Development of multi-way parametric array loudspeakerusing multiplexed double sideband modulation
Yuting GENG1 , Yusei NAKANO1 , Masato NAKAYAMA2, 3 , Takanobu NISHIURA4
1 Graduate School of Information Science and Engineering, Ritsumeikan University, Japan
2 College of Design Technology, Osaka Sangyo University, Japan
3 Research Organization of Science and Technology, Ritsumeikan University, Japan
4 College of Information Science end Engineering, Ritsumeikan University, Japan

ABSTRACTParametric array loudspeaker (PAL) can achieve a sharper directivity by utilizing ultrasonic wave than conventional dynamic loudspeakers. However, PAL has difficulty reproducing low-frequency sound because it utilizes
demodulation of ultrasound in the air. We have proposed the multiplexed double sideband (M-DSB) modulation
for PAL, which can enhance sound pressure level (SPL) by utilizing harmonic distortion in demodulation. However, in lower frequency, sound quality by PAL with M-DSB is still insufficient compared with one by dynamic
loudspeakers. Therefore, in this paper, we develop a new multi-way PAL with combining software and hardware
approaches, which can achieve both sharper directivity and powerful bass sound. Multi-way PAL consists of atweeter PAL (T-PAL) and woofer PALs (W-PALs), and each part is an aggregate of multiple ultrasonic transducers (UTs). T-PAL employs single sideband (SSB) modulation, which gives low-distortion but low-SPL. W-PAL
employs M-DSB modulation, which gives high-SPL but high-distortion. In order to achieve a flatter frequency
response, we conducted preliminary experiments to determine both a suitable number of UTs and an optimized
arrangement for T-PAL and W-PALs. Finally, we confirmed the effectiveness of the proposed method throughevaluation experiments.
Keywords: Parametric array loudspeaker, Multi-way speaker, Modulation, Hardware arrangement

1

INTRODUCTION

In recent years, parametric array loudspeaker (PAL) [1, 2] has received attention for its sharp directivity.
PAL emits an intense amplitude modulated (AM) wave synthesized by modulating an ultrasonic wave with
audible sounds. The emitted intense AM wave is demodulated from ultrasonic wave to audible sound by nonlinear interaction in the air, and the demodulated audible wave achieves the sharp directivity of ultrasonic wave.
Hence, PAL can reproduce audible sound in a particular area and is promising to be used in museums, stations
and so on. However, it is difficult for PAL to reproduce bass sounds, and the sound quality is degraded byharmonic distortion [3]. Conventionally, the sound pressure level (SPL) and sound quality are considered to be
influenced by the modulation method. For instance, double sideband (DSB) modulation [1] shows a higher SPL
and single sideband (SSB) modulation [4] shows a better sound quality. Therefore, weighted double sideband(W-DSB) modulation is proposed in which different modulation methods are utilized in different bands withweighting factors [5]. W-DSB can realize a flatter frequency response, but it has a limitation that the SPL ofdemodulated sounds is extremely low. In order to attain a better performance of low-frequency reproduction, we
have proposed the multiplexed double sideband (M-DSB) modulation [6], which utilizes harmonic distortions
to enhance the SPL. Nevertheless, in the lower frequency, the sound quality by PAL with M-DSB is stillinsufficient compared with the sound quality by dynamic loudspeakers, for music listening or other applications.
In this paper, we develop a new multi-way PAL based on the modulation method and hardware design
to realize a better performance of low-frequency reproduction. The proposed multi-way PAL consists of atweeter PAL (T-PAL) and woofer PALs (W-PALs). In the proposed method, M-DSB modulation is utilized for
its effectiveness on low-frequency enhancement. Moreover, focusing on the fact that the SPL of demodulated
sound increases with the number of ultrasonic transducers (UTs), we allocate much more UTs for low-frequency
1

gr0369sv@ed.ritsumei.ac.jp, is0224ff@ed.ritsumei.ac.jp

2, 3 nakayama@ise.osaka-sandai.ac.jp
4nishiura@is.ritsumei.ac.jp1069Construction of hardware

Selection of suitable modulation method
Audible sound

Carrier wave

High-passfilter

SSB
modulation

Low-pass
filter

M-DSB
modulation

Listener
W-PAL (for low-frequency sound)
T-PAL (for high-frequency sound)Figure 1 – Overview of the proposed multi-way PAL.

𝟎. 𝟏𝟗 𝐦𝒙𝐋 = 𝟎. 𝟑𝟑 𝐦
𝒙𝐇 = 𝟎. 𝟏𝟏 𝐦

W-PAL
(600 transducers)
T-PAL(200 transducers)
W-PAL(600 transducers)

Figure 2 – Arrangement of the trial multi-way PAL.
reproduction to amplify the SPL. Therefore, with the synergy of software and hardware, a better low-frequency
reproduction is promising.

2

PROPOSAL OF MULTI-WAY PARAMETRIC ARRAY LOUDSPEAKER USING MULTIPLEXED DOUBLE SIDEBAND MODULATION

2.1 Overview of Proposed Multi-way Parametric Array LoudspeakerIn this paper, we developed a multi-way PAL using M-DSB modulation. Both modulation method andhardware design are studied for a better performance on low-frequency reproduction for PAL. Figure 1 shows
an overview of the proposed multi-way PAL. A trial is constructed on the basis of this proposal, and thearrangement of it is shown in Fig. 2. The proposed multi-way PAL consists of a T-PAL and W-PALs: T-PAL for
the high-frequency reproduction, W-PALs for the low-frequency reproduction. We utilized different modulation
methods for each part: M-DSB modulation for W-PALs, SSB modulation for T-PAL. The modulation methodsof the multi-way PAL will be discussed in detail in Subsection 2.2. In addition, we study on the hardware
design based on the fact that the SPL of the demodulated wave will be higher if more UTs are deployed. It isable to enhance the low-frequency significantly by allocating more UTs for W-PALs than T-PAL. The hardware
design will be discussed in detail in Subsection 2.3 and the numbers of UTs for each part are determined on
the basis of a preliminary experiment which will be discussed in Section 3.
2.2 Modulation Method of Proposed Multi-way Parametric Array LoudspeakerIn proposed method, we utilized M-DSB modulation for low-frequency emphasis, and SSB modulation for abetter sound quality of high-frequency. As shown in Fig. 3, the audible sound is split into low-frequency soundsL (t) and high-frequency sound sH (t). sL (t) and sH (t) can be indicated as follows:sL (t) = s(t) ∗ hLPFΩ (t),

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(1)

Figure 3 – Flowchart of modulation method in proposed multi-way PAL.
sH (t) = s(t) ∗ hHPFΩ (t),(2)

where ∗ denotes the convolution operator, hLPFΩ (t) and hHPFΩ (t) denote the low-pass filter and high-pass filter
with a cut-off frequency Ω, and t denotes the time index.
For high-frequency, which is easy to reproduce, SSB modulation with better sound quality is utilized. A
SSB modulated wave can be generated by filtering out the upper sideband of a DSB modulated wave. The SSB
modulated wave which will be emitted from T-PAL can be indicated as follows:uH (t) = {1 + mSSB · sH (t)}c(t) ∗ hLPFC (t),(3)

where mSSB denotes the modulation factor of SSB modulation, hLPFC denotes a low-pass filter with a cutoff
frequency same as the carrier frequency, and c(t) denotes the carrier wave and can be indicated as follows:c(t) = AC cos(2π fCt),(4)

where AC and fC denote the amplitude and frequency of the carrier wave.
For low-frequency, which is difficult to reproduce, M-DSB modulation is utilized because it makes use of
the second harmonic distortion for low-frequency emphasis [6]. M-DSB is a combination of DSB modulation,
which generates more harmonic distortions, and DSB-SC modulation, which can achieve frequency compression.
As shown in Fig. 3, sL (t) is compressed into sLF/2 (t) with 1 octave. When the target sound is a cosine tone
wave, sL (t), sLF/2 (t) can be indicated as follows:sL (t) = AL cos(2π fLt),(5)

sLF/2 (t) = AL cos(π fLt),(6)

sL (t) and sLF/2 (t) are modulated by DSB modulation and DSB-SC modulation, respectively. And the two modulated waves are added to generate the M-DSB modulated wave. The modulated waves which will be emitted
from W-PALs can be indicated as follows:uL (t) = uDSB (t) + uSC (t)= {1 + mDSB · sL (t) + mSC · sLF/2 (t)}c(t)(7)

mDSB AL ACmSC AL AC= AC cos(2π fCt) +cos(2π( fC ± fL )t) +cos(2π( fC ± fL /2)t),22where mDSB and mSC denote the modulation factor of DSB and DSB-SC modulation respectively.
In Eq. (7), it is known that the M-DSB modulated wave consists of the carrier wave (frequency: fC ),sidebands of DSB modulated wave (frequency: fC ± fL ) and sidebands of DSB-SC modulated wave (frequency:
fC ± fL /2). Target sound (frequency: fL ) is demodulated from the difference of one DSB sideband and carrierwave, and also from the difference between DSB-SC sidebands. On the other hand, a half frequency distortion(frequency: fL /2) is also generated from the difference of one DSB-SC sideband and carrier wave, and from thedifference of DSB sideband and DSB-SC sideband. Since the second harmonic distortion of this half frequency
distortion has the same frequency with target sound, it is considered that the target sound will be enhanced indemodulation.

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W-PAL (for low-frequency sound)
T-PAL (for high-frequency sound)

Target area𝑥#

Focal point

Non-target area𝑥"𝑥#

Target area’s depth

Target area’s width

Listener(a) Overview.

(b) Geometry of target area.

Figure 4 – Sectional view of relationship between multi-way PAL and demodulated sound.
2.3 Hardware Design of Proposed Multi-way Parametric Array Loudspeaker
The hardware design of proposed multi-way PAL is also studied for a better reproduction performance. The
arrangement of multi-way PAL influences the size and position of target area where the sounds of T-PAL and
W-PALs can be heard at the same time. The number of UTs influences the SPL of the demodulated sounds.
Since PAL has a very sharp directivity, the audible areas of W-PALs and T-PAL must be overlapped. In thissubsection, the parameters of the target area can be calculated theoretically. Figure 4 shows a sectional viewof the relationship between demodulated sounds and the arrangement of multi-way PAL. In this proposal, as
shown in Fig. 4(a), W-PALs are divided into two parts in vertical, and are closely spaced to create a focal
point. We have confirmed that the demodulated sound at the focal point does not attenuate though the W-PALs
are set separately in vertical. Due to the creation of the focal point, the target area becomes small, but the
demodulated sound quality can be improved at the target area around the focal point. Based on the preliminary
experiment in Section 3, the number of UTs is set under a proportion of 3:1:3 for upper W-PALs, T-PAL, andlower W-PALs.
In Fig. 4(b), xF denotes the distance between multi-way PAL and focal point, xL and xH denote the array
length of W-PALs and T-PAL respectively, θL and θH denote the directional angle of W-PALs and T-PAL
respectively. The angle between W-PALs and T-PAL is denoted with φ and can be indicated as follows:




xL
xH
φ = arctan+ arctan
.
(8)
2xF
2xF
The distance between T-PAL and beginning of target area (line segment OB) can be indicated as follows:
OB =xH
tan(90◦ − φ − θL ).
2(9)The propagation area at the focal point (line segment AD) can be indicated as follows:AD =xL+ xF tan θL .
2

(10)

The width of the target area is the same as the propagation area of T-PAL and can be calculated with Eq. (10).
By utilizing the law of sines in triangle ACD, the distance between the focal point and the end of the target
area (line segment AC) can be calculated as:
AC =

x

L

2

+ xF tan θL sin(90◦ + θ )Lsin(φ − θL )

.

(11)

In the case φ ≤ θL , the point C does not exist any more, and the demodulated sounds of W-PALs overlaps withthe demodulated sound of T-PAL endlessly. Except of this case, the depth of the target area (line segment BC)
is limited and can be calculated as:
BC = OA + AC − OB,(12)where OB and AC can be calculated with Eq. (9) and (11), OA can be set manually because the focal point A
is created by adjusting the direction of W-PALs and the position of focal point A can be controlled.

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3

PRELIMINARY EXPERIMENT ON NUMBER OF ULTRASONIC TRANSDUCERS
FOR MULTI-WAY PARAMETRIC ARRAY LOUDSPEAKER

3.1 Conditions of Preliminary Experiment on Number of Ultrasonic Transducers
A preliminary experiment is carried out to determine the proportion of UTs for W-PALs and T-PAL. The
demodulated SPL is extremely low if the number of UTs is small, so we set 100 UTs in a certain unit ofmulti-way PAL. 1 unit of the proposed multi-way PAL is shown in Fig. 5. There are 4 or 5 UTs in verticaland 22 UTs in horizontal, to achieve the closest packing for a better performance of wavefront synthesis. Units
adjoin on the long side and constitute W-PALs and T-PAL.
In the preliminary experiment, we first measured the power spectrum of demodulated sound. Then the proportion of UTs is calculated based on the average SPL of low-frequency and high-frequency in demodulated
sound. Because of the array effect in PAL, with the increase of UTs, the SPL becomes higher than the calculation. Hence, we also calculated the average SPL with different numbers of UTs and confirmed the necessary
proportion of UTs. The experimental conditions and equipment to measure the power spectrum are shown in
Tables 1 and 2. The experimental conditions to measure the average power with different number of UTs areshown in Table 3. The modulated waves are normalized to reach a maximum amplitude of (215 −1) and emitted
under the maximum permissible voltage (16 V). The necessary UTs for low-frequency is calculated with thefollowing equation to reach the same level of demodulated SPL with high-frequency.
r
PH
.
(13)
nL = nH
PL
Here, nL and nH denote the number of UTs for low-frequency and high-frequency respectively, PL and PH
denote the average power of low-frequency and high-frequency respectively. PL and PH can be indicated as:
PH =

fmax
1
P( f ),
fmax − Ω f∑
=Ω

(14)

PL =

Ω
1
P( f ),∑Ω − fmin f = fmin

(15)

where P( f ) denote the power spectrum with frequency index f , fmin denotes the minimum frequency of target
sound (0.1 kHz), fmax denotes the maximum frequency of target sound (8 kHz).
3.2 Results of Preliminary Experiment on Number of Ultrasonic Transducers
The power spectrum of demodulated sound is shown in Fig. 6. It is observed that the demodulated SPL
under 1 kHz is extremely lower than that of 2, 3 kHz. Therefore, in this paper, we set Ω = 1 kHz andenhance the sound under 1 kHz. Moreover, the measured average power of low-frequency (0.1~1 kHz) and

Figure 5 – One unit of the proposed multi-way PAL.
Table 1 – Experimental conditions to measure the power spectrum.
Environment
Ambient noise level
Temperature / Humidity
Distance between microphone and PAL
Sampling frequency / Quatization
Sound source
Number of UTs
Modulation

Office room (T60 = 650 ms)
LA = 32.4 dB
24.0◦ C / 33.7 %2.0 m
192 kHz / 16 bits
White noise (0.1~8 kHz)200
SSB ( fC = 40 kHz / mSSB = 1)

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Table 2 – Experimental equipment to measure the power spectrum.
Ultrasonic transducer
Power amplifier
Microphone
A/D, D/A converter

SPL (Hong Kong) Limited, UT1007-Z325R
JVC, PS-A2002
SENNHEISER, MKH 416-P48
RME, FIREFACE UFX

Table 3 – Experimental conditions to measure the average power.
Crossover frequency
Number of UTs
ModulationΩ = 1 kHz
100, 200, 300, 400, 500, 600, 900, 1200 and 1500
SSB ( fC = 40 kHz / mSSB = 1),
M-DSB( fC = 40 kHz / mDSB = 1, mSC = 1)

Figure 6 – Power spectrum of demodulated sound.

Figure 7 – Average SPL of demodulated sounds.

high-frequency (1~8 kHz) are 51.4 dB and 67.5 dB respectively. It is known that the difference in average
power is 16.1 dB. From Eq. (13), it is necessary to set W-PALs 6.4 times as many UTs as T-PAL. The
average SPL of demodulated sound is shown in Fig. 7. From Fig. 7, it is known that when (nL , nH ) =(500, 100), (1200, 200), the low-frequency and high-frequency reach the same level of SPL. Hence, in thispaper, we set (nL , nH ) = (1200, 200) for the proposed multi-way PAL to achieve a higher SPL of demodulated
sound.

4

EVALUATION EXPERIMENT ON SOUND QUALITY FOR MULTI-WAY
PARAMETRIC ARRAY LOUDSPEAKER

4.1 Conditions of the Trial Multi-way Parametric Array Loudspeaker
Based on the results of preliminary experiment in Section 3, we assembled a trial multi-way PAL as shownin Fig. 2. The number of UTs is set to (nL , nH ) = (1200, 200) as discussed, so the array length of W-PALs
and T-PAL are set to (xL , xH ) = (0.33 m, 0.11 m). The position of focal point is set to xF = 2.0 m.

(a) Woofer PAL(600 UTs, xL =0.33 m).

(b) Tweeter PAL(200 UTs, xH =0.11 m).

Figure 8 – SPL distribution of trial multi-way PAL.

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We first carried out an experiment measuring the SPL distribution to confirm the directivity of the trial
multi-way PAL. The measurement is under the same condition as shown in Tables 1 and 2. Figures 8(a) and8(b) show the SPL distribution of W-PAL and T-PAL respectively. The directional angles are calculated fromthe SPL distribution, θL = 15.8◦ and θH = 7.9◦ . The directivity angle is defined as the angle to the point
where the SPL of the demodulated sound is attenuated 6.0 dB in the horizontal direction of the focal point. By
substituting these parameters into Eq. (8), it is calculated that φ = 6.3◦ . Therefore, under the condition φ ≤ θL ,it is known that the demodulated sounds of W-PALs and T-PAL will coincide all the way in the propagation
direction. Moreover, the width of target area is 0.7 m, which is large enough for the size of a human head.
4.2 Conditions of Objective Evaluation Experiment on Frequency Response
An objective evaluation experiment is conducted to confirm that the proposed multi-way PAL can achievea flat frequency response by using M-DSB modulation and multi-way hardware design. In this experiment,
demodulated sounds are recorded at the focal point, and the experimental conditions and equipment are sameas that shown in Tables 1 and 2. As a comparison, we prepared 4 patterns as shown in Table 4. Conventional
method (W-DSB modulation) utilizes DSB modulation for low-frequency, so it is able to say that M-DSB ismore effective if M-DSB can enhance low-frequency better than DSB. Then, to measure the flatness of power
spectra, the average error of power spectra Perr is calculated as follows:
Perr =fmax
1|P( f ) − Pµ |fmax − fmin f =∑
fmin

(16)

where Pµ denotes the average of the power spectrum. A smaller value of Pµ implies a flatter frequency response.
4.3 Results of Objective Evaluation Experiment on Frequency Response
The power spectra and the average error of demodulated sounds at the focal point are shown in Fig. 9 and
10 respectively. The average SPL of demodulated sounds at the focal point are shown in Table 5. From Fig.
9 and Table 5, it is known that M-DSB can achieve a higher SPL than conventional DSB modulation at both
low-frequency (1.1 dB) and high-frequency (1.8 dB). The second harmonic distortions are generated less at lowfrequency, so the enhancement at low-frequency may be less effective than high-frequency. It is also known thatthe proposed method reaches a much higher SPL at low-frequency (6.0 dB) since it utilizes exclusive W-PALs.
And from Fig. 10, it is observed that the proposed method achieves a lower average error than other methods,
and it implies that the proposed method has a flatter frequency response than other methods. Therefore, it
is confirmed that it is possible to enhance the target SPL with M-DSB modulation and multi-way hardware
Table 4 – Comparison in objective evaluation experiment.
Name
SSB
DSB
M-DSB
Proposed

Modulation for W-PAL(low-frequency)
SSB
DSB
M-DSB
M-DSB

Modulation for T-PAL(high-frequency)
SSB
DSB
M-DSB
SSB

Figure 9 Power spectra of demodulated sounds at focal point.
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Figure 10 Average error of demodulated sounds at focal point.
Table 5 – Average SPL of demodulated sounds at focal point [dB].
Low-frequency soundHigh-frequency sound

SSB
64.8
85.9

DSB
69.9
88.0

M-DSB
71.0
89.8

Proposed
77.0
72.3

construction, especially at low-frequency. Moreover, it is confirmed that the flattest frequency response at the
focal point is realized with the proposed method.

5

CONCLUSIONSIn this paper, we propose a multi-way PAL to improve the low-frequency which is difficult to reproduce. MDSB modulation is proposed for low-frequency reproduction, and a hardware design which employs more UTs
for low-frequency than high-frequency is studied as well. The effectiveness of the proposed method is confirmedby evaluation experiments, and it is known that the proposed method can achieve a flat frequency response. In
the future, we will carry out an evaluation on directivity, and subjective evaluation on sound quality.

ACKNOWLEDGEMENTS
This work was partly supported by JST COI and JSPS KAKENHI Grant Numbers JP18K19829, JP18K11365
and JP19H04142.

REFERENCES[1]. T. Kamakura, M. Yoneyama and K. Ikegawa, "Developments of parameteric loudspeaker for practical use,"
Proceeding of 10th International Symposium on Nonlinear Acoustics, Kobe, Japan, pp. 147-150, 1984.
[2]. C. Shi and W. S. Gan, "Development of parametric loudspeaker: a novel directional sound generation
technology," Proc IEEE Potentials, vol. 29, no. 6, pp. 20-24, 2010.
[3]. P. J. Westervelt, “Parametric acoustic array,” The Journal of the Acoustical Society of America, vol. 35, no.
4, pp. 535–537, 1963.
[4]. S. Sakai, T. Kamakura, H. Nomura and S. Yoshida, "Dynamic SSB Modulator for Parametric Loudspeaker," The IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences,vol. 91, no. 12, pp. 1166-1173, 2008.
[5]. D. Ikefuji, M. Nakayama, T. Nishiura and Y. Yamashita, "Weighted double sideband modulation toward
high quality audible sound on parametric loudspeaker," IEEE International Conference on Acoustics, Speech,
and Signal Processing 2013, pp.843-847, 2013.
[6]. Y. Nakano, T. Fukumori, M. Nakayama and T. Nishiura, "A study on audible low-frequency sound emphasis based on multiplexed double sideband modulation in parametric loudspeaker," INTER-NOISE andNOISE-CON Congress and Conference Proceedings. Institute of Noise Control Engineering, pp.2054-2065,2018.

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