Arrayed Synthetic Aperture Radar

142 Pages·2015·2.44 MB·English

Department of Electrical and Electronic Engineering
Communications and Array Processing Group
Arrayed Synthetic Aperture Radar
Karen Mak
A Thesis submitted in ful(cid:133)lment of requirements for
the degree of Doctor of Philosophy and Diploma of
Imperial College London
September 2014
Supervisor: Prof. A. Manikas
Abstract
In this thesis, the use of array processing techniques applied to Single Input
MultipleOutput(SIMO)SARsystemswithenhancedcapabilitiesisinvestigated.
In Single Input Single Output (SISO) SAR systems there is a high resolution,
wide swath contradiction, whereby it is not possible to increase both cross-range
resolution and the imaged swath width simultaneously. To overcome this, a
novel beamformer for SAR systems in the cross-range direction is proposed. In
particular, this beamformer is a superresolution beamformer capable of forming
wide nulls using subspace based approaches.
SIMO SAR systems also give rise to additional sets of received data, which
includes geometrical information about the SAR and target environment, and
can be used for enhanced target parameter estimation. In particular, this thesis
looks at round trip delay, joint azimuth and elevation angle, and relative target
power estimation. For round trip delay estimation, the use of the traditional
matched (cid:133)lter with subspace partitioning is proposed. Then by using a joint
2D Multiple Signal Classi(cid:133)cation (MUSIC) algorithm, joint Direction of Arrival
(DOA) estimation can be achieved. Both the use of range lines of raw SAR
data and the use of a Region of Interest (ROI) of a SAR image are investigated.
However in terms of imaging, MUSIC is not well-suited for SAR, due to its
target response not corresponding to the target(cid:146)s true power return. Therefore a
joint DOA and target power estimation algorithm is proposed to overcome this
limitation.
Thesealgorithmsprovidetheframeworkforthedevelopmentofthreeprocessing
techniques. These allow sidelobe suppression in the slant range direction, along
with the reconstruction of undersampled data and region enhancement using
MUSIC with power preservation.
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Declaration of Originality
Iherebydeclarethatthisthesisismyownwork. Whereothersourcesofinformation
have been used, they have been acknowledged.
The copyright of this thesis rests with the author and is made available under a
Creative Commons Attribution Non-Commercial No Derivatives licence.
Researchers are free to copy, distribute or transmit the thesis on the condition
that they attribute it, that they do not use it for commercial purposes and that
they do not alter, transform or build upon it. For any reuse or redistribution,
researchers must make clear to others the licence terms of this work.
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Acknowledgments
Firstly I would like to o⁄er my most sincere gratitude to my supervisor, Prof.
Athanassios Manikas, who has helped me during this research and has been
supportingmeuntiredlythroughoutmystudysincemyundergraduatedays. Also
Iwouldliketogivemyappreciationforbeingo⁄eredanEngineeringandPhysical
Science Research Council (EPSRC) Doctoral Training Award for the funding of
my Postgraduate study at Imperial College.
A special thank you to B. Richards, D. Lancashire, M. Cohen and D. Hall
of Astrium Ltd, who have started my interest in SAR Maritime Mode, which is
leading to the fruitful results in this research.
I would also like to extend my sincere thanks to my fellow researchers and
friends at the Communications and Signal Processing Group at Imperial College,
in particular Marc, Harry and Kai, for their support throughout these years. In
addition I would like to thank Thulasi and Ste¢ for their enthusiastic encourag-
ement and friendship since my undergraduate days.
Finally I would like to thank my parents and grandmother for their endless
support and encouragement.
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Contents
Abstract i
Acknowledgments iii
Contents iv
List of Figures vi
List of Tables x
Notation xi
Abbreviations xii
1 Introduction 1
1.1 Current State of Array Processing Applied to SIMO SAR . . . . . 4
1.1.1 Focusing Bistatic SAR System Data . . . . . . . . . . . . 5
1.1.2 Applications using Beamforming with SIMO SAR . . . . . 6
1.1.3 Use of Superresolution Techniques on SAR Data . . . . . . 7
1.2 Thesis Scope and Organisation. . . . . . . . . . . . . . . . . . . . 7
2 Mathematical Modelling of SAR Systems 12
2.1 SISO SAR Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.1 Stripmap SAR . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 ScanSAR . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.3 Spotlight SAR . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.4 TOPSAR . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.5 Discrete Time Modelling . . . . . . . . . . . . . . . . . . . 23
2.2 SIMO SAR Systems . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 SIMO SAR System Mathematical Modelling . . . . . . . . 26
2.2.2 Discrete Time Modelling . . . . . . . . . . . . . . . . . . . 30
iv
CONTENTS v
3 Beamforming in SIMO SAR Systems 34
3.1 SIMO SAR with Steering Vector Beamforming . . . . . . . . . . . 35
3.2 SIMO SAR with Superresolution Wide Null Beamforming . . . . 39
3.3 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 SimulationEnvironment1: CollocatedArrayofK Beamformers 46
3.3.2 Simulation Environment 2: Sparse Array of K Beamformers 49
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Appendix 3A: Proof of reconstruction technique . . . . . . . . . . . . . 52
4 Target Parameter Estimation Using SIMO SAR 58
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2 Round Trip Delay Estimation . . . . . . . . . . . . . . . . . . . . 59
4.2.1 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Joint Direction of Arrival and Slant Range Estimation . . . . . . 68
4.3.1 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Joint Direction of Arrival and Relative Power Estimation . . . . . 83
4.4.1 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . 84
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5 Proposed Algorithms for SIMO SAR Systems Enhancement 91
5.1 Sidelobe Suppression in Slant Range Direction . . . . . . . . . . . 91
5.2 Sidelobe Suppression with Undersampling Reconstruction . . . . . 96
5.3 RegionEnhancementusingDOAestimationwithPowerPreservation102
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6 Conclusions and Future Work 107
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2 List of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Appendix 112
References 119
List of Figures
1.1 Geometry of a SAR system with a single beamformer. . . . . . . . 2
1.2 Summary of proposed algorithms (highlighted in red) . . . . . . . 9
1.3 Focused image of raw data from a single receiver beamformer,
showing how a slant range cut and cross-range cut will be used
for analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Log cross-range and slant range cuts of the image given in Figure
1.3 taken along the horizontal and vertical red lines respectively. . 11
2.1 Single transmitter planar array and single receiver planar array
SAR system geometry. . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 The real and imaginary parts of a complex chirp signal. . . . . . . 15
2.3 Stripmap operational mode . . . . . . . . . . . . . . . . . . . . . 16
2.4 ScanSAR operational mode. . . . . . . . . . . . . . . . . . . . . . 20
2.5 Spotlight operational mode. . . . . . . . . . . . . . . . . . . . . . 21
2.6 TOPSAR operational mode. . . . . . . . . . . . . . . . . . . . . . 23
2.7 3DdatacubeofthereceivedsignalsatallN elementsofthereceiver
beamformer after discretisation. . . . . . . . . . . . . . . . . . . . 24
2.8 The received signals after beamforming is applied to all N array
elementsofthereceiverbeamformerafterdiscretisinginthedirection
perpendicular to the cross-range direction, i.e. the range direction. 25
2.9 Single transmitter planar array and K receiver planar array SAR
system geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.10 An example of a SIMO SAR system. . . . . . . . . . . . . . . . . 28
2.11 3D datacube of the received signals at all KN elements of the
SIMO SAR system after discretisation. . . . . . . . . . . . . . . . 31
2.12 The outputs of the K receiver beamformers after discretisation in
the range direction . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Representationofsuppressionofsubbands,wherethebluesubbands
are desired. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
vi
LIST OF FIGURES vii
3.2 Log slant range cut of image from undersampled received data. . . 47
3.3 Log slant range cut of reconstructed image using steering vector
beamformer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Logslantrangecutofreconstructedimageusingproposedbeamformer. 49
3.5 Focused images of undersampled data from receiver beamformer 1
and 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Logslantrangecutofreconstructedimageusingproposedbeamformer
without shift correction, where K = 2 with 40m separation. . . . . 51
3.7 Logslantrangecutofreconstructedimageusingproposedbeamformer
with shift correction, where K = 2 with 40m separation. . . . . . 51
3.8 Systemrepresentationofreconstructionalgorithm,wheref indicates
o;k
the Doppler frequency to shift to. . . . . . . . . . . . . . . . . . . 53
4.1 Transmit and receive timing of a SAR system. . . . . . . . . . . . 60
4.2 RoundtripdelayestimationoftwotargetswithR = 25693mand
o;1
R = 25668m using a matched (cid:133)lter in the slant range direction. 65
o;2
4.3 Round trip delay estimation of two targets with R = 25693m
o;1
and R = 25668m using subspace partitioning. . . . . . . . . . . 65
o;2
4.4 RoundtripdelayestimationoftwotargetswithR = 25693mand
o;1
R = 25691m using a matched (cid:133)lter in the slant range direction. 66
o;2
4.5 Round trip delay estimation of two targets with R = 25693m
o;1
and R = 25691m using subspace partitioning. . . . . . . . . . . 67
o;2
4.6 Changein3dBwidthoftarget(cid:146)sresponsewithSNRusingamatched
(cid:133)lter (shown in blue) and with subspace partitioning (shown in red). 68
4.7 Joint azimuth and elevation angle estimation at range line index
p = 750. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.8 Joint azimuth and elevation angle estimation contour plot at range
line index p = 750. . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.9 Joint azimuth and elevation angle estimation surface plot at range
line index p = 1052. . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.10 Joint azimuth and elevation angle estimation contour plot at range
line index p = 1052: . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.11 Joint azimuth and elevation angle estimation contour plot using
N = 21 and with p = Np rounded to the nearest integer. . . . . . 78
rl 2
4.12 Squared error of azimuth angle estimates with changes in range
line block size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.13 Squared error of elevation angle estimates with changes in range
line block size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
LIST OF FIGURES viii
4.14 Range history variation of a single target with range line index p
for p = 1;2;:::;N . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
p
4.15 Joint azimuth and elevation angle estimation surface plot using a
ROI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.16 Joint azimuth and elevation angle estimation contour plot using a
ROI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.17 Joint squint angle and relative power estimation using range lines
of data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.18 Squint angle estimation using range lines of data, with P = 3:69. 87
s
4.19 Target power estimation using range lines of data with (cid:18) = 1:04o. 87
sq
4.20 Relative power estimate of target 1 using a ROI. . . . . . . . . . . 89
4.21 Relative power estimation of target 2 using a ROI. . . . . . . . . . 89
5.1 Focused image of raw data from a single receiver beamformer. . . 94
5.2 Focused image after incorporating subspace partitioning in the
slant range direction with the range compression stage of the CS
algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3 Log cross-range cuts at target 1: a) after image formation using
theCSalgorithm, b) afterimageformationusingtheCSalgorithm
with additional subspace partitioning in the slant range direction. 95
5.4 Focused image formed from raw data received by beamformer 1. . 99
5.5 Focused image formed from raw data received by beamformer 1
with additional subspace partitioning in the slant range direction. 99
5.6 Focused image formed from the reconstruction of K = 2 sets of
undersampledSARdatausingthesuperresolutionbeamformerand
with additional subspace partitioning in the slant range direction. 100
5.7 Log cross-range cuts at target 1: a) after image formation using
theCSalgorithm, b) afterimageformationusingtheCSalgorithm
with additional subspace partitioning in the slant range direction
and undersampling reconstruction. . . . . . . . . . . . . . . . . . 101
5.8 Log cross-range cuts at target 1: a) after image formation using
the CS algorithm on undersampled data received by beamformer
1, b) after image formation using the CS algorithmwith additional
subspacepartitioningintheslantrangedirectionandundersampling
reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.9 Surface plot of ROI containing a single target. . . . . . . . . . . . 104
5.10 Joint azimuth and elevation angle estimation surface plot using a
ROI of focused data. . . . . . . . . . . . . . . . . . . . . . . . . . 104
LIST OF FIGURES ix
5.11 Relative power estimate of imaged target in the ROI. . . . . . . . 105
5.12 Joint azimuth and elevation estimation surface plot with correct
power estimate using a ROI. . . . . . . . . . . . . . . . . . . . . . 105
6.1 GUI for designing the SIMO SAR system parameters. . . . . . . . 113
6.2 GUI for beampattern plotting. . . . . . . . . . . . . . . . . . . . . 114
6.3 GUI for selecting target parameter and (cid:135)ight path length. . . . . 115
6.4 GUI for forming raw SAR data. . . . . . . . . . . . . . . . . . . . 116
6.5 GUI for forming a focused image from simulated raw data using
the Chirp Scaling algorithm. . . . . . . . . . . . . . . . . . . . . . 117
6.6 GUI for image analysis. . . . . . . . . . . . . . . . . . . . . . . . . 118