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IEEE SIGNAL PROCESSING MAGAZINE [85] MARCH 2015

the loudspeaker weights and solved using the least-absolute

shrinkage and selection operator [16]. The assumption here is that

the desired sound field can be reproduced by a few loudspeakers,

which are placed close to the direction of the virtual source and

are sparsely distributed in space. This can produce low sound lev-

els outside the bright zones and hence can reduce the interference

to the dark zone.

Further Remarks

While the reproduction error has been widely used to quantify the

performance of sound field rendering methods, a planar wavefront

may be reproduced whose direction of propagation does not coin-

cide with the desired direction, which may give a high reproduc-

tion error. In [18], the cost function of the ACC method is refined

to optimize the extent to which a sound field resembles a plane

wave. A constraint is imposed on the plane-wave energy within the

bright zone over a range of incoming directions, thus optimizing

the spatial aspects of the sound field for ACC. Simulation results

demonstrate that a circular array of 48 equally spaced loudspeak-

ers produces consistently high contrast and a planar target sound

zone of radius 0.15 m for frequencies up to 7 kHz.

ACTIVE ROOM COMPENSATION

One challenge in the personal audio problem is room reverbera-

tion. A strong wall reflection may ruin the personal audio listening

experience [14]. Room reverberation can be corrected by using

active room compensation, provided the acoustic transfer function

(ATF) matrices are determined. For static room environments

these matrices may be premeasured but for time-varying environ-

ments they must be determined adaptively. In this section, meth-

ods for determining and correcting for these matrices to

compensate for room responses over spatial regions are described.

The room compensation approaches described here are more

robust at low frequencies. At high frequencies, a reverberant

sound field is diffuse. Compensation is extremely sensitive to small

changes within the room and cannot be practically compensated

for without very fast filter adaptation. Personal sound systems may

not be able to compensate for these variations. Instead, diffuse

components may be treated as noise and the system made robust

to them.

We summarize the advances made for the case of a single zone

with the ATF matrix,

,HH

/ using wave-domain or modal-space

processing. These approaches demonstrate the challenges inher-

ent in applying room compensation to the multizone problem. We

also review a crosstalk-cancelation approach to the multizone case

that utilizes impulse response reshaping.

MODAL-SPACE PROCESSING

Based on the wave-domain sound field representation (S1), the

sound field

(, )xp

~ can be expressed as in (3). The ATF ( , )xH ~

from each loudspeaker , to a point x inside the sound control

zone can also be parameterized as

(, ) ( ) ( ) ( ),expxH kr iJ

()

~c~ oz=

(8a)

(, ) ( ) ( ) (, ),xH kr YJ

()

~c~ iz=

=-=

(8b)

where ( )w

and ( )c~

are ATF coefficients. The sound

pressure vector p and ATF matrix H can then be written in

matrix form

,pB

a= (9a)

,HBC= (9b)

where B is the M N# matrix of basis functions evaluated at

each of the M microphone positions defined [ ] ( , ),

mn n m

a is an M -long vector of sound field coefficients, C is the

LN # matrix of the ATF coefficients defined

[] ,

cC =

and N

is either N

or .N

The PM problem of (5a) in the mode

domain becomes ,g

des

aC = where

des

a is the N -long vector of

coefficients for the desired sound field. The compensation prob-

lem can then be solved in offline manner by determining the

least-squares solution [19].

An adaptive mode-domain approach was devised in [20].

The ATF matrix can be further parameterized

,HUJC= (10)

where U is a tall Vandermonde matrix (2-D) or spherical harmonic

matrix (3-D) with the property that UU I

= and J is a diagonal

matrix of the mode amplitudes at the microphone positions. The

vector of microphones’ signals

pHg= are hence transformed into

mode-domain coefficients through .JUp

a =

For modest levels

of room reverberation, C can be expressed as the sum of an

anechoic room component and a small reverberant component. By

approximating the reverberation as small, a simple iterative proce-

dure for choosing

g to drive

a to

des

a can be formulated. Reverber-

ant compensation methods [19], [20] may have difficulties in practice

with preringing artefacts, but these artefacts may be reduced by

using more advanced multiple-input, multiple-output polynomial fil-

ter designs [21].

ACTIVE LISTENING ROOM COMPENSATION

WITH WAVE-DOMAIN ADAPTIVE FILTERING

Active listening room compensation can be used to make a rever-

berant room problem look like an anechoic room problem [22].

By applying a compensation filter matrix to the input loudspeaker

signals, the uncompensated anechoic-room driving signals can

then be used. The essence of the problem as depicted in Figure 3 is

to minimize the error energy

,ee

where

,e H g HCg

is the anechoic-room ATF matrix, and C is an LL# compen-

sation filter matrix. This effectively chooses the filter matrix C to

drive the net transfer function matrix HC to the anechoic-room

ATF matrix .H

In massive multichannel problems for which the number of

loudspeakers L and microphones M are large, the resultant

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