Statistical Analysis of the Multichannel Wiener Filter Using a Bivariate Normal Distribution for Sample Covariance Matrices

Journal article


Publication Details

Author(s): Zheng C, Deleforge A, Li X, Kellermann W
Journal: IEEE/ACM Transactions on Audio, Speech and Language Processing
Publication year: 2018
Volume: 26
Journal issue: 5
Pages range: 951-966
ISSN: 2329-9290
eISSN: 2329-9304
Language: English


Abstract


This paper studies the statistical performance of the multichannel Wiener filter (MWF) when the weights are computed using estimates of the sample covariance matrices of the noisy and the noise signals. It is well known that the optimal weights of the minimum variance distortionless response beamformer are only determined by the noisy sample covariance matrix or the noise sample covariance matrix, while those of the MWF are determined by both of them. Therefore, the difficulty increases dramatically in statistically analyzing the MWF when compared to analyzing the MVDR, where the main reason is that expressing the general joint probability density function (p.d.f.) of the two sample covariance matrices presented a Hitherto unsolved problem, to the best of our knowledge. For a deeper insight into the statistical performance of the MWF, this paper first introduces a bivariate normal distribution to approximately model the joint p.d.f. of the noisy and the noise sample covariance matrices. Each sample covariance matrix is approximately modeled by a random scalar multiplied by its true covariance matrix. This approximation is designed to preserve both the bias and the mean squared error of the matrix with respect to a natural distance on covariance matrices. The correlation of the bivariate normal distribution, referred to as the sample covariance matrices intrinsic correlation coefficient, captures all second-order dependencies of the noisy and the noise sample covariance matrices. By using the proposed bivariate normal distribution, the performance of the MWF can be predicted from the derived analytical expressions and many interesting results are revealed. As an example, the theoretical analysis demonstrates that the MWF performance may degrade in terms of noise reduction and signal-to-noise-ratio improvement when using more sensors in some noise scenarios.



FAU Authors / FAU Editors

Deleforge, Antoine
Professur für Nachrichtentechnik
Kellermann, Walter Prof. Dr.-Ing.
Professur für Nachrichtentechnik
Zheng, Chengshi
Lehrstuhl für Multimediakommunikation und Signalverarbeitung


External institutions
Institute of Acoustics, Chinese Academy of Sciences (CAS)


How to cite

APA:
Zheng, C., Deleforge, A., Li, X., & Kellermann, W. (2018). Statistical Analysis of the Multichannel Wiener Filter Using a Bivariate Normal Distribution for Sample Covariance Matrices. IEEE/ACM Transactions on Audio, Speech and Language Processing, 26(5), 951-966. https://dx.doi.org/10.1109/TASLP.2018.2800283

MLA:
Zheng, Chengshi, et al. "Statistical Analysis of the Multichannel Wiener Filter Using a Bivariate Normal Distribution for Sample Covariance Matrices." IEEE/ACM Transactions on Audio, Speech and Language Processing 26.5 (2018): 951-966.

BibTeX: 

Last updated on 2018-08-08 at 02:17