Article
A ClippingBased SelectiveTap Adaptive Filtering Approach to Stereophonic Acoustic Echo Cancellation
Tarbiat Modares Univ., Tehran, Iran
IEEE Transactions on Audio Speech and Language Processing (Impact Factor: 2.48). 09/2011; 19(6):1826  1836. DOI: 10.1109/TASL.2010.2102752 Source: IEEE Xplore
Fulltext
Available from: Mojtaba Lotfizad1826 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 19, NO. 6, AUGUST 2011
A ClippingBased SelectiveTap Adaptive
Filtering Approach to Stereophonic
Acoustic Echo Cancellation
Mehdi Bekrani, Andy W. H. Khong, Member, IEEE, and Mojtaba Lotﬁzad
Abstract—Stereophonic acoustic echo cancellation remains one
of the challenging areas for tele/videoconferencing applications.
However, the existence of high interchannel coherence between the
two input signals for such systems leads to considerable degrada
tion in misalignment convergence of the adaptive ﬁlters. We pro
pose a new algorithm for improving the convergence performance
and steadystate misalignment by considering robustness to the
source position in the transmission room. We achieve this by ex
ploiting the inherent decorrelating properties of selectivetap adap
tive ﬁltering as well as employing a variable clipping threshold
for the unselected taps. Simulation results using colored noise and
speech signals show an improvement over existing algorithms both
in terms of convergence rate as well as steadystate normalized mis
alignment.
Index Terms—Center clipping, convergence rate, interchannel
coherence, partial updating, selectivetap, stereophonic acoustic
echo cancellation (SAEC).
I. INTRODUCTION
T
HERE has been increasing interest in employing stereo
phonic audio communication systems for video/telecon
ferencing, home entertainment, and Elearning applications
in order to achieve better perception of sound [1], [2]. Such
systems have become increasingly popular since a stereophonic
audio system provides spatial information, leading to better
perception of the transmitted speech as well as improving the
ambience of the transmission room. These systems mitigate,
to a certain extent, the cocktail party problem that exists in
a multiparty conferencing scenario [2]. One of the problems
that should be addressed in such systems is the cancellation
of stereophonic acoustic echo using a pair of adaptive ﬁlters.
Stereophonic acoustic echo cancellation (SAEC) has issues
that are considerably more challenging to overcome than the
Manuscript received October 09, 2009; revised June 18, 2010; accepted
November 29, 2010. Date of publication February 10, 2011; date of current
version June 03, 2011. This work was supported in part by the Singapore
National Research Foundation Interactive Digital Media R&D Program under
research grant NRF2008IDMIDM004010 and in part by the Research Insti
tute for ICT. The associate editor coordinating the review of this manuscript
and approving it for publication was Prof. Sharon Gannot.
M. Bekrani was with Tarbiat Modares University, Tehran, Iran. He is now with
the School of Electrical and Electronic Engineering, Nanyang Technological
University, Singapore 639798 (email: mbekrani@ntu.edu.sg).
A. W. H. Khong is with Nanyang Technological University, Nanyang Tech
nological University, Singapore 639798 (email: andykhong@ntu.edu.sg).
M. Lotﬁzad is with the Department of Electrical and Computer Engineering,
Tarbiat Modares University, P.O. Box 14115143, Tehran, Iran (email: lot
ﬁzad@modares.ac.ir).
Digital Object Identiﬁer 10.1109/TASL.2010.2102752
monophonic case [3]. The fundamental problem is the poor
mismatch between adaptive ﬁlter coefﬁcients and the receiving
room acoustic impulse responses. It has been shown [4] that, in
a practical scenario, the adaptive ﬁlter misalignment converges
poorly, leading to a performance degradation. The misalign
ment problem is caused by the high interchannel coherence that
exists between the two transmitted stereo signals [4].
A variety of methods have been proposed to address the mis
alignment problem. These methods revolve around reducing
the interchannel coherence between the two transmitted signals.
One of the ﬁrst methods involved adding controlled quantities
of independent noise to each input channel [5], or modulating
them [6]. These two approaches are however not feasible since
distortion can be heard even when the added noise level is very
low [7]. Another approach involves the use of comb ﬁltering
[8], where frequency components of the left and right channels
are separated in order to reduce the interchannel coherence.
Although this method improves the performance of the adap
tive ﬁlters, it degrades the quality of the stereophonic sound,
especially at lower frequencies.
To address the disadvantages of the methods described above,
a preprocessor has been proposed to add a nonlinear (NL) func
tion of the transmitted signal in each channel to the signal it
self [4], [9]. This method employs a halfwave rectiﬁer and is
attractive in terms of improving the misalignment behavior of
the adaptive ﬁlters as well as its simplicity in implementation.
Although less distortion was introduced compared to the other
techniques discussed above, this distortion is still found to be
objectionable in some cases for music applications [4], [10].
An adaptive nonlinearity control was subsequently proposed to
maintain the desired level of misalignment and to minimize the
audio distortion [11].
It is apparent by now that algorithms proposed for SAEC
need to decorrelate the transmitted signals without degrading
the quality of the speech signals or destroying the stereophonic
image of the transmission room. In view of this, the use of time
varying allpass ﬁltering of the stereophonic signals has been
proposed [12] with the aim of signal decorrelation while main
taining the stereophonic perception. The use of psychoacoustic
properties to reduce perceived distortion while achieving signal
decorrelation has also been proposed, including the use of spec
trally shaped random noise [7], [13], gain controlled phase dis
tortion [14] and the combination of comb ﬁltering and allpass
ﬁltering with respect to the masking effect [15]. These methods
exploit a perceptual property of the human auditory system,
called “noise masking.”
15587916/$26.00 © 2010 IEEE
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BEKRANI et al.: CLIPPINGBASED SELECTIVETAP ADAPTIVE FILTERING APPROACH TO SAEC 1827
More recent advances in SAEC research involve a decorre
lation procedure for the adaptive weight update [10], [16]–[19].
These approaches decorrelates the tapinput vectors of the adap
tive ﬁlters as opposed to decorrelating the transmitted signals.
Among these methods, the exclusivemaximum (XM) tapselec
tion algorithm proposed in [17] appeared to be an attractive solu
tion. This algorithm achieves update signal decorrelation by en
suring that only an exclusive set of ﬁlter coefﬁcients from each
channel is selected for adaptation. In order to reduce any degra
dation in convergence performance due to this subselection pro
cedure, the XM tapselection strategy further ensures that the
energies of these exclusive tap inputs are maximized. The XM
tap selection has been incorporated with the NL halfwave rec
tiﬁer and the resulting XMNL normalized leastmeansquare
(XMNLNLMS) algorithm has been shown to achieve a higher
rate of misalignment convergence compared to that of nonlinear
NLMS (NLNLMS) [17].
We propose to further improve the convergence performance
of the XM tapselection algorithm. This motivation is derived
from the degradation in convergence performance of the XM
tapselection algorithm when the interchannel coherence be
tween the two tapinput vectors is relatively low. This can occur,
for example, when the source in the transmission room is lo
cated away from the centroid of the stereophonic microphone
pair. We note that the robustness issue of XMNLNLMS to
the source position has not been investigated and that, in this
work, we present insight into this problem. Utilizing this new
knowledge, we propose to improve the misalignment conver
gence of XMNLNLMS by employing a centerclipping algo
rithm so that the low interchannel coherence and maximization
of tapinput energy criteria can be jointly optimized. The pro
posed algorithm ensures that the misalignment convergence and
steadystate misalignment of the adaptive ﬁlters will be robust
to the source position in the transmission room.
In [7] and references therein, the authors evaluated the adap
tive signal decorrelation ﬁlter as a preprocessor and reported
that
complete decorrelation in the frequency domain cannot be
achieved unless one or both of the stereophonic signals are zero
at every frequency. This process is undesirable since it destroys
the stereophonic image of the transmitted signals, which is im
portant to the listeners in the receiving room. Therefore, they
concluded that complete decorrelation is not applicable in prac
tice. Our proposed method, as opposed to the technique dis
cussed in [7], does not apply decorrelation ﬁltering to the trans
mitted signals. We instead operate on the tapinput vector of
the adaptive ﬁlters. Therefore, similar to XMNLNLMS, the
stereophonic image is preserved. We also note that the decor
related tapinput vectors of both algorithms may prevent some
of the adaptive ﬁlter coefﬁcients from adaptation in some iter
ations. However, this effect will not signiﬁcantly degrade the
convergence of weights since any signiﬁcant reduction in the in
terchannel coherence due to our centerclipping approach will
bring about an improvement in convergence rate. It is also im
portant to note that, similar to the approach in [17], the use of the
NL preprocessor is required to provide a solution to the illposed
SAEC problem, while our proposed centerclipping approach
improves the convergence rate and robustness of XMNLNLMS
to the source position.
Fig. 1. Stereophonic acoustic echo cancellation for teleconferencing applica
tion.
II. R
EVIEW OF
STEREOPHONIC
ACOUSTIC ECHO
CANCELLATION
Fig. 1 shows the stereophonic acoustic echo canceller. For
simplicity, we consider only one microphone in the receiving
room, since similar analysis can be applied to the other channel
[4]. Microphones in the transmission room receive signals pro
duced by the sound source
via acoustic impulse responses
and giving transmitted signals and , re
spectively, where
for Channel and is the length of the transmission room im
pulse responses, while
is deﬁned as the transpose operator.
The transmitted signal to the receiving room for Channel
can
then be expressed as
(1)
where
. These
signals produce an echo
in the receiving room given by
(2)
where
is
the
th channel receiving room impulse response and
is the
th channel tapinput vector while is the length of .
Similar to singlechannel AEC, adaptive ﬁlters are employed
to estimate
and . In this paper, we assume, similar
to that of [4], [17], that the adaptive ﬁlters are each of length
,
which is of the same length as that of
and . For real
istic applications where the adaptive ﬁlters are shorter than that
of
, residual echo will be transmitted back to the transmis
sion room due to the unmodeled “tails” of
.
The error between the echo and its estimate can then be ex
pressed as
(3)
where
, 1, 2, is
the vector of adaptive ﬁlter coefﬁcients for the
th channel.
A. Nonlinear Normalized LeastMeanSquare Algorithm
In order to efﬁciently reduce
, adaptive algorithms are
employed for SAEC. Deﬁning
as the expectation operator,
the NLMS algorithm [20] is the result of minimizing
,
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1828 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 19, NO. 6, AUGUST 2011
and is popular because of its simplicity in computational efﬁ
ciency and ease of implementation. The twochannel NLMS al
gorithm is expressed as
(4)
where
and
are the concatenated twochannel
tapinput vector and ﬁlter coefﬁcient vector, respectively, while
is the stepsize, which controls the rate of convergence, and
is a regularization parameter to prevent division by zero.
Unlike singlechannel AEC, estimation of
and
for the stereophonic case is challenging. As shown in [4], when
, the adaptive ﬁlters coefﬁcients is of the form
(5)
where
, 1, 2 are vectors given
that
is appended with zeros and is a scalar
quantity. Equation (5) indicates that multiple solutions exist and
that
and are linearly related to and .
The dependency of
and on these multiple solu
tions due to
and is known as the nonuniqueness
problem. In practical cases where
, the nonuniqueness
problem is mitigated [4]. However, even in such cases, direct ap
plication of the standard adaptive ﬁltering is normally not suc
cessful because
and are highly correlated, giving
rise to an illconditioned system identiﬁcation problem. As a
result, the misalignment convergence of the adaptive ﬁlters is
impaired signiﬁcantly. This degradation is known as the mis
alignment problem [4].
In order to address the misalignment problem, a nonlinear
(NL) preprocessor is proposed [4], [21]. This preprocessor op
erates on
and such that the modiﬁed transmitted
signals
and are given by
(6)
(7)
where
controls the amount of nonlinearity to be added. It has
been shown in [4] that a value of
is a good compromise
between speech quality and misalignment convergence of the
NLMS algorithm.
Due to its simplicity in implementation and the low distortion
introduced, the NL preprocessor has become an intrinsic part of
SAEC and has been incorporated into several recently proposed
algorithms for SAEC [10], [17]. For the remainder of this paper,
the NLMS algorithm employing this NL preprocessing will be
referred to as NLNLMS.
B. ExclusiveMaximum (XM) TapSelection Algorithm
The XMNLNLMS update [17] can be expressed as
(8)
where
1, 2 is the channel index,
is the NLpre
Fig. 2. Locations of the source and the microphone pair in the transmission
room.
processed tapinput vector of the
th channel deﬁned
by (6) and (7),
, while
is a tapselection matrix and
with elements
given by
otherwise
(9)
otherwise
(10)
where
, denote the elemental indices of
and , respectively, and ,
.
As can be seen, the XM algorithm [17] incorporates a tapse
lection scheme that reduces the interchannel coherence by se
lecting exclusive ﬁlter coefﬁcients for updating in each channel.
It is important to note that the selected tap inputs are only used
for updating the coefﬁcients and hence no distortion is intro
duced. However, with any tapselection updating strategy, con
vergence performance of the adaptive ﬁlters will be reduced.
This degradation is then minimized by jointly maximizing the
norm of the selected tap inputs across both channels. The use
of the NL preprocessor is required to provide a solution to the
illposed SAEC problem, while the XM approach improves the
convergence rate of NLNLMS. As a result of this combination,
which we refer to as XMNL, better misalignment convergence
of the adaptive ﬁlter can be achieved. Alternatively, the XM tap
selection can be seen as an effective approach to achieve good
misalignment convergence with lower distortion brought about
by a smaller nonlinearity factor
.
III. E
FFECT OF SOURCE POSITION ON MISALIGNMENT
CONVERGENCE
One of the problems that has yet been considered for
XMNLNLMS is its robustness to the position of the source
in the transmission room. We now illustrate the misalignment
convergence of XMNLNLMS by considering different source
positions. Fig. 2 shows an experimental setup where two mi
crophones are placed at
positions (2.7,2,1.5) m and
(3,2,1.5) m in a room with dimensions 7 m
7m 4m.We
vary the
position of the source starting from the front of the
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BEKRANI et al.: CLIPPINGBASED SELECTIVETAP ADAPTIVE FILTERING APPROACH TO SAEC 1829
Fig. 3. Misalignment convergence of the XMNLNLMS algorithm (solid) for
different positions of the source, as compared to NLNLMS (dashed).
array centroid at m to the front of the right micro
phone at
m. The positions in the receiving room are (3, 2,
1.5) m for the microphone and (2.85, 1.8, 1.6) m and (2.4, 1.1,
1.7) m for the two loudspeakers. For the purpose of illustration,
all room impulse responses are generated synthetically using
the method of images [22] such that
and
samples and these synthetic impulse responses have lengths
that correspond to their reverberation times. At a sampling
rate of
Hz, this corresponds to 23 ms and 36 ms,
respectively. A stationary colored noise source signal
is
obtained by ﬁltering white Gaussian noise through a lowpass
ﬁnite impulse response (FIR) ﬁlter with coefﬁcients given
by
[23] which was chosen to generate a
speechlike spectrum. The convergence of the algorithms is
quantiﬁed by the normalized misalignment
(11)
where
. Fig. 3 shows the misalign
ment convergence of XMNLNLMS averaged over ten indepen
dent trials, for the different source positions. The convergence
performance of NLNLMS for
m, when it is directly
in front of the microphone pair centroid, has been included for
comparison. Additional tests conducted have shown that the
misalignment convergence of NLNLMS for various source po
sitions is comparable to that shown in Fig. 3. A stepsize of
was used for XMNLNLMS, while the stepsize of
NLNLMS was adjusted to
so that its steadystate mis
alignment reaches that of XMNLNLMS. As shown in Fig. 3,
XMNLNLMS outperforms the fullupdate NLNLMS when
the source is directly in front of the microphone pair centroid at
m. On the contrary, the convergence rate of XMNL
NLMS is reduced signiﬁcantly when the source is located away
from the microphone pair centroid such as when
m.
To gain further insight into the degradation in convergence
rate of XMNLNLMS with respect to the source position, we
consider both the interchannel coherence as well as the ratio of
selected tapinput energy to the total tapinput energy.
Fig. 4. Average interchannel coherence of the NLNLMS (dashed) and
XMNLNLMS (solid) algorithms for various positions of the source.
A. Effect of XM Tap Selection on Interchannel Coherence
We ﬁrst investigate the effect of XM tapselection on the in
terchannel coherence for various source positions. We denote
the XM subselected tapinput vector in (8) as
(12)
The interchannel coherence between
and is then
deﬁned by
(13)
where
is the cross power spectrum between and
while is the normalized frequency. For the same condi
tion as in Figs. 3 and 4 shows the mean interchannel coherence
between
and , across different frequencies for var
ious source positions, obtained by averaging over ten indepen
dent trials.
As can be seen, when the source is in front of the microphone
pair centroid
m , the XM tapselection criterion is
utilized efﬁciently to decorrelate input vectors
and ,
giving a low interchannel coherence of 0.43. Due to this efﬁ
cient decorrelation, a good misalignment convergence shown in
Fig. 3 is achieved. For this source location, the modest amount of
degradation due to tap selection does not signiﬁcantly outweigh
the beneﬁts brought about by the reduction in interchannel co
herence due to the exclusivity criterion. Fig. 5(a) shows an ex
ample of the XM selected taps
and in this case. For
clarity, we show only the ﬁrst 80 samples of
and ,
each of length
samples. As can be seen, most of the se
lected taps in the ﬁrst channel correspond to elements in
being greater than zero, whereas for the second channel, most
of the active taps correspond to elements in
being less
than zero. This is due to the intrinsic effect of NL preprocessing,
which increases the magnitude of the positive elements in the
ﬁrst channel and the negative elements in the second channel.
As a result of XM tap selection on
and , low inter
channel coherence of 0.43 is achieved as shown in Fig. 4.
As shown in Fig. 4, the interchannel coherence between
and employing XM tap selection increases from
m to approximately m. To understand this increase
in interchannel coherence even after XM tap selection is ap
plied, Fig. 5(b) shows a plot of
and for m.
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1830 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 19, NO. 6, AUGUST 2011
Fig. 5. Selected tap inputs
and for the XMNLNLMS algorithm
for various source position
. (a)
m. (b)
m. (c)
m.
As can be seen, the effect of NL preprocessing on XM tap se
lection reduces and the similarity between
and in
creases. The increase in interchannel coherence between
and in turn reduces the convergence rate for XMNL
NLMS, as can be seen from Fig. 3.
Fig. 5(c) illustrates
and when the source is in
front of the right microphone at
m. Due to the source
being further away from the left microphone, elements in
have magnitudes much lower than those of . In addition,
it is expected that
differs from . As a result of this
difference, the interchannel coherence is lower for
m
compared to
m, as shown in Fig. 4. It is therefore expected
that the misalignment convergence of XMNLNLMS should in
crease when the source moves from
mto m.
On the contrary, however, the XMNLNLMS convergence rate
continues to reduce with increasing
position, as can be seen
from Fig. 3. In Section IV, we gain better insight into this con
tradictory behavior by studying the effect of XM tap selection
on the energies of the active tap inputs for different source po
sitions.
B. Effect of XM Tap Selection on TapInput Energies
In order to further illustrate how XM tap selection affects the
energies of the tap inputs, we employ the
ratio criterion [17]
deﬁned as
(14)
where
for the XM tap se
lection, with elements deﬁned by (9) and (10). Our intention is
not to show the exact relationship between
and the misalign
ment convergence rate, but to illustrate that the loss of tapinput
energy has an undesirable effect on the convergence rate of the
adaptive ﬁlters. Fig. 6 illustrates how
varies with source po
sition for XMNLNLMS and NLNLMS, obtained by averaging
over all frames in the signal where each frame is calculated using
Fig. 6. Variation of against source position for NLNLMS (dashed) and
XMNLNLMS (solid).
(14). As can be seen, NLNLMS has
for all source po
sitions since all tapinputs are used for weight update. On the
other hand, for XMNLNLMS,
and increases with
position of the source.
We can now see from Figs. 4 and 6 why XMNLNLMS
achieves poorer convergence performance when the source
is far from the centroid of the microphone pair: although the
interchannel coherence is relatively low, the
ratio is not
sufﬁciently high to reduce the degradation in convergence rate
due to tap selection. As a consequence of this conﬂict between
the need to reduce interchannel coherence and maximization
of tapinput energies, the overall result is a reduction in con
vergence rate of XMNLNLMS, as can be seen from Fig. 3.
On the other hand, when
m, the degradation in con
vergence rate due to a reduction in
is offset by a signiﬁcant
reduction in interchannel coherence, as shown in Figs. 6 and
4, respectively. As a result of this joint effect, good overall
convergence performance can be obtained for XMNLNLMS,
as can be seen in Fig. 3.
As an additional note, the position of the source affects not
only the misalignment convergence of XMNLNLMS, but also
its steadystate value. As can be seen from Fig. 3, the steady
state normalized misalignment is higher than that of NLNLMS
for increasing
position since the weight update is performed
using only a fraction of the tap inputs. This causes an additional
error in the weight update, resulting in an increase in the steady
state normalized misalignment.
IV. C
ENTERCLIPPING APPROACH TO SAEC
We now propose a centerclipping algorithm that has the
ability to reduce the interchannel coherence according to
the source location in the transmission room. We exploit the
decorrelation properties of XM tap selection, similar to that of
XMNLNLMS. In addition we propose an errorbased com
pensation technique that addresses the additional steadystate
normalized misalignment resulting from XM tap selection.
A. CenterClipping Exclusive Maximum Tap Selection
We propose to apply centerclipping to the tapinput vectors
in order to increase the energies of the “inactive” tap inputs
when the interchannel coherence between
and is
relatively low, such as when the source is in front of one of the
microphones. This is to reduce the degradation in misalignment
convergence brought about by the XM tapselection process. As
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BEKRANI et al.: CLIPPINGBASED SELECTIVETAP ADAPTIVE FILTERING APPROACH TO SAEC 1831
Fig. 7. Schematic diagram of the proposed structure.
will be shown in Section IVD, the clipping threshold is based
on indirect estimation of the similarity between the energies of
and . This similarity reﬂects how close the source
is to the microphone centroid, which in turn affects the con
vergence behavior. The proposed approach ensures a softop
timization constraint, which makes it robust to source position.
A schematic diagram of the proposed method is as shown in
Fig. 7.
The proposed clippingbased XMNLNLMS algorithm
(cXMNLNLMS) updates the ﬁlter coefﬁcients using
(15)
(16)
where
is deﬁned in (6) and (7), is the XM tap
selection matrix with diagonal elements deﬁned in (9) and (10),
and the
matrix is deﬁned by
(17)
The matrix
is used to identify the tapinput elements
not selected by XM. The purpose of the proposed centerclip
ping strategy is to increase the energies of tap inputs corre
sponding to the “inactive” (unselected) taps. We achieve this by
ﬁrst deﬁning
as the clipped vector whose elements are computed by (18),
as shown at the bottom of the page, where
controls the
amount of clipping for
. In Section V, we discuss how this
clipping threshold can be determined for our SAEC application.
B. Effect of
on TapInput Energy
The range of
for each tapinput vector can be
bounded between zero and the maximum magnitude of any el
ement within that vector, i.e.,
, where
(19)
Fig. 8. Variation of and
against
for the XM tap
selection algorithm and centerclipping algorithm, respectively.
It can be seen from (18) that when ,wehave
, which results in the second term of (16)
having values equivalent to the unselected tap inputs, so that
and the proposed cXMNLNLMS algorithm be
comes the fullupdate NLNLMS algorithm. On the other hand,
when
,wehave , causing the
second term of (16) to vanish, hence reducing cXMNLNLMS
to XMNLNLMS.
In order to illustrate how the clipping threshold
affects
the energies of the tapinput vectors
and , we em
ploy a
ratio criterion similar to the one deﬁned by (14)
(20)
where the subscript
in denotes centerclipped signals.
Fig. 8 illustrates how
and vary with ,
using signals generated by convolving the previously deﬁned
colored speechlike noise sequence with
and when
the source position is at (2.85,1.85,1.6) m. If
for both
channels,
and therefore the convergence behavior of
the centerclipped cXMNLNLMS algorithm will be equivalent
to NLNLMS. On the other hand, when
,
we have
and hence the performance of the proposed
cXMNLNLMS algorithm will be equivalent to XMNLNLMS.
C. Effect of Clipping Threshold on Interchannel Coherence
As illustrated in Section III, the misalignment conver
gence of XMNLNLMS depends on both the tapinput
energy as well as the interchannel coherence between
and . As such, we investigate the effect of on
the interchannel coherence between
and .We
convolve the same colored Gaussian noise sequence with
and , where , with the source po
sitioned at coordinates (2.85,1.85,1.6) m. A total of ten
(18)
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1832 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 19, NO. 6, AUGUST 2011
Fig. 9. Interchannel coherence versus clipping threshold for colored noise
signal.
Fig. 10. Variation of against horizontal position of the source in the
transmission room for four cases of vertical positions
.
independent trials are averaged and Fig. 9 illustrates how the
mean interchannel coherence across frequency varies with
, where we constrain and such
that
. As can be observed,
the interchannel coherence reduces with increasing values of
clipping threshold. This is as expected since with increasing
, less energy will be allocated to the unselected taps
brought about by the XM tapselection criterion, thus reducing
the similarity between
and , which as a conse
quence causes a reduction in interchannel coherence.
D. SoftDecision Rule for Clipping Threshold
As shown in Figs. 8 and 9, a high value of will re
duce both
and interchannel coherence. As described in
Section III, a reduction in interchannel coherence is crucial
when the source position is near the centroid of the microphone
array pair, while the need to increase
becomes important
when the source is nearer to one microphone. Hence,
enables a tradeoff between interchannel decorrelation and
degradation of misalignment convergence due to tap selection.
Therefore, high
is desirable when the source is near the
centroid of the microphone pair, while low
is desirable
when the source is near one of the microphones. As was pointed
out, the similarity between the energies of
and
contributes to the high convergence rate of XMNLNLMS
when the source is near the microphone pair centroid. On the
other hand, considerable difference in the energies as well as
low interchannel coherence between
and cause the
convergence rate of the XMNLNLMS to reduce signiﬁcantly.
Fig. 11. Clipping threshold
versus
.
We therefore propose to use the difference between absolute
values of the two channels as a measure of energy dissimilarity.
It is foreseeable that when the source is near the microphone
array centroid, the relative absolute values of
and
are approximately equal. On the contrary, when the source is
nearer to one microphone, the relative absolute values of these
tapinput vectors differ from each other. Thus, the dissimilarity
measure is deﬁned as
(21)
where
, 1, 2, is a moving average of the ab
solute values of the input elements given by
(22)
Here, we use
to smooth so as to avoid the effects
of instantaneous changes of
on the value of the clipping
threshold. We see that
and that is close
to 0 when the received energy of the two microphones are ap
proximately equal and approaches 1 when the received energy
from one microphone is much larger than that of the other mi
crophone.
Fig. 10 shows four illustrative examples of how
varies
with different
and positions of the source in the transmission
room. In these examples, the room dimensions and the coordi
nates of microphones are given as shown in Fig. 2. As expected,
the value of
is small when the source is close to the cen
troid at
m. On the contrary, is large when the
source is near Microphone 2 at
m.
We now incorporate
into cXMNLNLMS by varying the
value of
as a function of . Since we desire a low
when the source is nearer to one microphone and vice versa,
should reduce with increasing . We therefore propose
a piecewise linear mapping
(23)
The relation between
and is plotted in Fig. 11. For
speech signals, we use values
and which
were determined empirically.
We note from (23) that
is independently determined for
each channel, and indirectly depends on the relative position of
the source and the microphones. In addition, when
,
such as when the source is near the microphone pair centroid,
increases with reducing . This reduces the effect of
the second term in (16) and as a result, the proposed algorithm
converges in the same manner as XMNLNLMS. On the other
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BEKRANI et al.: CLIPPINGBASED SELECTIVETAP ADAPTIVE FILTERING APPROACH TO SAEC 1833
Fig. 12. Comparison of and for NLNLMS, XMNLNLMS, and
cXMNLNLMS.
hand, when increases, such as when the source is near one
of the microphones,
reduces to zero. As shown in Fig. 8,
this has the effect of increasing the energy of the unselected taps,
which in turn reduces the degradation in misalignment conver
gence due to XM tap selection in situations where reducing the
interchannel coherence cannot further improve the convergence
rate of the adaptive algorithm.
Fig. 12 further illustrates how degradation in
, and
consequently the convergence performance due to tap se
lection, can be reduced by incorporating
into the
proposed cXMNLNLMS algorithm. As described earlier in
Section IIIB, the degradation of convergence performance
for XMNLNLMS when the source is far away from the mi
crophone pair centroid
is due to a reduction of
compared to NLNLMS. In this scenario, the proposed
cXMNLNLMS algorithm ensures that
is closer to the
value 1 achieved by NLNLMS. On the other hand, when the
source is near the centroid
m , cXMNLNLMS at
tains the beneﬁcial properties of the XM tapselection strategy
to maximally decorrelate the tapinput vectors. The overall
joint result is a fast converging cXMNLNLMS that is robust
to the source position in the transmission room.
V. E
NHANCEMENT OF THE STEADYSTATE PERFORMANCE
As noted from Fig. 3 and Section III, the steadystate nor
malized misalignment of XMNLNLMS is higher than that of
NLNLMS. This is due to the unselected ﬁlter coefﬁcients in
troducing an error during adaptation since there is now a mis
match between
, which drives the unknown system, and
the selective tapinput vector
. This error occurs
regardless of the source position. It is therefore expected that
cXMNLNLMS also suffers from increased steadystate mis
alignment since the proposed clipping method generates a signal
that is different from .
To illustrate this, we consider input vectors
deﬁned by
(17) each of length
. A colored noise source signal
generated as described in Section III, is positioned at coordi
nates (2.89,1.85,1.6) m. As before, the room is of dimension
as shown in Fig. 2. This steadystate normalized misalignment
is achieved by allowing the algorithm to reach its steadystate
and averaging over the last 5000 samples. Fig. 13 shows how
the steadystate normalized misalignment varies with normal
ized clipping thresholds
.
Fig. 13. Relation between steadystate misalignment and normalized clipping
threshold in NLNLMS, XMNLNLMS, and cXMNLNLMS, when the source
is at (2.89,1.85,1.6) m.
As can be seen, the steadystate normalized misalignment for
NLNLMS is
29 dB, and 24 dB for XMNLNLMS. If we
employ
deﬁned by (23) for the above source position,
we obtain
, so the proposed cXMNL
NLMS algorithm gives an additional 1 dB of steadystate nor
malized misalignment improvement over XMNLNLMS.
As a ﬁnal improvement, we propose to enhance the
steadystate normalized misalignment performance of
cXMNLNLMS. We note that the steadystate performance of
cXMNLNLMS depends on the source position and therefore
when
, we need to reduce the additional steadystate
normalized misalignment. Hence, we propose to reduce
to zero after convergence of the meansquare error (MSE).
To estimate the convergence of the algorithm, we employ the
following recursive relation for estimating the MSE [24]
(24)
where
is related to the timeconstant of the averaging
process. We consider
for our experiments. Hence,
when
reaches below a lower limit, will be set to zero.
In this case, the normalized misalignment reduces towards the
steadystate misalignment of NLNLMS. We therefore propose
to incorporate
into (23) giving (25),
otherwise
(25)
where
is an empiricallyderived lower limit that aims to
achieve a low level of MSE after convergence. Fig. 14 shows
an example of MSE and misalignment convergence for a single
trial when the source is at coordinates (2.87,1.85,1.6) m. As can
be seen, setting
based on (23) brings about a higher initial
convergence rate than NLNLMS, while reducing
to zero
using (25) after MSE convergence will bring about additional
reduction in steadystate normalized misalignment. Additional
tests revealed that although the convergence of MSE occurs
before convergence of misalignment, exact knowledge of MSE
is not required. The proposed cXMNLNLMS algorithm is
summarized in Table I.
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1834 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 19, NO. 6, AUGUST 2011
Fig. 14. Estimated MSE and misalignment for the cXMNLNLMS algorithm.
TABLE I
T
HE cXMNLNLMS ALGORITHM
VI. FURTHER SIMULATION AND EXPERIMENTAL RESULTS
We evaluate, by way of further simulation, the performance
of cXMNLNLMS under different source positions. In order
to simulate the SAEC system, impulse responses
,
, , and were generated using the method
of images [22]. To evaluate the robustness of the algorithms,
TABLE II
S
PECIFICATIONS OF THE
SIMULATED ENVIRONMENT IN
SAEC
we ﬁxed the location of the microphones while the source
position in the transmission room was varied across three
cases shown in Table II. A sampling rate of
Hz
was used throughout the experiment. The source signal was
generated by ﬁltering a white Gaussian noise signal through a
lowpass ﬁnite impulse response (FIR) ﬁlter with coefﬁcients
, as was used in Section III.
We compare the convergence performance of the pro
posed cXMNLNLMS algorithm with NLNLMS and
XMNLNLMS. Since the steadystate normalized misalign
ment for XMNLNLMS varies with the source position, we
chose its stepsize so that its steadystate normalized mis
alignment reaches that of NLNLMS and cXMNLNLMS
when the source position is in front of the microphone array
centroid at (2.85,1.85,1.6) m. This corresponds to
for both NLNLMS and cXMNLNLMS and for
XMNLNLMS. White Gaussian noise (WGN) is added to
to achieve an dB. For all simulations, we have used
dB for cXMNLNLMS. The normalized misalign
ment curves, obtained by averaging over ten independent trials,
are plotted for Cases 1, 2, and 3 (Table II) in Fig. 15(a)–(c)
respectively.
Fig. 15(a) shows the convergence performance of the algo
rithms where the source is directly in front of the right micro
phone. In this case,
and are signiﬁcantly different
and hence a high value of
deﬁned in (21) is expected.
As shown in Fig. 11, this translates to a low
, and con
sequently, as shown in (18),
. As a result,
the convergence performance of cXMNLNLMS is equivalent
to that of NLNLMS. The proposed cXMNLNLMS algorithm
thus achieves an initial convergence of nearly 8 dB better than
XMNLNLMS and reaches a steadystate normalized misalign
ment of 4 dB lower as expected.
Fig. 15(b) shows convergence results when the source posi
tion is midway between the microphone pair centroid and the
right microphone at (2.88,1.85,1.6) m. Now, the interchannel
coherence increases relative to the previous case and as can be
seen from this result, cXMNLNLMS achieves the highest rate
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BEKRANI et al.: CLIPPINGBASED SELECTIVETAP ADAPTIVE FILTERING APPROACH TO SAEC 1835
Fig. 15. Normalized misalignment of the NLNLMS, XMNLNLMS, and
cXMNLNLMS algorithms for a colored noise source signal. (a) Source directly
in front of right microphone at (3,1.9,1.55) m. (b) Source at (2.88,1.85,1.6) m.
(c) Source in the center of microphone pair at (2.85,1.85,1.6) m.
of initial convergence, improving that of NLNLMS by nearly 4
dB during initial convergence. We note that when compared to
XMNLNLMS, cXMNLNLMS achieves approximately 3 dB
improvement during initial convergence and about 2 dB lower
steadystate normalized misalignment.
Finally, when the source position is in front of the micro
phone pair centroid at coordinates (2.85,1.85,1.6) m,
and
are similar and the interchannel coherence between
and is high. As can be seen from Fig. 15(c), the conver
gence of cXMNLNLMS achieves the highest rate of conver
gence with an improvement of approximately 4 dB over that
of XMNLNLMS and nearly 10 dB over that of NLNLMS. In
terms of steadystate normalized misalignment, the NLNLMS
algorithm requires nearly 10 s more than that of cXMNLNLMS
to reach
30 dB.
To further illustrate the convergence performance of the
proposed cXMNLNLMS algorithm, we simulated the SAEC
system using a speech signal as shown in Fig. 16. In this ex
ample, the speech signal is sampled at 11 025 Hz and a WGN is
added to
to achieve an SNR dB. The position of the
source in the transmission room is (2.88,1.85,1.6) m. As can be
seen from this result, cXMNLNLMS achieves approximately
6 dB lower misalignment than NLNLMS and 4 dB lower than
XMNLNLMS during initial convergence.
We consider using recorded impulse responses, where the di
mensions of the transmission room is 6.5 m
8.75 m 2.65 m,
the source was positioned at (3.25,4.37,1.15) m while the
two microphones were placed at (3.11,2.37,1.2) m and
(3.39,2.37,1.2) m for Case 1 and at (3.25,2.37,1.2) m and
(2.83,2.37,1.2) m for Case 2. The estimated reverberation time
was 280 ms. These impulse responses were of length 3087
samples and subsequently truncated to 512 samples. Fig. 17
Fig. 16. Normalized misalignment for the NLNLMS, XMNLNLMS, and
cXMNLNLMS algorithms when the source is at (2.88,1.85,1.6) m for a speech
signal.
Fig. 17. Illustration of measured transmission room impulse response .
Fig. 18. Normalized misalignment of the NLNLMS, XMNLNLMS, and
cXMNLNLMS algorithms for real room impulse responses. (a) Case 1: source
in the center of microphone pair. (b) Case 2: source approximately in front of
the right microphone.
shows one of the measured impulse responses in the trans
mission room. For this experiment, the sampling frequency,
stepsizes as well as the SNRs were the same as that of the
previous simulations. The results are shown in Fig. 18. As
can be seen from Fig. 18(a), cXMNLNLMS achieves nearly
3 dB improvement in convergence performance compared to
XMNLNLMS when the source is in front of the microphone
centroid. In Fig. 18(b), when the source is in front of the right
microphone, the proposed algorithm achieves nearly 6 dB
improvement in convergence compared to XMNLNLMS.
VII. C
ONCLUSION
We presented a new approach to improve the misalignment
convergence as well as the steadystate performance and ro
bustness of adaptive ﬁlters for SAEC. This approach retains
the decorrelation properties of the XM selectivetap algorithm
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1836 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 19, NO. 6, AUGUST 2011
when the source is located near the microphone centroid, but
employs a variable centerclipping threshold whose value is de
rived based on the absolute values of the received microphone
signals in order to work better, when the source is located closer
to one of the microphones. The proposed approach achieves
better convergence performance for different source positions
in comparison to both NLNLMS and XMNLNLMS.
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Mehdi Bekrani was born in Gorgan, Iran, in 1979.
He received the B.Sc. degree from Ferdowsi Uni
versity of Mashhad, Mashad, Iran, in 2002, and the
M.Sc. and Ph.D. degrees from Tarbiat Modares Uni
versity, Tehran, Iran, in 2004 and 2010, respectively,
all in electrical engineering.
He is currently a Research Fellow at Nanyang
Technological University, Singapore. His current
research interests include acoustic signal processing
and their applications.
Andy W. H. Khong (M’06) received the B.Eng. de
gree from Nanyang Technological University, Singa
pore, in 2002 and the Ph.D. degree from the Depart
ment of Electrical and Electronic Engineering, Im
perial College London, London, U.K., in 2005. His
Ph.D. research was mainly on partialupdate and se
lectivetap adaptive algorithms with applications to
mono and multichannel acoustic echo cancellation
for handsfree telephony.
He is currently an Assistant Professor in the
School of Electrical and Electronic Engineering,
Nanyang Technological University, Singapore. Prior to that, he served as
a Research Associate in the Department of Electrical and Electronic En
gineering, Imperial College London, from 2005 to 2008. His postdoctoral
research involved the development of signal processing algorithms for vehicle
destination inference as well as the design and implementation of acoustic
array and seismic fusion algorithms for perimeter security systems. He has also
published works on acoustic blind channel identiﬁcation and equalization for
speech dereverberation. His other research interests include humancomputer
interfaces, source localization, speech enhancement, and blind deconvolution.
Mojtaba Lotﬁzad was born in Tehran, Iran, in 1955.
He received the B.S. degree in electrical engineering
from AmirKabir University of Technology, Tehran,
in 1980, and the M.S. and Ph.D. degrees from the
University of Wales, Cardiff, U.K., in 1985 and 1988,
respectively.
He joined the Department of Electrical and
Computer Engineering, Tarbiat Modares University,
Tehran, Iran. He has also been a Consultant to sev
eral industrial and governmental organizations. His
current research interests are in signal processing,
adaptive ﬁltering, speech processing, and specialized processors.
Page 11
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 "Here, the channel acoustic response parameters are updated adaptively to produce an estimate of echo. Among different adaptive filter algorithms, the gradient based least mean squares (LMS) algorithm and its modifications, such as normalized LMS (NLMS) and variable step size LMS (VLMS) algorithms, are widely used for their satisfactory performances, less computational burden, and ease of implementation [2, 9, 10]. A faster algorithm is the recursive least mean squares (RLS) algorithm which is, however, computationally expensive [9]. "
Article: Gradient Based Adaptive Algorithm for Echo Cancellation from Recorded Echo Corrupted Speech
[Show abstract] [Hide abstract] ABSTRACT: An offline single channel acoustic echo cancellation (AEC) scheme is proposed based on gradient based adaptive least mean squares (LMS) algorithm considering a major practical application of echo cancellation system for enhancing recorded echo corrupted speech data. The unavailability of a reference signal makes the problem of single channel adaptive echo cancellation to be extremely difficult to handle. Moreover, continuous feedback of the echo corrupted signal to the input microphone can significantly degrade the quality of the original speech signal and may even result in howling. In order to overcome these problems, in the proposed scheme, the delayed version of the echo corrupted speech signal is considered as a reference. An objective function is thus formulated and thereby a modified LMS update equation is derived, which is shown to converge to the optimum WienerHopf solution. The performance of the proposed method is evaluated in terms of both subjective and objective measures via extensive experimentation on several reallife echo corrupted signals and very satisfactory performance is obtained. 
Conference Paper: Echo canceller with both doubletalk detector and path change detector
[Show abstract] [Hide abstract] ABSTRACT: An echo canceller with both doubletalk detector (DTD) and echo path change detector (PCD) is put forward. Doubletalk detector is based on the activity detection of speech, using subfilter to detect the near end talk, and enhancing its performance by adding a sliding window. The path change detector works by comparing the performance between mainfilter and subfilter. There is a problem when an echo canceller has both detectors: It's hard to discriminate between echo and near end speech after path changes, which can cause the echo of far voice increase suddenly and this echo is similar to the near end voice. To solve this problem, we propose to change doubletalk detection threshold after path change happened. In addition, using the short silence mute at the beginning of a call, some random sequences will be sent to initialize the filter. The simulation results show that the proposed echo canceller has a satisfactory performance during doubletalk and path change. 
Conference Paper: Convergence analysis of clipped input adaptive filters applied to system identification
[Show abstract] [Hide abstract] ABSTRACT: One of the efficient solutions for the identification of long finiteimpulse response systems is the threelevel clipped input LMS/RLS (CLMS/CRLS) adaptive filter. In this paper, we first derive the convergence behavior of the CLMS and CRLS algorithms for both timeinvariant and timevarying system identification. In addition, we employ results arising from this analysis to derive the optimal stepsize and forgetting factor for CLMS and CRLS. We show that these optimal stepsize and forgetting factor allow the algorithms to achieve a low steadystate misalignment.