Active control of scattering effects in 2.5D multizone reproduction
Junqing ZHANG(1) , Wen ZHANG(1) , Lijun ZHANG(1) ,Mengyao ZHU(2)(1) Center of Intelligent Acoustics and Immersive Communications and School of Marine Science and Technology, Northwestern

Polytechnical University, Xi’an China, E-mail: junqingzhang@mail.nwpu.edu.cn, wen.zhang@nwpu.edu.cn,
zhanglj7385@nwpu.edu.cn(2) School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China, E-mail:zhumengyao@shu.edu.cn.

Abstract
Multizone reproduction has gained signiﬁcant interest in recent years for its advantage that listeners can enjoy
their personal audio without physical isolation or wearing headphones. However, study of multizone reproduction has been focused on reproducing sounds in an empty listening space. The scattering effects of the humanand objects in sound zones are often neglected, causing degraded system performance. In this work, we focus
on reproduction on a 2D horizontal plane using 3D secondary sources, i.e., 2.5D reproduction. Through experiments we show how scatterers such as human head and body in sound zones inﬂuence reproduction results.
A modal-domain method for 2.5D multizone reproduction with an active control strategy to correct the scattering effects is proposed. The method is based on modelling the human head as a rigid sphere, based on whichanalytical expressions are developed to represent the scattered sound ﬁeld. The method is validated throughexperiments using a 48-element circular loudspeaker array. Experimental results especially show the improved
acoustic contrast performance using the proposed method.
Keywords: 2.5D multizone reproduction, mode matching, scatterer

1

INTRODUCTION

Nowadays, the development of multizone sound ﬁeld reproduction has attracted more and more attention. It can
provide a variety of different experiences for listeners in open space, such as listening to music or watchingmovies in speciﬁc areas, and simultaneously generating quiet regions using a single array of loudspeakers [1, 2].
It provides signiﬁcant ﬂexibility because there is no need for listeners to wear headphones or set separate
isolation. Lots of methods have been proposed to achieve multizone sound ﬁeld control, among which therepresentative ones are: acoustic contrast control (ACC) [3], pressure matching (PM) [4], the combination of
ACC and PM [5] , and model-domain based reproduction [6, 7, 8]. A practical implementation is to control
2D desired ﬁelds using 3D point sources, known as 2.5D reproduction [9, 10]. Algorithms proposed in recent
years have gradually evolved from single frequency based design to broadband reconstruction [11, 12]. Such
improvement will promote the implementation and applications of multizone sound ﬁeld reproduction.
Multizone reproduction is usually designed in an empty listening space, and most existing works assumed that
there is no scatterer within the control region. In practice, the listener exists in these sound zones, producing
scattered sound ﬁelds which will inevitably leak into adjacent pre-deﬁned reproduction regions. Similar to theeffects due to reverberation, the scattering effects generally degrades the reproduction performance. Experimental
results proved that the scattering effects from listeners causes around 8 dB acoustic contrast loss [13]. Until
now, only a few research works have been carried out to test and correct the inﬂuence of scatterers. Betlehem
and Poletti [14] devised a method for sound ﬁeld reproduction around a solid object in a reverberant room.
Chang provided an improving control method to correct the scattering effects on the sound focused personal
audio system [15]. However, both of these methods are based on multi-point control method, which requires
many microphones to be placed at the control points which are uniformly placed within the sound zone. A
modal-domain approach was recently developed to correct the scattering effects and achieve optimal control

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Virtual source

Global region ofinterest
BrightScattered
zone
Field

Incident
Field

r0

o

ob
obd=ob- od

od
x

rb

rd

Dark zone

R

Figure 1. Geometry of multizone sound control with a scatterer inside the bright zone.
over the entire region [16]. Simulation results showed that the proposed method can improve the reproduction
performance over a wide frequency range and a certain angle range in the free ﬁeld environment.
The research works mentioned above are mainly base on theoretical studies and computer simulations, and very
few experimental validations have been provided. In this paper, we present experimental validation of the proposed active scattered ﬁled control in [16] using a circular loudspeaker array. In the reproduction stage, theacoustic transform function (ATF) is measured by a spherical microphone array, and the generated sound ﬁeld
is measured by an electret condenser microphone array in a semi-anechoic environment enclosed by acoustic
bafﬂes. In addition, the actual scattering effects and effectiveness of the active control were discussed. The
remainder of this paper is organized as follows: the scattered ﬁeld control theory for 2.5D multizone reproduction is revisited in Section 2. Section 3 introduces the experimental implementation of the proposed method.
The experiment results and the detailed discussion are showed in Section 4. Finally, we summarize the research
work in Section 5.

2

ACTIVE CONTROL OF THE SCATTERED FIELD

The geometry of multizone sound control with a scatterer inside the bright zone is shown in Figure 1. Whenthe virtual source comes from the exterior of the control region, the sound ﬁeld at an arbitrary point includes
two parts: the incident ﬁeld coming from the virtual source directly and the scattered ﬁeld caused by the humanhead and body inside of the bright zone.
2.1 Sound ﬁeld modal
The sound ﬁeld at the observation point x can be represented as [16],P(x, k) = Pin (x, k) + Psc (x, k).

(1)where k = 2π f /c is the wave number with c the speed of sound and f being the temporal frequency, andsuperscript (·)in and (·)sc denote the incident ﬁeld and scattered ﬁeld, respectively.

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2.1.1 Incident sound ﬁeld
In 2.5D reproduction, the desired ﬁeld is on a 2D plane, i.e., the plane is at elevation angle θ = π/2, thus theincident sound pressure can be expressed in the form [17],N0Pin (x, k) ≈N0in(k) jn (k x)Ynm eimφx ,∑ ∑ βnm(2)m=−N0 n=|m|where Ynm = Cnm Pnm (0) and Cnm = ((2n + 1)(n − |m|)!)/(4π(n + |m|)!). jn (·) is the spherical Bessel function ofin (k) is the modal coefﬁcient. The truncation order N = ekr /2 [18], where r is the radiusorder n, and βnm000of the region of interest, e is the Euler’s number, and · denotes the ceiling function. Similarly, the incident
sound ﬁeld at any observation point xb ≡ (xb , φxb ) within the bright zone can be written as,
Pbin (xb , k) ≈

Nb

Nb

μ

∑ ∑ ανinμ (k) jν (k xb )Yν eiμφxb ,(3)

μ=−Nb ν=|μ|where ανinμ is the corresponding sound ﬁeld coefﬁcients. The truncation order is Nb = ekrb /2, where rb is theradius of the bright region.
Using the Bessel function addition formula [19], the bright zone sound ﬁeld coefﬁcients ανinμ in (3) can bein in (2) as,
related to the global sound ﬁeld coefﬁcients βnm
N0

N0

in
(k)Tnν (ob , k) = ανinμ (k),∑ ∑ βnmmμ(4)m=−N0 n=|m|where ob is the vector that points from the global origin to the origin of the bright zone, and∞

2m−μTnν (ob , k) = 4πiν−nW1W2 ∑ il (−1)
mμ

=0



with
W1 =

n
0

ν
0



j (k ob )Y(μ−m) (θob , φob )

l
0




,W2 =

n
ν
m −μ

(2n + 1)(2ν + 1)(2 + 1)/4π,l(μ − m)(5)



denoting the Wigner 3 − j symbol, and (·) represents the complex conjugate.
We can represent (4) in matrix form as,
Tb b = ain
b.

(6)

(7)

in
T
in
in
in
in
T
where b = [β0in , . . . , βnin2 +n+m+1 , . . . , β(N2 ] , ab = [α0 , . . . , α1+ν 2 +ν+μ , . . . , α(N +1)2 ] , and Tb is the (Nb +0 +1)
b1)2 × (N0 + 1)2 translation matrix. Similarly, the matrix Td denotes the translation matrix from the global region

to the dark zone.
2.1.2 Scattered sound ﬁeld
In order to parameterize the scattered ﬁeld, we model the human head as a rigid sphere. By applying theboundary condition on its surface, which is the particle velocity perpendicular to the surface is zero [17], thescattered ﬁeld at the observation point xb within the bright zone can be written as,
Pbsc (xb , k) ≈

Nh

Nh

(1)

μ

∑ ∑ ανscμ hν (k xb )Yν eiμφxb ,(8)μ=−Nh ν=|μ|(1)

where hν (·) represents the outing spherical Hankel functions. The scattered ﬁeld modal coefﬁcients ανscμ can be(1)

calculated using the relationship ανscμ = (− jν (ka)/hν (ka))ανinμ , where (·) denotes the corresponding derivative.
The truncation order is Nh = eka/2 with a the radius of the human head.

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For observation points within the dark zone, the scatterer can be viewed as an exterior source. Thus, the soundpressure of the observation point xd within the dark zone can be written as,
Pdsc (xd , k) ≈NdNd∑ ∑ ζvusc jv (k xd )Yvu eiuφxd ,(9)u=−Nd v=|u|where Nd = ekrd /2, and rd is the radius of the dark zone. Analogous to (4), based on the corresponding(1)μaddition theorem for hν (k xb )Yν (θxb , φxb ) [19], we have
Nh

Nh

μu

∑ ∑ ανscμ Sνv (obd , k) = ζvusc ,(10)μ=−Nh ν=|μ|

where
μu

∞

2μ−u

Sνv (obd , k) = 4πiv−ν W3W4 ∑ il (−1)
=0h (k obd )Y(u−μ) (θobd , φobd ) (2ν + 1)(2v + 1)(2 + 1)/4π,

with the vector obd = ob − od , and W3 and W4 denote Wigner 3 − j symbol.
The matrix-vector notation of (10) issc
Sbd ascb = cd .

(11)

(12)

sc
sc
sc
T
sc
sc
sc
sc
T
where asc
b = [α0 , . . . , αν 2 +ν+μ+1 , . . . , α(N +1)2 ] , cd = [ζ0 , . . . , ζv2 +v+u+1 . . . , ζ(N +1)2 ] , and Sbd is the (Nd +1)2 × (Nh + 1)2 translation matric.

hd

2.2 Modiﬁed formulation and control
In the previous work [10], we formulated the multizone reproduction problem in the modal domain as obtaining
the global sound ﬁeld coefﬁcients b to generate a desired sound ﬁeld within bright zone which characterisedby its local coefﬁcients ainb . The energy of the dark zone and entire global sound ﬁeld were set as constraints
for the optimization problem. Then, we proposed a modiﬁed formulation, which reduced the energy of both theincident and scattered ﬁelds in the dark zone [16]. That is,2
min Tb b − ain
b
b

(13)

subject to (Td + Rd )b ≤ ed(13a)b ≤ eg ,

(13c)

2

2

According to (12), the scattering components are linked to the incident sound ﬁeld and the global components,that is(14)
csc
d = Rd b
where Rd = Sbd QETb represents the translation matrice from the bright zone to the dark zone. The matrix




(1)
(1)
Q = diag − j0 (ka)/h0 (ka), . . . , − jNh (ka)/hNh (ka) is a diagonal matrix, and the matrix E is used to pick theﬁrst (Nh + 1)2 elements of the vector Tb b given the truncation order of the scattered ﬁeld in the bright zone isNh . Solving this constrained optimization problem, we can obtain the global coefﬁcients b.
2.3 2.5D weighted mode matching reproduction
The aim of the multizone sound ﬁeld reproduction is to choose the loudspeaker driving signals to generate adesired sound ﬁeld Pin (x, k) at each position x in the control region D. The control region shall be circular of3066

MM-4XP Miniature
Loudspeakers array

Mac proRednet3

Bright zone
Switch

Dark
zone

KEMAR
Head & Torso
ELectret microphone
Array

ADA8200
MPS-488P Power Supply Front Panel

(b)

(a)

Figure 2. (a) Illustration of the setup of the 2.5D reproduction system, (b) experimental layout: A KEMAR
Head and Torso Simulator is placed at the center of the bright zone within a 48-channel circular loudspeakerarray in a semi-silent environment.
radius r0 centered about the origin as shown in Figure 1. The global sound ﬁeld generated by an array of L
loudspeakers can be represented as,
LP(x, k) = ∑ d (k)G (x, k),

(15)

=1

where G (x, k) represents the ATF between the th loudspeaker and the observation point x in the global system.
d is the th loudspeaker driving signal.
We adopt the weighted mode matching approach to minimize the weighted least squares error over the entire
control region [16]. By referring to (2) and (15), the cost function can be written as,
J(d, k) =

1
2π

 
D

2


P(x, k) − Pin (x, k) dx.

(16)

Until now, we can obtain the loudspeaker driving signals by solving this cost function. The reader is encouraged
to refer to [16] for a detailed derivation of the theory behind the design.

3

IMPLEMENTATIONAs mentioned in Section 2.1.2, the proposed active scattered ﬁeld control is based on assuming the human headas a rigid sphere. However, for human listeners, the effects of the scatterer are not only due to the human head,but also the human body (including shoulders, neck, and clothes, etc.). Therefore, it is necessary to validate
the proposed theory on a human body, such as a head and torso simulator. The illustration of the measurement
setup and experimental layout are showed in Figure 2(a) and (b), respectively.
3.1 Acoustic transform function measurement
In the reproduction stage, we measure the ATF between the loudspeakers and observation points [16] to obtainthe loudspeaker driving signals. The room environments and sensor errors are very sensitive to sound ﬁeld
reconstruction, so the accurate measurement of ATF is very important. High order spherical microphone arrayis a good choice in 3D sound ﬁeld coefﬁcient extraction [20]. In our experiment setup, the global control region
is a circular area of radius 1 m. Due to the limited observation range of a single microphone array, we often
need a distributed microphone arrays to complete ATF measurement over this large area [21].
In our experiment, we use the MH Acoustics’ Eigenmike EM32 to capture the sound pressure produced by the
loudspeaker. We move a single Eigenmike along a horizontal circle (assuming stationary conditions) [21] tocapture the global sound ﬁeld. This strategy not only reduces the hardware costs, but also avoids perturbations

3067

of the scattering effects when Eigenmikes are set nearby for the measurement. A ﬁve second-long exponential
sweep from [20,20000] Hz frequency range is feed to each loudspeaker as an excitation signal [22].
3.2 Hardware implementation
The experiment is conducted in the Acoustics and Audio Lab at the Center of Intelligent Acoustics and Immersive Communications (CIAIC), Northwestern Polytechnical University. The measurements are performed at asampling frequency of 48 kHz using a Dante audio interface. As shown in Figure 2(a), Dante network provides
all the experimental equipments with a synchronized clock. The loudspeaker driving signals are sent by the
Mac Pro to the switch, then to the sound card Focusrite Rednet3. Finally, the signals are sent to the speakerthrough the sound card. The Meyer Sound MM4XP miniature analog loudspeakers are powered by MPS-488P
Power Supply devices, and we use the ADA8200 as the D/A converter to convert the digital driving signals tothe loudspeaker analog input signal. In Figure 2(b), a circular array of 48 loudspeakers are used to synthesize
sound ﬁeld in a two dimensional 2D plane levelled with the listener’s (or the mannequin’s) ears. The GRAS
45BB KEMAR Head and Torso Simulator wearing a T-shirt is placed at the original of the local bright zone.
The loudspeakers are equally spaced on a circle with a radius of 1m. The acoustic barriers enclose the circular
loudspeaker array to create a semi-anechoic environment, which is used to match the simulation condition usedin [16]. After the ATF encoding is completed, we send the driving signals to the loudspeaker array to reproduce
the global sound ﬁeld. Finally, an electret condenser microphone array is used to measure the reproduced soundﬁeld within different listening zones.

4

EXPERIMENTAL VALIDATIONIn this section, we present the experimental setup and discuss the measurement results.
4.1 Experimental measurement setup
We evaluate the reproduction performance over a broadband frequency range [100,1000] Hz and angle range[0o , 180o ]. The desired ﬁeld is a plane wave with an amplitude of A = 1 coming from the azimuth angle φ pw .
For the evaluation along with frequency, the coming angle of the plane wave is φ pw = 120o . For the evaluation
along with angle, the frequency of the plane wave is 600 Hz. For both cases, we set the energy constraints
in the dark zone and global region to ed = 0 dB and eg = 20 dB. Each sound zone has a radius of 0.15 m.
The bright zone and dark zone are located at ob = (0.4, 0) and od = (−0.4, 0) with respect to the global origin,respectively.
4.2 Evaluation indicator
The evaluation indicator is the acoustic contrast κ(k) between the bright zone and dark zone,
2



1
k)
 dx
P(x,
D
Vb
b
κ(k) = 10log10
2



1
Vd Dd P(x, k) dx(17)

where P(x, k) represents the reproduced sound ﬁeld at a point within the bright zone Db or the dark zone Dd .
Vb and Vd denote the area of the bright zone and the dark zone, respectively.
4.3 Experiment results and discussion
We evaluate the acoustic contrast over a broadband frequency range and a certain angle range. The blue, blackand red lines correspond to the case that there is no scatterer (Incident) [10], using the traditional method
without scattered ﬁeld control (Scattered), and using the proposed scattering control method (Proposed) [16].
Performance results in Figure 3(a) shows that the scattering effects of the KEMAR mannequin head and bodyon the reproduction performance can not be ignored, the acoustic contrast has 0.1 − 4.8 dB loss when the3068

Figure 3. Acoustic contrast along with a broadband frequency range and a wide angle range.
KEMAR mannequin is inside the bright zone. Especially at 600 Hz, the acoustic contrast loss is up to 4.8 dB.
Using the proposed method, about 0.1 − 3.1 dB gain in acoustic contrast is achieved in the frequency range[500,1000] Hz. In Figure 3(b), the acoustic contrast has 0 − 3.5 dB loss over the angle range [0o , 180o ]. The
proposed active control method can improve the performance within the range [70o , 130o ]. It is noteworthy that
there is around 6.5 dB acoustic contrast improvement at 100o .

5

CONCLUSIONSIn this work, we presented an active control of scattering effect in 2.5D multizone reproduction with experimental validation. Based on wave modelling theory and translation theorem, we developed analytical expressionsof the incident and scattered ﬁelds for the global region and each sound zone. We then proposed an active
control strategy to correct the scattering effects and used the weighted mode matching approach for reproduction. The experimental results showed that the scattering effects produced by the human head and body severely
degrade the reproduction performance. The proposed scattered ﬁeld control method is based on the assumptionof modeling the human head as a rigid sphere and can achieve acoustic control improvement over a broadband
frequency and angle range. Future work will investigate incorporating the human torso scattering effect into thecontrol and examine the proposed method in reverberant environments.

ACKNOWLEDGEMENTS
This work was supported by the National Natural Science Foundation of China (NSFC) funding scheme under
Project No. 61671380.

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