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Distributed Speech Presence Probability Estimator in Fully Connected Wireless Acoustic Sensor Networks

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Abstract

This paper presents a Gaussian-based distributed speech presence probability (DSPP) estimator which is applied in fully connected wireless acoustic sensor networks (WASNs). In WASNs, we are primarily interested in optimally utilizing all available information of recorded signals. In this work, under the Gaussian statistical assumption of signals, each node computes the DSPP using its own local signals along with the compressed signals from other nodes. We evaluate the effect of DSPP estimation on noise reduction from both the simulated and the real recorded signals. The performance of the proposed DSPP estimator is compared to that of local SPP estimation, where each node only uses its noisy signals, and to that of centralized SPP estimation, where each node uses all recorded noisy signals of the whole network. It is shown that the proposed method exhibits good performance, while the computational complexity is considerably reduced.

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Notes

  1. The ratio of clean signal variance to noise signal variance.

  2. A priori knowledge, indicating whether speech segments are more probable or silence.

  3. The ratio of noisy signal variance to noise signal variance

  4. Central limit theorem states that when independent random variables are added, the summation tends toward a Gaussian distribution regardless of the distribution of the original variables.

  5. In Souden et al. [32], it is shown that when the noise is a mixture of both coherent point source interference (e.g., non Gaussian babble, pink or factory noises) and non-coherent additive white noise, the SPP estimator is theoretically able to achieve an estimate close to one when speech is present. Interested readers are referred to Souden et al. [32] for theoretical proof.

  6. In the local case, there is no cooperation and consequently no transmitted signals between nodes, and each node only uses the recorded signals by its own microphones. Indeed, in this case instead of \( {\mathbf {y}}, {\varvec{\Phi }}_{{\mathbf {v}}},\) and \({\varvec{\Phi }}_{{\mathbf {x}}} \) in (14), the information of each node, i.e., \( {\mathbf {y}}_{k}, {\varvec{\Phi }}_{{\mathbf {v}}_{k}},\) and\( {\varvec{\Phi }}_{{\mathbf {x}}_{k}} \), are utilized to compute the SPP. Since the procedure is similar to that of CSPP and it is only required to replace the parameters, we explain this case briefly.

  7. Since the first microphone in the first node was considered as the reference microphone, the input full-band SNRs is computed for this microphone.

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Acknowledgements

We would like to express our appreciation to Iran National Science Foundation (INSF) for supporting this work under Grant number 96000455. We are also grateful to the Department of Medical Physics and Acoustics, University of Oldenburg, for allowing access to their recorded data.

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  1. Electrical Engineering Department, Yazd University, Yazd, Iran

    Raziyeh Ranjbaryan & Hamid Reza Abutalebi

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Correspondence to Hamid Reza Abutalebi.

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Ranjbaryan, R., Abutalebi, H.R. Distributed Speech Presence Probability Estimator in Fully Connected Wireless Acoustic Sensor Networks. Circuits Syst Signal Process 39, 6121–6141 (2020). https://doi.org/10.1007/s00034-020-01452-4

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