Using Three Receivers
Genyuan Wang, Xiang-Gen Xia, Senior Member, IEEE, and Victor C. Chen, Senior Member, IEEE
AbstractThe conventional ISAR image is a two-dimensional
(2-D) projection of a three-dimensional (3-D) object surface. The
image (projection) plane is related to the motion of a target with
respect to the line of radar sight (LOS). In general, the image plane
and the image scale in the cross range direction can not be de-
termined by the traditional ISAR system with one receiver unless
the target motion knowledge is known. In this paper, we propose
a new ISAR system with three receivers. Using the three-receiver
ISAR system, 3-D images of maneuvering targets can be generated,
where the knowledge of the target motion is not required.
Index TermsISAR imaging, maneuvering targets.
I. I
NTRODUCTION
M
OST OF the current inverse synthetic aperture radar
(ISAR) imaging techniques form two-dimensional
(2-D) images of moving targets, which are 2-D projections of
three-dimensional (3-D) moving targets. The fine resolution
in the range direction is obtained by transmitting a wide band
signal and the high cross range resolution is achieved by
exploiting the relative motion between the radar and targets.
The absolute scale in the cross range, however, depends on the
angular rotation of the target. When the rotation is uniform,
the scale depends on the rotation velocity that is usually not
known. When the rotation is nonuniform, the scale is even
more complicated to determine. In both cases, the scale in the
cross range of an ISAR image is not known in the conventional
ISAR. Since the absolute scale in ISAR imaging is not known,
the true locations of scatterer can not be determined even in the
image projection plane. Furthermore, in the conventional ISAR,
it is only possible to form one image plane. Therefore, even the
scale in this image plane is known, it is still not possible to form
other image planes with different orientations, and therefore it
is not possible to form a 3-D image of a maneuvering target
through the conventional ISAR. Recently, there are a few
algorithms on the 3-D ISAR imaging [5], [6], [16][21]. The
algorithms in [5], [6] are proposed for the near field turning
table targets with the knowledge of the target motions through
the measurements. The algorithms in [16][20] require the
knowledge of the relative positions of the radar and target, and
Manuscript received March 16, 2000; revised November 16, 2000. This work
was supported in part by the 1998 Office of Naval Research (ONR) Young
Investigator Program (YIP) under Grants N00014-98-1-0644 and N00014-0-
110059 and the Air Force Office of Scientific Research (AFOSR) under Grant
F49620-00-1-0086.
G. Wang and X.-G. Xia are with the Department of Electrical and Com-
puter Engineering, University of Delaware, Newark, DE 19716 USA (e-mail:
gwang@ee.udel.edu; xxia@ee.udel.edu).
V. C. Chen is with the Radar Division, Naval Research Laboratory, Wash-
ington, DC 20375 USA (e-mail: vchen@radar.nrl.navy.mil).
Publisher Item Identifier S 1057-7149(01)01666-9.
several different view angles and different heights of the air-
craft. In [21, sec. 8.5, p. 596], multiple antenna ISAR imaging
is proposed, where it is proposed that the motion parameters of
a target are first estimated before the ISAR imaging.
In this paper, we propose a new ISAR imaging system with
three receiving antennas, where we propose a method to solve
for the 3-D scatterer position information and therefore we are
able to form 3-D ISAR images. The principle is as follows. Two
receivers and one transmitter that is also a receiver, are located in
the same plane orthogonal to the LOS as shown in Fig. 1. Using
the three receivers, three conventional 2-D complex ISAR im-
ages are obtained. All of them have the same range and the cross
range resolutions but with different phases that contain the po-
sition information of the scatterer. Using the phase information,
the 3-D geometric positions of scatterer can be solved. If all the
3-D geometric positions of the scatterer are correctly solved,
the 3-D ISAR image can be, of course, formed. However, in
our system, there may be a few scatterer positions not correctly
solved as we will see the reason later, which may affect the 3-D
ISAR image quality. The method to resolve this issue is that,
from the majority of the correctly detected scatterer locations,
the scale of a 2-D ISAR image in the cross range direction in
any image plane can be obtained, which allows us to form im-
ages with different image planes (projections) of the three di-
mensional target. From the image collection at different image
plane orientations the actual 3-D information can be obtained.
This paper is organized as follows. In Section II, received
signals of the three receivers are described. In Section III, the
2-D and 3-D ISAR imaging algorithm of maneuvering targets is
described. In Section IV, some simulation results are presented.
II. R
ECEIVED
S
IGNALS FROM A
T
HREE
R
ECEIVER
ISAR
S
YSTEM
A three-receiver ISAR system is shown in Fig. 1. The coor-
dinate system is defined as in Fig. 1, i.e., the location of the
transmitter as well as the first receiver is chosen at the origin,
the LOS is the axis
, the second and the third receivers are lo-
cated on the
axis and
axis with the coordinates
and
, respectively.
Suppose that the radar transmits a linear frequency modulated
(LFM) signal
(2.1)
where
amplitude;
carrier frequency;
10577149/01$10.00 © 2001 IEEE WANG et al.: THREE-DIMENSIONAL ISAR IMAGING OF MANEUVERING TARGETS
437
Fig. 1.
Geometry in the three receiver ISAR system.
chirp rate;
time length of the chirp pulse.
The complex envelope of the received signal at the
th
(
) receiver from a point scatterer
located at
is
(2.2)
where
is the fast time for the range dimension,
is the slow
time for the cross-range dimension, the fast time delay at the
slow time instant
is
(2.3)
where
is the wave propagation velocity and
is the
distance from the
th receiver of the radar to the point scatterer
at time . These distances are
(2.4)
(2.5)
(2.6)
where
is the change of the distance between the target
and the radar due to the translational motion from the time in-
stant 0 to the time instant .
is independent of a point
,
i.e., the same for all the scatterer of the target.
is
the coordinate of
at
.
,
, and
are the shifts of scatterer
from time instant 0 to the time in-
stant in the
,
and
directions, respectively, due to the ro-
tation of the target with respect to some reference scatterer
located at
of the target. The scatterer
is
chosen as the auto-focus point of the target, which will be men-
tioned later. Now, let us give an example to see how large the
shifts
,
and
may be. As the size of a
target is less than 20 m and the rotation of the target with the line
of radar sight is about 0.1 degree. The quantities of
,
and
are less than 2 m. If
is
chosen as the center of the target, they are less than 1 m.
After the range compression, the received signals in (2.2) be-
come
sinc
rect
(2.7)
where
is the wave length of the transmitted signal
and rect
stands for the unit rectangular signal. From the above
formulas, one can see that, at different slow time , a received
signal
has different time delay in the fast time .
III. I
MAGING
A
LGORITHM AND
3-D G
EOMETRIC
P
OSITION
D
ETERMINATION
In this section, we want to present the conventional ISAR
imaging algorithm that generates high resolution images of a
maneuvering target as well as preserves the phases. Note that
these preserved phases are used to solve for the three dimen-
sional geometric positions of scatterer as we shall see later in
this section. Since there are three ISAR images from the three
receivers, in order to preserve the phases the motion compen-
sation has to be uniform to all the three receivers, which is the
main goal in the next subsection.
A. Uniform Motion Compensation at Three Receivers
The purpose of motion compensation is to remove the effect
of the translational motion of target from the received signals.
The motion compensation has two parts, namely range align-
ment and auto-focus. Range alignment is to compensate the fast
time delay at different slow time such that the received signals
of a scatterer are in the same range cell. The argument of the sinc
function in (2.7) is the term to work with for range alignment
while the phase in (2.7) is the term to work with for auto-focus
as we shall see later.
Consider, for example, a target of size about 2040 m and the
distance of the target to the radar is more than 10 000 m, and the
distance
of the receivers to the transmitter is about 12 m. Let
and
be the coordinates of the autofocus point
in
and 438
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO. 3, MARCH 2001
(a)
(b)
Fig. 2.
Target model and time-variant ISAR image. (a) Target model and (b) image with a time-variant Doppler algorithm.
axes with
and
, then the last term in (2.5) and
(2.6) satisfy
m
and
m
When the radar resolution in the range is about 0.10.5 m; the
distance differences of a scatterer to the three different receivers
are much smaller than the range resolution size. This implies
that the range alignment of the three received signals can be
achieved by using the same compensation function, i.e, the same
range alignment [1], [22] compensation function. As a remark,
the above approximations are used only for explaining the range
alignment and these two terms in (2.5) and (2.6) are still main-
tained in the following analysis.
After the range alignment, from (2.7) the received signal of
all scatterer in the th range cell can be written as
(3.1)
where t