Synthetic Aperture Radar - uniroma1.it · Synthetic Aperture Radar Pierfrancesco Lombardo. Sistemi Radar RRSN –DIET, Università di Roma “La Sapienza” MTI extra –2 2 Outline

Sistemi Radar

RRSN – DIET, Università di Roma “La Sapienza” MTI extra – 1

Synthetic Aperture Radar

Pierfrancesco Lombardo

Sistemi Radar


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


Principles of SAR Image Formation

Sample image from ASI - Italian Space Agency (www.asi.it)

Sistemi Radar


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


Radar Antenna Footprint

aFsF RD

aNsN RD

NRFR

h

a

e

Operation from a high platform

Sistemi Radar


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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

Sistemi Radar


fast time

slow

tim

e …

4

3

2

1

Focused SAR processing scheme

slow

-tim

e co

mpr

filte

r

fast-time compression filter

Sistemi Radar


slow

tim

e

focused SAR Processing scheme (II)

fast time

Sistemi Radar


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

Sistemi Radar


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


-

fast time

slow

tim

e

Range cell migration (RCM)

Sistemi Radar


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

Sistemi Radar


-

fast time

slow

tim

e

RCM compensation (II)

Sistemi Radar


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

Sistemi Radar


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


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/

Documents

Synthetic Aperture Radar - uniroma1.it · Synthetic Aperture Radar Pierfrancesco Lombardo. Sistemi Radar RRSN –DIET, Università di Roma “La Sapienza” MTI extra –2 2 Outline