1IWAENC 2006 – PARIS – SEPTEMBER 12-14, 2006

PERFORMANCE EVALUATION OF SPARSE SOURCE SEPARATION
AND DOA ESTIMATION WITH
OBSERVATION VECTOR CLUSTERING IN REVERBERANT ENVIRONMENTS
1,2

Shoko Araki, 1 Hiroshi Sawada, 1 Ryo Mukai, and 1,2 Shoji Makino

shoko@cslab.kecl.ntt.co.jp
NTT Communication Science Laboratories, NTT Corporation
2-4 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237, Japan
2
Graduate School of Information Science and Technology, Hokkaido University
Kita 14, Nishi 9, Kita-ku, Sapporo-shi, Hokkaido 060-0814, Japan
1

ABSTRACTThis paper investigates the effects of real world acoustic environments on sparse source separation and direction of arrival(DOA) estimation performance. The time-frequency mask technique is widely studied as an approach for sparse source separation and DOA estimation. The approach relies on source sparseness, which can easily be affected by, for example, reverberation. In fact, most proposed approaches assume an anechoic
condition, which is difficult to maintain in a real acoustic environment. We investigate how the performance of such methods is affected when the problem does not meet the assumed
conditions. We show that strong reverberation and a large distance between the sources and sensors degrade the separation
performance, however, the DOA estimation performance is not
so severely affected.

1. INTRODUCTION
The time-frequency mask approach to blind sparse source
separation (BSS) is being widely studied (e.g. [1, 2]).
Some authors have also proposed direction of arrival (DOA)
estimation methods for sparse sources [3, 4]. The timefrequency mask approach is attractive because it can handle the underdetermined problem where the sources outnumber the sensors. With regard to these problems, wehave also already proposed the time-frequency mask approach, which is based on observation vector clustering[5], and a DOA estimation method [6] for sparse sources.
In order to estimate the time-frequency mask for the
separation, all the cited methods rely on the assumptionof source sparseness, and some methods adopt an anechoic assumption. Moreover, all the above DOA estimation methods utilize an anechoic assumption. In practice,
however, these assumptions cannot hold due to such factors as reverberation and noise.
To study the effects of such practical issues, in this paper, we investigate how the performance of a time-frequency
mask approach degrades when the problem becomes far
from holding the assumptions. We focus particularly on
the reverberation variations caused by changing the room

reverberation time and the distance between sensors andsources.
2. PROBLEM DESCRIPTION
Suppose that sources s1 , . . . , sN are convolutively mixed
and observed at M sensors
xj (t) =

PN

P

k=1

l hjk (l) sk (t − l), j = 1, . . . , M,

(1)where hjk (l) represents the impulse response from source
k to sensor j. In this paper, we look especially at a situation where the number of sources N can exceed the number of sensors M (N > M ). We assume that N and M
are known, and that the sensor alignment does not cause
the spatial aliasing problem. We have two goals. One
is to obtain separated signals yk (t) that are estimationsof sk solely from M observations. The other is to estimate the DOAs qk of signals sk (k = 1, · · · , N ) using
the knowledge of the sensor alignment. Here qk is a 3dimensional vector of a unit-norm representing the direction of the source sk [6].
This paper employs a time-frequency domain approach.
Using a short-time Fourier transform (STFT), the convolutive mixtures (1) can be converted to instantaneous mixtures at each frequency f :PN
xj (f, τ ) ≈ k=1 hjk (f )sk (f, τ ),(2)or in vector notation,
x(f, τ ) ≈PN

k=1 hk (f )sk (f, τ ),(3)

where hjk (f ) is the frequency response from source k tosensor j, sk (f, τ ) is the STFT of a source signal sk , and τ
is a time index. We call x = [x1 , . . . , xM ]T an observation vector and hk = [h1k , . . . , hM k ]T is a vector of thefrequency responses from source sk to all sensors.
3. METHOD REVIEWIn this section, first we explain the assumptions that havebeen widely employed for solving the underdetermined

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IWAENC 2006 – PARIS – SEPTEMBER 12-14, 2006

x1(t)

...
xM(t)

]

STFT

yk(f,τ)x(f,τ)]

x(f,τ)

Sensorlocations

D

yk(t)

x̄(f, τ ) ← x̄(f, τ ) / ||x̄(f, τ )||Mk(f,τ)Normalization

ClusteringckThen, we apply unit-norm normalization
ISTFT

Ck Maskdesign

DOA estimation

qk

Figure 1: Flow of our method.
problem (e.g. [1, 5]). Then, we briefly describe our separation and DOA estimation methods [5, 6] (Fig. 1).
3.1. Assumptions
ASSUMPTION 1: Source sparsenessWe assume the sparseness of sources in the time-frequency
domain. When the signals are sufficiently sparse, we canassume that the sources rarely overlap at each time-frequency
point, and (3) can be approximated asx(f, τ )≈ hk (f )sk (f, τ ), k ∈ {1, · · · , N }, (4)where sk (f, τ ) is a dominant source at the time-frequency
point (f, τ ). For instance this is true for speech signals in
the time-frequency domain [1].
ASSUMPTION 2: Anechoic model
We also assume an anechoic environment. If the source is
Dirac’s delta function sk (t) = δ(t), its observation at thej-th sensor isxj (t) ==hjk (t)δ(t)hjk (t) = λjk δ(t − τjk )where λjk ≥ 0 and τjk are the attenuation and the timedelay from source k to sensor j. If we assume an anechoic environment, λjk and τjk are determined solely by
the geometric condition of the sources and sensors. In thefrequency domain, an impulse response hjk (f ) is represented by
hjk (f ) ≈ λjk exp [−2πf τjk ].

(5)

3.2. Sparse source separation
Here we employ the method proposed in [5], which
employs the above two assumptions as discussed below.
First, we normalize all observation vectors x(f, τ ) for
all time-frequency points (f, τ ) such that they form clusters, each of which corresponds to an individual source.
The normalization includes phase-normalization with respect to a sensor J and the frequency-normalization,¸·
arg[xj (f, τ )/xJ (f, τ )]x̄j (f, τ ) ← |xj (f, τ )| exp 
4f c−1 dmax
(6)
where c is the propagation velocity and dmax is the maximum distance between sensor J and a sensor j ∈ {1, . . . , M }.

(7)

to x̄(f, τ ) = [x̄1 (f, τ ), . . . , x̄M (f, τ )]T .
Considering the sparseness assumption (4) and the anechoic assumption (5), the normalized vector can be writtenas·¸π(τjk − τJk )
λjk
,
(8)
exp −
x̄j (f, τ ) ≈A
2c−1 dmax
qP
M2
where A =j=1 λjk . We can see that the normalized
observation vector x̄(f, τ ) depends only on the source geometry λjk and τjk of the source sk , which is dominantat the time-frequency point (f, τ ). This means the normalized observation vectors can be clustered based on thesource geometry.
Therefore, the next step is to find clusters C1 , . . . , CNformed by all normalized vectors x̄(f, τ ). After setting
appropriate initial centroids ck (k = 1, · · · , N ), clustering is realized by the following iterative updates:Ckck= {x̄(f, τ ) | k= argmini ||x̄(f, τ ) − ci ||2 } (9)(10)← E[x̄(f, τ )]x̄∈Ck , ck ← ck /||ck ||,where E[·]x̄∈Ck is a mean operator for the members ofa cluster Ck . This minimization can be performed efficiently with the k-means clustering algorithm [7] with agiven source number N .
Because each resulting cluster corresponds to an individual source, finally, we obtain separated signals yk (f, τ )= Mk (f, τ )xj (f, τ ) where j is an arbitrary selected sensor
index j ∈ {1, . . . , M } and½
1 x̄(f, τ ) ∈ Ck
Mk (f, τ ) =(11)
0 otherwise
Then we have time-domain outputs yk (t) by using an inverse STFT (ISTFT).
3.3. DOA estimation [6]When qk and dj are 3-dimensional vectors representing
the k-th source DOA and the j-th sensor position, respectively, the delay τjk in (5) normalized by the delay τJk forthe sensor J is
τjk − τJk = c−1 (dj − dJ )T qk .

(12)

On the other hand, from (8) and (10), the delay τjk canalso be derived as
2c−1 dmax
τjk − τJk = −arg{ck }j(13)πwhere {ck }j is the j-th component of the centroid ck .
From (12) and (13), we obtain the DOA
2dmax +
qk = −
D rk .
(14)π
where r k = [arg[{ck }1 ], · · · , arg[{ck }M ]]T , D = [d1 −dJ , · · · , dM − dJ ]T , and ·+ denotes a pseudo-inverse.

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IWAENC 2006 – PARIS – SEPTEMBER 12-14, 2006

445 cm

4

x 10

120o

(a)

1.5
1

2
Frequency (Hz)Frequency (Hz)2

• Reverberation time (RT) : 128 ms or 300ms• Room height: 250cm

210o

4

x 10

Microphone (120cm height, omni-directional)
Loudspeaker (120cm height)

4cm

256cm

0

4cm

1
0.5

0

4cm

180cm

0.2

0.4
0.6
Time (sec.)

0

0.8

4

0.2

0.4
0.6
Time (Sec.)

0.8

x 10

45o
2

R = 50, 110, 170 (cm)Figure 2: Experimental setup.
If rank(D) ≥ 3, we can estimate the 3-dimensional DOA.
Note that the DOA estimation procedure also assumes source
sparseness and an anechoic condition.
4. PERFORMANCE INVESTIGATIONS
4.1. General conditions
We investigated how the performance of a time-frequency
mask approach is affected by reverberation. We performedexperiments under an anechoic condition and some reverberant conditions. Here, we only tested the 3-microphone
and 4-source case. For the anechoic test, we simulated
the mixture by using the anechoic model ((5) and (13))
and the mixture model (1). For the reverberant tests, observations were simulated by following (1) with impulse
responses hjk measured in a room (Fig. 2). The room reverberation times RT were 128 and 300 ms. For both RTs,
we utilized the same room but changed the wall condition. We also changed the distance R between the sensors
and sources. The distances variations were R=50, 110,
and 170 cm (see Fig. 2). The sources sk (t) were 5-second
English speech signals sampled at 8 kHz. We investigatedeight speaker combinations and averaged the results for all
the outputs. The STFT frame size was 512 and the frame
shift was 128(= 512/4).
4.2. Properties of impulse responses of reverberant conditions
Figure 3 shows example impulse responses under different reverberant conditions; (a) RT=128 ms, R=50 cm, (b)RT=128 ms, R=170 cm, (c) RT=300 ms, R=50 cm, (d)RT= 300 ms, R=170 cm. The impulse response becomeslong as RT and R increase. Figure 3 also includes theclarity index [8]:R 80ms 2
h (t)dt
C = 10 log10 R0∞
2 (t)dth
80ms
which explains the ratio between direct sound and reverberant sound. Small (large) C means the reverberant sound(direct sound) is large. We can see that the clarity C be-2(b)Frequency (Hz)

R cm

0

4

x 10

315o

Frequency (Hz)

355cm

0.5

(c)

1.5

1.5
1
0.5
0

(d)

1.5
1
0.5

0

0.2

0.4
0.6
Time (Sec.)Clarity
RT=128ms
RT=300ms

00.8

R=50cm
45.5
40.5

0

0.2

R=110cm
40.8
34.9

0.4
0.6
Time (Sec.)

0.8

R=170cm
36.6
32.7

Figure 3: Example impulse responses. (a) RT=128 ms,
R=50 cm, (b) RT=128 ms, R=170 cm, (c) RT=300 ms,
R=50 cm, (d) RT=300 ms, R=170 cm.
comes small as the reverberation and distance R increase.
That is, when the reverberation is long and R is large, theanechoic assumption becomes corrupted.
4.3. Source sparseness under reverberant conditions
Here, we investigate how the sparseness changes undersome of the reverberant conditions. For the sparsenessmeasure, we employed the approximate W-disjoint orthogonality [9]:P
2(f,τ ) ||Φ(k,z) (f, τ )sk (f, τ )||P
rk (z) =× 100 (15)2(f,τ ) ||sk (f, τ )||where Φ(k,z) is a time-frequency binary mask that has aparameter z½
1 20 log (sk (f, τ )/ŷk (f, τ )) > z
Φ(k,z) (f, τ ) =(16)
0 otherwiseihPNand ŷk (f, τ )=STFT
i=1,i6=k si (t) (sum of interferencecomponents). The approximate W-disjoint orthogonalityrk (z) means the percentage of the energy of source k fortime-frequency points where it dominates the other sourcesby z dB.
Figure 4 shows the rk (z) values under some reverberant
conditions. The sparseness decreases when the contribution of the direct sound is small (see Fig. 3). That is, thesparseness decreases as a result of both the reverberationand distance R.
4.4. Separation performance
The separation performance was evaluated in terms of thesignal-to-interference ratio (SIR) improvement. Moreover,4

IWAENC 2006 – PARIS – SEPTEMBER 12-14, 2006

5

100

4

90

.]g
e3
d
[
r
o
rr 2
E

80
] 70
%
[
60
k
_
r

50
40
30
20

anechoic
128ms, 50cm
128ms, 170cm
300ms, 170cm-10 -50

510

10 15 20 25 30
z [dB]

Figure 4: Source sparseness for some reverberant conditions. rk (z)is calculated for N = 4.
18anechoic
128ms,50cm
128ms,110cm
128ms,170cm
300ms,50cm
300ms,110cm
300ms,170cm

[dB]

12
10
8
6
4
0
SDR

Figure 5: Separation performance for each condition.
we also evaluated the sound quality with the signal to distortion ratio (SDR). The definitions of SIR improvement
and SDR can be found in [5].
Figure 5 shows the result for each condition. The performance degrades as the reverberation becomes long. Moreover, performance degradation was observed as the distance R became large. Both phenomena were expectedfrom the clarity values in Fig. 3 and from the sparsenessevaluation in the previous subsection. The performancetends to worsen as the direct sound contribution becomes
smaller.
4.5. DOA estimation performance
For DOA evaluation, we converted the estimated DOAs
qk as follows
qk = [cos θk cos φk , sin θk cos φk , sin φk ]T

,s
m
mc
8 0
2 1
1 1

,s
m
mc
8 0
2 7
1 1

s
mm
0 c
0 0
3 5

,s
m
mc
0 0
0 1
3 1

,s
m
mc
0 0
0 7
3 1

Figure 6: DOA estimation error in degrees. The error bar
shows the standard deviations.

5. CONCLUSION

2
SIR

,s
mm
8 c
2 0
1 5

tion and distance R are large, the DOA estimation error
increases, however, the DOA estimation error is still notvery large even under difficult conditions.

16
14

c
i
o
h
c
e
n
a

(17)

where θk and φk are the azimuth and the elevation of thek-th source, respectively. Because the elevations φk werealways zero with our setting, we evaluated only the azimuth θk .
The azimuth values were set as shown in Fig. 2, however, there were small differences between the drawn DOA
and real DOA because they were set manually for every
RT and R. Therefore, we evaluated the estimation error
Errork = |θk − θ̂k |where θ̂k represents the approximated true directions, whichwere estimated by the MUSIC algorithm [10] when there
was only one source signal.
The result is shown in Fig. 6. When the reverbera-

We investigated the time-frequency mask approach for BSS
and DOA estimation with respect to reverberation. As
our test was only for the 3-microphone and 4-source case,further investigations are required for more complicatedcases (more sources, more sensors, longer reverberation,etc.). The performance degradation caused by diffusednoise should also be investigated in the future.
6. REFERENCES[1] Ö. Yılmaz and S. Rickard, “Blind separation of speech
mixtures via time-frequency masking,” IEEE Trans. Signal
Processing, vol. 52, no. 7, pp. 1830–1847, July 2004.
[2] N. Roman, D. Wang, and G. J. Brown, “Speech segregation
based on sound localization,” Journal of Acoustical Societyof America, vol. 114, no. 4, pp. 2236–2252, 2003.
[3] S. Rickard and F. Dietrich, “DOA estimation of many
W-disjoint orthogonal sources from two mixtures using
DUET,” in Proc. SSAP2000, Aug. 2000, pp. 311–314.
[4] M. Matsuo, Y. Hioka, and N. Hamada, “Estimating DOA
of multiple speech signals by improved histogram mapping
method,” in Proc. IWAENC2005, Sept. 2005, pp. 129–132.
[5] S. Araki, H. Sawada, R. Mukai, and S. Makino, “A novel
blind source separation method with observation vector
clustering,” in Proc. IWAENC 2005, Sept. 2005.
[6] S. Araki, H. Sawada, R. Mukai, and S. Makino, “DOA
estimation for multiple sparse sources with normalized observation vector clustering,” in Proc. ICASSP2006, May
2006, vol. 5, pp. 33–36.
[7] R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, Wiley Interscience, 2nd edition, 2000.
[8] “ISO 3382: Acoustics-Measurement of the reverberation
time of rooms with reference to other acoustical parameters,” 1997.
[9] S. Rickard and Ö. Yılmaz, “On the approximate W-disjoint
orthogonality of speech,” in Proc. ICASSP2002, may 2002,
vol. I, pp. 529–532.
[10] R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas and Propagation, vol. 34, pp. 276–280, Mar. 1986.