Speech enhancement aims at noise reduction and extracting the desired target speaker from the noisy mixture in a complex recording environment. Microphone array (MA) beamforming is commonly used in almost all acoustic equipment, such as hearing aids, surveillance device, teleconference system, mobile phone, voice controlled, smart home. MA beamforming techniques use the a priori information about the properties of surrounding environment, the designed MA distribution, the direction of arrival (DoA) of interest useful signal to achieve a better noise reduction and speech enhancement at the same time. Generalized Sidelobe Canceller (GSC) beamformer eficiently remove background noise while saving the original clean speech component in an annoying recording scenario. However, due to undetermined factors, the overall GSC beamformer's performance often degraded in realistic recording schemes. In this paper, the authors proposed exploiting the Bayesian estimator of short time spectral amplitude (STSA) to gain the amplitude of beamformer's output signal. The results obtained showed that the suggested method can use the Bayesian estimator to improve the speech quality in the term of the signal-to-noise ratio (SNR) from 7.9 to 15.3 dB and reduce the speech distortion to 14.1 dB. The numerical results indicate the advantage of the author's approach to overcome the drawback of GSC beamformer in real-life application as compared to state-of-the-art solutions.
Nowadays, the perceptual metric listener, the speech quality or speech intelligibility are afected by
numerous types of noise, as shown in figure 1. Speech enhancement aims at the precise estimation of
the clean speech component from its noisy mixture of interference, background noise, non-directional
noise source, competing talker in an adverse environment. The single-channel algorithm is often based
on the spectral subtraction method, which has the simplicity of performing. However, this approach
leads to speech distortion in complex and annoying recording situations, where the non-stationary noise
can not be exactly calculated. Therefore, the microphone array (MA) beamforming [
GSC beamformer [
Unfortunately, due to the complex undetermined environment, the diferent MA sensitivities, the error of MA displacement, the inaccurate calculation of DoA seriously afect the GSC beamformer’s evaluation, that decreases the speech quality, speech intelligibility and listener perception.
In this article, the author proposes using the STSA estimator for gaining the output signal to recover
the obtained signal approximate to the original speech signal. Ephraim and Malah [
The rest of this contribution is organized as follows. The first section introduces the problem of speech enhancement and the MA beamforming technology. The section 2 presents the principal working of GSC beamformer in the frequency-domain. The author proposed the using of STSA estimator for improving the GSC beamformer’s evaluation in reducing the speech distortion. The perspective experiment was conducted in section 4. The section 5 concludes the numerical results and the author’s direction of research in the future.
In this section, the author presents the scheme of traditional structure of GSC beamformer [
The representations of observed MA signals in the short-time Fourier transform (STFT) can be expressed as follows: 1(, ) =(, )Φ + 1(, ), 2(, ) =(, )− Φ + 2(, ), (1) (2) where = 2 and , denote the current considered frequency and frame; (, ) is the original speech component; 1(, ) and 2(, ) present the additive noise component, unwanted interferences; Φ = 0 cos( ), 0 = / and is the range between two microphones; = 343 (m/s) is the sound speed propagation in the air; is the direction of arrival of useful talker relative to the DMA2 geometry. (3) (4) (5) (6) (7) (8)
The traditional GSC beamformer own three parts: (1) the fixed beamformer (FBF), which concerns the steerable beampattern towards the direction of sound source, (2) the block matrix (BM) that aims at suppressing the speech component to achieve the only noise, (3) adaptive noise canceller (ANC) that it used to extract the target speaker from FBF’s output with using BM’s output as reference signal. The upper branch usually implements delay and sum beamformer and lower branch uses signal subtraction.
The upper branch signal (, ) and lower branch signal (, ) can be calculated as: (, ) = (, ) = 1(, )− Φ + 2(, )Φ
2 1(, )− Φ − 2(, )Φ 2 , .
The auto-cross power spectral densities (PSD) between (, ), (, ) can be derived in the following way: (, ) = (1 − ) (, − 1) + (, )*(, ) (, ) = (1 − ) (, − 1) + (, )*(, ) where is a smoothing parameter, which is in the range of {0..1} and * denote the conjugate operator.
The determined Wiener filter’s coeficient yields as: (, ) = (, ) (, ) .
The obtained signal by applying GSC beamformer is given by:
(, ) = (, ) − (, ) * (, ).
Because of the undetermined recording conditions, as well as the complex and annoying environment,
the displacement of MA’s configuration, the error of sampling rate, the inaccurate estimation of preferred
steering vector, the diference of microphone quality, the overall GSC beamformer’s performance in
adverse noisy situations often degraded. There is still existing speech distortion, unacceptable noise level
or musical noise, which decreases the speech quality for perceptual metric listener. Consequently, in
the next section, the author proposes using the observed phase diference of MA to form an appropriate
gain function to preserve the clean speech data at the GSC beamformer’s output.
where ( |, ) denotes the captured MA signals conditional PDF and () expresses the STSA prior
distribution and means for the possible value of spectral amplitude. As in single-channel approach
the STSA prior, the presented formulation of these factors can be derived as:
[
, ( |, ) = ︂(
1 2 exp − 2 | − |2 ,
︂) () =
︃( 2 2 exp − 2 2 )︃ ,
In the broadside recording situation, the observed noisy MA signals can be represented as: (, ) = (, ) + (, ), = 1, 2, ..., at the current frequency-frame (, ). = 2 . The speech spectral component (, ) can be expressed as (, ) = (, ) (,) with (, ) ≥ {[− ]} the spectral phase, is the number of microphones. 0 being the spectral amplitude, , ∈
From the received noisy spectral (, ), STSA estimator calculates the original amplitude (, ).
By applying the Bayesian rule [
=1 ︃( ∑︁ 2, cos( − ,) − 2 − 2, )︃
. (13) 2
The described equation of MMSE STSA estimator is given by: where (.) expresses the Gaussian error and =
1 2
+ ∏︁
1 =1 2, , = − =1 2, ∑︁ , cos( − ,).
With the introduced MMSE STSA estimator, the author’s proposed gain function for enhancing GSC beamformer’s performance as: − 2 2 + 1 2 − ︁( 2 2+ )︁ √︁ 5 exp ︁( 2 )︁ (︁ 1 − ︁( ︁) √
︁( ︁) √︁ exp 2 ︁( 2 )︁ (︁ 1 − ︁( ︁) √ (, ) = ︁( ˆ )︁ 2
1 (, )Φ− 1 (,)(, ) where is the Hermitian operator, (, ) = [Φ − Φ ] and Φ (, ) = { (, ) (, )} is the covariance matrix of observed MA signals.
And the enhanced GSC beamformer’s output signal is given by:
ˆ (, ) = (, ) × (, ).
The method proposed by the author uses the additive gain function, which based on the STSA estimator of phase diference. Therefore, it is referred as aaSTSA. In the next section, an experiment to verify the efectiveness of the aaSTSA technique in realistic recording scenario is described. = (17)
In this section, the author illustrate the performance of the proposed multi-channel microphone speech enhancement technique for reducing the speech distortion, improving the speech quality and speech intelligibility of GSC beamformer’s output signal.
The author chooses the clean speech from the TIMIT database [
The observed MA signals are presented in figure 6.
By applying coGSbe, the output signal is shown in figure 7.
It is seen from figure 9 that, the speech distortion occurred, due to the diferent microphone mismatches, the inaccurate estimation of preferred DoA of target talker, the displacement of MA significantly degrade the GSC beamformer. As a result, the amplitude of output signal at frames, where the speech component exists, was degraded.
Using the additive gain function, which is based on the amplitude Bayesian estimator, the final output signal is given in figure 8.
The comparison of energy and speech quality between the original MA signals, the signals processed by coGSbe, and aaSTSA was shown in figure 9 and table 1.
Based on the assumption that, the speech component is distributed as the Gamma distribution and
the additive noise is distributed according to the Gaussian model, the WADA (Waveform Amplitude
Distribution Analysis) SNR [
From the noisy mixture of MA signals, the suggested method aaSTSA calculated the a priori information about the amplitude of the original speech signal for forming an efective gain function to reduce speech distortion to 14.1 dB, recover the amplitude of output signal and increase the speech quality from 7.9 to 15.3 dB. Compared to coGSbe, aaSTSA allows obtaining better speech enhancement in preserving the speech component while suppressing background noise. The illustrated experiment was performed in the realistic living room with MA configuration broadside. The numerical results demonstrate that, the author’s approach can be integrated into other multi-channel signal processing to solve several complicated problems of MA beamforming.
In this paper, the author have proposed the exploiting STSA estimator, which uses the spectral phase estimation for improving the GSC beamformer’s speech enhancement by adding a gain function for recovering clean speech components. The suggested method addressed the problem of speech distortion in realistic annoying recording scenarios for increasing the SNR ratio. In addition to providing superior evaluation in comparison with the traditional GSC beamformer, the author’s proposed method is found to enhance performance in a complex noisy environment. The efectiveness of the suggested method allows decreasing the speech distortion to 14.1 dB and improves the speech quality from 7.9 to 15.3 dB. From the numerical results, the suggested technique can be installed in various types of acoustic equipment to obtain better noise reduction, speech enhancement. The future work will be aimed at enhancing signal processing by incorporating STSA estimators with diferent types of noise properties. Declaration on Generative AI: The author have not employed any generative AI tools.