Performance Analysis of Multichannel Wiener Filter-Based Noise Reduction in Hearing Aids Under Second Order Statistics Estimation Errors

Abstract

The speech distortion weighted multichannel Wiener filter (SDW-MWF) is a promising multi-microphone noise reduction technique, in particular for hearing aid applications. Its benefit over other single- and multi-microphone techniques has been shown in several previous contributions, theoretically as well as experimentally. In theoretical studies, it is usually assumed that there is a single target speech source. The filter can then be decomposed into a conceptually interesting structure, i.e., into a spatial filter (related to other known techniques) and a single-channel postfilter, which then also allows for a performance analysis. Unfortunately, it is not straightforward to make a robust practical implementation based on this decomposition. Instead, a general SDW-MWF implementation, which only requires a (relatively easy) estimation of speech and noise correlation matrices, is mostly used in practice. This paper features a theoretical study and experimental validation on a binaural hearing aid setup of this standard SDW-MWF implementation, where the effect of estimation errors in the second-order statistics is analyzed. In this case, and for a single target speech source, the standard SDW-MWF implementation is found not to behave as predicted theoretically. Second, two recently introduced alternative filters, namely the rank-one SDW-MWF and the spatial prediction SDW-MWF, are also studied in the presence of estimation errors in the second-order statistics. These filters implicitly assume a single target speech source, but still only rely on the speech and noise correlation matrices. It is proven theoretically and illustrated through experiments that these alternative SDW-MWF implementations behave close to the theoretical optimum, and hence outperform the standard SDW-MWF implementation.

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Katholieke Universiteit Leuven
Departement ElektrotechniekESAT-SISTA/TR 10-81
Performance analysis of multichannel Wiener filter based
noise reduction in hearing aids under second order
statistics estimation errors1
Bram Cornelis2, Marc Moonen2, Jan Wouters3
Published in IEEE Transactions on
Audio, Speech and Language Processing,
Vol. 19, No. 5, July 2011
1This report is available by anonymous ftp from ftp.esat.kuleuven.ac.be in
the directory pub/sista/bcorneli/reports/IEEETranASL MWFperf.pdf.
10.1109/TASL.2010.2090519. (c) 2010 IEEE. Personal use of this material is
permitted. Permission from IEEE must be obtained for all other uses, in any
current or future media, including reprinting/republishing this material for ad-
vertising or promotional purposes, creating new collective works, for resale or
redistribution to servers or lists, or reuse of any copyrighted component of this
work in other works.
DOI:
2K.U.Leuven,
Arenberg 10,
16 321970,
bram.cornelis@esat.kuleuven.ac.be.
grant of the Institute for the Promotion of Innovation through Science and
Technology in Flanders (IWT-Vlaanderen). This research work was carried
out at the ESAT Laboratory of Katholieke Universiteit Leuven in the frame
of the Belgian Programme on Interuniversity Attraction Poles, initiated by
the Belgian Federal Science Policy Office IUAP P6/04 (DYSCO, ‘Dynamical
systems, control and optimization’, 2007-2011), Concerted Research Action
GOA-MaNet and research project FWO nr.
and network design for wireless acoustic sensor networks’).
responsibility is assumed by its authors.
Dept.
3001 Leuven,
WWW:
of Electrical
Belgium. Tel. +32 16 321797,
http://www.esat.kuleuven.ac.be/sista,
Bram Cornelis is funded by a Ph.D.
Engineering(ESAT),Kasteelpark
Fax +32
E-mail:
G.0600.08 (’Signal processing
The scientific
3K.U.Leuven, Dept. of Neurosciences, ExpORL, Herestraat 49/721, 3000 Leu-
ven, Belgium.

Page 2

Abstract
The Speech Distortion Weighted Multichannel Wiener Filter (SDW-MWF)
is a promising multi-microphone noise reduction technique, in particular for
hearing aid applications. Its benefit over other single and multi-microphone
techniques has been shown in several previous contributions, theoretically
as well as experimentally. In theoretical studies, it is usually assumed that
there is a single target speech source. The filter can then be decomposed
into a conceptually interesting structure, i.e. into a spatial filter (related
to other known techniques) and a single-channel postfilter, which then also
allows for a performance analysis. Unfortunately, it is not straightforward
to make a robust practical implementation based on this decomposition.
Instead, a general SDW-MWF implementation, which only requires a (rel-
atively easy) estimation of speech and noise correlation matrices, is mostly
used in practice. This paper features a theoretical study and experimen-
tal validation on a binaural hearing aid setup of this standard SDW-MWF
implementation, where the effect of estimation errors in the second order
statistics is analyzed. In this case, and for a single target speech source, the
standard SDW-MWF implementation is found not to behave as predicted
theoretically. Second, two recently introduced alternative filters, namely the
rank-one SDW-MWF and the spatial prediction SDW-MWF, are also stud-
ied in the presence of estimation errors in the second order statistics. These
filters implicitly assume a single target speech source, but still only rely on
the speech and noise correlation matrices. It is proven theoretically and
illustrated through experiments that these alternative SDW-MWF imple-
mentations behave close to the theoretical optimum, and hence outperform
the standard SDW-MWF implementation.

Page 3

IEEE TRANSACTIONS ON AUDIO, SPEECH AND LANGUAGE PROCESSING1
Performance analysis of multichannel Wiener
filter based noise reduction in hearing aids
under second order statistics estimation errors
Bram Cornelis*, Student Member, IEEE,
Marc Moonen, Fellow, IEEE
Katholieke Universiteit Leuven
Department of Electrical Engineering (ESAT–SCD)
Kasteelpark Arenberg 10, B-3001 Leuven, Belgium
Tel: +32/16/321927
E-mail: bram.cornelis@esat.kuleuven.be;
marc.moonen@esat.kuleuven.be
Jan Wouters
Katholieke Universiteit Leuven
Dept. of Neurosciences, ExpORL
Herestraat 49/721, 3000 Leuven, Belgium
E-mail: jan.wouters@med.kuleuven.be
Copyright (c) 2010 IEEE. Personal use of this material is permitted. However, permission to use this material for any other
purposes must be obtained from the IEEE by sending a request to pubs-permissions@IEEE.org.
B. Cornelis is funded by a Ph.D. grant of the Institute for the Promotion of Innovation through Science and Technology in
Flanders (IWT-Vlaanderen).
This research work was carried out at the ESAT Laboratory of Katholieke Universiteit Leuven in the frame of the Belgian
Programme on Interuniversity Attraction Poles initiated by the Belgian Federal Science Policy Office IUAP P6/04 (DYSCO,
‘Dynamical systems, control and optimization’, 2007-2011), Concerted Research Action GOA-MaNet and research project FWO
nr. G.0600.08 (’Signal processing and network design for wireless acoustic sensor networks’). The scientific responsibility is
assumed by its authors.
May 16, 2011DRAFT

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IEEE TRANSACTIONS ON AUDIO, SPEECH AND LANGUAGE PROCESSING2
Abstract
The Speech Distortion Weighted Multichannel Wiener Filter (SDW-MWF) is a promising multi-
microphone noise reduction technique, in particular for hearing aid applications. Its benefit over other
single and multi-microphone techniques has been shown in several previous contributions, theoretically
as well as experimentally. In theoretical studies, it is usually assumed that there is a single target speech
source. The filter can then be decomposed into a conceptually interesting structure, i.e. into a spatial
filter (related to other known techniques) and a single-channel postfilter, which then also allows for a
performance analysis. Unfortunately, it is not straightforward to make a robust practical implementation
based on this decomposition. Instead, a general SDW-MWF implementation, which only requires a
(relatively easy) estimation of speech and noise correlation matrices, is mostly used in practice. This
paper features a theoretical study and experimental validation on a binaural hearing aid setup of this
standard SDW-MWF implementation, where the effect of estimation errors in the second order statistics
is analyzed. In this case, and for a single target speech source, the standard SDW-MWF implementation
is found not to behave as predicted theoretically. Second, two recently introduced alternative filters,
namely the rank-one SDW-MWF and the spatial prediction SDW-MWF, are also studied in the presence
of estimation errors in the second order statistics. These filters implicitly assume a single target speech
source, but still only rely on the speech and noise correlation matrices. It is proven theoretically and
illustrated through experiments that these alternative SDW-MWF implementations behave close to the
theoretical optimum, and hence outperform the standard SDW-MWF implementation.
Index Terms
Noise reduction, speech enhancement, microphone arrays, hearing aids, binaural hearing aids, multichan-
nel Wiener filtering
I. INTRODUCTION
A major problem for hearing aid users is the degradation of their speech understanding in a noisy
environment. Sensorineural hearing loss is most often accompanied by a loss of spectral and temporal
resolution in the auditory processing, which results in a SNR loss of about 4-10 dB [1], [2]. Noise reduc-
tion in hearing aids has therefore been an active area of research for several years. Besides hearing aids,
noise reduction also has many other applications such as hands-free communications and teleconferencing.
The first noise reduction techniques applied in hearing aids were single-microphone techniques [3].
Although these techniques may improve the SNR, this comes at the price of a high speech distortion [4].
Maybe as a consequence, single-microphone noise reduction techniques do not seem to increase speech
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IEEE TRANSACTIONS ON AUDIO, SPEECH AND LANGUAGE PROCESSING3
intelligibility significantly [1], [5]. The noise reduction does increase the overall listening comfort, so that
hearing aid users generally find single-microphone noise reduction useful [5]. Single-microphone noise
reduction is therefore usually included as a postfiltering stage.
In order to achieve the initial goal of increasing the speech intelligibility, hearing aids are fitted with
multiple microphones, so that spatial information can be utilized in addition to temporal and spectral
information to reduce the noise. Theoretically, a SNR improvement can then be achieved without distorting
the target speech signal [4]. In practice, a speech intelligibility improvement can indeed be obtained [1],
unlike with single-microphone techniques.
A popular multi-microphone noise reduction technique is the linearly constrained minimum variance
(LCMV) beamformer. The LCMV minimizes the output power while imposing linear constraints on
the beamformer response towards a target direction. The problem can be transformed into an easier
unconstrained optimization problem by using the Generalized Sidelobe Canceller (GSC) technique [6].
The initial approach assumed freefield propagation, but this was extended into arbitrary transfer functions
in the Transfer Function GSC (TF-GSC) technique [7]. For hearing aid applications, the GSC technique
may be viewed as the current state of the art, and it leads to a significant benefit in certain scenarios [8].
However, it relies on a priori knowledge or assumptions about the target signal location and microphone
characteristics. These assumptions are usually violated in practice so that performance may degrade
significantly [9].
A different class of multi-microphone noise reduction techniques is based on Multichannel Wiener
Filtering (MWF) [10]–[12], which is basically a generalization of single-channel procedures [3], [13]. The
MWF produces a minimum-mean-square-error (MMSE) estimate of the speech component in a reference
microphone signal, by exploiting speech and noise correlation matrices. To provide an explicit tradeoff
between speech distortion and noise reduction, the Speech Distortion Weighted Multichannel Wiener Filter
(SDW-MWF) was also proposed in [10]–[12]. This extension is equivalent to applying additional single-
channel noise reduction to the spatial filter output, which, as already mentioned, is generally considered
useful by hearing aid users. As the SDW-MWF does not require a priori knowledge or assumptions about
the target signal location and microphone characteristics unlike the GSC, it is expected to be more robust,
which was indeed demonstrated in [9]. A frequency-domain adaptive implementation of the SDW-MWF
was also proposed in [12]. This approach is computationally advantageous as every frequency bin can
be processed separately. The SDW-MWF thus offers a robust and computationally efficient alternative to
the GSC.
In the near-future, the number of microphone signals available in a hearing aid will increase as a
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