Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 1
Synthetic Aperture Radar
Pierfrancesco Lombardo
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 22
Outline
• SAR Basics• SAR System parameters, range resolution and swaths • Real Aperture Radar (RAR)• Doppler Frequency approach to SAR• Synthetic antenna approach to SAR
• SAR Focusing algorithms• Range Cell Migration and focus parameter variation • Range-Doppler Algorithm• Chirp Scaling Algorithm• Range Migration Algorithm
• SAR imaging modes• Fundamental limitation of SAR• Squinted SAR• Spotlight SAR Inverse SAR
• Examples of advanced SAR applications • Coherent Multichannel SAR/ISAR using multiple platforms • Passive SAR and ISAR
EUSAR 2012
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 3
Principles of SAR Image Formation
Sample image from ASI - Italian Space Agency (www.asi.it)
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 4
Radar Antenna Beam
ee d
aa d
ad
ed
d
87.9)(1722.018.0031.0 rad
dee
987.0)(01722.08.1
031.0 radda
a
airborne case
2487.3)(0567.01
0567.0 radde
e
32487.0)(00567.0100567.0 rad
daa
spaceborne case
Example airborne SARWavelength () 3.1 cm (X band)
Antenna (da de) 1.8 m 0.18 m
Altitude 10 kmOff-nadir angle () Adjustable 15° - 60°
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 5
Radar Antenna Footprint
aFsF RD
aNsN RD
NRFR
h
a
e
Operation from a high platform
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 6
Air-borne SAR: ground range swath
h
0
N F)(M
0 M FF NN
The incidence angle is coincident with the local off-nadir angle
eF d20
eN d20
NgN tghR
FgF tghR
)2
()2
( 00ee
gR dtgh
dtghS
- ground swath width
Example airborne SARWavelength () 3.1 cm (X band)
Antenna (da de) 1.8 m 0.18 m
Altitude 10 kmOff-nadir angle () Adjustable 15° - 60°
kmS
kmS
gR
gR
06.760
85.115
0
0
• Swath • approx:
kmS
kmS
gR
gR
89.625.0
1017.0
85.193.0
1017.0
h0
N F)(M
gRS
RS
02
0
0
coscos
h
dR
dS
eegR
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 7
Azimuth antenna footprint
aFsF RD aNsN RD
aNsN RD
NRFR
h
a
e
NN
hRcos
F
FhRcos
kmRd
DkmRd
DkmRd
D
kmRkmRkmR
kmRd
DkmRd
DkmRd
D
kmRkmRkmR
Ne
sFNe
sNe
sN
FN
Ne
sFNe
sNe
sN
FN
407.0637.10017.0344.0353.10017.0301.0156.10017.0
604.23)17.012/cos(
10000.20)12/cos(
10463.17)17.012/cos(
1060
183.0637.10017.0178.0353.10017.0175.0156.10017.0
637.10)17.012/cos(
10353.10)12/cos(
10156.10)17.012/cos(
1015
0
00
0
00
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 8
Radar pulses & range resolution
h
N F
)cos()cos( NFNFR
hhRRS
- The radar operates in time domain (“fast time”) by sending RF pulses:
- Slant-range is direct transposition of time to space (scale factor c/2)- Pulses come back from distances going from RN to RF- SR=RF-RN is the slant-range swath corresponding to SgR
F
N
NN
hRcos
FF
hRcos
slant range swath
- Slant range resolution: R = c/2 (= pulse length)
all scatterers with echo from a distance inside slant range resolution cannot be resolved
n
gR
R- Ground range resolution: gR = c/(2sin)
all scatterers with ground range inside groundrange resolution cannot be resolved
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 9
Range ambiguities
RSc
PRT 2- To avoid ambiguities:
PRT (time between RF pulses)
h
N F
F
N
h
N F
F
N
Ambiguities: echoes to subsequent pulses from these ranges reach the receiver at the same time
Potentially ambiguous pulse is outside the antenna beam
OK!
NO!
RSc
PRTPRF
21
- Pulse Repetition Frequency (PRF)(assume <<2SR/c negligible)
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 10
Pulse compression and range resolution
2time
time
Non- modulated Rectangular pulse:
time µS
sidelobes
1.0
-20 -16 -12 -8 -4 0 4 8 12 16 20
peak sidelobe level
Practical1
time
Phase-modulated rectangular pulse with overall bandwidth B
)sin(2
Bc
gR
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 11
Single pulse radar echo
NRFR
h
a
e
kmS gR 06.7
- Any desired value is achievable using a pulse with B large enough!
mDs 3440
Bck
gR 3
fast time
600
- Vector collecting “fast time” samples: not a matrix – not an image !!!!
Example: B = 450 MHzk= 1.3 Hamming (PSL 43 dB)
gR=0.5 m
- 1 pixel represents a ground patch of: 0.5 m × 344 m !!!!
Two problems:
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 12
Real Aperture Radar
Exploit platform motion in “slow time”
pulses collected from different positions a matrix an image !!!!
Still wide pixel along slow time !!!
fast timesl
ow ti
me
1
2
3
4
…
4
3
2
1
Note: along slow time … space = V * timebeing V the platform velocity
Between two pulses displacement of V PRT
V
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 13
Real Aperture Radar (II)
NRFR
h
a
e
kmS gR 06.7
- To shrink resolution cell increase antenna length da
Example: to achieve Ds0=0.5 m
Reduce beamwidth 344/0.5=688 times!
Increase antenna length da 688 times:
da=1.8*688= 1238.4 dm !!!!!!!! IMPOSSIBLE!!!
Using platform motion:
a matrix an image !!!!
with 0.5 m × 0.5 m ground resolution
fast time
slow
tim
e …
4
3
2
1
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 14
Angle-Doppler frequency relationship
- There is a one-to-one relationship between Doppler frequency and sin of angle
- Since sinis linear with along-track displacement x, Doppler frequency is linear with x
yR
h
V
fd>0
fd<0fd=0
yRx
sin
sin22 Vvf rd
xRVf
yd
2
xsinVvr
V
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 15
Doppler frequency bandwidth
Doppler frequency bandwidth:
aaaMAXMAXd d
Vd
Vd
VVf 2
2)2
sin(2sin2
aMAX d2
aMINMINd d
VVf
sin2
aMINdMAXdd d
VffB 2
- Minimum PRF
ad d
VBPRF 2
ad
aMIN d2
x
fd
Bd
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 16
Frequency approach to SAR
The isodops: flight parallel to flat Earth
y
x,v
fr=0
fr=0.5
fr=0.95
Non-squintedsquinted
DOPPLERCENTROID
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 17
Along-track resolution by Doppler
- Doppler frequency resolution (Fourier Transform)
NPRF
PRTNTf
ossd
11
xRV
Tf
yossd
21
NPRF
VR
TVR
fVR
x y
oss
yd
y
21
22
ND
RdNdN
VVR
x syy
aa
y
122
- N pulses at min PRF: FFT provides N Doppler filters
sin21 VT
foss
d
NPRF
VTVf
V ossd 2
122
sin
NdNdNV
Va
aa
12
2sin
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 18
Synthetic antenna principle
- By exploiting platform motion emulate “synthetic antenna array”
NNdNPRTVNPRTV a
a
2112
sin1sin2
ad
1
0)(
N
nkats
-Using V PRT = da / 2: Synthetic antenna beam N times narrower than real antenna beam
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 19
Synthetic antenna principle (II)- By exploiting platform motion emulate “synthetic antenna array”
-To steer in direction , add all returns of the N pulses after compensating a linear phase term both in TX and in RX (twice as in standard array):
sin2 dk
NNdNPRTVNPRTV a
a
2112
sin1sin2
ad
sin2
1
0
sin41
0
sin22()()( PRTVk
N
n
PRTVnjN
n
ndj
ka PRTnsFFTePRTnsets
-Using V PRT = da / 2: Synthetic antenna beam N times narrower than real antenna beam
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 20
fast-time FFT
fast-timeIFFT
slow-timeFFT
Reference for fast-time chirp fast time
slow
tim
e …
4
3
2
1
Unfocused SAR Processing scheme
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 21
Limit to Doppler frequency resolution
Longer Toss = longer pulse sequence Higher Doppler frequency resolution
NPRF
Tf
ossd
1
2
2)(
12
2
yoss
yoss
oss
yoss
RTV
RTV
TVR
xTV
- This all applies as long as the platform motion does not force motion of point on ground out of the Doppler filter
oss
y
TVR
x 12
ossTV1
2sin
y
y
R
Rx
2sin
2
Maximum resolution:
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 22
Max unfocused SAR resolution
Longer Toss = longer pulse sequence Higher Doppler frequency resolution
NPRF
Tf
obsd
1
mRmRmR
RTV
F
Ny
oss
13.192/61.172/45.162/
2 0
0.04642
0.05402
2sin
13.192/61.172/45.162/
2 0
F
N
y
F
Ny
R
RR
mRmRmR
Rx
Maximum resolution:
222 y
aaobsdobsobs
Rdd
VTBTPRFTN
mDs 3440
25.212/
2/
56.192/
2/
28.182/
2/
0
a
F
a
a
N
dR
dR
dR
N
mx 61.17
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 23
Maximum observation time for point target
aMAX d2
- Maximum Tobs for the echo to be received inside the antenna beam
ad
aMIN d2
V
ya
sy Rd
D
ya
sy Rd
D
VR
dVD
T y
a
syobs
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 24
Slow-time Chirp signal from point target
aMAX d2
adV
ad d
VB 2
- For long Toss the geometry induces a chirp signal in the slow time ta
ad
aMIN d2
V
adV
ta
fd
ya
sy Rd
D
Doppler filter width
Received echo from point target migrates through Doppler frequency filters in the slow time ta
VR
dVD y
a
sy
22
V
RdV
D y
a
sy
22
Chirp slope: (LFM rate) yy
a
aobs
dt R
V
VR
ddV
TB
a
2212
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 25
Slow-time Chirp signal from point target (II)
- Chirp signal in the slow time ta
ya
sy Rd
D
atVx
2
)()( aat
obs
tjaTa etrectts
2
)()( xjD exrectxs
sy
yt R
Va
22
yR 2
VR
dT y
aobs
- Chirp signal in the along-track space domain x
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 26
Focused SARTo exploit long Toss we can think in terms of:
- Compress the chirp signal in the slow time ta domain
Resolution in slow time
Resolution in along-track range
Vd
Bt a
da 2
1
2a
ad
tVx
- Compensate for the liner frequency modulation + narrow Doppler filter at zero Doppler using the whole Toss
21
21
21
22a
y
a
y
sy
y
oss
yd
y d
VR
dVR
VDV
RTV
Rf
VR
x
VR
dVD
T y
a
syoss
- To achieve high resolution - Small-sized ANTENNA appears better !
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 27
Synthetic antenna principle (II)
- By exploiting platform motion emulate “synthetic antenna array”
-For long sequence of pulses, to steer in direction , compensating a linear phase term is not enough: SECOND ORDER TERM is needed Quadratic phase of the Fresnel area
ad
Synthetic antenna beam N times narrower than real antenna beam
Fresnel approximation (near-field) focusing term is required
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 28
Range variation of aperture and slope (I)
aFsF RD
aFsF RD
aNsN RD
aNsN RD
NRFR
h
aN
N R 2
asF
FsN
N
A dDD
r21
FF R
2
Dsy and vary with range:
The maximum resolution does not vary with range
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 29
Range variation of aperture and slope (II)
The maximum resolution does not vary with range
2SD
2SD
2sFD
2sFD
2sND
2sD
2sD
2sND
fS
x
Far Range
Near Range
- Note: compression filter length and filter parameter (beta) vary from N to F a different slow-time filter must be applied for every fast-time sample
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RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 30
fast time
slow
tim
e …
4
3
2
1
Focused SAR processing scheme
slow
-tim
e co
mpr
filte
r
fast-time compression filter
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RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 31
slow
tim
e
focused SAR Processing scheme (II)
fast time
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 32
fast time
slow
tim
e
frequency domain SAR processing scheme
fast-time FFT
fast-timeIFFT
slow-timeIFFT
Reference for fast-time chirp
Reference for slow-time chirp
slow-timeFFT
slow
-tim
e co
mpr
filte
r
fast-time compression filter
ta
fa
fa
f
ta
f
)( aa ft
)( aa ft
)( f )( f
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RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 33
Radar-point target range varies with slow-time
aMAX d2
Note: the quadratic term in x (ta) is the same term responsible for the slow-time chirp:
- quadratic phase term- linear frequency modulation
ad
aMIN d2
Vy
asy R
dD
if the echo from the point target migrates throughrange bins
Ry
ya R
Rd
2
12
2
yy
yyy
y
ay
y
ayaya
RxR
RxRxRxR
RtV
RR
tVRtVRtR
21)(
21)(
2
2
222
22
2
22222
RyR
x 2
2
2
2
8 a
yR d
R
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 34
-
fast time
slow
tim
e
Range cell migration (RCM)
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 35
RCM compensationHyperbolic shaped (approx. quadratic) range cell migration appears unless range resolution is coarse enough
For the sample airborne SAR case(using worst case Far range distance)
Note:
1) Range Cell Migration shape is range dependent ! different compensation fron N to F2) For targets at same range and different along-track displacement RCM compensation is
different Compensation in time domain must be repeated continuously in slow-time
If higher rage resolution is required, it is necessary to compensate the point target migration through range bins
mdR
a
yR 5.3
8 2
2
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RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 36
-
fast time
slow
tim
e
RCM compensation (II)
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RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 37
V
STRIPMAP Mode SPOTLIGHT Mode
V
Spotlight Mode SAR
Spotlight Mode SAR steers the real antenna toward the scene center to exceed the limit on the synthetic aperture of the stripmap mode
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RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 38
ScanSAR Mode
ScanSAR Mode acquisition are performed by using the same azimuth antenna steering of the stripmap mode, but switching the beam in elevation after each burst to cover a wider swath h
Flight path
Sistemi Radar
RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 39
Fundamental limitation of SAR
aa d
Avoidance of Range Ambiguities: 1/PRF > 2 SR/cAvoidance of Azimuth Ambiguities: PRF>2v/ *Antenna beamwidth AZ
Range Swath:Antenna beamwidth AZ
cos/cos/ oeoeR RdRS
o
e
a RdcPRF
dv
cos
22
o
e
a Rdc
dv
cos
22
cos
4 oae
Rcvdd
vc
dS
a
R
22/