2018 26th European Signal Processing Conference (EUSIPCO)

Time-Frequency-Bin-Wise Beamformer Selection
and Masking for Speech Enhancement in
Underdetermined Noisy Scenarios
Kouei Yamaoka∗ , Andreas Brendel† , Nobutaka Ono‡ , Shoji Makino∗ ,Michael Buerger† , Takeshi Yamada∗ , and Walter Kellermann†∗ University of Tsukuba, 1-1-1 Tennodai, Tsukuba-shi, Ibaraki, 305-8577 Japan,{yamaoka@mmlab.cs, maki@tara, takeshi@cs}.tsukuba.ac.jp† Friedrich-Alexander University Erlangen-Nürnberg, 91058 Erlangen, Germany,{andreas.brendel, michael.buerger, walter.kellermann}@FAU.de‡ Tokyo Metropolitan University, 6-6 Asahigaoka, Hino-shi, Tokyo, 191-0065 Japan, onono@tmu.ac.jp

Abstract—In this paper, we present a speech enhancement
method using two microphones for underdetermined situations.
A conventional speech enhancement method for underdeterminedsituations is time-frequency masking, where speech is enhancedby multiplying zero or one to each time-frequency component
appropriately. Extending this method, we switch multiple preconstructed beamformers at each time-frequency bin, each of which
suppresses a particular interferer. This method can suppress
an interferer even when both the target and an interferer
are simultaneously active at a given time-frequency bin. As aswitching criterion, selection of minimum value of the outputs of
the all beamformers at each time-frequency bin is investigated.
Additionally, another method using direction of arrival estimationis also investigated. In experiments, we confirmed that the
proposed methods were superior to conventional time-frequency
masking and fixed beamforming in the performance of speechenhancement.

I. I NTRODUCTION
Beamforming and blind source separation (BSS) [1] arecommonly used in speech enhancement and can yield a good
performance as long as a sufficient number of microphones areavailable. Automatic speech recognition can be improved byapplying these methods (e.g., [2]). However, the capability ofthese microphone array methods to suppress multiple interferers depends on the number of microphones M . If there are N
sound sources consisting of one target and (N −1) interferers,
we need the same number of microphones (M = N ) to suppress all interferers by null steering. However, commonly-usedsmall recording devices such as voice recorders often have
only two microphones. Although several conventional methods
such as time-frequency masking [3], [4], multichannel Wiener
filtering [5], and the statistical modeling of observations using
latent variables [6] can work well in underdetermined situations (M < N ), they face a tradeoff between a low signal
distortion and high noise reduction performance.
In this paper, we propose a new method of speech enhancement realizing a high performance by selecting one
out of multiple pretrained beamformers as an extension of
conventional speech enhancement based on time-frequency
masking. If M microphones are available, a single beamformer
can generally form (M − 1) nulls. This means that a single

ISBN 978-90-827970-1-5 © EURASIP 2018

beamformer can suppress only one interferer in the two microphone case (M = 2). However, if we can construct (N −1)
beamformers, each suppressing one of the (N − 1) interferers,
we can improve the speech enhancement performance byusing a combination of these beamformers rather than a single
beamformer.
In [7], the combination of multiple beamformers with different steering directions for audio zooming was considered.
However, in this study, we combine multiple beamformers
with the same steering direction (the same target) but different
null directions. Speech enhancement by Wiener filtering andfrequency-bin-wise combination of multiple fixed null beamformers using a square microphone array was proposed in[8], [9]. However, this method tends to generate target signal
distortions. The reduction of mechanical noise, such as thesound of actuators and motors in a robot, by selecting themost suitable noise covariance matrix at each time-frequency
bin for the computation of maximum signal-to-noise ratio(MaxSNR) beamformers has also been proposed [10]. Thismethod requires the clustering of multichannel mechanicalnoise covariance matrices in a training phase under the assumption that the number of the patterns of the actuator isusually limited. In contrast to the methods presented above, we
switch multiple signal-dependent beamformers at each timefrequency bin for underdetermined speech enhancement witha low amount of target distortions such as minimum variancedistortionless response (MVDR) beamformers [11], [12].
In this paper, we propose two criteria for selecting a suitablebeamformer from a set of previously trained beamformers,
namely, minimum value selection (MIN), that is, the choiceof the beamformer corresponding to the minimum absolute
output among the outputs of these multiple beamformers,
and its extension based on the direction of arrival (DOA)
estimation. If a time-frequency bin is occupied by either
the target and one of the interferers or by a single source,i.e., it fulfills the W-disjoint orthogonality (W-DO), MIN can
suppress the interferer. The combination of MIN and DOA
estimation can also suppress noise in a time-frequency bin
when no target is present. We evaluate the performance of1596

2018 26th European Signal Processing Conference (EUSIPCO)

Interferer B

Interferer A

TABLE I: Combinations of the input signals andcorresponding output signals

TargetFig. 1: Combination of two beamformers with a spatial nullfor each interferer
each proposed method and confirm its effectiveness.
II. C ONVENTIONAL LINEAR BEAMFORMING
We model the microphone signals in the short-time Fouriertransform (STFT) domain. Here, let xi (ω, t) be the ith microphone signal at the angular frequency ω in the tth time frame.
When two microphones observe one target and one interferer,
we can perform conventional speech enhancement using, e.g.,a MaxSNR beamformer [11], [13] or an MVDR beamformer[11], [12], which steers a spatial null in the direction of theinterferer, as described by the following equations:y(ω, t) =wH (ω)x(ω, t),(1)Tx(ω, t) =[x1 (ω, t), x2 (ω, t)] ,w(ω) =[w1 (ω), w2 (ω)] ,

T

(2)
(3)

where y(ω, t) is the output signal of the beamformer, w(ω)
denotes the spatial filter vector, (·)T denotes the transpose, and(·)H denotes the Hermitian transpose. However, only (M − 1)sources can be suppressed using M microphones. Hence, theperformance of linear speech enhancement may be degradedunder an underdetermined situation with M < N , i.e., when
we have fewer microphones than sound sources N .
III. P ROPOSED SPEECH ENHANCEMENT METHOD BASEDON SELECTION FROM MULTIPLE BEAMFORMERS

Without loss of generality, we consider a situation with
M = 2 microphones and N = 3 sound sources consistingof a target signal, interferer signal A, and interferer signal
B (hereafter referred to as tgt, iA , and iB , respectively). In
this situation, we cannot construct a null beamformer thatsuppresses both interferers. However, if only tgt and iA are
observed, we can construct beamformer A that suppresses iA
using a conventional beamforming method, and analogously
beamformer B that suppresses iB (see Fig. 1). Then, we
obtain the following two output signals yA and yB from an
observation x consisting of tgt, iA , and iB :yA (ω, t) =yB (ω, t) =wH
A (ω)x(ω, t),HwB (ω)x(ω, t),

(4)
(5)

where wA and wB are the spatial filters defining the beamformers A and B, respectively.
For every time-frequency bin of the observed signal x, thedominant sound comprises the seven patterns listed in Table I
with the corresponding beamformer outputs yA and yB , where
the trivial case with no active sources is not considered here.
If only tgt is dominant in x(ω, t), both beamformers output
tgt (see the second row of Table I). If only iA is dominant,beamformer A suppresses the input signal and beamformer

ISBN 978-90-827970-1-5 © EURASIP 2018

x
tgt
iA
iB
tgt, iA
tgt, iB
iA , iB

yA
tgt
0*
iB
tgt
tgt, iB
iB

yB
tgt
iA
0*
tgt, iAtgt
iAtgt, iA , iB

tgt, iB

tgt, iA* suppressed

yMIN
tgt
0*
0*
tgt
tgt
iA or iB
tgt, iAor tgt, iB

yDOA
tgt
0 **
0 **
tgt
tgt
0 **
tgt, iAor tgt, iB** masked

B outputs a slightly altered version of iA . At time-frequency
bins consisting of tgt and iB , beamformer B outputs tgt only,
whereas beamformer A outputs both tgt and iB .
In our proposed method, we perform speech enhancementby choosing the output from yA and yB , which means that
we choose the best result from multiple beamformers in eachtime-frequency bin. Here, the important issue is how to selectthe appropriate beamformer. Under the assumption of W-DO,
either tgt, iA , or iB is active in a time-frequency bin. Then,the requirement for the selection strategy is that the output
should be tgt if it is dominant, otherwise zero as an interferer isdominant in this case. In this paper, we propose two methodsof selecting beamformers satisfying this requirement, which
we call MIN and its extension DOA.
A. Minimum value selection of multiple beamformers
The magnitude of the output of beamformer A (B) is smaller
than that of beamformer B (A) when iA (iB ) is dominant in
the respective time-frequency bin. Thus, the following MIN
selection criterion satisfies the requirement described above:{yA (ω, t) if |yA (ω, t)| ≤ |yB (ω, t)|,yMIN (ω, t) =(6)yB (ω, t) otherwise.
This formula implies that MIN selects the output of the
beamformer with the smaller magnitude. The rationale behind
MIN is that it suppresses the interferer signal in a timefrequency bin consisting of tgt and one interferer signal under
the assumption that the magnitude of tgt is smaller than themagnitude of the sum of tgt and the interferer signal, which isa valid assumption when considering statistically independent
target and interferer signals. However, if a time-frequency bin
contains iA and iB , MIN will select iB or iA (see the seventh
row of Table I). Thus, although the magnitude of the output of
MIN is smaller than iA and iB , one of the interferers remains.
MIN is similar to time-frequency masking, in which a softor hard mask is applied to time-frequency bins dominated byinterferers. Thus, masking methods require W-DO in general.
In contrast, MIN selects the beamformer that suppresses aninterferer in each time-frequency bin, i.e., it can also suppress
noise in a time-frequency bin that contains both the target and
one interferer. Therefore, the proposed method is applicableeven if the assumption of W-DO is not satisfied. From theabove, it can be concluded that the MIN-based selection
is an extension of time-frequency masking overcoming thelimitation of requiring W-DO.

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2018 26th European Signal Processing Conference (EUSIPCO)

B. Extension of minimum value selection by DOA estimation
Speech enhancement by MIN, which is a simple selection
rule, is expected to show high speech enhancement performance. However, when a time-frequency bin contains multiple
noise signals, it is not possible to suppress all of them. If there
is no target in such a bin, the respective signal component
should be suppressed completely similarly to time-frequency
masking (see the last column of Table I), i.e.,yDOA (ω, t) = M (ω, t)yMIN (ω, t),(7)where M (ω, t) is a soft mask. To construct M (ω, t), we
estimate the activity of the sound sources by evaluating a
trained probabilistic model that describes the DOAs of thesound sources.
In this paper, we use a one-microphone-pair version of [14]for this task, which has been used as a baseline algorithm forthe DOA estimation methods in [15] and [16]. Here, the relative phase ratios (RPRs) ϕ(ω, t) of the observed microphonesignals defined aswhere C is the number of frequency bins. Here, ηkL (ω, t) isa Boolean variable that indicates whether the sound source
active in time-frequency bin (ω, t) belongs to cluster k.
SAEk (t) is smoothed by applying linear weighted moving
average (LWMA) as
SAEk (t)←T∑(T + 1 − |i|)SAEk (t + i),
T + 1 − |i|

(15)

i=−T

where T is the number of time frames taken into account for
LWMA. Then, the global DOA estimation, i.e., the estimationof a DOA associated with a time frame, is performed byapplying a fixed threshold to the SAE estimates.
{
1 if SAEk (t) > threshold,Gηk (t) =(16)
0 otherwise,
M G (t) =SAEk=target (t),∑K
k=1 SAEk (t)(17)

x2 (ω, t) |x1 (ω, t)|·,(8)
x1 (ω, t) |x2 (ω, t)|
are clustered by a Gaussian mixture model (GMM). The meanµk (k = 1, . . . , K) of each complex Gaussian distribution N c
is an expected RPR associated with a DOA from a predefined
grid, where K is the number of clusters/grid points{}
1|ϕ(ω, t) − µk |2
N c (ϕ(ω, t); µk , σ 2 ) =
exp
−
, (9)
πσ 2
σ2

where ηkG (t) and the soft mask M (t)G are global counterpartsof ηkL (ω, t) and M L (ω, t), respectively. The global DOA
estimation works even if some time-frequency bins do notsatisfy W-DO owing to the averaging of local DOA estimates.
Finally, the local DOA estimate is chosen if W-DO isfulfilled and the global DOA estimate otherwise, i.e.,{⟨⟩ηkL (ω, t)if η L (ω, t), η G (t) = 1,
ηk (ω, t) =(18)
ηkG (t)otherwise,

where σ 2 is the variance common to all Gaussian components,
which can be user-defined without performance loss [17].
Then, the mean of the Gaussian component with the maximum
likelihood given the observation ϕ(ω, t) is chosen as the timefrequency-bin-wise DOA estimate

where ⟨·, ·⟩ is the standard inner product operator. Then, thesoft mask M in (7) is constructed as
if ηk=target (ω, t) = 1,
1⟨⟩L
M (ω, t) = M (ω, t)if η L (ω, t), η G (t) = 1, (19)
M G (t)otherwise.

ϕ(ω, t):=

DOAL (ω, t) =argmax N c (ϕ(ω, t); µk , σ 2 ). (10)µkHereafter, we abbreviate the local, i.e., time-frequency-binwise DOA, as DOAL , and the global, i.e., time-frame-wise
DOA as DOAG . Note that DOAL (ω, t) is a RPR associatedwith the DOA corresponding to the time-frequency bin (ω, t).
Then, a soft mask M L (ω, t) based on the local DOA estimatesis computed as
N c (ϕ(ω, t); µk=target , σ 2 )
,
(11)
∑K
2
c
k=1 N (ϕ(ω, t); µk , σ )where µk=target is the mean corresponding to the target
direction. This procedure, based on bin-wise estimates, isjustified in time-frequency bins satisfying W-DO.
Next, source activity estimation (SAE) of each sourceis performed per time frame by averaging the local DOA
estimates as follows:C1∑ L
η (ω, t),SAEk (t) =(12)
C ω=1 k{1 if DOAL (ω, t) = µk ,ηkL (ω, t) =(13)
0 otherwise,
M L (ω, t)=

η L (ω, t) =L[η1L (ω, t), · · · , ηK(ω, t)]T ,ISBN 978-90-827970-1-5 © EURASIP 2018

(14)

IV. E XPERIMENTAL EVALUATION
A. Experimental conditions
To evaluate the effectiveness of our proposed method, we
conducted experiments using the “Underdetermined-speech
and music mixtures” test data from the community-based
Signal Separation Evaluation Campaign (SiSEC) [18]. These
data contain two mixtures with three male or female speakers.
We conduct speech enhancement experiments for each speakeras a target sound. The experimental conditions are listed inTable II.
We used two signal-dependent beamformers to produce
time-invariant filters: a MaxSNR beamformer [11], [13] andan MVDR beamformer [11], [12]. We gave the same targetactive period and noise-active period as prior information forboth beamformers to evaluate the beamformers on the same
basis. Using these periods, we calculated the interferenceplus-noise covariance matrix for the computation of both the
beamformer filters and the target covariance matrix for the
MaxSNR beamformer. Besides, we performed the eigenvalue
decomposition for the spatial correlation matrix of the targetactive period and used the eigenvector corresponding to the
maximum eigenvalue as the estimate of the transfer function,1598

2018 26th European Signal Processing Conference (EUSIPCO)TABLE II: Experimental conditions
Number of microphones
Distance between microphones
DOAs
Reverberation time
Sampling rate
FFT frame length / shift
Training period
Test period

25 cm
40◦ , 80◦ , and 105◦
250 ms
16 kHz2048 / 512 samples
5s
35 s (5 s × 7)

which is assumed to be prior information for the MVDR
beamformer.
We evaluate the performance by comparing the results ofthree conventional speech enhancement methods and fouralgorithmic variants of the proposed method. As conventional
methods, we evaluate MaxSNR SOL and MVDR SOL, which
are the underdetermined speech enhancement methods using
a single MaxSNR and an MVDR beamformer, respectively.
We also investigate the performance of the degenerate unmixing estimation technique (DUET) [19] as a conventional
method of time-frequency binary masking with a stereo microphone. We discuss the combinations of a MaxSNR and an
MVDR beamformer with the MIN and DOA selection strategy
and abbreviate these algorithmic variants as MaxSNR MIN,MVDR MIN, MaxSNR DOA, and MVDR DOA, respectively. We therefore require a target-active period and twonoise-active periods (for iA and iB separately) for the computation of the beamformer filters.
For the DOA estimation, the variance was set to 10 for all
Gaussians. Here, only the frequency bins corresponding to 1–
4 kHz were considered as they contain most of the signals
energy. For the SAE, we used nine time frames (384 ms) forsmoothing by LWMA.
To validate the effectiveness of our proposed method, weinvestigate the performance of the considered algorithms in allseven combinations of the source signals, as shown in Table I.
Here, all observed signal mixtures can be assumed to besparse (and therefore W-DO is satisfied in most time-frequencybins) because the target and noise signals are speech. We use
objective criteria, namely, the signal-to-distortion ratio (SDR),
signal-to-interference ratio (SIR), and signal-to-artifacts ratio(SAR) [20] to quantify the results. A concise representation of
the results is obtained by averaging these criteria over speakers
for the period consisting of all speakers. Here, the reference
signal is the source image, i.e., the noise-free reverberant
speech signal.
B. Results and discussion
The results of speech enhancement using the algorithms
discussed above are shown in Fig. 2 for the test period that
includes three speakers. The conventional single beamformers
can suppress only one interferer but generate a low amount ofartificial noise. Therefore, they only show good performancefor SAR. The proposed method shows a high performancein SDR and SIR, and is superior to DUET as well as to
MaxSNR SOL and MVDR SOL. Moreover, the extension of
MIN with DOA estimation results in a significant improvementof the SIR. Considering these results, it can be concluded

ISBN 978-90-827970-1-5 © EURASIP 2018that our proposed methods, particularly MVDR MIN and
MVDR DOA, improve the speech enhancement performance.
The fact that the best performance is achieved by the MVDR
beamformer in combination with MIN or its extension can beunderstood by investigating the properties of MIN and the two
beamforming methods. MaxSNR only maximizes SNR and
imposes no constraint on the target direction. Thus, the magnitude or phase of the target in yA and yB may be different,
which is a serious problem when choosing different outputs inneighboring time-frequency bins. We show the selected beamformers using MVDR MIN in Fig. 3(a) examplary. According
to this figure, the selected beamformer switches frequently inthe time-frequency plane. Hence, if the magnitude or phase of
the target in the two outputs is different, it causes distortionsof the target if different beamformer outputs are chosen intime-frequency bins close to each other, which is an effectsimilar to that occurring in time-frequency masking. On theother hand, since the MVDR beamformer outputs the target
source without distortion, both the magnitude and the phasematch. Thus, no distortion due to the switching of the beamformers occurs. This explains the higher SDR of MVDR MIN(and DOA) than of MaxSNR MIN. Considering only the
SIR performance, the MaxSNR beamformer, which does not
impose a constraint on the target direction, may be superior
to the MVDR beamformer. However, it results in a greater
distortion. Thus, it can be concluded that MVDR MIN and
its extension realize a high performance with a low distortionof the target signal in underdetermined situations.
Now, we discuss the extension of MIN by DOA estimation.
Figure 3(b) shows the selected beamformers and masked timefrequency bins. The main benefit of DOA estimation is the
improvement of SIR by using a soft mask (see the red timefrequency bins in the figure). Although the SAR performancedecreases because the masking generates artificial noise, theSDR performance is almost the same as that for MVDR MIN.
Thus, we can conclude that the extension with DOA estimation
is effective for improving noise reduction performance.
V. C ONCLUSIONSIn this paper, we have proposed a new method of speechenhancement for underdetermined scenarios and performeda performance evaluation for the 2-microphone case. Thismethod achieves high speech enhancement performance byselection from multiple preconstructed beamformers and timefrequency masking. We proposed two methods for selecting
the pretrained beamformers: MIN, which can suppress noisein the presence of one target and one interferer in each timefrequency bin, and its extension based on speaker activity
detection from the spatial information of the sources. Bothmethods can be considered as extensions of time-frequency
masking.
We demonstrated the effectiveness of the proposed methodby performing experiments in a reverberant environment containing one target and two interferers. The MVDR beamformer
combined with MIN and DOA estimation showed the highest
performance with approximately 3 dB improvement in SDR
and 7 dB improvement in SIR. This means that our proposed
method is superior to the conventional methods we used for1599

2018 26th European Signal Processing Conference (EUSIPCO)

4
3

MVDR_DOAMaxSNR_DOA

MVDR_MINMaxSNR_MIN

0

MVDR_DOA

1

0

DUET

2

2

MVDR_SOL

4

5

MaxSNR_SOL

SAR [dB]

6

MaxSNR_DOA

MVDR_DOAMVDR_MINMaxSNR_DOA

MaxSNR_MIN

DUET

MVDR_SOLMaxSNR_SOL

08

MVDR_MIN

1

6

MaxSNR_MIN

2

7

10

DUET

3

8

12

MVDR_SOLSIR [dB]

SDR [dB]

4

14

MaxSNR_SOL

5

Fig. 2: Results of speech enhancement for the test period consisting of three speakers

(a)

(b)

Fig. 3: Selected beamformers in (a) MVDR MIN and (b)MVDR DOA for each test period. Green, beamformer A;
blue, beamformer B; red, masked by (7)benchmarking our results in terms of the speech enhancement
performance.
Acknowledgments
This work was supported by the Japan Society for the
Promotion of Science (JSPS) under Grant 16H01735, SECOM
Science and Technology Foundation, and the Tsukuba-DAAD
Joint Research Program.
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