a FFT and reconstructed with a random phase. The signal was the phonetically balanced Lafon’s lists (www.extpdf.com/lafon-pdf/html) classically used in the French clinical tests. Each list has 17 three-phoneme words, leading to 51 phonemes. A total of 20 lists are available.

The noise was presented at the input of the system, from one of the five loudspeakers (Figure 16.1). The input angle was θ. Lafon’s lists were always presented from the front LS (θ = 0°).

Then, the signal was recorded on the KEMAR head. Consequently, the ITD and the ILD effects were present. The distance head-LS was 1 m; azimuth ranged from − 90° to 90°, with five positions (− 90°, − 45°, 0°, 45°, 90°). A sample frequency was fs = 44.1 kHz; then it was downsampled to fs = 16 kHz. The intensity was 70 dB SPL, allowing a good dynamic for the recording. The recorded signal was then processed and the final signal, represented by s₁″(t) and s₂″(t) in Figure 16.1, was burned on a CD. All subjects followed two successive stages: first, a training session; and second, an assessment (test) session.

2.2.2 Training session

Each subject listened to the vocoded speech (VOC) with no noise added, and was asked to repeat each three-phoneme word. The percentage of correct recognition of phonemes (PCRPs) was recorded for each of the 20 lists. This training task lasted until each subject reached a performance of at least 80% of correctly repeated phonemes. The training session for all the subjects lasted less than 15 min.

2.2.3 Phoneme recognition test

Then, subjects were instructed to listen to a total of 150 lists; each list corresponded to a given experimental condition (as described next). The lists were chosen randomly in the data bank (the 20 Lafon’s lists), and each list was equally represented throughout the different 150 conditions indicated here:

1. Three algorithms: Beamformer (BF), Doerbecker + Ephraim and Malah (DOEM), and Doerbecker + Scalart (DOS)

2. Three reinjection percentages: α = 0% (denoted 00), 20% (20), and 40% (40)

3. Five angles for the noise: θ = -90°, -45°, 0°, + 45° and + 90°

4. Three SNRs: − 6 dB, 0 dB, and 6 dB

This leads to 3 × 3 × 5 × 3 = 135 situations. Consequently, the parameters of the study were the algorithm, the reinjection, the noise angle, and the SNR. The corresponding condition codes were BEAM00, BEAM20, BEAM40, DOEM00, DOEM20, DOEM40, DOS00, DOS20, and DOS40, indicating the algorithm and the reinjection.

Furthermore, speech perception was tested in the VOC situation, yielding another 15 experimental conditions (3 SNRs * 5 noise angles). At the beginning of a session, a test was made without any processing to stand up as a reference (UNPROC).

The whole listening experiment lasted 3 h, including at least one break per hour (and more upon the subjects’ request). Programs were developed on Matlab® software and graphical user interface (GUIDE).

The full recognition percentages of the phonemes PCRP (Percentage Correct Recognition Phoneme) are presented in Table 16.3. These results will be analyzed and compared to the source localization.

3.2.2 Specific recognition

As the angle of the noise perturbation did not strongly affect the percentage recognition, the results indicated here were averaged on θ (Table 16.4) for clarity purposes. Table 16.5 shows the mean values (over the SNRs) according to the algorithm and the reinjection. The corresponding value for “Voc only” was 33%.

The overall representation of the reinjection is shown in Figure 16.6.

In order to show the influence of the algorithms, PCRPs are reorganized as shown in Figure 16.7, after averaging on the SNR and on the noise angle.

Beam and DOEM led to the best PCRP (Figure 16.7). Results were clearly above those obtained with the vocoder only (VOC). The difference between Beam and DOEM was very small, suggesting that time strategy and spectrum processing present similar behaviors.

The Adaptive Directional Microphone (ADM) strategy was clearly an advantage for the sounds coming in front of the listener (Van den Bogaert et al., 2008).

4.2.2 Influence of SNR

When no reinjection was done, the beamformer algorithm led to the best PCRPs (Table 16.4). When a reinjection was introduced, the recognition was improved with all the algorithms, but BEAM stayed ahead. (Note: SNR = − 6 dB.) In this adverse condition (low SNR), the algorithms were not efficient (compared to VOC).

In the case of SNR = 0, recognition led to better results (the noise and the signal were at the same level). Without reinjection, BEAM results were the best. With reinjection, DOEM PCRPs were greatly improved (Table 16.4).

Compared to the VOC (vocoder only) situation, PCRP recognition percentages were clearly better when a noise reduction strategy was used; reinjection leveled the recognition percentages among the algorithms.

In the case, of SNR = 6 dB, the results obtained with the different strategies were rather equivalent (Table 16.4). Reinjection had a positive influence (α starting from 20%). The VOC situation was far inferior. Similarily, Kokkinakis and Loizou (2010) indicated that when SNR was high, the improvements according to the strategies were leveled.

The reinjection factor α improved the phoneme recognition (Figure 16.6). It is interesting to point out that the best results were always obtained with α = 40% in PCRP recognition.

About localization, reinjection favored the beam strategy but lowered the PCRPs obtained with the DOEM algorithm (Figure 16.5). Consequently, α improved the perception results PCs (PCRPs and PCLs) with the beam processing, which is based on the temporal properties of the signal, in both localization and recognition.

If we consider spectrum processing (Doerbecker), α lowered the source localization ability with DOEM and improved the phoneme recognition. Using DOEM processing, the choice seems to be that either we want to recognize or we want to localize—improving one reduced the other. For DOS, the results were more even with α for the localization and similar to DOEM for phoneme recognition (improvement), compared to VOC.

4.3.2 Noise angle

The noise angle (Table 16.3) did not change the behavior drastically in all the conditions. Nevertheless, it may be seen that results were slightly better when the noise was stimulating the right ear rather than to the left ear (θ > 0). Is it linked to the brain hemisphere preference? The noise reaching the right ear goes mostly to the left hemisphere, which is more specialized in terms of language. The left brain may be more efficient to separate noise and speech. The ear preference is an interesting issue (Poeppel, 2003; Saoud et al., 2012).