On in situ beamforming in an automotive cabin using a planar loudspeakerarray
Martin Bo MØLLER(1,2) ; Martin OLSEN(3)(1) Bang & Olufsen a/s, Denmark, mim@bang-olufsen.dk(2) Aalborg University, Denmark, marbm@es.aau.dk(3) Harman Lifestyle Audio, Denmark, martin.olsen@harman.com

Abstract
Compact loudspeaker arrays are often used in applications where control of the sound dispersion is required, e.g.
in audio reproduction systems and aspects of sound field control. An example of the latter is sound zoning where
the goal is to deliver individual audio content to one listener without disturbing another. Typical approaches
are based on filter-and-sum beamforming applied to control the resulting directivity of the array. However,directivity is defined in free field while sound zones are generally of interest in listening spaces with reflective
boundaries such as domestic rooms and automotive cabins. In order to address this discrepancy, in situ zonal
control can be utilized. This relies on measured impulse responses from each array element to the spatial
control points defining the zones. Such methods increase the solution specificity and can lead to non-causal
control filters. In the present paper, methods based on controlling the flow of acoustic energy are applied to aplanar loudspeaker array located on the dashboard inside a car cabin. A comparison study including directivity
and in situ zone control is presented, and the solutions are evaluated in terms of the resulting sound zoning
performance.
Keywords: Sound field control, Sound zones, Beamforming, Automotive audio

1

INTRODUCTION

Reproduction of high quality audio content in automotive listening spaces is associated with numerous challenges. Prominent examples are the spatially confined and complex acoustical environment as well as restricted
loudspeaker placement options. Furthermore, a significant shift might occur in applications and user scenarios
compared to today, in response to the expected prevalence of autonomous driving in the near future. Therefore,
new functionalities have recently received much attention such as reconfigurable seating areas with preserved
sound quality, or the ability to provide personal sound to individual occupants. Many aspects of these applications can be aided by introducing spatial sound field control solutions. The topic of the present paper concerns
fundamental investigations of a 19 channel compact loudspeaker array, which was positioned on the dashboard
inside an automotive cabin. Different sound field control strategies have been formulated and applied in an
in situ comparison study. The objective was to investigate specific setup scenarios and to assess the resulting
performance, related to controlling the sound content reproduced at each individual front seat. Performance assessment was based on the acoustic separation achieved between the front seats. This scenario can be attainedby means of in situ zonal control, which relies on measured impulse responses from each array loudspeaker tothe spatial control points, defining the spatially confined zones, as introduced in e.g. [1]. Other control methods
have been proposed for in situ control, where vectorial metrics are included in the optimization cost functions,such as particle velocity [2], and sound intensity [3]. The resulting control filters inherently reflect the acoustical complexity of the listening space, which is a general characteristic of most in situ methods. The listening
space information is captured in the measured impulse responses, and consequently the solution specificity isoften high.
Another approach is to control the sound field by focusing the sound energy flow towards the target listening
position, which effectively increases the acoustical separation. The beamforming control methods based on1109

the assumption of free field sound radiation, implicitly assumes a high degree of resemblance between the
setup scenario and the acoustical environment in which the compact array should be operating. The mismatch
between a free field setup scenario and operation in reverberant environments has previously been considered ine.g. [4]. However, in automotive audio systems the positioning of control loudspeakers is restricted to confined
regions along the interior boundaries, which often results in areas of highly complex geometrical and acoustic
impedance features in close proximity to the array. This is likely to affect the control problem since some of
the adjacent physical components should be considered a part of the array structure. Some aspects of theseeffects have been addressed in [5] in relation to cross-talk-cancellation, but not disclosed in details.
In the present paper, a comparative study is presented where a time-domain pressure matching control algorithm
has been applied, and control filters were determined in different setup configurations. In addition, a simple
delay-and-sum beamforming solution, based on free field analytical plane wave model has been included as
reference [7]. The following specific setup methods for the control algorithm are considered:• Free field beamforming where the control filters are based on impulse response measurements conductedunder free field conditions in a grid of microphone positions, that captures the radiation characteristics.
A subset of microphone positions is selected as the bright and dark points, respectively. In the caseof beamforming, the bright points define the main sound energy flow direction whereas the dark points
form the directions where ideally no sound radiation should occur. This definition is followed consistently
throughout this paper when beamforming methods are considered.
• In situ beamforming was applied to include the effects of the reflecting interior boundaries of the reproduction scenario inside the car cabin. Here, the impulse responses are measured in a plane in front of
the loudspeaker array. Constraining the sound field in points in this plane, according to the definition ofbright and dark directions, resembles the control strategy proposed for the free field case. The hypothesis
investigated here was that the in situ setup method potentially provides a beamforming solution due to a
relatively short distance between the loudspeaker array and the control points.
• In situ P-U beamforming has been considered since controlling the sound field in a single plane introduces the risk of accurately controlling only that plane without focusing sound propagating towards thelistener. To cope with this, a method including a vectorial control metric was defined, constraining boththe pressure and particle velocity in order to steer the sound energy flow.
• In situ zonal control based on measurements of impulse responses between the array loudspeakers andmicrophones inside the two control regions at the front seats in the unoccupied cabin. A bright zone wasdefined where the sound pressure level should be higher compared to the dark zone at the adjacent seat.
In general, the setup measurements for the in situ methods were conducted inside a regular unoccupied car
cabin. In addition, measurements series were performed with an anechoic termination for setting up special
versions of the in situ beamforming and P-U. A head-and-torso-simulator (HATS) was utilized in order tocreate a more realistic performance assessment in the comparison of the different setup methods investigated inthis paper.

2

THEORYIn this section, the applied sound field control algorithms are introduced along with the primary performance
evaluation metric. The latter is defined in the frequency domain as the mean square pressure in the bright zone
relative to the mean square pressure in the dark zone, commonly referred to as the acoustic contrast, written as,
MBcontrast( f ) = MB−1 ∑ |pmB ( f )|2
mB =1

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MD

MD−1 ∑ |pmD ( f )|2 ,
mD =1

(1)

where the subscript (·)B and (·)D denotes the bright and dark zone respectively, pm ( f ) is the complex pressure
at microphone position m and frequency f , and MB and MD are the number of microphone positions sampling
the bright and dark zone respectively.
The fundamental aspects of the control methods are presented in the sections below. The delay-and-sum method(based on the microphone equivalent in [7]) is regarded the simpler beamforming solution, whereas the timedomain pressure (and particle velocity) matching is the basis for all the remaining sound field control methods
investigated in the current work.
2.1 Time-domain pressure matching
In the following, it is assumed that the loudspeaker and listening space interaction behaves as a linear timeinvariant system. Furthermore, it is assumed that the input signal is a unit sample sequence. The pressure
impulse response at microphone m due to loudspeaker ` is expressed ashm` [0]
···
0


..
..
..




.
.
.
w` [0]
hm` [I − 1] · · ·0..
 , w` = (2)pm` = Hm` w` , Hm` = 
,

.


0
·
·
·
h
[0]
m`


w
[N
−
1]


..
..
` w
..


.
.
.
0

···

hm` [I − 1]

where hm` [i] is the ith sample of the impulse response. The combined pressure at the microphone due to the L
loudspeakers isT
pm = Hm w, Hm = Hm1 · · · HmL , w = wT1 · · · wTL .
(3)
Finally, the pressures at all the microphones can be concatenated asT
pB = HB w, HB = HT1 · · · HTMB ,(4)

where subscript B denotes the bright zone. The dark zone pressure can equivalently be expressed with the corresponding microphones and denoted by the subscript D. The pressure matching cost-function to be minimized
is thenJp (w) = (1 − ξ )kpt − HB wk22 + ξ kHD wk22 + αe kRe wk22 + αb kBwk22 ,(5)where ξ ∈ [0, 1] controls the tradeoff between attaining the target pressure pt in the bright zone and silence inthe dark zone and the penalties kRe wk22 and kBwk22 are introduced to control the shape of the resulting finite
impulse response (FIR) filters and the frequency range where the loudspeakers should be active as suggested
in [8] and [9], respectively. The FIR filters which minimize this quadratic cost-function can be expressed inclosed-form as
−1 T
(6)
HB pt .
wp = (1 − ξ )HTB HB + ξ HTD HD + αe RTe Re + αb BT B
2.2 In situ P-U beamforming
Constraining both the sound pressure and particle velocity at the control points of concern, provides a formulation which includes a vectorial control component. The particle velocity component of the sound field in agiven direction can be estimated from the finite difference approximation to Euler’s equation of motion between
two pressure measurements displaced along the axis of interest as [7]ux (t) = −Z tt p (t) − p (t)1 ∂ p(t)x2x1dt ≈ −dt.
ρ∆x−∞ ρ ∂ x
−∞

Z

(7)

In the above, x1 and x2 denotes points on the axis of interest, ∆x = x2 − x1 , and ρ is the density of air. As
the pressures are available as impulse responses from a causal system, the particle velocity is zero before the1111

beginning of the impulse responses, hence, the integral only needs to start at t = 0. Furthermore, as the pressure
is only known at discrete time intervals, the integral must be evaluated as a numerical integration using e.g. thetrapezoidal rule. The particle velocity impulse responses can then be expressed as


1/2 0
0
···
0
1/2 1/2 0
···
0 


∆T
1/2 1 1/2 · · ·0 (8)um`,x = Um` w` = −(1 − η)T(Hm`,x2 − Hm`,x1 )w` , T = 
,
 ..
ρ∆x
..
..
.. 
.
.
 .
.
.
.
. 
1/2 1
1
· · · 1/2
where T is the chosen integration rule (here trapezoidal) expressed in a matrix, η ∈ [0, 1] is a weight forcontrolling the relative importance of controlling the pressure and the particle velocity, and ∆T is the samplinginterval (here 1/48 kHz). Extending Um`,x to all microphones and loudspeakers of concern, the P-U matching
cost function is written as   2
  2
ηpt
H̄B
H̄D
−
w +ξ
w + αe kRe wk22 + αb kBwk22 ,(1 − η)ut
UBUDJpu (w) = (1 − ξ )

2

(9)

2

where ut is the target particle velocity in the bright zone and H̄B = ηHB . The resulting solution is−1
wpu = (1 − ξ )(H̄TB H̄B + UTB UB ) + ξ (H̄TD H̄D + UTD UD ) + αe RTe Re + αb BT B(η H̄TB pt + (1 − η)UTB ut ).

(10)

The performance of the in situ beamforming and in situ P-U beamforming relies on the sound field characteristics captured in the measured impulse responses. Thereby, the main difference between the investigatedmethods in this paper is the geometry defining the bright and dark zone, as well as the environment in which
the impulse responses were measured.

3

EXPERIMENTAL METHODOLOGY

3.1 Setup
The compact loudspeaker array employed in this work includes a total of 19 elements in a planar configuration,
as illustrated in 1d, each comprised by a 35 mm ‘full-range’ loudspeaker in a closed box cabinet.
To determine control filters for the free field beamforming method, the compact loudspeaker array was positioned in the center of a free field measurement system. Anechoic impulse responses from each loudspeaker
were measured to control points on a hemicylindrical surface (half-circles stacked), as illustrated in Fig. 1d.
The points representing the bright zone were selected relative to the positions representing the target direction
towards the listener, whereas the remainder of the hemicylindrical surface was selected as the dark zone.
The impulse responses estimated in the car cabin were based on measurements sampling the cabin in a 3-D
control point grid, using a planar array of quarter-inch microphones. The loudspeaker array was positioned andcentered on the dashboard, and the 3-D measurement grid was covering the front-row seat area from positionsin close proximity to the loudspeaker array and along the length-dimension, according to the layout shown in
Fig. 1b. The filters for the in situ beamforming and P-U methods were calculated using the impulse responses
from the first and the first two planes in front of the loudspeaker array, respectively, as illustrated in Fig. 1b.
Furthermore, an additional version of these two methods were based on impulse response measurements wherea wall of open-cell foam wedges was installed immediately in front of the front seats. Hence, an anechoic
termination was introduced, valid above approximately 700 Hz at normal incidence, and is shown in Fig. 1c.
The purpose of introducing the termination was to effectively separate the front seat area from the remainder ofthe car cabin, and to eliminate reflections from the front seats. The in situ zonal control was based on impulse
response measurements inside the desired control regions, as illustrated in Fig. 1b.

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Loudspeaker array

Loudspeaker array

Loudspeaker array

Microphonesampling
grid

Microphonesampling
grid

Microphonesampling
grid‘Anechoic’ Termination

55 mm(a) Full cabin - in situ zonal control.

(b) Full cabin - in situ zonal and beamforming. (c) Anechoic terminated cabin - in situ beamforming and P-U.

Loudspeaker array

Reference
loudspeaker

65 mm
1m
Loudspeakerarray - (front view)

Microphonesampling
grid

Loudspeakerarray - (top view)(d) Loudspeaker array and free field setup.

(e) Full cabin - head and torso simulator

Figure 1. Topview and sideview illustrations of the different setups considered for control filter calculation(details provided in sub-captions) and evaluation points. The open black circles represent the unconstrained
control points. Open blue circles represent the bright zone control points utilized for the beamforming methods,
whereas the closed blue circles indicate the dark points. The control points used for setting up the zonal control
method follow the same convention, but with green circles.
In all the methods investigated here, the target pressure and particle velocity were defined as the response fromthe reference loudspeaker to the points sampling the bright zone, delayed by 100 samples at 48 kHz sampling
frequency. The length of the control filters were 350 taps for all√ methods and the parameter adjusting the weightof bright vs. dark zone was ξ = 0.9. The parameter η was 0.04, αe and αb were set to 10−9 and 10−3 for
the P-U method and to 10−7 and 10−1 for the remaining methods. Furthermore, the impulse responses used for
estimating the particle velocity were lowpass filtered using a 4th order Butterworth filter with cutoff frequency
2 kHz [7], due to the errors inherently introduced in the finite difference approximation of the pressure gradient.
A separate set of impulse responses were measured at the positions used for the zonal control. Additionally, thisset of measurements was also used to evaluate the performance of the control strategies in driver and passenger
seat positions of the unoccupied car. To provide a more realistic evaluation scenario, a measurement series was
conducted with a head and torso simulator, Brüel & Kjær Type 4100, with in-ear microphones. The sound field
was sampled in 3 heights and 5 head rotations, with superposition between the HATS and a traditional manikinon the front seats, as indicated in Fig. 1e.

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4

RESULTS

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Contrast [dB]Contrast [dB]To evaluate the idealized separation as well as a more realistic separation, the contrast results are evaluatedfor both the occupied and unoccupied car cabin, as introduced in the previous section. Additionally, the meansquare pressure in the bright zone is reported to show the spectral emphasis introduced with the control methods.

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Figure 2. Experimental results depicting the contrast between the front seats in the unoccupied cabin or occupied by HATS. The middle plots show the mean square pressure in the unoccupied driver’s seat as sound): Delay-and-sum
pressure levels (SPL). All results are smoothed by a 1/12 octave moving average fliter. (beamformer. (): free field beamformer. (): In situ beamformer. (): In situ beamformer, anechoic.
(): In situ p-u beamformer. (): In situ p-u beamformer, anechoic. (): Zonal control. (): Reference
loudspeaker response.
The results are shown in Fig. 2 where the in situ beamforming and P-U methods are compared in the left1114

column. The reference loudspeaker response is included as reference in the middle row. The response fromthis loudspeaker was used as target pressure and particle velocity in the bright zone. Results are reported using
impulse responses measured both with and without the anechoic termination. It is seen that the methods allprovide similar contrast results, both when evaluated in the unoccupied cabin and when evaluated with the
HATS measurements. The main difference is observed in the mean square pressure in the bright zone between
2.5 and 6 kHz, where the in situ P-U method provides a boost.
In the right column of Fig. 2, the zonal control is compared with the delay-and-sum beamforming method, thefree field beamforming, and the in situ P-U method based on the impulse responses measured with anechoic
termination installed. It is seen that the zonal control is superior in terms of contrast evaluated in the unoccupiedcabin. However, when the contrast is evaluated based on the HATS measurements, the methods provide overall
more similar results. It is seen that the delay-and-sum solution is slightly suboptimal, when the acoustic contrast
is evaluated throughout the frequency range of interest. However, it is also found that the resulting mean squarepressure generated in the bright zone in general is more uniform when compared to the other methods.

5

DISCUSSION

From the experimental results, a number of observations can be made regarding the specific application of soundfield control in this work. The first point relates to the sound field control by means of the in situ beamforming
approaches. Only minor differences in the resulting performance are found, when comparing filters determinedbased upon impulse responses measured in the full car cabin and with an anechoic termination. Likewise,
adding a constraint on the particle velocity on top of the pressure also fails to significantly alter the resulting
solution. From these results it is assumed that the measurements were taken in such close proximity to theloudspeaker array, that they are dominated by the direct sound. Thereby, the anechoic termination does notprovide significant changes in the responses, as the reverberation is already significantly attenuated relative tothe direct sound in the particular source/receiver configuration. Furthermore, the particle velocity component
in the length direction of the car is already heavily dominated by the direct sound impinging towards themeasurement microphone planes, and the introduction of a vectorial physical control parameter proves to beless significant in this specific case.
It is seen that the conditions, under which the acoustic separation between the two front seats is evaluated,heavily influence the observed differences between the proposed methods. When evaluated in the unoccupied
volumes at each seat, the zonal control is seen to provide superior contrast. This is expected as the measurements used in this method very closely resemble the measurements used to evaluate this result. However, when
the seats are occupied by a HATS, it is seen that the observed separation is much more similar between theinvestigated methods. It is interesting to observe that introducing listeners in the intended bright and dark zone,
removes most of the expected benefits from impulse responses measured within the car cabin. This implies thatin order to attain the additional benefit of in situ measurements, the measurements should closely resemble thereproduction scenario i.e. including information about how the current occupancy of the cabin affects the soundfield from the loudspeakers to the ears of the occupants.
The frequency range of the control performance seems to be divided into three regions. Below 1.5 kHz theresults indicate that significant interaction occurs between the car cabin and the control loudspeakers. This isobserved from the zonal control being the only method providing high separation in that particular range andthat the response of the reference driver exhibits increased frequency variation in the mean square pressure in
the bright zone. Between 1.5 kHz and 4-5 kHz, the beamforming approaches become capable of effectively
focusing sound towards one seat relative to the other as seen from the improved performance of the delay-andsum method in this region. Finally, above 4-5 kHz the contrast is seen to decrease with frequency. This canbe explained by the spatial aliasing due to the horizontal and vertical displacement of the drivers. Given thevertical displacement of 65 mm and horizontal displacement of 27.5 mm, the expected frequencies for onset ofsidelobes are around 2.6 kHz and 6.2 kHz respectively.

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6

CONCLUSION

Throughout this paper a number of methods were investigated for reproducing audio to one of the front seats ina car using a planar loudspeaker array. The in situ beamforming and P-U methods were shown to yield almost
identical results, which can be attributed to the direct sound having the most significant contribution in themeasured impulse responses. The acoustic separation performance was seen to lie between the delay-and-sum
beamforming and the zonal control method, indicating that constraining the sound field in close proximity toloudspeaker array generates a beamforming solution.
The best choice of control method depends on the availability of the impulse responses accurately representing
the reproduction scenario. The delay-and-sum beamforming provides a uniform mean square pressure relative
to the in situ methods and is a suitable approach when representative system characterization is not available.
If accurate knowledge of the reproduction scenario inside the control regions is available, the zonal control
provides the highest possible separation between the zones, among the investigated methods. The associatedvariation of the mean square pressure in the target zone, could then be equalized in a global sense.

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