High Resolution Radar Imaging using
Coherent MultiBand Processing Techniques
Philip van Dorp, Rob Ebeling, Albert G. Huizing
Radar Department
T
NO Defence, Security and Safety
The Hague, The Netherlands
philip.vandorp@tno.nl
Abstract— High resolution radar imaging techniques can be
used in ballistic missile defence systems to determine the type of
ballistic missile during the boost phase (threat typing) and to
discriminate different parts of a ballistic missile after the boost
phase. The applied radar imaging technique is 2D Inverse
Synthetic Aperture Radar (2D-ISAR) in which the Doppler
shifts of various parts of the ballistic missile are employed to
obtain a high cross-range resolution while the resolution in
downrange is achieved with a large radar bandwidth. For a
10 cm downrange resolution, a radar bandwidth of more than
1.5 GHz is required. However, this requirement is not
compatible with EM frequency spectrum allocations for long
range ballistic missile defence radars that operate in the L, S,
and C frequency band. In this paper, a novel coherent
multiband ISAR imaging technique is proposed that employs
two or more narrowband radar systems that operate in different
frequency bands. The coherent multiband imaging process uses
an advanced interpolation technique to achieve a very high
downrange resolution and produces little artifacts due to noise.
I. INTRODUCTION
F
or an effective battle management and command &
control process in ballistic missile defense systems, detailed
information about the location and type of threat and the
timing of events such as the separation of the warhead and the
booster is crucial. Non-Cooperative Target Recognition
(NCTR) techniques which estimate the geometry of the object
require a high range resolution for identifying individual
object scatterers for correct classification. For this purpose,
phased array radars are needed that not only detect and track
ballistic missiles during boost phase but also provide high
resolution images of these missiles with resolutions on the
order of 10 cm. 2D Inverse Synthetic Aperture Radar (2D-
ISAR) is a radar imaging technique that employs the Doppler
shifts of various parts of the ballistic missile to obtain a high
cross-range resolution while the resolution in downrange is
achieved with a large radar bandwidth. For a 10 cm
downrange resolution, a radar bandwidth of at least 1.5 GHz is
required. However, this bandwidth requirement is not
compatible with Electro Magnetic (EM) frequency spectrum
allocations for radars that operate in the L, S, and C frequency
band, as is shown in Table I. Only X-band radars are able to
provide the desired range resolution.
TABLE I. MAIN RADAR FREQUENCY BANDS
R
adar
Band
Frequency
(MHz)
Resolution
(cm)
L
S
C
X
1215 – 1400
2700 – 3400
5250 – 5820
8500 – 10400
81
21
25
8
L - S 1215 – 3400 7
In 1997, Cuomo et al. described an ultra wideband (UWB)
coherent processing technique that allows high resolution
images of radar targets to be made using sparse frequency
subband measurements [1]. This technique allows the desired
range resolution of 10 cm to be achieved by using
measurements in the L-band and S-band which are compatible
with frequency spectrum allocations and long range radar
operations, see Table I. To obtain the desired resolution with
sparse frequency subband measurements, Cuomo et al. use a
model fitting and parameter estimation technique to
interpolate between the measured target frequency data.
However, this procedure is sensitive to noise and leads to
artifacts in the radar image. In this paper, a different approach
is described in which cross-range imaging is performed first
and then the interpolation of the downrange measurements is
performed. This approach is less sensitive to noise and
produces less artifacts in the high resolution radar image.
The paper is organized as follows. Section II gives an
overview of the ISAR imaging technique. Section III
discusses coherent multiband processing. Section IV shows
bandwidth interpolation applied on real measurements and
ISAR simulation results and section V draws conclusions.
II. ISAR IMAGING
H
igh range resolution radars transmit waveforms which
are designed to optimize the range resolution. This is achieved
by transmitting pulses with frequency and/or phase
modulation. One of these waveforms is the Linear Frequency
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981
Modulated (LFM) pulse with bandwidth B. On receive,
stretch processing can be used to obtain a range profile of a
target with a high range resolution. Details of stretch
processing are provided by Tait [2], Schikorr [3] and Blanton
[6]. The stretch processing measurements is a sinusoidal
output signal where the frequency is proportional to the range
and range processing with Fourier transform is applied. The
similarities between stretch processing radars and processing
for linear Frequency Modulated Continuous Wave (FMCW)
radars mean that the proposed approach is applicable to both
radar types.
In the next subsections the ISAR processing is introduced
followed by the ISAR accuracies.
A. ISAR processing
Wide band radar scattering from a target is often used to
form an image of the target. The image is a synthetic aperture
radar image (SAR image) or an inverse synthetic aperture
radar image (ISAR image) because the transformation behaves
as if a very large aperture radar antenna is synthesized from a
set of incremental data taken over the domain of the (synthetic)
a
perture. The SAR image is formed by moving the radar
system while the target remains stationary, and the ISAR
image is formed by holding the radar at a fixed location while
the orientation angle of the target changes. The image
transformation involves first transforming the time domain
data to the range domain using a spectral estimation usually
based on an Fourier transform. Then the complex cross-range
data for each range value is transformed to the Doppler
domain using another spectral estimation, also usually a
Fourier transformation. For a rotating target, some points on
the target are moving toward the radar (positive Doppler) and
some are moving away (negative Doppler). The down range
and cross range data are combined and give the image domain
of the target.
There are many implementations of the SAR/ISAR
concept. Some use the two independent Fourier
transformations as described (possibly in reverse order), while
others use a 2-D version of the Fourier transform. If the
increments are (or can be made) uniform and equal (often
including a transformation to Cartesian frequency then the fast
Fourier Transform (FFT) can be used. Fig. 1 presents the
ISAR processing architecture. The digitized measurements
enter the architecture in the top left corner. M sweeps (first
index) are stored with N samples (second index) in the linear
sweep. The architecture presents two routes which are
reversible with linear transformations.
• The blue route (clock wise) weights each sweep with
a range window and succeed with the range FFT. This
step gives the range response. The cross-range
processing selects one range cell (column), weights
each range response with a cross-range window, and
succeeds with the cross-range FFT. The result is the
ISAR response.
• The green route (anti clock wise) selects one received
frequency (column), weights each frequency response
with a cross-range window and succeeds with the
cross-range FFT. This processing step gives the cross-
range response. The range processing weights each
cross-range response with a range window, and
succeeds with the range FFT. The result is the ISAR
response.
y
1,1
y
1,2
…
y
1,N
y
2,1
y
2,2
…
y
2,N
…
…
… … … … …
… … … … …
y
M,1
y
M,2
…
y
M,N
…
Range FFTWeighting Y
1,1
Y
1,2
…
Y
1,N
Y
2,1
Y
2,2
…
Y
2,N
…
…
… … … … …
… … … … …
Y
M,1
Y
M,2
…
Y
M,N
…
Range FFTWeighting
Range FFTWeighting
Range FFTWeighting
Range FFTWeighting
Cross R FFT
Weighting
Z
1,1
Z
1,2
…
Z
1,N
Z
2,1
Z
2,2
…
Z
2,N
…
…
… … … … …
… … … … …
Z
M,1
Z
M,2
…
Z
M,N
…
Cross R FFT
Weighting
Cross R FFT Weighting
Cross R FFT Weighting
Cross R FFT Weighting
Cross R FFT
Weighting
z
1,1
z
1,2
…
z
1,N
z
2,1
z
2,2
…
z
2,N
…
…
… … … … …
… … … … …
z
M,1
z
M,2
…
z
M,N
…
Cross R FFT
Weighting
Cross R FFT Weighting
Cross R FFT Weighting
Cross R FFT Weighting
Range FFTWeighting
Range FFTWeighting
Range FFTWeighting
Range FFTWeighting
Range FFTWeighting
Sweep 1
Sweep 2
Sweep M
Radar
receiver
Range
response
ISAR
response
Cross-range
response
Figure 1. ISAR processing architecture.
B. ISAR Processing with Bandwidth Interpolation
Irregular motion of the object disturbs phase of the
measurements and range migration gives unaligned range
responses. Compensation techniques are applied which
reduce the effects of these disturbances on the ISAR image.
The quality of the ISAR image is very sensitive for these
compensation techniques. Normally, the phase correction is
applied before the range processing and the range alignment is
applied after the range processing.
The bandwidth interpolation applied to measurements of
different radar bands extends the bandwidth. The resulting
bandwidth comprises all the other bands and gives a high
range resolution ISAR image. The bandwidth interpolation
introduces errors which disturb the ISAR image. There are
two possible approaches for bandwidth interpolation in the
ISAR imaging process. The first approach is to perform
bandwidth interpolation before range processing and cross-
range processing (the clockwise approach). The Fourier
transforms are linear processes and the bandwidth
interpolation errors add twice. The second approach is to
perform bandwidth interpolation before the cross-range
processing (the anti-clockwise approach). The bandwidth
interpolation errors add only once in the cross-range
processing. These approaches are now described in more
detail.
Cuomo [1] presents a HRR processing approach with
bandwidth interpolation applied on the range response. His
approach with additional cross-range processing is presented
in Fig 2. The LFM pulses of each band are digitized. The
measurements are the input of the bandwidth interpolation
(BWI). The output of BWI is a signal which contains the
individual bands and interpolated signals in the gaps between
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982
the bands. The processing continues with range processing,
range alignment and cross-range processing.
BWI
Cross-range processing
Interpolation
AR model fit
Motion compensation
Uncompressed
Input band 1
Uncompressed
Input band 2
Uncompressed
Input band M
Range Processing
Frequency Frequency
Frequency
Range responses
Pre-processing
ISAR image
Figure 2. ISAR processing approach with range BWI before cross-range
processing.
In this paper, we propose a different approach to minimize
the bandwidth interpolation errors, see Fig 3. The phase
correction and range alignment are applied onto each band
individually before cross-range processing. The range
alignment is a complex multiplication in the frequency
domain. The cross-range processing is applied on each band
and results in cross-range responses of each individual band.
The cross-range responses contain no bandwidth interpolation
errors and gives optimal cross-range object separation. The
bandwidth interpolation is applied onto each cross-range
response. This process generates errors in range not in the
cross-range response. The final step is the range processing
applied onto each interpolated cross-range response.
Cross-range
processing
Motion
compensation
Cross-range
processing
Motion
compensation
Cross-range
processing
Motion
compensation
Range Processing
Uncompressed
Input band 1
Uncompressed
Input band 2
Uncompressed
Input band M
Frequency Frequency Frequency
Cross-range
responses
BWI
Interpolation
AR model fit
Pre-processing
ISAR image
Figure 3. ISAR processing approach with range BWI after cross-range
processing.
C. I
SAR Accuracies
The linear sweep FMCW range resolution ∆r is related
with the bandwidth B of the transmitted sweep [2]:
B
c
wr
range
2
=∆ (1)
where c is the speed of light and w
range
a window correction
factor. It follows from this equation that a better range
resolution can be achieved by increasing the bandwidth. The
window function is applied to reduce strong sidelobes which
mask weak signals from other objects. A rectangular shaped
window has w = 1 with -13.2 dB sidelobes, a Hamming
window has w = 1.3 with -40 dB sidelobes. The cross-range
resolution ∆r
cross
given by the change in aspect angle ∆
ψ of
the target during the M sweeps of one ISAR image [2]:
ψ
λ
∆
=∆
2
crosscross
wr (2)
where λ is the average transmitter frequency wavelength and
w
cross
a window correction factor. The reason of the cross-
range window and range window are equivalent. The cross-
range resolution is independent of the range but depends on
the target motion. Correction of the cross-range is possible
with the target track.
The ISAR imaging is induced by changes in the aspect angle
of the target. During the imaging time, the scatterers must
remain in their range cells. Reflectivity density function won’t
remain the same over a wide range of radar viewing angles.
Therefore we cannot use an arbitrary large integration time to
achieve the highest possible cross-range resolution and
prevent defocusing in the image.
III. COHERENT MULTIBAND PROCESSING
T
his section describes the pre-processing, AR model fit
and interpolation techniques of coherent multiband
processing.
A. Pre-Processing
Different radar bands cause systems errors which depend
on the radar circuits. Common system errors are offsets,
unequal power and phase alignment. These systems errors are
removed before the ISAR processing.
The radar measurements have multiple bands. The
frequency spacing of the bands differs and the grids have no
common factors. The analysis is more complicated than that of
regularly sampled data. We resample the irregularly
measurements onto a regular grid with the Fourier transform.
By computing the Fourier coefficients at all required discrete
frequencies and then Fourier-transforming back, a kind of
interpolation can be obtained.
B. AR model fit
Kauppinen [4] presents a good overview of signal
extrapolation without a detailed description of the Burg
method. Roth and Keiler [5] give a good description of the
Burg's method applied onto one band. The Burg method
estimates a model in a recursive manner with reduced
computational effort. We adapt this for our problem.
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983
First, we describe the single band AR filter estimation and
multiband AR filter estimation.
1) Single Band AR Filter Estimation
The auto-regressive (AR) model is defined by the
equation:
∑
=
=
−
+−=
Pm
m
nmnmn
eyay
1
(3)
where y
n
are the signal samples, P
is the model order, a
m
are
the model coefficients, and e
n
is the residual. The model
coefficients a
m
are calculated by minimizing the total energy
of the residual:
∑
=
nall
n
eE
2
(4)
The Burg method is one method to solve this problem and
described by Roth [5]. The errors in the forward and backward
directions are:
∑∑
=
−
=
−
=+=
P
m
mnm
P
m
nmnmn
yayyae
01
(5)
where a
1
= 1. This FIR filter is implemented with a lattice
filter structure. The equations of the lattice filter are:
1
1
1 −
−
−
+=
l
n
l
n
n
l
n
bkff (6)
1
1
1 −
−
∗−
+=
l
n
n
n
l
n
fkbb
l
(7)
Where f
n
l
and b
n
l
are the forward and backward prediction
errors and k
l
are the reflection coefficients of the l stage. The
*
denotes the complex conjugate operation. The initial values
for the residuals are f
n
0
= b
n
0
= y
n
. Burg's method calculates the
reflection coefficients k
l
so that they minimize the sum of the
forward and backward residual error. This implies an
assumption that the AR coefficients can predict the signal
forward and backward. The sum of the residual error in the l-
th stage is:
∑
−
=
+=
1
22
N
ln
l
nn
l
nnl
bwfwE
(8)
Minimizing E
l
with respect to the reflection coefficient k
l
y
ields ∂E
l
/∂k
l
= 0. The reflection coefficient that full fills the
partial derivative is given by:
( )
( ) ( )
∑
∑
−
=
∗−
−
−
−
∗−−
−
=
∗−
−
−
+
−
=
1
1
1
1
1
1
11
1
1
1
1
2
N
n
l
n
l
nn
l
n
l
nn
N
ln
l
n
l
nn
l
bbwffw
bfw
k (9)
The AR coefficients a
m
can be obtained from the reflection
coefficients k
l
via the Levinson-Durbin algorithm. The
recursion is initialized with a
0
0
= 1 and
1,,2,1
11
−=+
=
∗−
−
−
lmforakaa
l
mll
l
m
l
m
L (10)
l
l
l
ka = (11)
This process is repeated for l = 1,2, …, P. At the end of the
iterations a
m
p
gives the desired prediction error filter
coefficients a
m
of the AR filter.
2) Multi-band AR filter estimation
The multiple band approach has M bands. The
measurements are indicated with f
j
and b
j
each with N
j
elements where j is the band index. The Burg method has M
datasets which are related to each other. The FIR filter is
applied on each of the M chirps. The sum of the residual error
in the l stage is the sum of all forward measurements error and
the sum of all backward measurements error. The combined
error function is:
∑∑
=
−
=
+=
M
j
N
ln
l
njnj
l
njnjl
bwfwE
1
1
2
,,
2
,,
. (12)
The solution of the partial derivative is:
( )
( ) ( )
∑∑
∑∑
=
−
=
∗−
−
−
−
∗−−
=
−
=
∗−
−
−
+
−
=
M
j
N
n
l
nj
l
njnj
l
nj
l
njnj
M
j
N
ln
l
nj
l
njnj
l
bbwffw
bfw
k
1
1
1
1
1,
1
1,,
1
,
1
,,
1
1
1
1,
1
,,
2
. (13)
The a update is equivalent with the single band approach
applied to each band:
1
1,
1
,,
−
−
−
+=
l
njl
n
nj
l
nj
bkff (14)
1
1,
1
,,
−
−
∗−
+=
l
nj
n
nj
l
nj
fkbb
l
(15)
The results of the combined Burg estimation is one FIR filter
applicable on all bands.
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984
C. Interpolation and Extrapolation
Band-width interpolation is a extension to extrapolation.
Assume that the forward extrapolated signal in a missing band
is y
n
f
and the backward extrapolated signal is y
n
b
. The missing
band is a weighted sum of both extrapolated signals:
(
)
b
nn
f
nnn
ywywy −+= 1 , (16)
where w
n
is a scale factor which controls the transition
b
etween the two band. We use a linear scale factor starting
with one at the beginning of the band and zero at the end of
the band. This weighting is depicted in Fig 4. The Figure
shows a linear weighting in case of interpolation starting at
one and zero at the end of the band. The Extrapolation has no
weighting, it contains the predicted signals.
Interp.Extrap. Interp. Extrap.
frequency
frequency
frequency
frequency
Band 1
Band 2
Band 3
Total band
(sum)
Linear weight interpolation
Figure 4. Bandwidth interpolation with linear weights and bandwidth
extrapolation.
IV. RESULTS
Two experiments are carried out applying the described
method. The first experiment contains a three corner test
measurement with range processing. The second experiment
contains a simulated ballistic missile trajectory with FMCW
measurements succeeded with ISAR processing.
A. Test Measurements
The test measurement contains three corners with different
height and positioned in the near field antenna and radar cross
section (RCS) measurement facility of TNO. The FMCW
frequency is 10-20 GHz with 10 MHz frequency step. The
corresponding range resolution is 0.015 m. We remove 80%
of the total band. The remaining lower band is 10-11 GHz and
higher band is 19-20 GHz. The resolution of both bands is
0.15 m. The model order P is chosen one third of the number
of measurements in the shortest band according to Roth and
Keiler [5]. Fig 5 presents the results of the interpolation. The
measurement contains five heights with each 40 angle
measurements with a total angle deviation of approximately
30 degrees. The five height measurements show the varying
ranges of the three corners as a function of the aspect angle.
The middle corner is the rotation centre of the measurement.
Figure 5. Interpolated three corners test measurements. Left top the original
full band range measurement. Right top the lower band range measurement.
Right bottom the higher band range measurement. Left bottom the
interpolated range measurement.
The lower band and higher band range resolution causes
indistinguishable corners which are distinguisable in the
origional full band. The interpolated range response shows the
three corners. The interpolated range response show besides
the three corners other distortions which are also visible in the
full band range measurement. The interpolated measurement
shows no artifacts caused by the applied method. The selected
model order is not critical. The applied Burg method
converges to the correct solution regardless of the chosen
number of poles. In our case the number of poles is larger than
the three corners. This prevents that the number of poles has to
be estimated. One of the reasons of the covergence is the
minimizing of the forward and backward prediction errors of
the Burg method. The recursive Burg method does nor
requires much computation time compared with other AR
estimation methodes.
B. Simulated Ballistic Missile Measurements
For the simulated Ballistic Missile Measurements a
software program is used which is capable of generating LFM
pulse measurements. The program which is used is called
RAPPORT (Radar signature Analysis and Prediction by
Physical Optics and Ray Tracing) and is developed in house at
TNO. It uses a combination of Geometrical Optics (GO) and
Physical Optics (PO) methods to calculate the radar return of a
specified object. The object is a 3D CAD model, consisting of
a large number of triangular facets. RAPPORT uses GO to
determine which facets of the CAD model are hit by rays from
the radar’s EM radiation. The PO calculating method is then
used to determine the amount of reflected radiation for each
facet which is hit by the radar’s EM radiation. This is done for
all facets and the returning radiation is summed over all facets,
resulting in one amplitude and phase. This can be done for all
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985
