Advances in Bistatic Inverse Synthetic Aperture
Radar
(Invited Session on Advances in Inverse Synthetic Aperture Radar)
M. Martorella1 , J. Palmer2 , F. Berizzi1 , B. Bates2,3
1
Dept. of “Ingegneria dell’Informazione”, University of Pisa, via Caruso, 16, 56122 Pisa, Italy
2
Defence Science and Technology Organisation, Edinburgh, SA 5111, Australia
3
School of EEE, University of Adelaide, SA 5005, Adelaide, Australia
Abstract—Bistatic geometries are enabled in scenarios where
multiple separated transmitters and receivers are employed as
well as when illuminators of opportunity are exploited. Bistatic
Inverse Synthetic Aperture Radar (B-ISAR) becomes the radar
imaging tool for obtaining non-cooperative target images in
arbitrary bistatic configurations. Theoretical aspects and real
data experiments have been conducted in recent years that have
proven the effectiveness of B-ISAR. A review of both theory
and results is provided in this paper and new perspectives are
indicated.
β
x2
x1
O
x
iMB(t)
iBI(t)
iMA(t)
x3
RA(t)
V
Radar A
RB(t)
BIApp
I. I NTRODUCTION
A significant amount of interest has been given to bistatic
radar imaging in recent years; specifically to Bistatic Synthetic
Aperture Radar (BiSAR). Theoretical aspects have been developed and experiments conducted that have demonstrated the
capabilities of BiSAR systems. It will not be long before a
BiSAR imagery will be consistently produced [1].
Bistatic radar imaging of non-cooperative targets and, in a
more general sense, bistatic radar imaging that rely on the target motion, such as Bistatic Inverse Synthetic Aperture Radar
(B-ISAR) has also progressed in the last years, pushed by the
need of exploiting the availability of multiple sensor systems.
Such systems tend to minimise the number of transmitters by
using multiple receivers that exploit the signal transmitted by
one or more platforms. In order to function, such systems must
be able to form B-ISAR images.
The main difference between BiSAR and B-ISAR, as with
SAR and ISAR, is the fact that the target motion provides a
significant contribution to the image formation process; and
this motion is, in general, not known a priori. This subtle difference causes major problems when defining suitable image
formation algorithms.
In this paper, the latest results in the area of B-ISAR are
summarised and future developments are indicated.
II. B ISTATIC G EOMETRY AND S IGNAL M ODELLING
In this section the terminology and theory for Bistatic ISAR
imaging is introduced.
Bistatic Geometry
The geometry of the problem is illustrated in Fig. 1. In order
to consider the most generic case, let Radar A and Radar B
be two radars that can transmit radar signals and receive the
Radar B
Figure 1.
Bistatic Geometry
reflected signals from either radar. In this case, three potential
radar configurations can be obtained:
1) Monostatic configuration, Radar A: i.e. Transmit and
receive using Radar A;
2) Monostatic configuration, Radar B: i.e. Transmit and
receive using Radar B;
3) Two equivalent bistatic configurations (BI) involving
either Radar A as the transmitter and Radar B as the
receiver or vice versa.
Signal Modelling
After suitable signal pre-processing [2], including motion
compensation, the received signal, for a generic radar configuration, can be written in a time-frequency format as follows:
Z
SR (f, t) = W (f, t)
ζ(x)ejϕ(x,f,t) dx
(1)
³
V
´
³
´
t
0
where W (f, t) = rect Tobs
rect f −f
, f0 represents
B
the carrier frequency, B is the transmitted signal bandwidth,
Tobs is the observation time, V is the spatial region where
the reflectivity function, ζ(x), is defined, and function rect(x)
yields 1 when |x|<0.5, and is 0 otherwise.
The phase term (ϕ(x, f, t)) in Eqn 1 is dependent on the
radar configuration being considered. The phase terms relative
to the three configurations, i.e. Radar A (MA), Radar B (MB)
and the bistatic radar (BI), can be written as follows:
ϕM A (x, f, t) =
4πf
[RA (t) + x · iM A (t)]
c
(2)
ϕM B (x, f, t) =
4πf
[RB (t) + x · iM B (t)]
c
(3)
ϕBI (x, f, t) =
=
(ϕM A (x, f, t) + ϕM B (x, f, t))
2
2πf
[RA (t) + x · iM A (t) + RB (t) + x · iM B (t)]
c
·
¸
4πf RA (t) + RB (t)
=
+ K(t)x · iBI (t)
(4)
c
2
2) short integration time. These assumptions avoid the need
for the consideration of non-constant target rotation vectors
and the use of polar reformatting, and are generally satisfied
in typical ISAR scenarios where the resolutions required are
not exceptionally high.
When the target rotation vector is constant, the received
signal backscattered by a single ideal scatterer located at a
generic point may be rewritten (after motion compensation)
in the following way:
Z Z
ζ̄(x1 , x2 )ejϕBI (x10 ,x20 ,f,t) dx1 dx2
SR (f, t) = W (f, t)
(8)
where:
Z
ζ̄(x1 , x2 ) =
ζ(x1 , x2 , x3 )dx3
(9)
where
and where the phase ϕBI (x10 , x20 , f, t) may be written as:
¯
¯
¯ iM A (t) + iM B (t) ¯
¯
¯ = cos θ(t)
K(t) = ¯
¯
2
2
(5)
θ = arccos(iM A (t) · iM B (t))
(6)
iM A (t) + iM B (t)
|iM A (t) + iM B (t)|
(7)
and
iBI (t) =
In Eqns 2 - 7, θ is the bistatic angle, c is the speed of light
in free space, RA (t) and RB (t) are the distances between the
two radars (Radar A and Radar B) and a focusing point O
on the target, iM A (t) and iM B (t) are the unit vectors that
indicate the LoS for the two radars, and x is the vector that
locates a generic point on the target.
By substituting Eqns 2-4 into Eqn 1, the received signal
model for the three configurations is obtained. The two
monostatic configurations (MA and MB) can be treated in
the same way in order to produce an ISAR image by means
of any available ISAR technique. In fact, the two received
signal models differ only in their aspect angle and their radartarget focusing point distance. The bistatic configuration (BI),
whilst employing the same signal processing techniques, as its
monostatic counterparts requires a little more attention. This
is because the bistatic ISAR image is distorted by the bistatic
geometry, as is indicated in the term K(t) (Eqn. 5). An analysis
of the effects of the bistatic geometry on the ISAR image Point
Spread Function (PSF) follows.
III. B ISTATIC ISAR I MAGE F ORMATION AND P OINT
S PREAD F UNCTION
The term K(t) carries information about the change in time
of the bistatic geometry. This change in the bistatic angle
during the coherent integration time significantly affects the
B-ISAR image PSF. In this section the B-ISAR image PSF
will be derived and the distortion introduced by the bistatic
geometry will be related to the bistatic angle variation.
In deriving the PSF, two assumptions are made that will
allow the application of the Range Doppler technique when
reconstructing the ISAR image (following motion compensation). These two assumptions are: 1) far field condition, and
4πf
[K(t) (x10 sin Ωt + x20 cos Ωt)]
c
(10)
In Eqns 8 - 10, Ω is the target rotation vector, and
(x10 , x20 , x30 ) are the coordinates of a generic scatterer on
the target with respect to a reference system centred on the
target itself (see Fig. 1).
It is worth noting that the axis x3 has been chosen in
order to be coincident with the effective rotation vector [3].
This choice of reference system is arbitrary, yet it greatly
simplifies the mathematical relations without introducing any
new constraints.
Under assumptions 1) and 2) above, bistatic angle changes
are relatively small, even when a target covers relatively large
distances within the integration time. In particular, the bistatic
angle can be well approximated with a first order Taylor
(Maclaurin) polynomial:
ϕBI (x10 , x20 , f, t) =
θ(t) ∼
= θ(0) + θ̇(0)t
(11)
where −Tobs /2 ≤ t ≤ Tobs /2, and θ̇ = dθ
dt .
As a result, the term K(t) can also be well approximated
with its first order Taylor (Maclaurin) polynomial, and by
using Eqn. 5 the following equation may be obtained:
K(t) ∼
= K(0) + K̇(0)t =
·
·
¸
¸
θ(0)
θ̇(0)
θ(0)
cos
−
sin
t = K0 + K1 t
2
2
2
(12)
Therefore, Eqn. 10 becomes:
ϕBI (x10 , x20 , f, t) =
4πf
[(K0 + K1 t)
c
(x10 sin Ωt + x20 cos Ωt)]
(13)
which for small integration angles (short integration time
hypothesis) can be approximated as:
ϕBI (x10 , x20 , f, t) ≈
4πf0
[(K0 + K1 t) Ωtx10 ] +
c
4πf
[(K0 + K1 t) x20 ]
(14)
c
The ISAR image may be reconstructed by performing the
following steps:
1) Radial motion compensation.
2) Image formation (by means of the RD technique)
a) Range Compression: Fourier Transform (FT) along
the frequency coordinate f
b) Cross-range compression: FT along the time coordinate t.
Radial Motion Compensation
In the absence of synchronisation errors, the radial motion
compensation
can be obtained
by compensating the phase
h
i
4πf RA (t)+RB (t)
. Any parametric or non-parametric
term c
2
technique used for monostatic ISAR is able to compensate
this term with the desired accuracy [4].
has been largely studied in [5], where a new technique was
proposed that eliminated such effects.
Details about the limits of applicability of Range-Doppler
to B-ISAR imaging have been studied in [6].
IV. S YNCHRONISATION E RRORS
Phase synchronisation errors can be modelled in terms
of frequency errors, which will be addressed in this work
as Frequency Jitter (FJ). The FJ that will be taken into
consideration is composed of an offset (η0 ), a linear term (η1 t)
and a random term δF (t), as formalised in (22):
∆f (t) = η0 + η1 t + δF (t)
Eq. (4) is therefore modified by introducing the FJ term, as
modelled in (23):
ϕBI (x, f, t)
=
Image Formation (derivation of the PSF)
After calculating the FT along the two coordinates, the BISAR system PSF is obtained, as shown in (15):
·
¸
Z
4πf
2
−j c 0 (K0 +K1 t)Ωtx10
P SF (τ, ν) = e
δ τ − K0 x20 ⊗τ
c
W 0 (τ, t)e−j2πtν dt
(15)
¸
·
2
= CH [ν, α0 , α1 ] δ τ − K0 x20 ⊗τ ⊗ν w(τ, ν)
c
w(τ, ν) = BTobs e
sinc [Tobs ν] sinc [Bτ ]
(17)
ch [ν, α0 , α1 ] = e−j2π(α0 t+α1 t )
·
¸
2f0 Ωx10
θ(0)
α0 =
cos
c
2
·
¸
2f0 Ωx10
θ(0) θ̇(0)
α1 = −
sin
c
2
2
(18)
2
(19)
· exp
© 4π
c
2
P SF (τ, ν) = CH [ν, α0 , α1 ] ⊗ν w(τ − K0 x20 , ν) (21)
c
It is worth recalling that a convolution between an infinite
duration chirp and a sinc function is equivalent to a FT of a
finite duration chirp, where the parameter of the sinc function
is equivalent to the duration of the chirp.
As can be seen from Eqns (18 - 20), the chirp rate depends
on the position of the scatterer along the cross-range direction.
The defocussing effect of a chirp signal on an ISAR image
RA (t)+RB (t)
2
i
+ K(t)x · iBI (t)
(23)
ª
(f0 + η0 ) K0 x20 Tobs sinc (Tobs ν)
N
ν
N
ν
£
δ ν−
2
c
(f0 − η0 ) K0 Ωx10
¤
D (η0 , η1 , K0 , K1 , x10 , x20 )
(24)
where
D (η0 , η1 , K0 , K1 , x10 , x20 )
(20)
and ⊗τ and ⊗ν are the convolution operator over the
variables τ and ν respectively.
Therefore the PSF of Eqn. 15 can be rewritten as:
h
© £
¤ª
P SF (τ, ν) = Bsinc B τ − 2c K0 x20 exp (−i2πf0 τ )
(16)
CH [ν, α0 , α1 ] = F T {ch [ν, α0 , α1 ]}
4π[f +∆f (t)]
c
In presence of FJ and bistatic angle changes, the distortion effects on the B-ISAR image cannot be separated into
distortion induced by only the synchronisation error or by
only the bistatic angle change, as highlighted by the analytical
expression of the PSF in (24) when neglecting the FJ term
∆f (t)
where
−j2πf0 τ
(22)
=
R
exp
© 4π ¡
c
γ1 t + γ2 t2 + γ3 t3
¢ª
exp {−j2πντ } dt
(25)
and
γ1 = (f0 + η0 ) (K0 Ωx10 + K1 x20 ) + η1 K0 x20
γ2 = (f0 + η0 ) K1 Ωx10 + η1 (K0 Ωx10 + K1 x20 )
(26)
γ3 = η1 K1 Ωx10
More details the effects of synchronisation errors on the
B-ISAR image can be found in [7].
Figure 2.
Emulated Bistatic Radar (EBR) geometry
V. A PPLICATION : E MULATED B ISTATIC ISAR
Figure 3.
C Band - HH Polarised
Figure 4.
C Band - VV Polarised
In certain cases, such as over the open ocean, an Emulated
Bistatic Radar (EBR) [8], [9], [10] configuration can be established. This may permit a B-ISAR image formation process
on a monostatic platform, as shown in Fig. 2. An EBR system
has the ability to provide both the standard monostatic radars
(i.e. Radar A and Radar B) via the direct (MC in Fig. 2) and
double indirect (EMC) paths and the bistatic radar element
via the direct-indirect (EBC) path, without requiring either a
secondary transmitter or receiver.
A. Emulated Bistatic SAR and signal phase noise
By using the sea surface multipath, as shown in Fig. 2,
an EBR system is able to form both monostatic and bistatic
ISAR images. The image quality of the EBC and EMC
paths are, however, contingent on the the sea surface reflected
signals maintaining coherence. Sea surface reflections have
been employed in a number of detection systems in recent
times, mostly for remote sensing purposes. These applications
have demonstrated the coherence aspect of certain sea surface
reflections (i.e. signals reflected in the specular and quasispecular reflection region) [11], [12], [13], [14], [15].
In contrast with the true bistatic system discussed above,
the principal difference of the EBR system is the source of
the signal errors. Whilst FJ is no longer an issue, as there
are no synchronisation difficulties between the transmitter and
receiver, phase noise on the indirect paths (i.e. EBC and EMC)
due to the sea surface is an issue that must be considered.
Visual estimates of the effects due to phase degradation as a
result of the roughened and moving sea surface may be taken
from the Emulated Bistatic SAR [16] images in Figs. 3 - 6.
In these figures, EB-SAR images of the Golden Gate bridge,
taken with NASA’s Jet Propulsion Laboratory’s AIRSAR CBand fully polarimetric radar, are displayed. In each figure, the
left hand bridge image corresponds to the standard monostatic
(MC) path, the middle bridge is from the bistatic (EBC) path
and the right hand bridge is from the emulated monostatic
(EMC) path.
As the target is static, and the standard monostatic image has
formed correctly (i.e. the platform’s motion has been properly
compensated), the causes of the image degradation present
in the EBC and EMC path images may be isolated. As all
other system effects are accounted for, the degradation of
these images can only be a result of the roughened surface
and the change in the surface during the coherent processing
interval (i.e. first and second order surface motion effects).
Whilst somewhat degraded, these images demonstrate that
even without phase compensation of the sea surface effects,
sufficient coherence to allow recognisable images to be formed
is retained for, at least, some sea states.
Figure 5.
C Band - HV Polarised
Figure 6.
C Band - Total Power
Table I
R ADAR PARAMETERS (S HIP )
No of sweeps
No of transmitted frequencies
Lowest frequency
Frequency step
Range resolution
Radar height
Target type
PRF/Sweep Rate
Figure 7.
Original ISAR image - Black scatterers on a white background
256
256
9.16 GHz
0.6 MHz
0.97 m
305 m
Bulk Loader
20 kHz / 78.13 Hz
B. Emulated Bistatic ISAR of maritime targets
The data used in the following analysis was collected using
a low power radar system developed by the DSTO. Table I
gives the relevant radar parameters. The data was acquired
using an airborne radar that illuminated a bulk carrier. In this
system, both the aircraft and ship movements contributed to
the total aspect angle variation that may be exploited for ISAR
image formation.
This data was processed to an intermediate stage using
the Image Contrast Based Autofocusing (ICBA) ISAR image
formation technique [17], the result of which is shown in Fig.
7. As with the EB-SAR images, three dominant bodies may
be identified in this image; corresponding to the three paths.
As the three bodies are separable in range-Doppler space,
each body was able to be extracted and processed separately.
This allowed the ICBA algorithm to determine the optimum
focus parameters for each path. The refocussed images for the
EBC and EMC paths are displayed in Figs. 8 and 9 accordingly. The automatically determined optimum parameters for
these images, as well as for the MC path (which has not been
displayed here due to space limitations) are displayed in Table
II. A comparison of the Beta and Gamma terms for the MC,
the refocused EBC and the refocused EMC, shows that the
distribution of parameters was not linear, as might be expected,
and the resultant refocused EBC path (Fig. 8) is rather blurry.
As a result, a second attempt was made to refocus the EBC
path image using Beta and Gamma parameters that were the
average of the alternate paths (“Theoret-re-focus” in Table
II). As can be seen in Fig. 10, this resulted in a significant
improvement in image clarity. This Emulated Bistatic ISAR
Figure 8.
Refocused ISAR image - EBC path
image may be considered an approximation of the B-ISAR
image that would result with two radars located in the MC
and EMC positions of the EBR (cf. Fig 2), and demonstrates
that B-ISAR image formation is indeed realisable.
VI. C ONCLUSIONS
The B-ISAR theoretical aspects have highlighted additional
issues with respect to those of monostatic (conventional)
Table II
VALUES OF THE F OCUSING PARAMETERS , I MAGE C ONTRAST AND I MAGE
P EAK
Data Set
Original Data
Crop
Original
MC
Re-focus
Crop
Original
EBC
Re-focus
Theoret-re-focus
Crop
Original
EMC
Re-focus
Beta
76.59
76.59
76.59
76.59
76.56
76.91
76.59
77.23
Gamma
5.05x10−2
5.05x10−2
5.05x10−2
5.05x10−2
4.61x10−2
0.22x10−2
5.05x10−2
-4.60x10−2
IC
5.61
10.13
10.13
7.28
7.43
11.14
6.63
8.65
IP(dB)
27.98
27.98
27.98
25.27
24.91
27.05
22.59
23.82
ACKNOWLEDGMENT
The authors would like to thank the Defence Science and
Technology Organisation (DSTO) of Australia and NASA’s Jet
Propulsion Laboratory for providing real data.
R EFERENCES
Figure 9.
Figure 10.
Refocused ISAR image - EMC path
Theoretically refocused ISAR image - EBC path
ISAR. The bistatic angle change and synchronisation errors
are two examples of problems that have been analysed in
the recent years. The analytical derivation of the B-ISAR
PSF in presence of bistatic angle changes and synchronisation errors suggests using parametric autofocusing techniques
[7] and Time-Frequency Analysis (TFA) for Range-Doppler
image formation [18]. Bistatic angle change estimation and
compensation must also be investigated in order to improve
image focus quality and resolution.
Results obtained in B-ISAR opens the way to multistatic
ISAR imaging systems where a number of monostatic and
bistatic configurations are enabled at the same time. Scenarios
where multiple transmitters, including illuminators of opportunity, and multiple receivers will be exploited in order to obtain
simultaneous multiview ISAR imaging and/or enhanced ISAR
image capabilities, such as higher resolution images and 3D
images.
[1] M. Zink, G. Krieger, H. Fiedler, and A. Moreira, “The tandem-x mission:
Overview and status,” pp. 3944–3947, IEEE International Geoscience
and Remote Sensing Symposium, 2007, 2007.
[2] F. Berizzi, “ISAR imaging of targets at low elevation angles,” Pisa Univ.
Italy, 2001.
[3] D. Wehner and B. Barnes, High resolution radar. Artech House,
second ed., 1994.
[4] F. Berizzi, M. M, H. B., D. M. E., and B. S., “A survey on ISAR
autofocusing techniques,” in Proceedings of the IEEE ICIP 2004,
(Singapore), 2004.
[5] F. Berizzi and E. Dalle Mese, “Sea-wave fractal spectrum for sar remote
sensing,” IEE Proceedings-Radar, Sonar and Navigation, vol. 148, no. 2,
pp. 56–66, 2001.
[6] M. Martorella, J. Palmer, J. Homer, B. Littleton, and I. D. Longstaff,
“On bistatic inverse synthetic aperture radar,” IEEE Tr on Aerospace
and Electronic Systems, vol. 43, no. 3, pp. 1125–1134, 2007.
[7] M. Martorella, “Bistatic ISAR image formation in presence of bistatic
angle changes and phase synchronisation errors,” in Proceedings of the
EUSAR 2008 Conference, (Friedrichshafen, Germany), 2008.
[8] J. Palmer, J. Homer, and B. Mojarrabi, “Improving on the monostatic
radar cross section of targets by employing sea clutter to emulate
a bistatic radar,” in IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings, 21-25 July 2003,
vol. vol.1 of IGARSS 2003. 2003 IEEE International Geoscience and
Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477),
(Toulouse, France), pp. 324–6, IEEE, 2003.
[9] J. Palmer, M. Martorella, and I. D. Longstaff, “Airborne isar imaging
using the emulated bistatic radar system,” in Proceedings of the EUSAR
2004 Conference, (Ulm, Germany), 2004.
[10] J. Palmer, M. Martorella, J. Homer, B. Littleton, and I. D. Longstaff,
“ISAR imaging using an emulated multistatic radar system,” IEEE Tr
on Aerospace and Electronic Systems, vol. 41, no. 4, pp. 1464–1472,
2005.
[11] J. L. Garrison, S. J. Katzberg, V. U. Zavorotny, and D. Masters,
“Comparison of sea surface wind speed estimates from reflected GPS
signals with buoy measurements,” in Igarss 2000, (IEEE Geosci), NASA
Goddard Space Flight Center Greenbelt MD USA, 2000.
[12] S. T. Lowe, P. Kroger, G. Franklin, J. L. LaBrecque, J. Lerma, M. Lough,
M. R. Marcin, R. J. Muellerschoen, D. Spitzmesser, and L. E. Young, “A
delay/doppler-mapping receiver system for GPS-reflection remote sensing,” IEEE Transactions on Geoscience and Remote Sensing, vol. 40,
no. 5, pp. 1150–1163, 2002.
[13] M. Martin-Neira, M. Caparrini, J. Font-Rossello, S. Lannelongue, and
C. S. Vallmitjana, “PARIS concept: An experimental demonstration of
sea surface altimetry using GPS reflected signals,” IEEE Transactions
on Geoscience and Remote Sensing, vol. 39, no. 1, pp. 142–150, 2001.
[14] V. Zavorotny and A. Voronovich, “Scattering of GPS signals from the
ocean with wind remote sensing application,” IEEE Transactions on
Geoscience and Remote Sensing, vol. 38, pp. 951–64, 2000.
[15] G. Ruffini, E. Cardellach, A. Rius, and J. Aparicio, “GNSS-OPPSCAT
WP1000 ESA Report : Remote Sensing of the Ocean by Bistatic Radar
Observations: a Review,” tech. rep., IEEC, 1999.
[16] J. Palmer and J. Homer, “SAR Generation through Bistatic Radar
Emulation,” in EUSAR 2004 Conference, (Ulm, Germany), pp. 589 –
592, 2004.
[17] M. Martorella, F. Berizzi, and B. Haywood, “A contrast maximization
based technique for 2D ISAR autofocusing,” IEE Proceedings-Radar,
Sonar and Navigation, vol. 152, no. 4, pp. 253–262, 2005.
[18] V. C. Chen and S. Qian, “Joint time frequency transform for radar rangedoppler imaging,” IEEE Transactions on Aerospace and Electronic
System, vol. 34, no. 2, pp. 486–499, 1998.