2008 adaptive wave ﬁeld synthesis for active sound ﬁeld reproduction: experimental results

8/11/2019 2008 Adaptive wave field synthesis for active sound field reproduction: Experimental results

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Adaptive wave field synthesis for active sound field reproduction:Experimental results

Philippe-Aubert Gauthiera and Alain BerryGroupe dAcoustique de lUniversit de Sherbrooke, Universit de Sherbrooke, 2500 boul. de lUniversit,

Sherbrooke, Qubec J1K 2R1, Canada

Received 31 May 2007; revised 28 January 2008; accepted 28 January 2008

Sound field reproduction has applications in music reproduction, spatial audio, sound environment

reproduction, and experimental acoustics. Sound field reproduction can be used to artificially

reproduce the spatial character of natural hearing. The objective is then to reproduce a sound field

in a real reproduction environment. Wave field synthesis WFS is a known open-loop technology

which assumes that the reproduction environment is anechoic. The room response thus reduces the

quality of the physical sound field reproduction by WFS. In recent research papers, adaptive wave

field synthesis AWFS was defined as a potential solution to compensate for these quality

reductions from which WFS objective performance suffers. In this paper, AWFS is experimentally

investigated as an active sound field reproduction system with a limited number of reproduction

error sensors to compensate for the response of the listening environment. Two digital signal

processing algorithms for AWFS are used for comparison purposes, one of which is based on

independent radiation mode control. AWFS performed propagating sound field reproduction better

than WFS in three tested reproduction spaces hemianechoic chamber, standard laboratory space,

and reverberation chamber. 2008 Acoustical Society of America. DOI: 10.1121/1.2875844

PACS numbers: 43.38.Md, 43.60.Tj, 43.50.Ki AJZ Pages: 19912002

I. INTRODUCTION

With the constantly evolving digital signal processing

and the relatively recent advent of multichannel audio, spa-

tial audio has gained more attention in the past decades from

researchers and practitioners for applications such as high-

fidelity sound reproduction, music reproduction, virtual real-

ity display, interactive multisensory environments, auraliza-

tion, and sound installations Camurri and Ferrentino, 1999;

Epain et al., 2004;AES Staff Writer, 2005;Woszczyket al.,2005;Keller et al., 2006; Blesser and Salter, 2007. The in-

terest in immersion and convincing multisensory environ-

ments is not new Grau, 2003 and various techniques for

spatial audio have been introduced in the past Kendall,

1995;Verheijen, 1997; Poletti, 2000; Rumsey, 2001; Davis,

2003.

Within spatial sound, sound field reproduction methods

attempt to reproduce physical stimulus wave field, thereby

avoiding any perceptual considerations in the implementa-

tion. Sound field reproduction was investigated by research-

ers in the past decades Berkhoutet al., 1993;Nelson et al.,

1997; Verheijen, 1997; Poletti, 2000; Choi and Kim, 2004;

Epain et al., 2004; Takane and Sone, 2004; Keller et al.,

2006. One of the most active and recent related matters is

room compensation Spors et al., 2003; Gauthier et al.,

2005a; Betlehem and Abhayapala, 2005; Spors et al., 2005;

Fuster et al., 2005; Gauthier and Berry, 2006, which is es-

sential for sound field reproduction in a real reproduction

space on the basis of objective, physically measurable, per-

formances. This is especially true when acoustical treatment

of the reproduction space is not possible, like for sound field

reproduction in vehicle mock-ups where the visual reproduc-

tion of the original space is important.

This paper deals with the problem of sound pressure

field reproduction using adaptive digital signal processing

applied to adaptive wave field synthesis AWFS originally

introduced by Gauthier et al. 2005b. More specifically it

validates by experiments the AWFS concept.

The concepts and results shown in this paper are not

limited to audio applications. Indeed, sound field reproduc-tion may also be applied to experimental acoustics Veit and

Sander, 1987; Bravo and Elliott, 2004, psychoacoustics

Epain et al., 2004;Keller et al., 2006, and sound environ-

ment reproduction or even used as a vibroacoustics design

tool. These are promising applications of sound field repro-

duction.

This paper is divided in four parts. In Sec. I, sound field

reproduction, WFS, and AWFS are described. The complete

experimental procedures and setups are described in Sec. II.

Results of experiments with AWFS are then reported in Sec.

III for three different reproduction spaces. Section IV dis-

cusses the results and exposes our conclusions.

A. Sound field reproduction

The main objective of sound field reproduction can be

generally stated as the aim to recreate a given acoustical

property of the sound field, such as sound pressure, sound

intensityChoi and Kim, 2004; Merimaa and Pulkki, 2005,

spatial diffusenessMerimaa and Pulkki, 2005, etc., over an

extended region of space. This can be achieved using a re-

production system including electroacoustical sources and

receivers, signal processing, and the desired physical targetaElectronic mail: [email protected]

J. Acoust. Soc. Am. 123 4, April 2008 2008 Acoustical Society of America 19910001-4966/2008/1234/1991/12/$23.00


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description. In several of these cases, use of adaptive filtering

implies the minimization of a cost function which is repre-

sentative of this reproduction objective Gauthier et al.,

2005a; Gauthier and Berry, 2006. Adaptive signal process-

ing for spatial sound reproduction has been considered invarious forms by researchers Asano and Swanson, 1995;

Takane et al., 1999; Radlovi et al., 2000; Santilla, 2001;

Epain et al., 2004; Choi and Kim, 2004; Gauthier et al.,

2005b;Spors et al., 2005;Gauthier and Berry, 2006.

B. Wave field synthesis

WFS research started with the theoretical propositions

by BerkhoutBerkhoutet al., 1993;Verheijen, 1997;Startet

al., 1999. From the simple source formulation of the

KirchhoffHelmholtz integral theorem Williams, 1999,

WFS operators are designed to link a given simple virtual

sourcetypically creating spherical or plane wave in an hori-zontal plane, the listening plane, fed by a monophonic sig-

nal, to a loudspeaker array which reproduces the acoustic

field of the virtual source that is the target, or virtual, sound

field. A schematic and simplified representation of the prob-

lem is shown in Fig. 1. The problem is usually limited to

reproduction in the horizontal plane with a finite number of

discrete reproduction sources using appropriate simplifica-

tions of the integral formulation Verheijen, 1997. WFS

studies have investigated: spatial aliasing de Vries et al.,

1994;Startet al., 1995;Spors and Rabenstein, 2006;Corteel,

2006a, objective performance, room effect, Klehs and

Sporer, 2003;Sporer and Klehs, 2004, acoustic room com-

pensationSporset al., 2003,2005;Fusteret al., 2005, WFS

equalizationCorteel, 2006b, and more.

On one hand, the benefit of current WFS prototypes is

their effectiveness in transmitting a spatial impression in

terms of sound localizationover a broad area surrounded by

loudspeakers. On the other hand, WFS drawbacks are related

to the definition of the synthesis operators: The reproduction

room response or electroacoustical system limits Corteel,

2006b are not considered in the definition of WFS. The

typical WFS system is consequently based on an open-loop

architecture assuming a free field as the reproduction space.

Active room compensation or system equalization for WFS

is an active research topic for objective sound field reproduc-

tion in real room Elliott and Nelson, 1989; Asano and

Swanson, 1995; Bouchard and Quednau, 2000; Santilla

2001;Sporset al., 2003;Gauthier et al., 2005b;Spors et al.,

2005;Fuster et al., 2005;Corteel, 2006b.

To lighten the present paper, which focuses on experi-

mental results, the readers are referred to Verheijen 1997

for a more detailed review of WFS. A complete description

of WFS adapted to the specific problem of AWFS was pub-

lished by Gauthier and Berry 2006.

C. Adaptive wave field synthesis and independentradiation mode control

In a recent paper Gauthier and Berry, 2006, AWFS was

suggested as a practical compromise between WFS and ac-

tive room compensation that usually requires a large amount

of sensors. AWFS is based on a cost function to be mini-

mized. Although implemented here in a specific configura-

tion, the AWFS concept described by this cost function can

readily be applied to any configuration. The cost function is

a quadratic function of: 1 the reproduction errors and 2

the adaptive filters departure from the WFS solution ex-pressed as a set of finite impulse response FIR filter coef-

ficients. The penalization of the departure from the WFS

filters is what makes AWFS original in comparison with

other research done on sound field reproduction using active

noise control techniques. The interest of such an approach

stems from a simple observation: The direct sound field re-

produced by WFS approaches the virtual sound field

Gauthier and Berry, 2007 and then allows for proper sound

localization on the basis of precedence effect Blauert,

1999. Accordingly, WFS can be taken as a starting point or

an a priori solution for the adaptive algorithm which will

minimize the reproduction errors caused by the room re-

sponse. Moreover, the weighted penalization of any depar-ture from the WFS solution may prevent the degradation of

sound localization since it limits the contribution of the sec-

ondary sources which are normally not activated by the WFS

solution, given the fact that the WFS solution already con-

tains spatial information that cannot be completely measured

using a limited number of error microphones. For example,

when using more reproduction sources than error sensors, the

WFS solution contributes to the proper reconstruction of the

direct sound field outside the control region defined by the

error sensor locations Gauthier and Berry, 2006. Finally,

this penalization, which is controlled by a set of penalization

parameters, can be used to control the balance between a

purely WFS solution and a closed-loop realization of Am-

bisonics sound field reproduction Gauthier and Berry,

2006.

This specific definition of a cost function for a multi-

channel adaptive system leads to a simple modification of the

leaky filtered-reference least-mean-square FXLMS algo-

rithmElliott, 2001. The modification is the inclusion of the

WFS solution in the adaptation rule. Here, we will refer to

modified FXLMS for AWFS when this algorithm is used.

Via the singular value decompositionSVDof the plant

matrix frequency response functions FRFs between repro-

FIG. 1. Term convention for WFS definition. The virtual source is located in

x0. L is the reproduction source line, the virtual source is on the left of the

source line and the reproduction space is on the right of the source line. All

sources and sensors are located in the x1 x2 plane.

1992 J. Acoust. Soc. Am., Vol. 123, No. 4, April 2008 P.-A. Gauthier and A. Berry: Experiments with adaptive wave field synthesis


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duction sources and error sensors involved in AWFS, it was

shown that the underlying AWFS mechanism is the indepen-

dent control of radiation modes Gauthier and Berry, 2006

using plant decoupling. It is also related to the Principal-

Components LMS PC-LMS algorithm Cabell and Fuller,

1999. This suggested a practical implementation of AWFS

signal processing which had already been textually described

byGauthier and Berry2006.This reference on signal pro-

cessing for AWFS should suffice for the purpose of this pa-

per, see also Gauthier and Berry 2008. In the case of

AWFS based on independent radiation mode control, a set of

analysis filters is used to transform the sound pressure in the

SVD basis and a set of synthesis filters is used to create the

loudspeaker signals from the SVD basis. In this transformed

domain a set of single-channel independent adaptive filters

operate to control each radiation mode individually. This re-

duces the computational burden and allows for a fine tuning

of the convergence properties of the algorithm i.e., indepen-

dent fine tuning of the radiation modes convergence proper-

ties. Adaptive sound reproduction using plant decoupling

via SVD was already proposed by Bai and Elliott 2004 via

simulations for cross-talk cancellation. The main differences

between Bais work and the present paper are 1 the experi-mental application to sound field reproduction, 2 further

considerations for the proper construction of the synthesis

and analysis filters from a signal processing perspective, and

3 the inclusion of an a priori solution the WFS solution.

The inclusion of the WFS solution in the cost function

Gauthier and Berry, 2006 significantly changes the algo-

rithm since the WFS solution must be projected on the SVD

basis radiation mode synthesis filters and nullspace synthe-

sis filters. The proper construction of the synthesis and

analysis filters is also what make this paper on AWFS origi-

nal. Moreover, this construction of the synthesis and analysis

filters had proven to be of critical importance for the efficient

projection of the WFS solution on the SVD basis. However,such detailed considerations for signal processing are beyond

the scope of this paper.

In this paper, the performance of AWFS based on modi-

fied FXLMS and independent radiation mode control algo-

rithms is derived from experiments with a real AWFS system

in three different acoustical situations. This paper therefore

validates the AWFS concepts, previously investigated in

theory Gauthier and Berry, 2006. See Elliott 2001 for a

general review on adaptive filtering for active noise control

and sound field reproduction.

II. EXPERIMENTAL PROTOCOL

A. Experimental setups

The tested system includes 24 reproduction sources and

4 reproduction error sensors. The complete system is shown

in Fig.2.The reproduction sources create a 2-m-diam circu-

lar array in the horizontal plane. Sources are separated by

26 cm, thus giving an approximate minimal spatial aliasing

frequency of 634 Hz /2=26 cm, where is the acoustical

wavelength Spors and Rabenstein, 2006. This minimal

spatial aliasing frequency gives the frequency range of focus

for the experiments. Above the spatial aliasing frequency, the

sound field reconstruction is impossible over the reproduc-

tion region. The error microphones form a cross, in the same

horizontal plane as the reproduction sources, and their sepa-

ration distance along x1 and x2 axes is 17.5 cm. Sources and

sensors stand 1.22 m above the floor.

The loudspeakers are studio monitors amplified two-

way cabinets. The error sensors are 1 /4 in. electret micro-

phones. For the off-line broadband AWFS implementation,

the loudspeakers and the microphones are connected to a

signal conditioner and a computer using a sound card 24

analog inputs and 24 analog outputs. In this setup, theAWFS signal processing operates off-line. The setup is sche-

matically shown in Fig. 3a.For the second setup involving

harmonic target wave fields, the loudspeakers and micro-

phones are connected to reconstruction and antialiasing fil-

ters 440 Hz low-pass, eighth order, Butterworth, respec-

tively, before being connected to a digital signal processing

station used for on-line harmonic AWFS. The station is built

around a Texas Instrument TMS320C40 floating point digital

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Sources

Error sensors

Monitoring sensors

Sources: 24

Sensors: 4

FIG. 2. Schematic AWFS setup made of 24 reproduction sources, 4 repro-

duction error sensors, and 8 monitoring sensors. Typical virtual source

position.

FIG. 3. Schematic representation of the AWFS instrumentations,a Broad-

band and b harmonic.

J. Acoust. Soc. Am., Vol. 123, No. 4, April 2008 P.-A. Gauthier and A. Berry: Experiments with adaptive wave field synthesis 1993


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signal processor. The setup is shown in Fig. 3b.The experi-

mental methods differ for these two setups. The system is

pictured in Fig.4.

B. Methods of experiments

Two types of reproduction methods and experiments are

reported. As for the first type, the AWFS algorithms operate

off-line. In this case, the experimental procedure is:1iden-

tification of the plant impulse responses from all reproduc-

tion sources to all error sensors. Sweep-sine identification

was used to cover from 0 to 600 Hz. The number of coeffi-

cients varies according to the reproduction environment. 2

Off-line running, by simulation, of the AWFS algorithms tex-

tually described by Gauthier and Berry 2006. 3 Render-

ing, with the real electroacoustical system, of the AWFS so-

lution after convergence of the control filters. 4

Measurement of the reproduced sound fields. The reproduced

sound field measurements are based on reproduced impulseresponses from the reference signal to the eight monitor

microphones see Fig. 2. Broadband AWFS results shown

in Sec. III include measurements of the reproduced sound

fields using swept sines.

As for the second type of reproduction methods and ex-

periments, the objective is to evaluate the performance of

AWFS with an on-line adaptation system. To reach this goal,

several practical trade-offs are included to reduce the com-

putational burden so that on-line adaptation can be per-

formed using the available hardware. In the case of harmonic

sound field reproduction, all the AWFS filters including

adaptive filters, target operators, synthesis, and analysis fil-

ters are implemented using two-coefficient FIR filters. The

algorithm then approaches the PC-LMS algorithm Cabell

and Fuller, 1999 with a supplementary penalization term

and an a priori solution. In this very specific situation, the

computational load is drastically reduced and on-line adap-

tation is possible using the algorithms as textually described

by Gauthier and Berry 2006.

For both types of AWFS realization, the convergence

coefficients used in the adaptive algorithms are set near the

maximum values, which guaranteed stability and conver-

gence of the adaptation.

III. AWFS EXPERIMENTS

A. Acoustical characteristics of the reproductionrooms

The three reproduction environments were selected to

cover a large spectrum of reverberation properties. These en-

vironments are: 1 a hemianechoic chamber, 2 a standardlaboratory space, and 3 a reverberation chamber.

The hemianechoic chamber Fig. 4 has a volume of

125 m3 6.556.253.05 m with a floor surface of 41 m2.

A typical frequency response function FRF transfer func-

tion between a reproduction source and an error microphone

is shown in Fig.5.In this situation, the FRFs are smooth and

the dip around 310 Hz is created by the destructive interfer-

ence with the floor reflection at this frequency. In the hemi-

anechoic chamber, the error sensor signals are mostly domi-

nated by the direct sound field of the reproduction sources.

The volume of the standard laboratory space is 469 m3

8.2314.024.06 m with a floor surface of 115 m2. The

typical FRF shown in Fig. 5 is more complex and showsvarious dips. The reverberation radius the distance from the

source at which the sound pressure level of the direct sound

field is equal to the sound pressure level of the diffuse sound

field was estimated to be more than 1.4 m with broadband

noise audio bandwidth. The approximation of the rever-

beration radius is derived from the spatial sound pressure

level decay curve from an omnidirectional loudspeaker array.

The mean curve was estimated from four measurement lines

in the horizontal plane 1.22 m above the floor randomly

selected in the room. From the mean curve, the sound source

power level is computed from the measured direct sound

field using a curve fitting with a theoretical free-field decay

curve. The homogeneous reverberation level is evaluated

from the last part of the decay curve. The approximation of

the reverberation radius is then derived from the crossing of

this homogeneous level and the theoretical free-field decay

curve for the approximated sound source power level. Given

a reverberation radius of more than 1.4 m in this laboratory

space, the error sensors at 1 m of the reproduction sources

are exposed to the direct sound field of the reproduction

source and the field reflected by the room walls with a well-

balanced proportion in comparison with the hemianechoic

space.

FIG. 4. Experimental AWFS setup in the hemianechoic chamber.

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ref.

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Hemi-anechoic chamberReverberant chamberArbitrary laboratory space

FIG. 5. Typical identified FRFs from a reproduction source to an error

microphone in the hemianechoic chamber, standard laboratory space, and

reverberation chamber.



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The volume of the reverberation chamber is 142 m3

with a floor surface of 46.5 m2 7.56.23.05 m. Several

sheets of damping material were placed in corners of the

room to reduce the excessively long reverberation time. The

typical FRF shown in Fig.5has gains that vary strongly with

frequency and the transitions from frequency to frequency

are very sharp. The reverberation radius was estimated to be

between 0.45 and 0.51 m for broadband signal. Therefore, in

this highly reverberant space, the error sensors are mostly

exposed to the diffuse sound field of the reproduction

sources. This is an hostile environment both for WFS and

AWFS.

B. Hemianechoic space

1. Broadband AWFS

The broadband off-line demonstration of AWFS is inter-

esting because it validates the complete AWFS concept, as

described in previous papers Gauthier and Berry, 2006. The

broadband nature of the off-line system places a general

point of view on the results.

In a preliminary stage, the system FRFs are identified

using swept sines with an average over 200 realizations. Theresulting impulse responses include 256 coefficients. The

sampling rate is 1200 Hz for all the broadband experiments.

Using the identified plant, the modified FXLMS algorithm

can readily be applied Elliott, 2001; Gauthier and Berry,

2006.

The independent radiation mode control implementation

requires an additional initialization step. Singular value de-

composition of the system plant in the frequency domain is

achieved as textually described by Gauthier and Berry

2006 for each frequency. This gives the radiation modes

source modes, singular values, and pressure modes at each

frequency. Radiation mode reordering and phase optimiza-

tion algorithms are then applied in the frequency domain tosmooth the source and pressure mode phase responses. This

creates a novelty in comparison with Bais work with broad-

band plant decoupling Bai and Elliott, 2004. Inverse

discrete-time Fourier transform is then applied to obtain the

synthesis filters and analysis filters to move to and from the

SVD basisin the time domain for AWFS based on indepen-

dent radiation mode control. Note that using such synthesis

and analysis filters, the plant is uncoupled but not whitened.

The synthesis filters Gauthier and Berry, 2006 for the first

four source modes are shown in Fig. 6. Each group of syn-

thesis filtersthere are 4 groups of 24 filtersproduces one of

the source modes at the reproduction source array. The

analysis filters for the four pressure modes are shown in Fig.

7. Each group of analysis filters there are 4 groups of 4

filters transforms the physical acoustical pressures in the

pressure mode basis SVD basis. Interestingly, the synthesis

and analysis filters show a sharp concentrated time response:

Time leakage is reduced in comparison with SVD filters pre-

sented by Bai and Elliott 2004, thanks to the radiation

modes reordering and to the phase optimization algorithms.

Figure8 shows the reproduced impulse responses from

the virtual source to the monitoring sensor array shown in

Fig.2 for WFS. The transfer function units are 1 /m sound

pressure Pa divided by virtual monopole amplitude

Pa m. The virtual source is a spherical source located at

xo = 0 , 4 , 0 m. Clearly, the direct field of the reproduced

impulse responses approaches the target impulse responses.

After the direct wave front passage, the reflection from the

floor appears and instants later the low frequency echo of the

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Source mode #1

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Source mode #2

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Source mode #3

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Source mode #4

Samples

FIG. 6. First synthesis filtersGauthier and Berry, 2006in the time domain

for source modes 14 in the hemianechoic chamber. Each plot includes 24synthesis filters to create the given source mode with 24 reproduction

sources. Each filter includes 256 coefficients.

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Pressure mode #1

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FIG. 7. Analysis filtersGauthier and Berry, 2006 in the time domain for

pressure modes 14 in the hemianechoic chamber. Each plot includes 4

analysis filters to catch the pressure mode with 4 pressure sensors. Each

filter includes 256 coefficients.



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hemianechoic chamber impinges the monitoring array. This

echo is caused by the chamber which is hemianechoic only

above 150 Hz. Moreover, another physical imperfection of

the WFS reproduced sound field appears: The direct wavefront has an undesirable coloration the impulse is spread

over two or three samples, passing from positive to negative

values, possibly caused by the loudspeaker response or the

WFS approximations.

The convergence coefficient was set to 0.00001 for the

modified FXLMS algorithm. The convergence coefficient

m, for the independent radiation mode control algorithm,

were set to 1 =0.0001, 2 =3 =0.0004, and 4 =0.002 for

the four radiation modes, where the subscript indicates the

radiation mode number. The penalization parameter for the

FXLMS algorithm was set to = 20 Gauthier and Berry,

2006. The penalization parameters for the AWFS based on

independent radiation mode control were 1 = 2, 2 =3 =0.2and 4 =0.1.

The impulse responses reproduced by AWFS are shown

in Fig.9a by FXLMS and Fig. 9b by independent radia-

tion mode control. Clearly, the imperfections of WFS shown

in Fig.8are partly corrected by AWFS even outside the error

sensor array note that the two central monitors see Fig.2

correspond to two of the error sensors. Both the modified

FXLMS and independent radiation mode control algorithms

reduce these imperfections. The floor reflection is attenuated

and the low frequency echo disappears from the sound field

reproduced by AWFS. Moreover, the direct sound field re-

produced by AWFS is closer to the target wave field than the

sound field reproduced by WFS. Therefore, AWFS compen-

sates for the room effects, for the loudspeaker colorations,

and for some classical WFS approximations which introduce

supplementary physical errors in the reproduced sound field.

According to Fig. 9, the independent radiation mode

control algorithm Fig. 9b achieves a better sound field

reproduction than the FXLMS algorithm Fig. 9a at the

farther monitoring sensors. This is visible for the direct

sound field reproduced by independent radiation mode con-

trol, in which case the negative sign excursion of the impulse

responses one or two samples after the direct wave front

passage is drastically reduced for nearly all monitoring sen-

sors. This is due to the ability to fine tune each of the radia-

tion modes with the independent radiation mode controller

realization of AWFS. In the FXLMS case, the higher-orderradiation modes are often far too penalized and their possible

beneficial contribution in the sound field reproduction pro-

cess is greatly diminished. Further explanations are pre-

sented in Sec. III D.

A different representation of the results allows for a gen-

eral comparison between WFS and the two AWFS algo-

rithms in terms of the reproduction error reduction as a func-

tion of space. Figure10shows the normalized energies of the

reproduction errors at each of the monitoring microphones.

They are computed from the differences between the virtual

and reproduced impulse responses IRs shown in Figs. 8

and 9 and from others IRs measured for different virtual

source positions. The normalized energies are computed as

the sums of the quadratic error signals differences between

virtual IRs and reproduced IRs in the time domain over the

length of the IRs normalized by the total quadratic sum of

the virtual IR, divided by the number of monitoring micro-

phones. The normalization is thus achieved through division

by the mean virtual IR energy at the monitoring micro-

phones. According to the results shown in Fig.10,the AWFS

algorithms reduce on average the reproduction errors in com-

parison with WFS by controlling the reproduction errors at

the four error sensors two of which are monitors 4 and 5.

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Im

p.

response

[1/m]

Time [s]

Direct and targetwave fronts

Floorreflection

Low frequencyreflection

Monitor no

FIG. 8. Reproducedthick gray lines and virtual thin black lines impulse

responses at the monitoring sensor array shown in Fig.2for WFS with the

system in the hemianechoic chamber.

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response

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response

[1/m]

(a)

(b)

FIG. 9. Reproduced thick gray lines and virtual thin black lines impulse

responses at the monitoring sensor array shown in Fig. 2 for AWFS a

FXLMS algorithm with a penalization parameter set to 20 and b indepen-

dent radiation mode control with the system in the hemianechoic chamber.



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AWFS based on independent radiation mode control effec-

tively provides a larger reproduction region since the higher-order modes are included in the controller in that case. Note

that the size of the effective control region is also blurred by

this type of representation which includes all the frequencies.

AWFS by modified FXLMS provides a significant reproduc-

tion error reduction at the two central monitoring micro-

phones, but the reproduction errors are not more important

for the other monitoring microphones. AWFS performs better

than WFS for all the reported virtual source positions.

2. Harmonic AWFS and radiation modes at220 Hz

Harmonic AWFS results in the hemianechoic space, not

reported in this paper for the sake of brevity, were in agree-

ment with the broadband results described in Sec. III B.2. To

support previous propositions Gauthier and Berry, 2006

concerning the shapes of the radiation modes, Fig. 11 pre-

sents the four pressure modes at the error sensor array.

Clearly, these pressure modes correspond to finite approxi-

mations of pressure, pressure gradients, and crossed second-

order spatial derivative. Accordingly, the interpretation of

AWFS based on independent radiation mode control or in-

dependent control of pressure, pressure gradients, and

crossed second-order spatial derivative originally presented

by Gauthier and Berry 2006 is supported by this experi-

ment. This also explains why, in the broadband experiments,

the size of the control region is larger for the AWFS algo-

rithm based on independent radiation mode control which

allows the higher-order radiation modes to converge. More

detailed harmonic AWFS experiments are reported in Sec.

III C.

C. Laboratory space and reverberation chamber

The following summarizes the results obtained for the

laboratory space and the reverberation chamber. As these two

reproduction environments enhance the room effect on WFS,

only parts of the results are shown to support the effective-

ness of AWFS to compensate for the room effect.

1. Broadband AWFS

Since the rooms IRs were longer than for the hemi-

anechoic space, the identified IRs and control filters were

selected to have 512 coefficients for the laboratory space and

1024 for the reverberation chamber with an average over 200

realizations. The resulting synthesis and analysis filters are

shown in Figs. 12 and 13 for the laboratory space. Once

again, a phase optimization algorithm is applied in the fre-

quency domain to smooth the source and pressure modes

phase responses before inverse discrete-time Fourier trans-

form. Moreover, a bandpass filter fourth-order Butterworth,

60540 Hz is applied to all synthesis and analysis filters to

reduce DC components that tend to appear in long SVD

filters. Clearly the responses of the synthesis and analysis

filters are longer than for the hemianechoic room. These fil-

ters are again concentrated impulses and show a reduced

time leakage, thanks to the phase optimization and radiation

modes reordering algorithms which avoid any abrupt phase

or gain transitions in the frequency domain before inverse

discrete-time Fourier transform.

Measured impulse responses reproduced by classical

WFS are shown in Fig. 14 for the laboratory space and in

Fig. 15 for the reverberation chamber. The difference be-

-0.6 -0.3 0 0.3 0.610

-1

100

Normalized energies of the errors

-0.6 -0.3 0 0.3 0.610

-1

100

-0.6 -0.3 0 0.3 0.610

-1

100

-0.6 -0.3 0 0.3 0.610

-1

100

x1

[m]

Position #1

Position #2

Position #3

Position #4

FIG. 10. Normalized energies of the error signals at each monitoring micro-

phone for four virtual source positions in the hemianechoic chamber. Posi-

tion 1: xo =0 , 4 , 0 m, position 2: xo = 4,0,0 m, position 3: x0= 0,1.5,0 m, and position 4: x0 =1.19,0.91,0 m. WFS errors; errors of AWFS by FXLMS; and errors of AWFS by independentradiation mode control.

Pressure mode 1 Pressure mode 2


FIG. 11. Measured pressure modes at 220 Hz in the hemianechoic chamber.

Sensor position; positive real part; negative real part;

positive imaginary part; and negative imaginary part. Symbol diameterillustrates the magnitude of the corresponding value. ---: Corresponding

computed free-field directivity.



8/12

tween the WFS reproduced sound field and the virtual sound

field at the monitor sensor array is increased when compared

with WFS in the hemianechoic room.

AWFS was tested to reduce the reproduction errors at

the four error microphones. The convergence coefficient was

set to 0.000002, and the penalization parameter was set to 30

for AWFS by FXLMS in laboratory space. The individual

convergence coefficients were set to 1 =0.0000075, 2 =3=0.00003, and 4 =0.00015, and the penalization parameters

were set to 1 = 2, 2 =3 =0.2, and 4 =0.1 for AWFS by

independent radiation mode control in the laboratory. The

convergence coefficient was set to 0.0000005, and the penal-ization parameter was set to 0 for AWFS by FXLMS in the

reverberation chamber. The individual convergence coeffi-

cients were 1 =0.0000125, 2 =3 =0.00005, and 4= 0.00025, and the penalization parameters were set to m=0 for AWFS by independent radiation mode control in the

reverberation chamber. Although the penalization parameters

are set to zero in the reverberation chamber, the WFS solu-

tion still contributes to the AWFS solution because the adap-

tive filters are initialized with the WFS solution. The conver-

gence coefficients are smaller than for the hemianechoic case

because the size of the control filters is increased.

The reproduced impulse responses by AWFS are shown

in Figs.16and17 Figs.16a and17a for AWFS by FX-LMS and Figs. 16b and 17b for AWFS by independent

radiation mode control. The imperfections of WFS shown in

Figs.14and15are partly corrected by AWFS even outside

the error sensor array. Both the modified FXLMS and inde-

pendent radiation mode control algorithms reduce these im-

perfections for the two reproduction spaces. Remarkably, the

100 200 300 400 500

-0.1

-0.05

0

0.05

Amp.

Source mode #1

100 200 300 400 500

-0.05

0

0.05

Amp.

Source mode #2

100 200 300 400 500

-0.04

0

0.04

Amp.

Source mode #3

1 128 256 384 512

-0.1

0

0.1

Amp.

Source mode #4

Samples

FIG. 12. First synthesis filters Gauthier and Berry, 2006 in the time do-

main for source modes 14 in the laboratory space. Each plot includes 24synthesis filters to create the given source mode with 24 reproduction

sources. Each filter includes 512 coefficients.

100 200 300 400 500

0

0.2

0.4

Amp.

Pressure mode #1

100 200 300 400 500-0.2

0

0.2

Amp.

Pressure mode #2

100 200 300 400 500

-0.1

0

0.1

Amp.

Pressure mode #3

1 128 256 384 512-0.4

0

0.4

Amp.

Pressure mode #4

Samples

FIG. 13. Analysis filters Gauthier and Berry, 2006 in the time domain for

pressure modes 14 in the laboratory space. Each plot includes 4 analysis

filters to catch the pressure mode with 4 pressure sensors. Each filter in-

cludes 512 coefficients.

12

3 4

56

78

0.02

0.04

0.06

0.08

-0.5

0

0.5

Monitor noTime [s]

Imp.

response

[1/m]

Direct wave front

Floorreflection

FIG. 14. Reproducedthick gray linesand virtualthin black linesimpulseresponses at the monitoring sensor array shown in Fig.2for WFS with the

system in the laboratory space.

12

34

56

78

0.02

0.04

0.06

0.08

-0.5

0

0.5

Monitor noTime [s]

Imp.

response

[1/m]

FIG. 15. Reproducedthick gray linesand virtualthin black linesimpulse

responses at the monitoring sensor array shown in Fig.2for WFS with the

system in the reverberation chamber.



9/12

room compensation is achieved over a wide time range.

Again, more than simply reducing the undesirable room ef-

fect in the reproduced sound field, AWFS more closely re-

produces the direct sound field than WFS.The normalized energies of the errors at each of the

monitor microphones are shown in Fig.18 for the laboratory

space. The AWFS algorithms reduce on average the repro-

duction errors in comparison with WFS by controlling the

reproduction errors at the four error sensors. AWFS based on

independent radiation mode control gives a larger reproduc-

tion region as the higher-order radiation modes typically

corresponding to higher-order spatial derivatives are in-

cluded in the controller in that case. This again highlights the

benefits of AWFS based on independent radiation mode con-

trol. AWFS performs better than WFS for all the reported

virtual source positions. Similar results were obtained for the

reverberation chamber with different virtual source positions.

2. Harmonic AWFS

The harmonic AWFS results are only reported for the

laboratory space. Consistent results were obtained for the

reverberation chamber. According to the typical FRF shown

in Fig.5,the following frequencies were selected for on-line

AWFS: 133, 160, 220, 280, 340, and 400 Hz.

Examples of pressure modes are shown for 220 Hz in

Fig. 19. Again the radiation modes approach simple multi-

pole directivity patterns: monopole, two orthogonal dipoles,

and tesseral quadrupole at the sensor array.

The convergence coefficient was set to 0.01 for all fre-quencies while the penalization parameter was fixed to 1

except at 133 and 160 Hz where they were set to 0.0005 and

0.005, respectively for AWFS by the modified FXLMS al-

gorithm. The convergence coefficients and penalization pa-

rameters for the AWFS algorithm based on independent ra-

diation mode control were then adjusted to reach a roughly

similar residual error level at the error sensors than for the

FXLMS algorithm. However, each higher-order radiation

modes were less penalized than for the FXLMS algorithm

when possibleto increase the performance outside the error

sensor location Gauthier and Berry, 2006. This was

achieved using either m = or m+1m. The coefficients

are shown in Table I.

The results are summarized in Fig. 20, for a virtual

source in xo = 0 , 4 , 0 m, where the color axis represents the

ELS normalized criterion at each of the monitor positions

along x1. The criterion ELS is the moving average of the

quadratic sum of the reproduction errors normalized by the

quadratic sum of the target signals at the monitor sensors. As

one can note, the WFS performance is reduced in compari-

son with the other algorithms. As for the hemianechoic re-

sults, using the FXLMS algorithm, the error is effectively

reduced near the error sensors. However, as frequency in-

12

34

56

78

0.02

0.04

0.06

0.08

-0.5

0

0.5

Monitor noTime [s]

Imp.

response

[1/m]

12

34

56

78

0.46

0.48

0.5

-0.5

0

0.5

Monitor noTime [s]

Imp.

response

[1/m]

(a)

(b)



FXLMS algorithm with a penalization parameter set to 20 and b indepen-

dent radiation mode control with the system in the laboratory space.

12

34

56

78

0.02

0.04

0.06

0.08

-0.5

0

0.5

Monitor noTime [s]

Imp.

response

[1/m]

12

34

56

78

0.88

0.9

0.92

0.94

-0.5

0

0.5

Monitor noTime [s]

Imp.

response

[1/m]

(a)

(b)



FXLMS algorithm with =0 and b independent radiation mode control

with m = 0 with the system in the reverberation chamber.



10/12

creases, this control region is spatially reduced. This is inaccordance with typical active noise control results. AWFS

based on independent radiation mode control advantageously

produces, as shown in Fig. 20, a larger control region since

the higher-order radiation modes which typically imply

higher-order spatial derivatives at the error sensor array see

Fig.19 are allowed to converge.

D. Importance of the higher-order radiation modes

The importance of the higher-order radiation modes is

highlighted by a specific set of experiments. The size of the

active sound field reproduction effective region is shown in

Fig. 21 in relation to the acoustic wavelength. In Fig. 21,

several harmonic AWFS results with the WFS solution

forced to zero are presented for a harmonic wave field at

400 Hz in the laboratory space. The WFS solution is forced

to zero to illustrate only the effects of the individual radiation

modes. Clearly, when AWFS based on independent radiation

mode control includes only one radiation mode, the results

correspond to AWFS by FXLMS. When the number of

-0.6 0.3 0 0.3 0.610

-1

100

Normalized energies of the errors

-0.6 0.3 0 0.3 0.610

-1

100

-0.6 0.3 0 0.3 0.610

-1

100

0.3 0 0.3 0.6

100

-0.6 0.3 0 0.3 0.610

-1

100

x1

[m]

Position #1

Position #2

Position #3

Position #5

FIG. 18. Normalized energies of the error signals at each monitoring micro-

phone for four virtual source positions in the laboratory space. Position 1:

xo = 0 , 4 , 0 m, position 2: xo = 4,0,0 m, position 3: xo = 0,1.5,0 m,

and position 5: xo = 2.8289,2.8234,0 m. WFS errors; errors of

AWFS by FXLMS; and errors of AWFS by independent radiation modecontrol.



FIG. 19. Measured pressure modes at 220 Hz in the laboratory. Sensor

position; positive real part; , negative real part; positive imagi-

nary part; and negative imaginary part. Symbol diameter illustrates the

magnitude of the corresponding value. --- Corresponding computed free-

field directivity.

TABLE I. Convergence coefficientsmand regularization parametersm

for harmonic AWFS based on independent radiation mode control in labo-

ratory space.

Freq.Hz m m

133 0.01, 0.1, 0.1, 0.5 0.1, 0.01, 0.01, 0.001

160 0.02, 0.1, 0.1, 0.5 0.1, 0.01, 0.01, 0.001

220 0.02, 0.2, 0.2, 0.5 0.1, 0.01, 0.01, 0.001

280 0.02, 0.1, 0.1, 0.5 0.1, 0.01, 0.01, 0.0005

340 0.02, 0.1, 0.1, 0.5 0.1, 0.01, 0.01, 0.001

400 0.02, 0.1, 0.1, 0.5 0.1, 0.01, 0.01, 0.001

-0.5

0

0.5

133160 220 280 340 400

WFS

x1

[m]

-0.5

0

0.5

133160 220 280 340 400

AWFS by FXLMS

-0.5

0

0.5

133160 220 280 340 400

AWFS by ind. radiation mode control

Freq. [Hz]

x1

[m]

x1

[m]

0 0.05 0.1 0.15 0.2 0.25

ELS

FIG. 20. Normalized ELS criterion at the monitoring sensors for various

frequencies and harmonic algorithms after convergence in the laboratory.

From top to bottom: WFS, AWFS based on FXLMS and AWFS based on

independent radiation mode control. . Measurement points. The

0.1 contour lines;--- the 0.25 contour lines; andthe 0.5 contour lines.



11/12

higher-order modes included in AWFS based on independent

radiation mode control increases, the size of the effectivecontrol region increases from a quarter wavelength to half

the wavelength. This supports the previous observation on

the importance of the higher-order radiation modes to en-

large the effective active sound field reproduction region.

The adaptation coefficients and penalization parameters are

shown in TableI.

IV. CONCLUSION AND PERSPECTIVES

This paper investigated the objective performances of

AWFS to compensate for the room effects or any sound

field reproduction errorson WFS in experimental situations.

The basic idea of AWFS is a simple combination of activenoise control principles and classic WFS. Such a combina-

tion is entirely contained in the AWFS general cost function

Gauthier and Berry, 2006, which consists of minimization

of the reproduction errors typically caused by the room re-

sponseKlehs and Sporer, 2003;Sporer and Klehs, 2004 or

the system limitation Corteel, 2006b at several points in

space, along with a regularization that penalizes the adaptive

solution departure from the classic WFS solution. This pe-

nalizing is what makes AWFS original in comparison with

other sound field reproduction techniques based on active

sound control and adaptive filtering.

The results presented in this paper show that the AWFS

system successfully achieves active sound field reproduction

in more or less reflective spaces: hemianechoic chamber,

laboratory space, and reverberation chamber. These experi-

ments validate the AWFS concept and demonstrate the physi-

cal possibility of progressive sound field reproduction in re-

flective rooms. For the three rooms, it was shown that AWFS

reduces the reproduction errors with respect to WFS repro-

duction errors in the reproduction region. AWFS based on

independent control provides an extended effective area of

sound field reproduction since each radiation mode conver-

gence is independently adjusted so that higher-order modes

converge in the allowed time. Since these higher-order

modes are of great importance to enlarge the effective repro-

duction region, the possibility to control them independently

is a major advantage of AWFS based on independent radia-

tion mode control in comparison with modified FXLMS,

which does not allow such independent control of each ra-

diation mode convergence.

One of the original contributions of these results is that

they establish, for the first time to the authors knowledge,

the validity of the AWFS concept based on independent ra-diation mode control including SVD broadband filters for

broadband impulse reproduction by the way of controlled

experiments.Bai and Elliott 2004 already considered SVD

plant decoupling for cross-talk cancellation, but their paper

was limited to theoretical investigations. Moreover, at the

heart of the AWFS concept, is the definition of an a priori

solutionWFSwhich, to the authors knowledge, was never

used or experimentally tested within an adaptive signal pro-

cessing or active noise control architecture. This paper on

experimental AWFS supports the practical interest of AWFS.

The reported experiments were performed with a spe-

cific reproduction source and error sensor configuration.However, AWFS is not limited to a specific configuration.

These experiments with AWFS were performed to evaluate

the method. AWFS could be tested with different configura-

tions or for different practical problems: sound environment

reproduction, mock-up with sound field simulation system,

etc. A typical AWFS extension would, for example, include

more loudspeakers and more error sensors. Indeed, we ex-

pect that a larger effective reproduction region is achievable

with a compact sensor array which would include more sen-

sors, like a dense circular microphone array. Three-

dimensional configurations of either loudspeaker or micro-

phone arrays could also be implemented within the AWFSframework.

The tested AWFS system and implementation should be

regarded as proto-AWFS. Indeed, before AWFS can be used

for a practical application, several modifications should be

done. For example, to reduce the obstruction of the error

sensors in the listening area, the control filters can be calcu-

lated off-line for the virtual source positions and saved, after

which the error sensors can be removed. An example of ef-

fective bank of compensation filters for WFS direct-sound-

field equalization has been reported by Corteel 2006b.

Moreover, several adaptive algorithms could be applied to

AWFS, such as frequency-domain adaptation, sparse adapta-tion, etc. Elliott, 2001 to improve the convergence proper-

ties of the algorithm or to reduce the computational burden.

Future research on AWFS should be conducted within a

specific practical application such as sound environment re-

production or sound reproduction in a dedicated listening

room to evaluate the potential of the method in real situa-

tions, possibly using more reproduction sources and more

error sensors. AWFS and the corresponding algorithms

should also be tested and evaluated on the basis of subjective

performance.

-0.5 0 0.510

-2

10-1

100

101

x1

[m]

E

LS

(monitors)

AWFS, FXLMS

SVD with first mode only

SVD with modes 1 to 3

SVD with all modes

/2

0.8575 m

/4

FIG. 21. NormalizedELS criterion at the monitoring sensors for harmonic

algorithms at 400 Hz after convergence in the laboratory space using AWFS

with the WFS solution forced to zero. The wavelength and some corre-

sponding fractions are included.



12/12

ACKNOWLEDGMENTS

This work was supported by NSERC Natural Sciences

and Engineering Research Council of Canada, NATEQ

Fond Qubecois de la Recherche sur la Nature et les Tech-

nologies, VRQ Valorisation Recherche Qubec, and Uni-

versit de Sherbrooke. This research was conducted in col-

laboration with CIRMMT Center for Interdisciplinary

Research in Music Media and Technology, McGill Univer-

sity. The authors acknowledge the contribution of Emman-

uel Corratg, who contributed to the construction of the har-monic AWFS system and harmonic experiments.

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