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HYBRID SAR/ISAR
FOR DISTRIBUTED ISAR IMAGING OF MOVING TARGETS
Victor C. Chen and Baokun Liu
Ancortek Inc
Fairfax, VA, USA
Abstract—The hybrid SAR/ISAR processing takes advantages
of both SAR and ISAR to generate high-resolution imagery of
moving targets. In this paper, we introduce the concept of hybrid
SAR/ISAR, discuss how to reform a high-resolution imagery of
moving targets and extract 3-D target feature through hybrid
processing of the data taken by multiple arbitrarily distributed
ISARs.
Keywords—hybrid ISAR/SAR; distributed ISAR; 3-D SAR
image; 3-D projection slice theorem
I.
mountain. In practice, multiple radars are usually arbitrarily
distributed at different levels of height. A general
configuration of arbitrarily distributed ground-based radars
watching a moving target is illustrated in Figure 1, where each
radar functions as an ISAR for imaging of the moving target.
If all of the ISARs are time synchronized and collecting data
at the same time frame, we should be able to coherently
combine multiple individual ISAR data collected with
different grazing angles and to synthesize a large aperture
SAR data for optimally extracting target features.
INTRODUCTION
The concept of hybrid SAR/ISAR was first proposed in
early 1990s [1]. SAR observes stationary targets through a
moving radar platform. Any target motion can degrade SAR
imagery. Conversely, ISAR is based on a stationary platform
to observe moving targets. Any radar platform's motion can
affect the ISAR imagery. As explained in [1], "it is desirable
to construct a theory of hybrid SAR/ISAR imaging which
treats target and platform motions on an equal footing, both to
analyze the degradation of conventional SAR and ISAR
images and to identify ways in which these hybrid images may
be processed optimally." The hybrid SAR/ISAR processing
(also called the combined SAR/ISAR processing) is such way
to optimally process SAR or ISAR data.
A. The Concept of Hybrid SAR/ISAR
Hybrid SAR/ISAR configurations may have two ways in
which radar data can be optimally processed to achieve highresolution and 3-D imagery of moving targets:
(1) Refocus moving target in SAR imagery: to do this,
ISAR processing is applied to SAR sub-apertures data and,
then, coherently combines the processed sub-aperture data into
a new SAR data to refocus moving targets. This hybrid
SAR/ISAR processing takes the advantage of ISAR
processing to generate focused imagery of a moving target in
SAR [2,3].
(2) Coherently combining multiple ISAR data to a SAR
data: SAR processing is applied to the combined data to
achieve enhanced cross-range resolution and extract 3-D
target feature. This hybrid SAR/ISAR processing takes the
advantage of SAR processing for ISAR data.
In this paper, we concentrate on the second way of the
hybrid SAR/ISAR processing for applications of arbitrarily
distributed multiple ISARs.
B. Arbitrarily Distributed ISARs
Arbitrary distributed radars are a number of nearby radars
distributed within a limited area along coast, shore or
Distributed ISARs for Imaging of Moving Targets
Figure 1 – Illustration of distributed multiple ISARs to reform a highresolution SAR imagery of a moving target.
Distributed ISARs located at different heights are similar
to the configuration of trajectory-deviated SAR. As we know,
serious trajectory deviation in a strip-map or spotlight SAR
can cause not only image blurring, but also geometric
distortion.
In [4], airborne ISARs are assumed flying in formation
along a row and viewing a target from separated azimuth
angle, but at the same grazing angle. A combined SAR/ISAR
processing scheme was proposed in [4] to coherently combine
multiple ISARs into a SAR data for the enhancement of the
cross-range resolution. In this paper, we extend the distributed
multiple ISARs from linearly flying in formation to "arbitrary"
distributed. The arbitrarily distributed multiple radars are
more suitable to applications to ground-based surveillance,
where the multiple ISARs are not necessarily arranged along a
row and at the same heights. The actual distribution is based
on the topography of the ground. The "trajectory" or "aperture
path" of the distributed ISARs is similar to a serious deviated
strip-map SAR or curved spotlight SAR.
In Section II, we will revisit distributed ISARs at the same
height, but not line-up on a row. We will discuss how to
remove phase errors induced by different distances between
radars and the target due to their "arbitrary" distribution and,
thus, generate a combined SAR data for the enhancement of
the cross-range resolution. In Section III, we will discuss
arbitrarily distributed ISARs with different grazing angles for
extraction of 3-D target feature.
As we know, an ISAR imagery of a target is the projection
of a 3-D target onto a 2-D image projection plane (IPP), which
is determined by the radar grazing angle as well as other
factors [5,2]. Therefore, 2-D ISAR images of a 3-D rotating
target taken at different grazing angles will have different
scales in the range domain, i.e., the elevated scatterers appear
closer in range, called the image layover phenomena as
illustrated in Figure 2. If we apply hybrid SAR/ISAR
processing to it, by combining multiple ISAR range profiles
taken at different grazing angles, the resulting SAR imagery of
a 3-D target has artifacts caused by these layover features.
3-D Target Model
2-D ISAR Image
Cross-Range
Layover
phenomena
Figure 3 is a generalized distributed ISAR configuration
including N radar platforms and a target composed of K
scattering centers. The target is simply defined by a 3-D RCS
reflectivity density function characterized by the pointscatterer model. The origin of the reference coordinates, O, is
located at the rotation center of the target. Ri , ξi and φi (i = 1,
2, … , N) are the range, azimuth angle, and grazing angle of
the ISAR-i, respectively.
We assume that the target has only rotations about its
center of rotation at the origin and the translational motion has
been compensated. For simplicity, the target has only yaw
motion with rotation rate  about the Z-axis. The k-th
scatterer of the target is represented by a range vector Pk from
the origin and an elevation angle k,. The rotation angle is a
function of time:
, where
is the initial
rotation angle. The azimuth angle for the i-th ISAR ξi is
measured counter clockwise from the Y-axis.
For monostatic ISARs, the signal transmitted from the
ISAR-i, reflected by the k-th scatterer, and received at the
ISAR-i is expressed by
, (1)
where
,
and
.
The distance between i and k is
Image Projection Plan
Slant-Range
Figure 2 - Layover phenomena after 3-D target projected on 2-D
ISAR image projection plane.
To deal with the problem caused by ISAR data collected at
different grazing angles, we will take the advantage of the
spotlight SAR with a curved aperture path to extract 3-D
target feature [6-9].
II.
ARBITRARILY DISTRIBUTED ISARS AT THE SAME HEIGHT
Before dealing with arbitrarily distributed multiple ISARs
at different heights and, thus, grazing viewing angles, we first
take a look at how to combine arbitrarily distributed multiple
ISARs at the same height or with nearly a constant grazing
angle.
ISAR-i
Z

 (t )   k0   t
Pk
Ri sin i
Ri,k
Scatterer k
Y
Ri
φi
ϕk
.
Because
(2)
, for small t,
.
Thus,
. (3)
After removing the extra constant phase term and add a
different additional phase term to each ISAR, such that the
distributed ISARs are rearranged along a preselected a virtual
circular-trajectory with their azimuth angles ξi (i=1,2,...N)
unchanged as illustrated in Figure 4, thus, the residual phase
term is a function of time that corresponds to the Doppler shift
of the scatterer k:
ξi
,
θk0
o
.
For nearly constant grazing angles, φi ≈ φ, we have
X
Figure 3 - Configuration of distributed ISARs and a target.
(4)
where
, which is
determined by the rotation rate , the distance |Pk| of scatterer
k from the origin, the grazing angle of ISAR-i i ≈ , the
elevation angle of the scatterer k, and the azimuth angle of
ISAR-i platform ξi . Then, the total received signal of the
ISAR-i from the target becomes
, (5)
where i = 1, 2,…, N. Thus, an ISAR image can be generated
through standard ISAR image formation processing of the
total received signal of the ISAR-i.
Actual Distributed
ISARs

0
Scatterer k
ISAR-i
Ri,k
Pk
θk0
Ri
ξi
Rj
Rj,k
Y
ISAR-j
Circular Virtually-Distributed
ISARs
X
Figure 4 - Rearranging to a circular virtually-distributed ISARs..
A. Combining View Angles of Multiple ISARs
In the configuration of distributed ISARs, each ISAR can
only see the target within a small view angle. By correctly
combining multiple small view angles, a large view angle can
be synthesized. However, because of overlapping, the
combined view angle is smaller than the sum of individual
ISARs view angles. Figure 5 shows these angles as functions
of time. As known, during the observation time T, the total
view angle of each ISAR is T and, thus, the cross-range
resolution is
, where λ is the wavelength. In a
distributed multiple ISARs, the way to increase the total crossrange resolution is to combine the received signals si(t), i =
1,2,...,N, such that the combined view angle can become a large
angle. It is easy to verify that the variation of this synthesized
view angle can be extended to
.
The overlapped angle from the adjacent ISARs is
B. Synthesizing SAR from Distributed ISARs
Similar to the discussion in [4], with arbitrarily distributed
multiple ISARs with nearly same grazing angles, we use three
steps to synthesize a large SAR data.
(1) Time-Shifting of Received Signals: To coherently
combine received signals si(t) (i=1,2,...,N) from the distributed
ISARs, we must smoothly and correctly connect these signals
without time breaking and view angle jumping. To extend the
view angle continuously as a function of time, the signals
must be properly time-shifted to t1, t2, ... tN. Actually, the time
shifts for signals are related to the ISAR platform locations
and are determined by the parameters ξi. It is sufficient to
show from Figure 5 that
.
(2) Time-Windowing of Received Signals: To achieve
enhanced cross-range resolution in the distributed ISARs,
received ISAR signals must be coherently combined to extend
the view angles. It is seen in Figure 5 that, due to the time
shifts of signals, the view angles and hence the receiving
ISAR signals may be overlapped or piece-wisely connected in
the best case during the combining process.The overlapped
angles (or times) of adjacent signals are generally not the same
since the radar platforms may not be equally spaced.
Therefore, received signals need to be time-windowing so that
a continuously extended view angle is formed.
(3) Coherent Combination of ISAR Signals: To combine
these signals in the sense of extending the view angle, without
loss of generality, we consider a single scatterer scenario.
After substituting the individual signal
along with
parameters derived earlier into scomb(t), the resulting combined
signal becomes
.
(6)
After summing the N-dependent windows, the combined
signal is further reduced to
.
Distributed Multiple ISARs
N
In fact, the distributed ISARs must be appropriately placed
such that the synthesized combining angle is continuously
extended to a maximal one. This implies that
, or
.
We can see that, if
, then
and
the maximum cross-range resolution is achieved, that is
, which is N times improved resolution of
a single ISAR.
Overlapped
T5
ISAR-5
ISAR-4
T4
ISAR-3
.
(7)
T3
T2
ISAR-2
N
T
T1
ISAR-1
t1
t2
T
ξ1
T1
n
n 1
t3
T
ξ2
 T2
t4
T
ξ3
T 3
t5
T
ξ4
T 4
 NT
Integration Time
T
ξ5
T 5
N
View Angle
   Tn  NT
n 1
Figure 5 - Combined view angle and integration time.
The combined signal is piecewise continuous in time and has
an extended viewing angle:
.
The combining view angle must be linearly extended
without time breaking and angle jumping. This implies that
the overlapped viewing angles from the adjacent platforms,
have to be greater or
equal to 0.
D. Example of Arbitrarily Distributed ISARs with the Same
Height
The geometry of arbitrarily distributed ISARs with the
same height looking at a target is illustrated in Figure 6. Each
ISAR is operating at X-band 10 GHz with range resolution of
0.1 m. The observation time is 2 sec and the number of
transmitted pulses is 64. For simplicity, the total number of
ISARs is N = 5. The locations of each ISAR are: ISAR no.1 at
(9.3, -1.6, 0.7); ISAR no.2 at (11.8, -1.2, 0.7); ISAR no. 3 at
(11.9, 0.0, 0.7); ISAR no. 4 at (10.4, 0.7, 0.7); and ISAR no. 5
o
at (11.2, 2.0, 0.7). Thus, the radar azimuth angles are at -10 ,
o
o
o
o
-6 ,0 ,4 , and 10 , respectively. Because of ISARs are
distributed, the same height does not mean the same grazing
angle. Their grazing angles are 3.0º, 2.4º, 2.4º, 2.7º, and 2.5º,
respectively. The target consists of 16 scatterers and sits at the
origin and rotates at 3º/sec anti-clockwise around the z-axis.
2
1.5
1.5
1
1
Range (meter)
Generally speaking, to generate an non-smeared ISAR
imagery, the observation time of ISAR should be less than 2
seconds for a target’s rotation rate  < 3º/sec. Thus, any two
adjacent ISARs cannot be located too far away to have large
difference between their view angles. However, the distance
between each individual ISAR to the target center can be
different. The range differences are compensated when
combining them.
(b) Combined full aperture range-Doppler image
(a) Range-Doppler image of ISAR no.3
2
0.5
0
-0.5
0.5
0
-0.5
-1
-1
-1.5
-1.5
-2
-2
-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
Doppler (Hz)
Doppler (Hz)
Figure 7 – (a) Range-Doppler image of ISAR-no.3, and (b) combined
full aperture range-Doppler image.
Doppler Resolution
0
Combined ISARs
ISAR no.3
-10
-20
Intensity (dB)
.
target rotation center. We can see that the Doppler resolution
can be improved about 5 times by using the full aperture
hybrid SAR/ISAR processing.
Range (meter)
C. Restriction on the Distribution of Multiple ISARs
As we discussed earlier, the distribution of ISARs is
restricted by the effective rotation rate of the target, , and the
difference of view angles between two adjacent ISARs
. During the observation time
T, the view angles of two adjacent ISARs must satisfy:
-30
-40
-50
-60
-15
-10
-5
0
5
10
15
Doppler (Hz)
Figure 8 - Comparison of Doppler resolution at the range cell of the
peak point near the target rotation center.
III.
ARBITRARILY DISTRIBUTED ISARS WITH DIFFERENT
GRAZING ANGLES
Geometry of Arbitrarily Distributed ISARs and Target Center
ISAR no.1
0.8
ISAR no.5
ISAR no.4
Z
0.6
0.4
0.2
0
Target
15
-4
(a)
-2
0
10
X
2
5
0
Range-Doppler Image of
(b)combined ISARs
with different grazing angles
Range-Doppler image of
combined ISARs with same grazing angles
2
2
1.5
1.5
Y
4
Figure 6 - Configuration of the distributed ISARs in the simulations.
Range (meter)
After coherently combining signals from all ISARs and
compensating for the phase terms incurred by the different
distances between each ISAR and the target center, the rangeDoppler imagery of the ISAR-no.3 is shown in Figure 7(a) by
taking FFT along pulses. The range-Doppler imagery of the
combined distributed ISARs is shown in Figure 7(b), where
enhanced Doppler resolution can be easily seen. Figure 8
compares the Doppler resolution at the peak point near the
1
1
Range (meter)
ISAR no.2
ISAR no.3
1
Arbitrarily distributed ISARs usually may not have the
same height. If we apply the same procedure in Section II to
combine the multiple ISAR data and produce an enhanced 2-D
range-Doppler imagery of a 3-D target, the resulting 2-D
image suffers from layover phenomena and becomes unclear
by artifacts due to displaying 3-D features in 2-D, as shown in
Figure 9. To deal with the situation, we should take the
advantage of processing a spotlight SAR with curved aperture
path to construct a 3-D SAR image and extract 3-D target
feature.
0.5
0
-0.5
0.5
0
-0.5
-1
-1
-1.5
-1.5
-2
-3
-2
-1
0
1
Doppler (Hz)
2
3
-2
-3
-2
-1
0
1
2
3
Doppler (Hz)
Figure 9 - Combined ISAR image: (a) the same as in the figure
8(b) and (b) with different grazing angles.
A. Spotlight SAR with Curved Aperture Path
In [6], radar tomography method for generation of 3-D
radar image was proposed. Generally speaking, radar EM
wave reflected from a target can be processed to produce an
image which maps the target's radar RCS density into an
image plane. Each observation provides a 1-D projection of
the RCS density. Based on the projection slice theorem, the
Fourier transform (FT) of each projection is equal to the
functional value of the 2-D FT of the RCS density along a
related projection. By accumulating the FT of many 1-D
projections, it is possible to accumulate a sample
representation of the FT of the RCS density as shown in
Figure 10. Then, image can be reconstructed using the
backprojection algorithm by taking the inverse FT of the
sampled transform function.
. (8)
However, in practice, only a limited number of projections
can be taken with limited samples of G(kx,ky,kz). Thus, only
limited samples of the target RCS density function can be
reconstructed. Figure 12 shows a curved aperture path can
generate data that reconstructs 3-D samples of target RCS
density from 3-D surface in Fourier space.
(a) CURVED APERTURE PATH
Elevation
(b) DATA FREQUENCY SPACE
(a) APERTURE PATH
Elevation
According to [6], by taking the FT of projections at an
infinite number of angles, the value of the 3-D FT of the
g(x,y,z), defined by G(kx,ky,kz), can be obtained at all points in
the Fourier space. Then, the target RCS density function can
be reconstructed by taking 3-D inverse Fourier transform
(IFT):
(b) DATA FREQUENCY SPACE
Spotlight SAR
2-D SAR Image
3-D Data in Frequency Space
SAR
Azimuth
Azimuth
Elevation
Elevation
3-D Target
3-D Target
2-D SAR
Image Plane
3D SAR
Data Surface
Azimuth
Azimuth
Figure 10 - SAR with leveled linear aperture path. (a) SAR aperture
path; (b) 2-D image plane in data frequency space.
3-D observation space
Z
Projection Observation
(observed
direction
radar return)
w
ky
Fourier transform
of the projection
v
Target
RCS density
g(x,y,z)
3-D Fourier space
pξ(u)

0
u
Pξ(ku)
Y
p (u)    g[ x(u, v, w), y(u, v, w), z (u, v, w)] dvdw
ky

0
ξ
X
ku
ξ
kx
P (ku )   p (u ) e  jku u du

  g ( x, y, z)dvdwe
 jku u
du
Figure 11 - 3-D observation space and Fourier space.
The projection slice theorem can be extended the
tomographic technique to the generation of 3-D images. As
discussed in [6], 3-D observation space and corresponding 3D Fourier space is shown in Figure 11. The observation
direction is along the u-axis and the radar return at any range
is the integral of the target RCS density g(x,y,z) in a plane that
parallel to the (v,w) plane and perpendicular to the u-axis. The
u-axis direction is defined by the azimuth angle ξ and the
elevation angle . The observed radar return pξ(u) and
corresponding Pξ(ku), which is 3-D FT of the g(x,y,z)
evaluated at spatial frequencies along the radial line defined
by ξ and , are all shown in Figure 11.
Figure 12 - SAR with curved aperture path. (a) curved spotlight SAR
aperture path; (b) 3-D image plane in data frequency space.
B. 3-D Feature Extraction Using Curved Aperture Path
In the case of arbitrarily distributed ISARs with different
heights, the combined SAR data is equivalent to radar data
generated by a spotlight SAR with curved aperture path. 3-D
SAR data surface as indicated in Figure 12(b) can be used to
extract 3-D locations of the target scatterers. Therefore, in this
case, we should take the advantage of the spotlight SAR with
curved aperture path to extract 3-D target feature instead of
simply enhancing the cross-range resolution as discussed in
[4]. Similarly, in [7-9], a single SAR aperture with curved
flight path, called a curvilinear SAR, has been demonstrated to
extract 3-D target features.
However, the spotlight SAR with curved aperture path
suffers from severe high sidelobes after using the Fourier
transform to form 3-D imagery. To reduce sidelobes, the
RELAX algorithm was proposed [7,10].
To illustrate how 3-D target feature can be extracted by
using spotlight SAR with a curved aperture path, we use an
experimental example given in [7] specially designed for this
purpose. Data set was collected using a radar carried on a
helicopter flying along a curved aperture as shown in Figure
13, where 64 viewing (azimuth and elevation) angles and 64
pulses during each view angle were taken. This collected field
data is very similar to our situation.
The target is on the ground and consists of 13 corner
reflectors on the ground plane and 7 corner reflectors mounted
on a tripod of 2.65m tall. Figure 14(a) is the true 3-D locations
of the 20 scatterers, where the squares represent locations of
the scatterers and the size of each square is proportional to the
RCS of the scatterer. The triangles are projections of the
scatterer locations onto the ground plane with their sizes
proportional to RCSs. Figure 14(b) is the calculated 3-D
scatterer locations of the target by using the 3-D projection
slice theorem and 3-D backprojection algorithm with the
RELAX. Compared with the true 3-D target in Figure 14(a),
we can see that 18 of 20 scatterers are approximately correct.
The last two missing scatterers could be in the shadows.
optimally. Therefore, if the arbitrarily distributed ISAR
platforms have the same height, the combined SAR can
largely enhance the cross-range resolution in 2-D imagery.
Otherwise, when ISAR platforms have different heights, the
combined SAR data is equivalent to the data generated by
SAR with curved aperture path. In this case, we should take
the advantage of the curved aperture path to capture 3-D
feature of the target. Although the combined full aperture can
largely enhance the cross-range resolution in 2-D imagery,
due to different grazing view angles make 2-D image blurring
and geometric distortion, it is not necessary to take this
advantage of 2-D imagery.
There are also other algorithms to reconstruct radar image
in 3-D: interferometric ISAR algorithm [11] and SAR stereo
algorithm [12]. However, both of them cannot not take the
advantage from the combined full aperture SAR data.
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Figure 13 - Curved SAR aperture path in the field data [7].
(a) True 3-D distribution of scatterers
(b) Target 3-D feature extracted by 3-D SAR
Figure 14 - (a) True 3-D distribution of scatterers [7]; (b) 3-D
scatterers extracted using 3-D SAR with curved aperture path [7].
IV.
CONCLUSION AND DISCUSSION
The hybrid SAR/ISAR takes the advantages of both ISAR
and SAR and make combined SAR/ISAR data to be processed
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