SEPARATION AND DEREVERBERATION PERFORMANCE OF
FREQUENCY DOMAIN BLIND SOURCE SEPARATION
Ryo Mukai

Shoko Araki

Shoji Makino

NTT Communication Science Laboratories
2-4 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237, Japanryo,shoko,maki @cslab.kecl.ntt.co.jp
ABSTRACTIn this paper, we investigate the separation and dereverberation performance of frequency domain Blind Source Separation (BSS) based on Independent Component Analysis(ICA) by measuring impulse responses of a system. Since
ICA is a statistical method, i.e., it only attempts to makeoutputs independent, it is not easy to predict what is goingon in a BSS system physically. We therefore investigate
the detailed components in the processed signals of a whole
BSS system from a physical and acoustical viewpoint. In
particular, we focus on the direct sound and reverberationin the target and jammer signals. As a result, we reveal thatthe direct sound of a jammer can be removed and the reverberation of the jammer can be reduced to some degree
by BSS, while the reverberation of the target cannot be reduced. Moreover, we show that a long frame length causes
pre-echo noise, and this damages the quality of the separated signal.

As a result, it is shown that frequency domain BSS basedon ICA can remove the direct sound and reduce the reverberation of the jammer signal, while it hardly ever reduces
the reverberation of the target signal.
2. FREQUENCY DOMAIN BSS OF
CONVOLUTIVE MIXTURES
When the source signals are    ), the signals
observed by microphone  are    , and theunmixed signals are      , the model can be
described by the following equations:%!" $#0   /#

'&)(

*

1&2(43+-,.

(1)

5 ,  5 +6(2)*

1. INTRODUCTION
Blind Source Separation (BSS) is a technique that separates and extracts target signals only from mixture signals
observed without using information on the characteristicsof the source signals and the acoustic system [1, 2]. Most
BSS algorithms are considerably effective for instantaneous(non-convolutive) mixtures of signals, and some attempts
have been made to apply BSS to signals mixed in convolutive environments [3, 4]. However, it has also been pointed
out that a sufficient performance cannot be obtained in environments with long reverberation where the filter lengths ofthe mixing and unmixing systems are on the order of thousands or higher [5, 6].
In this paper, we examine the performance of a separation system obtained by frequency domain BSS. We focus
our attention on the power of (1) the direct sound of the target signal, (2) the reverberation of the target signal, (3) the
direct sound of the jammer signal, and (4) the reverberationof the jammer signal, and evaluate each power separately.

where + is the impulse response from source  to microphone  , 5 is the coefficient when the unmixing system73
is assumed
as an FIR filter, and the operator , denotes
convolution.
In this paper, we consider a two-input, two-output convolutive BSS problem, i.e.,  =  = 2 (Fig. 1). In addition,
it is assumed that 8( 5 is separated to 9( 5 , and  :; isseparated to 8:< .
Because it is possible to convert a convolutive mixture
in the time domain into an instantaneous mixture in the frequency domain, frequency domain BSS is effective for separating signals mixed in a reverberant environment.
Using a = -point short-time Fourier transform for (1), we
obtain>5?@61AB$#BCD5?E FG?H6+AI+J(3)

We assume that the following separation has been completed in a frequency bin ? :
>
K

230

?H61AB$#

7

?G

?H6+AI+6(4)

sourcesignals

observed
signals

h11

s1

x2

+

h22

mixing systemw22

s1 h11 x1

+

y2

0.8

unmixing system

'V)( #

7

-W

X

L diag Y[ZH

K

KB\^]

-_`YZH

K

K

y1s1

PIR

PTR

K

\^] 7
N

(dB)

-20

y1s2

-40

0

125(ms)0125(ms)0125(ms)Fig. 2. Definitions of measurement factors.
(1) estimate unmixing matrix

7

?G for each frequency.

(2) by using IFFT, transform frequency domain unmixing
7
matrix
?G to time domain unmixing filter 5  .

(5)3(3) while driving with the impulse as a source signal,
measure four impulse responses, from  ( to  ( ,  (to  : ,  : to  ( , and  : to  : .



Khg W Kjg
(6)
WIced Re f
Wiced Im fK
and Im 
are the real and imaginary parts

PJ

-30

]

K

x1s1

0

-10

where Ya denotes the averaging operator,  is used to express
the value of the  -th step in the iterations, and X is the step
size parameter. In addition, we define the nonlinear function
ZH+a as
ZH

w11 y1
w11 y1s1 h11h21 w12h12 w12s2 h22-0.8

is thewhere
5 ?@61AB#
L M ( ?H6+AI+6+M : 5?@61ABONQP
K
observed signal in frequency bin ? ,5?@61AB#LSR-(T?@61AB16UR4:;?H61ABQNOP is the estimated source signal, and7
7
?E represents the unmixing matrix.
5?E is determined so that R!( ?H6+AI and R<:;5?@61AB become mutually independent. The above calculations are carried out for eachfrequency independently.
7
For the calculation of unmixing matrix, we use an
optimization algorithm based on the minimization of the7
Kullback-Leibler divergence [7, 8]. The optimal
is obtained by using the following iterative equation:
7

(c)

0

Fig. 1. Model of BSS system
>

(b)

y1

w12

h12

(a)

+

w21

h21

s2

w11

x1

+

unmixedsignals(4) investigate the four impulse responses in detail andcompare them to the responses of a null beamformer(NBF).

b#where Re Kof , respectively.
In general, it is necessary to solve the permutation problem and scaling problem when ICA is used. In our experiment, the effect of the permutation problem was negligible
and so we did not coordinate the permutation. The problemof scaling was solved by adjusting the power of the target
signal in the output signal to 0 dB.
3. EVALUATION METHOD

The performance of BSS is usually evaluated by the ratioof a target-originated signal to a jammer-originated signal.
This measure is reasonable for evaluating the separation
performance, but is unsuitable for evaluating the dereverberation performance because of its inability to distinguishthe direct sound and reverberation. Since we want to know
the detailed components in separated signals, i.e., the direct
sound and reverberation of the target and jammer, we takethe following procedure,

3.1. Definitions of performance measurement factors
We evaluate the performance of unmixing system in time
domain. We consider a separated signal  ( , target signal  ( ,and jammer signal  : . When the target  ( is an impulse k<
and the jammer  : #l , we call the observed signal  ( as
 (nmT( [Fig. 2(a)], and  ( as  (nmo( [Fig. 2(b)]. Similarly, when
 ( #l and  : #pk45 , we call  ( as  (nmq: , and  ( as  (nm1:[Fig. 2(c)].  (rmo( is an impulse response from  ( to  ( by themixing system C , and  (nmT( is an impulse response from  (7
to  ( bythe whole system
a5C . These are calculated by*using  and  as follows.
3b(nmT(s#* (nmq:*#9(nmo(u# (nm1:
#

([(
(t:

3

3

([($,
([( ,

*

*

([( W
(t:vW
3

3

(t:H,
(t: ,

*

*

(7)
(8)
:"(
::

(9)
(10)

From the viewpoint of source separation, we can consider (nmo( as the direct and reverberant sound of target  ( , and (nm1: as the remaining sound of jammer  : .

231

NBF

5.73 m

0.6

ICA

(a)

y1s1

(b)

y1s1

(c)

y1s2

(d)

y1s2

1.56 m3.12 m1.15 mloudspeakers(height : 1.35 m)

030

2.15 m

40

4 cm

-0.6
0.6

microphones 1.15 m(height : 1.35 m)
room height : 2.70 m

0Fig. 3. Layout of the room used in experiments. Reverberation time = 300 ms.
-0.6*

To simplify the evaluation, we normalize + so that thepower of the observed signals  (rmo( and  (nm1: is equal to 0
dB, and make the following definitions (Fig. 2).
wix-y[z: the power of the reverberant sound in  (nmT( ,: the power of the reverberant sound in {(nmo( ,wix-P|: the power of  (rm1: .
wixz

We also define the reduction of the reverberation of target
signal }and the reduction of jammer signal } | as follows
P

}
}

P
|

#
#

x z
_~
P
x|
_
J
_

x-y[z

(11)
(12)

4. EXPERIMENTS
In order to examine what is separated by an unmixing system based on ICA, and what remains as noise, we investigated impulse responses of a system. In frequency domain BSS, it has been confirmed that the separation performance changes according to the length of the frame [6], so
we chose the frame length and the frame shift as parameters.

0ms

125ms

0ms

Fig. 4. Target and jammer impulse responses of NBF andICA
speech signals were about eight seconds each. We used theentire eight seconds of the mixed data for learning according to (5).
In these experiments, we changed the frame length =from 32 to 4096 and investigated the performance for eachcondition. The sampling rate was 8 kHz, and analysis window was a Hamming window. The frame shift was =~o
and =~o8 , which correspond to double and 32 times oversampling.
The number of iterations for (5) was 100, except when
#=~o and =p# 1024, 2048, and 4096, where the iteration was stopped at 70, 30, and 20, respectively, because adeterioration of the performance was observed.
4.2. Experimental results
Figures 4(a) and (c) show examples of impulse responsesof the unmixing system obtained by a null
beamformer (NBF) that forms a steep null directivity pattern towards a jammer under the assumption of the jammer’s
direction being known. Figures 4(b) and (d) are results obtained by ICA.
For the target signal, we can see that the reverberation
passes the system in both cases (NBF and ICA) in Figs. 4(a)and (b). Figure 4(c) shows that the direct sound of the jammer is removed, but the reverberation is not removed by
NBF, as expected. On the other hand, Fig. 4(d) indicatesthat ICA not only removes the direct sound, but also reduces
the reverberation of the jammer.
Figure 5 shows the relationship between the frame
length = and the reduction ratios }and } | defined byP|(11) and (12). } ( and } ( are }and } | when the tar- (nmo( and  (nmq:4.1. Conditions for the experiments
The layout of the room we used to measure the impulse responses of the mixing system C is shown in Fig. 3. The
reverberation time of the room was 300 ms, which corresponds to impulse response of 2400 taps at 8 kHz samplingrate. We used a two-element array with inter-element spacing of  cm. The speech signals arrived from two directions,
i.e., _.8l and 8l . The contribution of the direct sound of****([( and :e( was 6.6 dB, and that of (t: and :[: was 5.7
dB.
Two sentences spoken by two male speakers selectedfrom the ASJ continuous speech corpus for research wereused as the source signals. The lengths of these mixed

125ms

P

232

P

reduction ratio (dB)20
15

reduction ratio (dB)

RJ1

10

x1s2
(≅x2s2)

observed
signal

0

RJ2
-0.06
0ms

5

250ms

0.6

0ms

y1s2

T=512

RT1
RT2
0

(b) ICA, S=T/32

0.06

250ms

frame length

0

RJ1

15

-0.06

-0.6
0ms

RJ2

250ms

0.6

10

0ms

y1s2

T=2048
0

5
0
15

0.06

0

-0.6

0
20

reduction ratio (dB)

0.6(a) ICA, S=T/2

250ms

0.06
frame length

0

RT1
RT2
-0.06

-0.6
0ms

(c) NBF

250ms

0.6

y1s2

T=4096

10

0ms
0.06

250ms

frame length

RJ1
RJ2
0

0

-0.6

-0.06

5
0

RT1
RT2
32

64

128

0ms

256 512 1024 2048 4096

250ms

pre-echo

0ms

250ms

frame length T
Fig. 6. Jammer impulse response of BSS system
Fig. 5. Relationship between frame length and reduction
ratio.
get signal is <( . } : and } | : are results when the targetP
signal is : . Figures 5(a) and (b) show results by ICA when
#=~o and #=~o8 , respectively. For the sake ofcomparison, the performance of NBF is shown in Fig. 5(c).
Note that these results are measured by the power of
impulse responses, and differ from the noise reduction rate
(NRR) [6] measured by using a speech signal having ahighly colored spectrum. Our results indicate seemingly
better values than the NRR of the speech signal. For example, the reduction ratio } | ( = 15.8 dB and } | : = 12.6 dB(=#8l886U#I=~o ) correspond to about 11 dB and 8 dBin the case of NRR, and } | ( = 19.5 dB and } | : = 16.6 dB(=#8l886U#=~o8 ) correspond to about 14 dB and 9dB of NRR.

5. DISCUSSIONFirst, we discuss the jammer reduction ratio } | . When=8 , the reduction performance of BSS is as poor asthat of NBF, and when 88=i8l88 , the reduction ratio
increases. In the case of =p#8l8 , #=~o8 , } | ( =19.5
dB, } | : =16.6 dB. This is greater than the contribution of
the direct sound, i.e., 6.6 dB and 5.7 dB. This means thatthe unmixing system by ICA can reduce not only the direct
sound of the jammer but also the reverberant sound of thejammer. In addition, comparing the results of #=~o
and D#=^T8 [Figs. 5(a) and (b)], we can see that oversampling improves the jammer reduction ratio. However, as
we describe later, the reverberation is not eliminated completely.
On the other hand, the reduction ratio of the reverberation of target }is low, and does not vary through the
P

233

0.6

observed
signalx1s1(≅x2s1)

0

0

-0.06

-0.6
0ms
0.6

250ms

0ms

y1s1

T=512

250ms

0.06
frame length

0

0

-0.06

-0.6
0ms
0.6

0.06

250ms

0ms

y1s1

T=2048250ms

0.06
frame length

0

0

-0.6

-0.06

= 512, 2048, and 4096. The best performance is obtained
when = = 2048. In the case of = = 512, the length of theunmixing system is much shorter than the length of the reverberation; accordingly, the reverberation longer than theframe cannot be reduced at all. On the other hand, when
= = 4096, which is longer than the reverberant time, theunmixing system can wholly cover the reverberation, but
because each tap of the filter has errors that derive from thestatistical method of ICA.
When the filter length becomes longer, the number ofcoefficients to be estimated increases while the number ofdata for learning in each frequency bin decreases. As a result, the amount of estimation errors escalates. Moreover,the pre-echo noise grows, and this causes the performance
to fall.
The target signal’s impulse response -(rmo( is shown in
Fig. 7. As we have described previously, the reverberation
is not removed. Furthermore, the target signal still suffersfrom a pre-echo noise, and this damages the quality of theseparated target signal.
6. CONCLUSION

0ms

250ms

0.6

T=4096

y1s1

0ms
0.06

0

0

-0.6

-0.06
0ms

250ms

250ms

frame lengthpre-echo

0ms

250ms

Fig. 7. Target impulse response of BSS system
entire frame length = . This means that dereverberation was
not achieved for the target signal.
7
From these results, it can be concluded that is not theapproximation of the inverse system of C , but a filter thatcan eliminate the jammer signal.
It has been pointed out that early reflections of the jammer signal are removed by BSS [9]. We obtained a slightly
stronger result that not only the early reflections but also
the reverberation of the jammer signal is reduced to somedegree. The reason for this is that frequency domain BSS
is equivalent to two sets of frequency domain adaptive microphone arrays, i.e., Adaptive Beamformers (ABF), which
adapt to minimize the jammer signal including reverberation in the mean square error sense [10].
Finally, we show the reason why the reduction ratio of
jammer signal } | declines when = is too long. Figure 6
shows the jammer signal’s impulse response  (nm1: , when =We investigated the performance of an unmixing system obtained by frequency domain BSS based on ICA using theimpulse responses of target and jammer signals.
As a result, we revealed that ICA not only removes the
direct sound of the jammer signal, but also reduces the reverberation, while the reverberation of the target is not reduced.
The jammer reduction performance increases as theframe length becomes longer. However, an overly long
frame length decreases the performance due to accumulating errors. The performance of the target dereverberation
does not depend on the frame length and is as poor as thatof NBF.

ACKNOWLEDGEMENTS
We would like to thank Dr. Hiroshi Saruwatari for his valuable discussions. We also thank Dr. Shigeru Katagiri for his
continuous encouragement.

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