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Reproducing Personal Sound Zones Using a Hybrid
Synthesis of Dynamic and Parametric Loudspeakers
Jacob Donley∗, Christian Ritz∗and W. Bastiaan Kleijn†
∗School of Electrical, Computer and Telecommunications Engineering, University of Wollongong,
Wollongong, NSW, 2522 Australia, E-mail: jrd089@uowmail.edu.au and critz@uow.edu.au
†School of Engineering and Computer Science, Victoria University of Wellington,
Wellington, 6140 New Zealand, E-mail: bastiaan.kleijn@ecs.vuw.ac.nz
Abstract—This paper proposes a hybrid approach to per-
sonal sound zones utilising multizone soundfield reproduction
techniques and parametric loudspeakers. Crossover filters are
designed, to switch between reproduction methods, through an-
alytical analysis of aliasing artifacts in multizone reproductions.
By realising the designed crossover filters, wideband acoustic
contrast between zones is significantly improved. The trade-off
between acoustic contrast and the bandwidth of the reproduced
soundfield is investigated. Results show that by incorporating
the proposed hybrid model the whole wideband bandwidth is
spatial-aliasing free with a mean acoustic contrast consistently
above 54.2dB, an improvement of up to 24.2dB from a non-
hybrid approach, with as few as 16 dynamic loudspeakers and
one parametric loudspeaker.
I. INTRODUCTION
Personal sound environments, such as provided by multi-
zone soundfield reproduction (MSR) [1] and parametric loud-
speakers (PL) [2], are of interest in applications such as vehicle
cabin entertainment/communication systems, cinema surround
sound systems, multi-participant teleconferencing and personal
audio in restaurant/caf´
es. As well as creating a target bright
zone, it is sometimes also desired to create a second, quiet
zone. In this case, it is important to ensure that the acoustic
contrast (energy ratio) between zones is maximised whilst
ensuring the error in the bright zone is minimised. However,
research in the area has shown performance limitations related
to audio leaking between zones, known as interzone audio
interference, which limits the bandwidth of low error, high
acoustic contrast, personalised audio.
The concept of personal sound from controlling multiple
loudspeakers has been around since 1997 [3]. A method [4]
was proposed later, in 2002, to maximise the ratio of energy
between two regions which was termed Acoustic Contrast
Control [1]. Afterwards, earlier multizone reproduction tech-
niques made use of least-squares pressure matching [5] and
cylindrical harmonic expansion [6]. Further research has made
improvements in spatial reproduction accuracy by utilising
planarity [7] and orthogonal basis planewaves [8].
Scenarios where a finite number of loudspeakers are used
as secondary sources for soundfield reproduction, are lim-
ited to accurate reproduction below a (spatial aliasing) fre-
quency [9]. A fundamental issue with MSR using discrete
secondary sources is that the spatial aliasing induces so-called
grating lobes which can interfere across zones [10]. Recent
research [6], [8], [11] suggests a full circle array of ≈300
loudspeakers are required to reproduce audio up to 8 kHz with
high acoustic contrast.
PLs, on the otherhand, are capable of providing high di-
rectivity at high frequencies [12] and were first theorised in
1963 [13]. PLs have gained interest due to their high directivity
with a relatively small physical size which is comparable to dy-
namic (conventional) loudspeakers. Practical implementations
have shown PLs can provide immersive spatial audio [14],
[15], however, neither of the hybrid approaches use MSR
with dynamic loudspeakers or consider spatial aliasing. When
comparing PLs to MSR from dynamic loudspeakers, PLs
lack directivity at low frequencies [12], contain higher Total
Harmonic Distortion (THD) [2], [16] and can have potential
health risks due to the high Sound Pressure Level (SPL) of
the ultrasonic carrier frequency [2].
A hybrid system utilising the better aspects of both MSRs
and PLs would allow for high acoustic contrast at low and high
frequencies. Reproduction of speech soundfields [11], [17],
[18] would require low carrier SPL in PLs due to the low
energy of high frequency components in speech [19], thus
reducing related health risks. Further, frequency dependent PL
distortions are less of a problem at higher frequencies [16].
In this paper novel contributions are made through an
analytical approach to a hybrid MSR and PL system with ap-
plication to personal sound zones. A zone dependent crossover
filter is designed to shift the loudspeaker signals between the
MSR and PL in the frequency domain. A wideband acoustic
contrast is presented for the hybrid system and the trade-
off between the acoustic contrast, crossover frequency and
reproduced bandwidth is discussed.
Beginning this paper, in Section II, is an explanation of the
MSR layout and soundfield reproduction aliasing. Section III
gives a brief overview of the PL directivity model used in this
work. In Section IV a hybrid method is formulated for MSR
and PL reproduction of personal sound zones with results and
discussion in Section V and conclusions in Section VI.
II. MU LTIZ ON E SOU ND FIE LD REPRODUCTION (MSR)
In this section a general MSR layout is described along with
a description of a recent MSR technique. The aliasing which
occurs from reproductions with spatial discretisation artifacts
is also explained for later use in the hybrid model.
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0°
φL
Rlφc
Rv
ψc
−ψ
2d
R
D
Du
rzq
rq
α
Q
Dq
rzb
rb
β
B
Db−θ
Fig. 1. MSR layout for a circular loudspeaker array (green) with
a companion PL (red) for hybrid soundfield reproduction in Db.
In this work, the acoustical brightness contrast between two
zones, Dband Dq, is defined as
ζR(k) =
dqRDb|Sa
R(x, k)|2dx
dbRDq|Sa
R(x, k)|2dx,(1)
where dband dqare the areas (sizes) of Dband Dq, respec-
tively. The mean square error (MSE) between the desired
soundfield, Sd(x, k), and the actual reproduced soundfield,
Sa
R(x, k), is [6], [20]
R(k) = RDb
Sd(x, k)−Sa
R(x, k)
2dx
RDb|Sd(x, k)|2dx,(2)
which is used to measure reproduction accuracy. These mea-
sures can be used for any actual soundfield, Sa
R(x, k), created
with any reproduction technique, R, such as MSR, PL or any
combination thereof.
A. MSR Layout
The geometry of a generic MSR layout is depicted in
Fig. 1 for a circular array with a companion PL. An MSR
reproduction region, D, of radius Ris shown and contains
three sub-regions called the bright, quiet and unattended zone,
labelled Db,Dqand Du=D\(Db∪Dq), respectively.
The centre of Dis the origin from which other geometrical
locations are related. The centres of Dband Dqhave radius and
angle pair polar coordinates (rzb, β)and (rzq , α), respectively.
The radius of Dband Dqis rband rq, respectively, and the
direction of the soundfield within the regions is θand ϑ,
respectively. The MSR loudspeaker arc has a centre located
at (Rl, φc)and subtends an angle of φL. The directional PL
has a centre located at (Rv, ψc)and is directed at an angle of
ψclockwise from the origin. In practice, the PL is a circular
array of transducers, with effective radius d, protruding normal
to the reproduction plane. In this work, the imaginary unit is
i=√−1and the Euclidean norm is denoted with k·k. The
wavenumber k= 2πf/c is interchanged with frequency, f,
under the assumption that the speed of sound, c, is constant.
B. MSR Technique
An infinite set of planewaves arriving from every angle is
capable of entirely describing any arbitrary desired sound-
field [21]. A soundfield fulfilling the wave equation, in this
work, is denoted by the function S(x, k), where x∈Dis an
arbitrary spatial sampling point. As shown in the orthogonal
basis expansion approach [8], [20] to MSR, an additional
spatial weighting function, w(x), can be used to set relative
importance between zones. The weighted MSR soundfield
function used in this work can be written as
S(x, k) = X
j
Pj(k)Fj(x, k),(3)
where the orthogonal wavefields, Fj(x, k), have coefficients,
Pj(k), for a given weighting function and desired soundfield,
Sd(x, k); and j∈ {1, . . . , J }where Jis the number of basis
planewaves [8].
The complex loudspeaker weights used to reproduce the
soundfield in the (temporal) frequency domain are [22], [8]
Ul(k) =
M
X
¯m=−M
2ei¯mφl∆φsPjPj(k)i¯me−i¯mρj
iπH(1)
¯m(kRl),(4)
where ρj= (j−1)∆ρare the wavefield angles, ∆ρ= 2π/J,
φlis the angle of the lth dynamic loudspeaker from 0°, ∆φsis
the angular spacing of the loudspeakers, H(1)
ν(·)is a νth-order
Hankel function of the first kind and the modal truncation
length [8] is
M=dkRe.(5)
Here, Pjis chosen to minimise the difference between the
desired soundfield and the actual soundfield [8].
The actual soundfield from MSR is the result from super-
position of all individual loudspeaker responses
Sa
MSR(x, k) = GMSR(k)X
l
Ul(k)T(x,ll, k),(6)
where GMSR(k)is introduced as an arbitrary weighting for
hybrid soundfields (described later in IV-A), the loudspeaker’s
2-D acoustic transfer function (ATF) is
T(x,ll, k) = i
4H(1)
0(kkx−llk),(7)
and llis the position of the lth dynamic loudspeaker. Setting
GMSR(k)=1in (6) will render the multizone soundfield.
C. Soundfield Reproduction Aliasing
A fundamental issue with reproducing soundfields using
a limited number of loudspeakers is spatial aliasing which
gives rise to grating lobes which may impede the quiet
zone at higher frequencies [10]. Due to this phenomenon,
the bandwidth of reproducible soundfields with high acoustic
contrast (which may be lost above the aliasing frequency)
is reduced. For a part-circle array, the minimum number of
dynamic loudspeakers to use before aliasing problems begin
to occur is given by [6], [8]
L≥φL(2M+ 1)
2π+ 1.(8)
Substituting (5) into (8) and rearranging to find an approxi-
mation for upper frequency limit k=ku, gives
ku=2π(L−1) −φL
2R0φL
,(9)
where, instead of R,R0is used which is the radius of the
smallest circle concentric with Dencompassing all zones. The
upper frequency from (9) agrees with [10] and is dependent
on the number of loudspeakers, the reproduction radius and
the angle subtending the loudspeaker arc.
III. PARAMETRIC LOUDSPEAKER (PL)
A few PL directivity models are reviewed in this section as
well as common disadvantages of PLs. The disadvantages are
discussed in regards to speech soundfields, further motivating
the use of a hybrid model for such applications.
A. Directivity Models
The literature provides a handful of directivity models for
PLs which are algorithmic approximations of the pressure at
different angles. Earlier models include Westervelt’s directivity
(WD) [13] and product directivity (PD) [23], [24], though,
these models do not accurately match measured directivity
from a PL. Recently a convolutional directivity (CD) model,
used in this work, was proposed [12], [25] utilising both WD
and PD which has better correlation to measured directivity.
The actual soundfield reproduced by the PL, where the PL
is located at p, is defined in this work as
Sa
PL(x, k) = GPL(k)E(x, k)D(x, k )eikkx−pk,(10)
where GPL(k)is introduced as an arbitrary weighting for
hybrid soundfields (described later in IV-A), D(x, k)is the
CD and the directivity coefficient is
E(x, k) = ˜
βk2/4π˜αs˜ρ0kx−pkc2,(11)
where ˜
βis the coefficient of non-linearity, ˜αsis the sum of
the absorption coefficients for both primary frequencies and
˜ρ0is the density of the medium.
The CD is defined as the convolution between the PD and
WD with the linear convolution operator, ∗, as [12], [25]
D(x, k) = [DG(x, kc)DG(x, kc+k)] ∗ DW(x, k),(12)
where kcis the ultrasonic carrier frequency, DGx,ˆ
kis the
Gaussian directivity [24]
DGx,ˆ
k=e(i
2dˆ
ktan (ρx+Ψ))2
,(13)
where ρxis the angle of vector x−pfrom 0°, Ψ=
(ψ+ψc−π)and WD is [25]
DW(x, k) = ˜αs/q˜α2
s+k2tan4(ρx+Ψ).(14)
The far-field PL soundfield can then be found using (11)
and (12) in (10) with GPL(k)=1. However, as kdecreases
Sa
PL(x, k)approaches that of a point source and ζPL (k)is
consequently reduced. It is assumed in this work that the PL
is designed such that grating lobes are negligible [26] and for
different virtual source locations, multiple steerable PL arrays
can be used [15], [26].
B. PLs for Speech Soundfields
While PLs have been studied extensively over the years
there are still some drawbacks when it comes to reproducing
loud and clear audible sound. Audible reproductions from
PLs are known to require a large carrier SPL (>110 dB)
for typical speech conversation levels of ≈60 dBA, which
has potential inadvertent health risks [2]. Fortunately, for
applications of speech soundfields, high SPLs from the PL
are not necessary for high frequency ('2 kHz) components
of speech [19], further, harmonic distortions are lower above
this frequency [16]. Taking into account the PL location so that
the far-field demodulated audio [27] overlays Dband under the
assumption that high SPL from the PL is not required over Db,
health risks from the PLs could be argued to be negligible.
IV. HYBRID MSR AN D PL S YS TE M
A hybrid MSR and PL system is presented in this section
for use in personal sound zone applications. A crossover filter
is designed to switch target audio in the (temporal) frequency
domain to each of the constituent reproduction techniques.
A. Crossover Filter Design
Ideally the combination of low and high frequency acoustic
contrast from Sa
MSR(x, k)and Sa
PL(x, k), respectively, is de-
sired for personal sound zones. The weightings, GMSR(k)and
GPL(k), are introduced in (6) and (10), respectively, in order
to facilitate a hybrid soundfield, Sa
H(x, k). When composing a
hybrid soundfield it is natural to limit spectral distortion of the
reproduction at the crossover frequency, for this, we propose
the use of Linkwitz-Riley (LR) filters. Here, a low-pass ˆnth
order LR filter with a roll-off of 6ˆndB/octave is a cascaded
Butterworth filter
Hq
LR(k) = Bˆn
2(k/ku)−2,(15)
where Bˆn
2are Butterworth polynomials of order ˆn
2and ku
from (9) is suggested as the crossover frequency. The matching
LR high-pass is
Hp
LR(k) = Bˆn
2(ku/k)−2(16)
and together the crossover magnitude response is
Hq
LR(k) + Hp
LR(k)
= 1.(17)
In this work, the arbitrary MSR weighting is set to
GMSR(k) = Hq
LR(k),(18)
and the arbitrary PL weighting is
GPL(k) = Hp
LR(k).(19)
Using the new weights from (18) and (19) in (6) and (10),
respectively, a hybrid, H, soundfield is defined as the super-
position of a set of reproduction methods, R(in this work the
cardinality of Ris 2), as
Sa
H(x, k) = X
R∈R
db|GR(k)|Sa
R(x, k)
RDb|Sa
R(x, k)|dx,(20)
where each component soundfield is normalised to the mean
amplitude over Db.ζR(k)and R(k)can be evaluated using
Sa
H(x, k)in place of Sa
R(x, k)in (1) and (2), respectively.
B. Loudspeaker Signals
The time domain loudspeaker signals (unmodulated for a
PL) are defined in general in this section for the reproduction
of speech input signals, y(n). The discrete Fourier transform
of the gth overlapping windowed frame of y(n)is ˜
Yg(k). The
overlapping windowed frame of each loudspeaker signal is
˜
QRlg(k) = ˜
Yg(k)GR(k)Ul(k),(21)
˜qRlg(n) = 1
K
K−1
X
m=0
˜
QRlg(kmˆ
f)eicnkm,(22)
where km,2πm/cK, the number of frequencies is K, the
maximum frequency is ˆ
fand each loudspeaker signal, qRl(n),
for a particular R, is reconstructed by performing overlap-add
reconstruction with the synthesis window on ˜qRlg (n). For the
case where there is a single loudspeaker, l={1}, for a given
R, such as for the PL in this work, Ul(k) = 1 is used.
V. RESULTS A ND DISCUSSION
A. Experimental Setup
Simulations were carried out using the geometry shown
in Fig. 1 with rzb =rzq = 0.6 m,rb=rq= 0.3 m,R= 1.0 m
and α=β/3 = 90°. The desired soundfield angle was θ= 0°
and in this work w(x)was set to one in Db,100 in Dqand 0.05
in Dubased on [8], [11], [20]. The target soundfield in Dbwas
a virtual point source located at the centre of the PL and Dq
was set to be quiet. The loudspeakers had Rl=Rv= 1.3 m,
φL= 180°, φc= 180° and ψ=ψc−180°= 27.5°. The
speed of sound in air was c= 343 m s−1.
The PL was designed with kc= 2π(40 kHz) /c,˜
β= 1.2,
˜αs= 2.328 m−1,˜ρ0= 1.225 kg m−3and d= 6.18 cm. In this
work, it was assumed that the PL had ultrasonic transducer
spacing less than 4.3 cm [26], thus avoiding spatial aliasing.
The LR filters used to reproduce Sa
MSR(x, k)and Sa
PL(x, k)
had order ˆn= 12. The number of MSR loudspeakers used
was L={16,24,32,134}where kuwas found from (9).
To compare with MSR, L= 134 was chosen to reproduce
the speech with no spatial aliasing. The hybrid reproduction
method used R={MSR,PL}to find Sa
H(x, k)using (20).
B. Wideband Spatial Error Reduction
Figure 2 shows MSR(k),PL(k)and H(k)computed
from (2) in (E)–(H) as dashed green, dashed red and solid
blue lines, respectively. The crossover frequencies are the
vertical dash-dot black lines. Comparing the proposed hybrid
TABLE I
WIDEBAND MEAN RAND ζRC OM PARI SON S AS A F UNC TI ON OF T HE
NU MBE R OF DY NAM IC LO UD SPE AKE RS (L)F OR ON E PL
L
R(dB)ζR(dB)
MSR PL HMSR PL H
16 −27.2−40.7−32.5 30.0 40.454.2
24 −32.7−40.7−31.7 38.1 40.458.1
32 −33.7−40.7−31.6 43.5 40.460.3
134 −36.4−40.7−35.6 79.6 40.4 79.3
approach, it can be seen in Fig. 2 that Hwas on average
similar to the aliasing free MSR. Table I confirms this by
showing that, on average, Hwas slightly less than MSR.
While this was partly due to the low MSE of PL at lower
frequencies, acoustic contrast was also reduced when using
a PL at those lower frequencies as seen in Fig. 2 (A)–(D).
The trade-off between MSE and acoustic contrast is shown in
Table I where Hreduces with L.
C. Wideband Acoustic Contrast Improvement
Figure 2 shows ζMSR(k),ζPL(k)and ζH(k), computed
from (1), in (A)–(D) as dashed green, dashed red and solid blue
lines, respectively. The crossover frequencies are the vertical
dash-dot black lines which clearly indicate the point where
ζMSR(k)begins to decrease due to spatial aliasing. Note that
the multizone occlusion problem [1], [11] (should it occur)
may be difficult to overcome with one PL, however, the MSR
grating lobes interfere less over Dqduring this phenomenon.
Also shown in Fig. 2 is the limited bandwidth with high
acoustic contrast when reducing L. The mean acoustic contrast
over the wideband bandwidth for all reproduction techniques
is given in Table I and the mean improvement using the
hybrid method can be deduced. While the MSR mean acoustic
contrast decreased significantly, from 79.6 dB to 30.0 dB, due
to spatial aliasing, the proposed hybrid method decreased to
only 54.2 dB. For all reduced loudspeaker cases the hybrid
approach outperformed both MSR and PL methods. The
maximum improvement was 24.2 dB when L= 16 and for all
cases the wideband acoustic contrast remained above 54.2 dB,
despite the fundamental spatial aliasing that occurred.
VI. CONCLUSIONS
This paper has proposed a hybrid approach to personal
sound zones, including speech soundfields. An analytical
solution to the combination of MSR and PL soundfields is
presented along with a solution to a robust crossover filter.
The crossover filter is analytically derived from the geometry
of the soundfield layout whilst taking into account spatial
aliasing artifacts. Experimental results show that a significant
improvement in acoustic contrast from non-hybrid MSR and
PL soundfields of 24.2 dB and 19.9 dB, respectively, is achiev-
able. The proposed hybrid method also yields mean wideband
acoustic contrast consistently above 54.2 dB with as few as 16
dynamic loudspeakers and a single PL. Some topics for future
work are improving speech intelligibility contrast (SIC) and
quality in private speech sound zones using hybrid techniques.
0
20
40
60
80
100
120
140
Acoustic Contrast (dB)
(A)
L= 16
MSR
PL
H
ku
0.1 1 8
-50
-40
-30
-20
-10
0
Mean Squared Error (dB)
(E)
L= 16
(B)
L= 24
0.1 1 8
(F)
L= 24
(C)
L= 32
0.1 1 8
(G)
L= 32
(D)
L= 134
Acoustic Contrast and Mean Squared Error for Reproduction Methods
0.1 1 8
Frequency (kHz)
(H)
L= 134
Fig. 2. Results are shown for three reproduction methods and four L. Acoustic contrast results (ζMSR,ζPL and ζH) are shown in (A)–(D).
Mean squared error results (MSR,PL and H) are shown in (E)–(H). The case where L= 134 is alias free up to 8 kHz.
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