sar signal processing

Canada Centre for Remote Sensing, Natural Resources CanadaNatural Resources Ressources naturellesCanada Canada

SAR SystemsandDigital Signal Processing

Canada Centre for Remote Sensing, Natural Resources Canada

What is Synthetic Aperture Radar (SAR)?

A side-looking radar system which makes a high-resolution image of the Earth’s surface (for remote sensing applications)

The basic image is complex-valued and 2-dimensional:

– range = distance from sensor (perpendicular to flight path)

– azimuth = distance along flight path

Digital signal processing is used to focus the image and obtain a higher resolution than achieved by conventional radar systems


Concept of Synthetic ApertureSynthetic Aperture

Distance SAR travelled while objectwas in view = synthetic aperture

Last time SARsenses object

Flightpath

GroundTrack

Swath

First time SARsenses object

Nadir

Object


SAR Real Aperture

The Real Aperture of a SAR is the slant range plane interval of the transmitted pulse for which all signals return to the receiving antenna at the same instant of time.

– All signals at the same range return to the radar at the same time and are separable only in Doppler shift.

– For a transmitted chirp of length τ, the instantaneous radar return at range R contains surface returns corresponding to slant range interval, c τ /2, each uniquely coded in chirp frequency.

– On a smooth Earth, the constant Doppler frequency contours form a family of hyperbolae and the constant range contours form a family of circles.

– The real aperture determines the range of influence of a radar saturation event.


Point Target Echo in a Synthetic Aperture Radar System

AZIMUTH

RANGE POINT TARGET

TRANSMITTEDWAVEFORM

ANTENNA

MOTION DATA RATE = PRF X NUMBER OF RANGE CELLS

POINT TARGETPHASE HISTORY

SPACECRAFT

RANGE

SYNTHETIC APERTURE LENGTH AZIMUTH

DATA RECORDING

CHIRPLENGTH


Airborne SAR Flight Geometry

R1

H = 2 - 10 km

R2

R1 = Minimum slant range

R2 = Maximum slant range

Flight path

Range

Offset = 5 - 100 km

Azimuth

Imaged swath width5 - 30 Km


SAR Squint Angle

RADAR SWATH

SQUINT ANGLE

ZERO DOPPLER

SQUINTDIRECTION

SAR

AZIMUTH ANGLE


Principles of SAR

Radar coherence

SAR System components

SAR signal generation

Coherent demodulation

How demodulation creates phase

Pulse after range compression

Target in computer memory

Sensor motion equations

Azimuth signal analysis

Doppler frequency

Doppler bandwidth

Azimuth resolution

Synthetic aperture concept

SAR signal processing


Radar Coherence

Consider 2 ways the radar can measure echo time delay:– by observing the time delay of the echo magnitude

(e.g. 56 nsec accuracy = 8 m)– by observing the phase of the echo

(e.g. 6 psec relative accuracy = 1 mm)

A coherent radar has the ability to measure phase, achieved through precise control over:– start time and phase angle of the transmitted pulse– frequency of the coherent oscillator (demodulator)– platform motion including motion compensation


Components of a SAR System

To Signal Processor

CoherentDemodulator

High Power Amplifier

CoherentOscillator

A/DConverter

Low NoiseAmplifier

Circulator

Antenna

Tx/Rx

Pulse Generator

The coherent oscillator (coho) is a very stable clock which provides timing for the signal generation, transmission time, sampling window, demodulation and A/D converter


Antennas

An antenna couples electromagnetic waves (signals) propagating in free space to and from a transmission line.– frequency dependent– directional– polarization dependent

For SAR applications the axis that defines the wave’s electric field orientation with respect to the antenna defines the wave polarization. The general case is elliptical polarized waves.An antenna focuses the radiated waves into a beam in three dimensions.– for efficiency the radiating aperture > 1 wavelength– large radiating areas (apertures) can make tight beams– the gain of an antenna is determined by

• electrical losses• beam area (solid angle)


SAR Signal Generation

X

Chirp: Bandwidth = 20 MHz

Transmitted Pulse

ModulatorTo HPA

Tx pulse looks like a sine wave, but is a chirp with low fractional bandwidth

Carrier from coho: Freq = 5.3 GHz


Coherent Demodulation

X

Received Signal

Demodulated Signal

DemodulatorTo ADC

Demodulated signal is just like the original chirp generated

Carrier from coho: Freq = 5.3 GHz


Received Signal

Stored Rx Signal Stored Demodulated signal

Range Time −−−−> Range Time −−−−>

<−−−

− A

zim

uth

Tim

e

30−May−99 12:0 demod_phase.eps

Received Signal

Stored Demodulated SignalStored Rx Signal

Range Time → Range Time →

←

Azim

uth

Tim

e

How Demodulation Turns Time Delay Into Azimuth Phase


SAR Processing 1Once the radar illumination beam has passed over a point on the ground, all of the information from that point has been acquired and stored as a two dimensional (range and azimuth) phase history.– In the absence of radar saturation, all of the phase histories of

all of the points in the image are linearly combined in a time series to form the SAR “signal” data.

– SAR processing decodes the phase signature of each point in range and azimuth and focuses this information into an impulse response. The range and azimuth widths of the impulse response are the range and azimuth resolutions.

– Nyquist’s theorem requires that the processed data be sampled at least twice per impulse response width. These samples are the radar image “pixels”.


SAR Processing 2Because the natural coordinates of the range and azimuth data are not separable, the range and azimuth processing steps are coupled.– Range walk and range curvature

• Resolution vs. beam width• Beam squint (antenna pointing angle βSQ, relative to zero-

Doppler)• Earth rotation

Processing is done in the natural coordinate system of the radar, the slant range plane.– Earth surface presentations of radar images require projection along

constant range arcs to the Earth surface elevation at each point. RADARSAT data are often projected to an ellipsoid model of sea level.

Calibration separates the radar and the gross imaging geometry from the radar data by inverting the radar equation.


Point Target Compression or Focussing

LOOK 1 LOOK 2 LOOK 3 LOOK 4

AZIMUTHCOMPRESSION RATIO

AZIMUTHCOMPRESSION

AZIMUTHRESOLUTION

CHIRPLENGTH

RANGECOMPRESSION

= SINGLE LOOK APERTURE LENGTHAZIMUTH RESOLUTION

SINGLE LOOKAPERTURE LENGTH

RANGEWALK

RANGECOMPRESSION RATIO

RANGERESOLUTION

CHIRP LENGTH

RANGE RESOLUTION

RANGECURVATURE

=


Signal before range compression

Range time −−−−>

Signal after rangecomp


19−May−99 12:39 comp_pulse.m

Signal before range compression Signal after range compression

Range time → Range time →

Range Compression of Received Signal


Point Target in Computer Memory

Real part of demodulated signal

at range R vs. azimuth time

Real part of demod. signal vs. range time

(azimuth time increases with each line)

R

Real part of demodulated signal vsrange time (azimuth time increases with each line)

Real part of demodulated signal at range R vs azimuth time

R


Signal Analysis in the Azimuth Direction

0 2 4 6 8 10 12

−1

−0.5

0

0.5

1

Sig

nal a

mpl

itude

−−

−−

>Case A Radar is stationary with respect to target

0 2 4 6 8 10 12−2

−1.5

−1

−0.5

0

0.5

1

Azimuth sample number −−−−>

Sig

nal a

mpl

itude

−−

−−

>

Case B Target moving away from the radar at a constant rate

Over this time, 2R has decreased by λ

When the azimuth signal is analyzed, a sine wave is observed in Case B as the target is moving.

The sine wave frequency = the TARGET DOPPLER FREQUENCY

Case A Radar is stationary with respect to target

Case B Target moving away from the radar at a constant rate

When the azimuth signal is analyzed, a sine wave is observed in Case B as the target is moving. The sine wave frequency = the TARGET DOPPLER FREQUENCY

Azimuth sample number →

Sign

al a

mpl

itude

→

Sign

al a

mpl

itude

→

Over this time, 2R has decreased by λ


Phase Change Induced by Sensor Motion

Phase vs Time:cycles

m

Range vs Azimuth Time:

( ) ( ) 220

0

2 2R t R Vt tRλ λ λ

φ = − ≅ − −

( )2

20

02VR t R tR

≅ +

m

Platform motion

Radar

Zero-Doppler Point

Target

Range

( ) 22 2 20R t R V t= +

R

0RVt


Doppler Frequency from Phase Change

Hz

Doppler frequency vs. azimuth time: Hz

This is a linear FM signal:

22d

a

d VF tdt R

K t

φλ

−= =

=

Azimuth Time

DopplerFrequency

Slope = Ka Hz/s

Total Doppler Bandwidthof target DBW

Total exposure time of target

Azimuth Time

Total exposure time of target

Total Doppler Bandwidthof target (DBW)

Slope = Ka Hz/s

DopplerFrequency


Total Doppler Bandwidth Generated

- independent of range and wavelength !- the smaller is D, the larger is the DBW !

Length of beam footprint:

Exposure Time:

Total Doppler Band Width:

Antennalength D

Satellitemotion

Azimuth beamwidth α

Length of beam footprint L= synthetic aperture

Range

R

seL RTV D

λ= =

Hz2

a eVDBW K TD

= =

metersRL R

Dλα= =


Azimuth Resolution

Thus the SAR has the remarkable property that its resolution is independent of distance and radar wavelength !

However, the SNR goes down with increasing rangeand increasing frequency, so higher power may be needed at long ranges.

Doppler Bandwidth Hz

therefore resolution in time s

and resolution in space units = resolution in time * V

m

2VD

=

2DV

=

2D=


SAR Signal Processing

Overview of processing algorithms availableStructure of the received SAR signalThe Range/Doppler algorithmRange pulse compressionRange resolution obtainedDoppler centroid estimationRange cell migration correction (RCMC)Azimuth compressionMulti-looking to reduce speckleThe SPECAN algorithm


SAR Processing Algorithms

Range/Doppler– a widely-used general-purpose algorithm– good compromise between accuracy and speed

SPECAN– for quick-look or ScanSAR processing

Chirp Scaling– for the highest phase accuracy and moderate squint

Wave Equation– for systems which operate with wide apertures and/or

large squint anglesPolar Format– for spotlight radar processing


Structure of Transmitted SAR SignalThe transmitted SAR signal is usually a linear FM pulse:

(1)

where η = azimuth time sτ range time sP(τ) envelope of range pulse (chirp)f0 radar carrier frequency HzKr range FM rate Hz/sτl duration of range chirp s

These pulses are repeated at the rate of Fa Hz, which we refer to as the Pulse Repetition Frequency (PRF).

Note that τ is continuous time, while η is a discrete time variable.

( ) ( ) ( ){ } [ ]20, cos 2 / 2 , 0,t r l lS P f Kη τ τ π τ π τ τ τ τ= + − =


Structure of Received SAR Signal

The ideal received signal from a single point target can be expressed as:

The ideal received signal is the same signal as was transmitted, but with a time delay τd proportional to the range R:

where R(η) is the range to the point target for the pulse transmitted at time η and c is the speed of light.

( ) { } ( ) ( ){ }[ ] ( )

20, cos 2 / 2 ,

, 2r d d r l d

d l d

S P f Kη τ τ τ π τ τ π τ τ τ

τ τ τ τ

= − − + − −

= −

( ) ( )2 / 3d R cτ η=


The Range EquationThe most important geometry relationship is given by the range equation:

which comes from the right-angled triangle with sides R0 and Vr (η - η 0 )and hypotenuse R(η), where the straight-line platform motion approximation is made. As Vr (η - η 0 ) << R0 we can use a Taylor series to approximate R(η) by the parabola:

( ) ( )22 220 0rR R Vη η η= + −

( ) ( ) ( )220 0 0/ 2rR R V Rη η η= + −

Target

Range

R0

Platform motionRadar position

Zero-Doppler Point

( )0rV η η−R (η)


Structure of Demodulated SAR Signal

After coherent demodulation, the signal from the point target can be expressed as:

where we have included A, the azimuth beam profile (gain) which is a function of the time from the beam centrecrossing time ηc.

( ) ( ) ( )( ){ }

[ ] ( )

20

,

exp 2 / 2 ,

, 4

d c d

d r l d

d l d

S A P

j f j K

η τ η η τ τ

π τ π τ τ τ

τ τ τ τ

= − −

− + − −

= +


SAR Data Acquisition

Flight path

SAR Signal Memory

A

B

Nadir

Azimuth

Range

Target

SAR

R(ηA)

R(ηB)

Beam along surface

SAR Signal Memory

Range

Ground Track

Azimuth

SAR

Flight path

Beam along surfaceTarget

R (ηB)

R (ηA)

A

B

Nadir


Received Data in SAR Signal Memory

When the echo from each pulse is received, it is written into one line in SAR signal memory (along constant azimuth time).As the platform (or target) moves, the echo from a given target shifts in range, and is written into the next range line in the memory (going up the slide).After the beam has finished illuminating the target, the locus of energy has the shape shown in red.The purpose of SAR signal processing is to compress this energy into a single point.

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

45

Slant Range (cells) −−−−>

Azi

mut

h (

cells

) −

−−

−>

Locus of point target energy in signal memory

η0

ηc

start of target exposure

end

Slant Range (cells) →

Locus of point target energy in signal memory

Azi

mut

h (c

ells

)

→

start of target exposure

η0

ηC

end


Simulation ParametersSize of azimuth array Na 256 complex samples Size of range array Nr 128 complex samples No. of samples in chirp 104 complex samples No. non-zero range lines 239 complex samples Duration of chirp τ l 5.20 µsecRange FM rate Kr 3.27 MHz / µsecRange sampling rate Fr 20.0 MHzRange bandwidth 17.0 MHz

Radar wavelength λ 1.036 cm Speed of wave prop. c 300.0 Km/msec Range of target R0 850 KmPRF Fa 1700 HzTotal Doppler bandwidth 1410 HzPlatform Velocity Vr 7050 m/s

Azimuth FM rate Ka -11289 Hz/s"PRF" duration 150.59 msecBeam offset ηc -6.34 sDoppler centroid Fcen 71613 HzDoppler centroid 42.125 PRFsDoppler centroid Ffrac 213 HzAntenna length D 10.0 mActual RCM 6.92 cells


Energy of Range Signal

020

4060

80100

120

0

50

100

150

200

250

0

0.2

0.4

0.6

0.8

geninp2.epsRange −−−−>

Envelope of Received SAR Signal etac = −6.34 s rcm = 6.92 cells

<−−−− Azimuth

Mag

nitu

de −

−−

−>

16−May−99 13:51

Envelope of Received SAR Signal ηc = -6.34 s RCM = 6.92 cells

←

Azimuth

Range →

Mag

nitu

de

→


The Range/Doppler AlgorithmSARSignalData

MLDIMAGE

SLC Image

UnpackEncodedData

BalanceI & Q

Channels

RangeCompression

AzimuthFFT

DopplerCentroidEstimation

Range CellMigrationCorrection

MatchedFilter

Multiply

Detection,Look Summation

LookExtraction,

Azimuth IFFT


Range Processing

Generate range matched filter– Get replica of ideal range pulse– Reverse sequence in time– FFT the sequence with zero padding– Conjugate the answer– Apply smoothing window

FFT each range lineMultiply by range matched filterInverse FFTSelect good output points


Range Matched Filter

−60 −40 −20 0 20 40 60

−350

−300

−250

−200

−150

−100

−50

0

Spectrum of signal in range line 128

Range frequency (bin no.) −−−−>

Pha

se (

radi

ans)

−−

−−

>

−60 −40 −20 0 20 40 60

0

50

100

150

200

250

300

350

Spectrum of matched filter


Pha

se (

radi

ans)

−−

−−

>

13−May−99 12:42 rangemf2.eps

Phas

e (r

adia

ns)

→

Spectrum of signal in range line 128

Spectrum of matched filter

Phas

e (r

adia

ns)

→

Range frequency (bin no.) →

Range frequency (bin no.) →−60 −40 −20 0 20 40 60

0

2

4

6

8

10

12

14

Spectrum of signal in range line 128 (fftshifted)


Mag

nitu

de −

−−

−>

−60 −40 −20 0 20 40 600

2

4

6

8

10

12

14

Spectrum of range MF, with & without window


Mag

nitu

de −

−−

−>

13−May−99 12:42 rangemf1.eps


Mag

nitu

de

→

Spectrum of signal in range line 128 (FFT shifted)

Spectrum of range MF, with & without window


Mag

nitu

de

→


Range Pulse Compression

Signal before range compression


Signal after rangecomp


19−May−99 12:39 comp_pulse.m

Signal before range compression Signal after range compression

Range time → Range time →


Range Compression Results 1

5055

6065

7075

0

50

100

150

200

250

0

20

40

60

80

rangcom2.epsRange −−−−>

Signal after range compression etac = −6.34 s RCM = 6.92 cells


Mag

nitu

de −

−−

−>

19−May−99 13:4

←

Azimuth

Range →

Mag

nitu

de

→

Signal after range compression ηc = - 6.34 s RCM = 6.92 cells

0 20 40 60 80 100 120

0

50

100

150

200

250

Range compressed signal

Range cell no. −−−−>

Azi

mut

h ce

ll no

. −

−−

−>

19−May−99 13:4 rangcom1.epsRange cell no. →

Azi

mut

h ce

ll no

. →

Range compressed signal

Az i

mut

h ce

l l no

.

→



The data is now range compressed, but a significant range migration remains.

50 55 60 65 70 75

50

100

150

200

250

Range cell number −−−−>

Azi

mut

h ce

ll nu

mbe

r −

−−

−>

Contour plot of magnitude of range compressed signal

19−May−99 16:18 contour4.eps

Azi

mut

h c e

ll n u

mbe

r

→

Range cell number →

Contour plot of magnitude of range compressed signal


Range Resolution

The slant range -3 dB resolution in seconds is equal to:

where BWr is the bandwidth of the range pulse

A weighting function is used in the matched filter to control the range sidelobes, and leads to the weighting factor Qr (typically 1.2)ρsr is multiplied by half the speed of light to get the slant range resolution in metresρsr is also divided by sin(θ ) to get the ground rangeresolution in metres:

rsr

r

QBW

ρ = s

( )( )

sinrgr

r

Qc BW

θρ = m



54 56 58 60 62 64 66 68−35

−30

−25

−20

−15

−10

−5

0Compressed pulse in range line 128

Time (samples expanded by 16) −−−−−>

Mag

nitu

de (

dB)

−−

−−

>

Pkindex

= 60.88 samples

Pkvalue

= 80 units

Pkphase

= 0.0 deg

Resolution = 1.189 cells

Maxlobe

= −18.0 dB

1D ISLR = −14.9 dB

15−May−99 12:57 pulse3.ep

Compressed pulse in range line 128

Time (samples expanded by 16) →

Pkindex = 60.88 samples

Pkvalue = 80 units

Pkphase = 0.0 deg


Maxlobe = -18.0 dB

1-D ISLR = -14.9 dB

Mag

nitu

de (d

B)

→



54 56 58 60 62 64 66 68−200

−150

−100

−50

0

50

100

150

200Compressed pulse in range line 128


Pha

se A

ngle

(de

g) −

−−

−>

15−May−99 12:57 pulse4.eps

Compressed pulse in range line 128


Phas

e An

gle

(deg

)

→


Azimuth FFT 1

Mag

nitu

de

→

4550

5560

6570

75

0

50

100

150

200

250

0

200

400

600

800

1000

1200

azfreqdm.epsRange position (cells) −−−−>

Signal magnitude after azimuth FFT

<−−−− Azimuth frequency (cells)

Mag

nitu

de −

−−

−>

15−May−99 13:27

Signal magnitude after azimuth FFT

Range position (cells) →

←

Azimuth frequency (cells)

Mag

nitu

de

→


Azimuth FFT 2

The azimuth FFT causes a circular rotation of the data around the azimuth axis, because of the conversion from time to frequency.

50 55 60 65 70 75

0

50

100

150

200

250

Contour plot of signal energy after the azimuth FFT

Range position (cells) −−−−>

Azi

mut

h fr

eque

ncy

(cel

ls)

−−

−−

>

19−May−99 16:18 contour2.epsRange position (cells) →

Contour plot of signal energy after the azimuth FFT

Azi

mut

h fr

eque

ncy

(cel

ls)

→


Doppler Centroid Estimation

The centre of the azimuth or Doppler energy is a function of the antenna squint angle and the Earth rotation and must be estimated now, as it is needed for RCMC and azimuth compressionThere are many ways of estimating the Doppler Centroid, e.g.:

– Curve-fitting the azimuth magnitude spectrum– Estimating the average phase increment– Beating two range looks together

The Doppler centroid is ambiguous, as the energy is aliased to the interval ( 0 : Fa ). Both the aliased centroid and the ambiguity number must be estimated.


Aliasing of the Doppler Spectrum

>

>

0 Fa M Fa (M+1) Fa

Azimuth frequency (Hz) −−−−>

Dop

pler

ene

rgy

Measured spectrum True spectrum

15−May−99 14:59 amb_illus.eps

Dop

p le r

ene

rgy

Measured spectrum

Azimuth frequency (Hz) →

Fa M Fa (M+1) Fa

True spectrum

0

*true meas aF F M F= +

If the Doppler energy could be observed as an analog signal, the red spectrum would be seen.But, as the Doppler spectrum is sampled at a rate of Fa Hz, the spectrum is aliased down to the interval (0 :Fa) as shown in blue. This blue spectrum is all we can observewith the sampled data.M is referred to as the ambiguity number.We must estimate M as it is needed for range cell migration correction.


The Doppler Ambiguity Number

>

>

0 Fa M Fa (M+1) Fa

Azimuth frequency (Hz) −−−−>

Dop

pler

ene

rgy

Observed spectrum True spectrum

>

Ffrac

>

Fcen

15−May−99 16:6 amb_illus2.eps

Dop

p le r

ene

rgy

Azimuth frequency (Hz) →

M Fa (M+1) Fa

True spectrumObserved spectrum

Fa

FfracFcen

0

*cen frac aF F M F= +

In general, the Doppler energy is not between integer Faboundaries.

The total or absolute Doppler centroid is Fcen

The observed Doppler centroid is Ffrac

In addition to Ffrac, we need to estimate the Doppler ambiguity number M, so that we can obtain:


Average Phase Method

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5Estimated F

frac = 211 Hz

Real part −−−−>

Imag

par

t −

−−

−>

Azimuth phase increments in DC range frequency cell

19−May−99 14:19 accc.epsReal part

Estimation of the Doppler Centroid by the average azimuth phase vectors method

Real part →

Imag

ina r

y pa

r t

→

Estimated Ffrac = 211 Hz


Finding the Doppler Ambiguity

−60 −40 −20 0 20 40 60

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

etac = −6.344 s

squint = −3.0 deg

Ffractrue

= 213 Hz

Ffracest

= 212 Hz

Range frequency (bins) −−−−>

AC

CC

ang

le (

radi

ans)

−−−

−>

DLR algorithm: ACCC angle vs. range frequency (fftshifted)

Fit Error = 13.71 mrads

Cubic Err = 0.065 mrads

Slope = 9.192 mrad/MHz

Fcentrue

= 42.13 PRFs

Fcenest

= 42.18 PRFs

19−May−99 14:39 dopcen1.eps

DLR algorithm: ACCC angle vs. range frequency (FFT shifted)

Range frequency (bins) →

AC

CC

an g

le (r

adia

n s)

→ηc = -6.344 sSquint angle = -3.0 degFfrac = 212 Hz

est

Ffrac = 213 Hztrue

Fit Error = 13.71 mradsCubic Err = 0.065 mradsSlope = 9.192 mrad/MHzFcen = 42.13 PRFs

trueFcen = 42.18 PRFs

est


Range Cell Migration Correction

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12Total Range Migration vs. Beam Squint

Beam centre offset magnitude |etac| (s) −−−−>

Tot

al R

CM

(ra

nge

cells

) −

−−

−>

Simulation value

Target exposure = 0.141 s

19−May−99 14:45 RCMtot.eps

T ota

l RC

M ( r

ange

ce l

ls)

→

Simulation value

Target exposure = 0.141 s

Total Range Migration vs Beam Squint

Beam centre offset magnitude | c| (s) →

range cells

The total range migration comes from the range equation. When expressed in range cells, we can determine when RCM correction is needed:

2

0

2 r rl c

V FRCMc R

η η=

Beam centre offset magnitude |ηc| (s) →


Azimuth frequency index0 50 100 150 200 250

70.8

71

71.2

71.4

71.6

71.8

72

72.2

72.4

Frequency vector for RCMC calculations

Azimuth frequency index −−−−>

Una

liase

d or

abs

olut

e fr

eque

ncy

(K

Hz)

−−

−−

>

DOPCEN = 71.61 KHz M = 42

19−May−99 14:52 favector.eps

0

1

2

3

4

5

6

7

RC

M n

eede

d (

rang

e ce

lls)

−−

−−

>

Frequency vector for RCMC calculations

Azimuth frequency index →

DOPCEN = 71.61 KHzM = 42

Una

liase

dor

abs

olut

e fr

eque

ncy

(KH

z)

→

RCM

need

ed (r

ange

cel

ls)

→

RCM Calculation1. Compute absolute frequency of each frequency sample2. Compute RCM needed in range cells:

( )2

2028 r

RR f fV

λ=


Coefficients of filter for interpolating 1/16 of a cell

Shift amount (1/16 cell) →

Coe

ffici

ent v

alue

→

Before weighting After weighting

RCMC Interpolator Design 1

To perform RCMC, we need an interpolator.We design one based on a weighted sinc function.


1 2 3 4 5 6 7 8

−0.2

0

0.2

0.4

0.6

0.8

1

16 sets of 8−point interpolators designed with Kaiser window, beta = 3

Coefficient number

Coe

ffici

ent v

alue

−−

−−

>

Only sets 1:8 are shown(sets 9:15 are symmetrical)(set 16 is the no−shift set)

17−May−99 16:29 fildes2.eps

16 sets of 8-point interpolators designed with Kaiser window, β = 3

Coefficient number

Only sets 1:8 are shown(sets 9:15 are symmetrical)(set 16 is the no-shift set)

Coe

ffici

ent v

alue

→

RCMC Interpolator Design 2The red curve of the previous slide is sub sampled, with an 1/16 cell shift to get the individual coefficient sets:


RCMC Results 1

0 50 100 150 200 2500

2

4

6

8

10

(a) Amount of RCMC needed

Azimuth frequency (bin no.) −−−−>

Ran

ge (

cells

) −

−−

−>

Total RCMCInteger RCMCFract RCMC

55 60 65 70 75 800

2

4

6

(b) Energy of target before RCMC

Range (cells) −−−−>

Mag

nitu

de −

−−

−>

17−May−99 17:4

45 50 55 60 65 700

2

4

6

(c) Energy of target after integer RCMC


Mag

nitu

de −

−−

−>

45 50 55 60 65 700

2

4

6

(d) Energy of target after total RCMC


Mag

nitu

de −

−−

−>

rcmc1.eps

(a) Amount of RCMC needed (c) Energy of target after integer RCMC

(b) Energy of target before RCMC (d) Energy of target after total RCMC

Range (cells) →

Azimuth frequency (bin no.) →

Mag

nit u

de (c

e ll s

) →

Mag

nit u

de (c

e ll s

) →

Mag

nit u

de (c

e ll s

) →

Range (cells) →

Range (cells) →

Ra n

ge (c

e lls

) →

Total RCMCInteger RCMCFract RCMC


RCMC Results 2

4550

5560

6570

0

50

100

150

200

250

0

200

400

600

800

1000

1200

rcmc2.epsRange position (cells)

Signal magnitude after RCMC (every 12th line is shown)


Mag

nitu

de −

−−

−>

17−May−99 16:54

Signal magnitude after RCMC (every 12th line is shown)


Mag

nitu

de

→

Range position (cells)


RCMC Results 3

0 20 40 60 80 100 120

0

200

400

600

800

1000

Mean Square energy of RCMCed signal vs. range


MS

Ene

rgy

−−

−−

>

45 50 55 60 65 70

0

200

400

600

800

1000

Blowup of graph above


MS

Ene

rgy

−−

−−

>

19−May−99 15:1 rcmc3.eps

Range cell no. →

MS

Ener

gy

→

Mean Square energy of RCMCed signal vs range

Blowup of graph above

Range cell no. →

MS

Ener

gy

→


45 50 55 60 65 70

0

50

100

150

200

250

Contour plot of signal energy after RCMC

Range position (cells) −−−−>

Azi

mut

h fr

eque

ncy

(cel

ls)

−−

−−

>

19−May−99 16:15 contour3.eps

Range position (cells) →

Azi

mut

h fr

e que

ncy

(cel

ls)

→

Contour plot of signal energy after RCMC

RCMC Results 4

The data is now well-aligned in the azimuth direction --the data lies mainly in one range cell.


Azimuth Compression

After RCMC, the azimuth energy is aligned vertically in the computer memoryAzimuth compression consists of:– generation of matched filter– look extraction, with weighting– inverse discrete Fourier transform (DFT)

The azimuth matched filter parameters are computed from the azimuth FM rate, the exposure time and the Doppler centroidThe azimuth matched filter is also a linear FM signal, and is applied with a fast convolution, much like the range compression operation.


Azimuth Matched Filter

To derive the matched filter: – generate replica of ideal received signal– reverse it in time– zero pad, and take its DFT

To apply the matched filter:– select portion of azimuth spectrum to utilize– multiply by window and matched filter– inverse DFT– select good output points


Azimuth Signal Properties

0 50 100 150 200 2500

2

4

6

8

10

12

14

Azimuth frequency cell −−−−>

Sig

nal m

agni

tude

−−

−−

>

Slice of signal data down range cell 57 (max energy)

0 50 100 150 200 250

−50

0

50

100

Azimuth frequency cell −−−−>

Ang

le (

radi

ans)

−−

−−

>

18−May−99 10:34 azimmf1.epsAzimuth frequency cell →

Ang

le (r

adia

ns)

→Si

gnal

mag

nitu

de

→

Azimuth frequency cell →

Slice of signal data down range cell 57 (max energy)


4550

5560

6570

20

30

40

50

0

5000

10000

azcomp2.eps

Range −−−−>

Compressed data after azimuth processing


Mag

nitu

de −

−−

−>

18−May−99 11:13

Compressed data after azimuth processing

Range →

Mag

nitu

de

→

←

Azimuth

Form of the Compressed Pulse After Azimuth Compression


Azimuth Compression

Results 2

Blue curve:-data summed in azimuth

Red curve:-data summed in range

0 20 40 60 80 100 120

0

50

100

150

200

250


Azi

mut

h sa

mpl

e no

. −

−−

−>

1−D integrations over range and azimuth

18−May−99 11:13 azcomp1.eps

Range cell no. →

Azi

mut

h sa

mpl

e no

. →

1-D integrations over range and azimuth


Azimuth Compression Results 3

20 40 60 80 100 120

20

40

60

80

100

120

2D expansion of compressed pulse

Range (samples expanded by 4) −−−−−>

Azi

mut

h (

sam

ples

exp

ande

d by

4)

−−

−−

−>

Peakmag

= 14748

Pkr−indx

= 57.25

Pka−indx

= 36.00

Pkphase

= −1.8

19−May−99 16:45 contour5.epsRange (samples expanded by 4) →

Az i

mu t

h ( s

a mp l

e s e

x pa n

d ed

b y 4

)

→

2D expansion of compressed pulse

Pkmag = 14748

Pkr-index = 57.25

Pka-index = 36.00

Pkphase = -1.8


AzComp Results -- Azimuth Slice

40 50 60 70 80 90−200

−100

0

100

200


Pha

se A

ngle

(de

g) −

−−

−>


40 50 60 70 80 90−35

−30

−25

−20

−15

−10

−5

0


Mag

nitu

de (

dB)

−−

−−

>

Pkindex

= 36.00 samples

Pkvalue

= 14748 units

Pkphase

= −1.8 deg


Maxlobe

= −18.0 dB

1D ISLR = −16.3 dB

18−May−99 18:59 pulse3.epsTime (samples expanded by 16) →


P has

e an

g le

(de g

) →

Ma g

n it u

d e ( d

B)

→


Maxlobe = -18.0 dB

1D ISLR = -16.3 dB

Pkindex = 36.00 samplesPkvalue = 14748 unitsPkphase = -1.8 deg


AzComp Results -- Range Slice

40 50 60 70 80 90−200

−100

0

100

200


Pha

se A

ngle

(de

g) −

−−

−>


40 50 60 70 80 90−35

−30

−25

−20

−15

−10

−5

0


Mag

nitu

de (

dB)

−−

−−

>

Pkindex

= 57.13 samples

Pkvalue

= 14893 units

Pkphase

= −1.8 deg


Maxlobe

= −18.1 dB

1D ISLR = −15.0 dB


P has

e an

g le

(de g

) →

Mag

n itu

d e (d

B)

→



Maxlobe = -18.1 dB

1D ISLR = -15.0 dB

Pkindex = 57.13 samplesPkvalue = 14893 unitsPkphase = -1.8 deg



Multi-Looking ConceptSingle look image uses all signal returns from a ground target to create a single image. The image will contain speckle but have the highest achievable resolutionMulti looking is used to reduce speckle in the final detected image, assuming that phase is not needed.

Independent images of the same area can be formed in the digital processing of SAR data by using sub-sets of the signal returns. Achieved by compressing subsets of the azimuth signal energy (spectrum) independently, and adding their detected images together after registration.In satellite SARs, 3 or 4 looks are typically taken, with the azimuth resolution and number of looks selected to make the azimuth pixel size approximately equal to the ground range pixel size.

Resulting image has lower resolution but reduced speckle


The SPECAN Algorithm

Optimal for low resolution, multi-look or ScanSAR processing

Following conventional range compression, azimuth compression is achieved by a matched filter multiply followed by an azimuth FFT

There is no azimuth IFFT, so the algorithm is very efficient

This saving is possible because of the linear FM structure of the received signal

http://www.ee.ubc.ca/sar/sqlp/sqlp.html


SummaryIllustrated SAR compression with the R/D algorithm

– Obtained well-focussed results

– Carefully-designed matched filters with weighting

– RCMC done correctly

– Doppler parameters estimated accurately

Other algorithms available for specialized purposes

– SPECAN

– Chirp scaling

– Wave Equation

– Polar Format

Advanced Topics - SAR Systems and Digital Signal Processing

Notes

Slide 2

A SAR system, as used in remote sensing, has two features which distinguish it from other radar systems:

• It makes a 2-dimensional image by having the radar platform move in a straight line during the data collection. The second dimension is given by measuring the time delay of the received radar pulse.

• It obtains high resolution in the motion direction by focussing or compressing the Doppler energy arising from the platform motion.

As the radar is a coherent system (preserving phase), it is convenient to perform the signal processing using complex numbers. Also, the pulse repetition frequency (PRF) is kept low to obtain large swath widths, so complex numbers are needed to properly sample the received signal.

In the early days of SAR, users were only interested in the magnitude of the processed image, but now they are also very interested in the phase. So the final processed image is usually stored in the form of complex numbers.

One of the features that distinguishes a modern radar system from its predecessors is digital signal processing (DSP). With digital processing, focussing can be precise, and image quality maintained at a high level.

Slide 3

What does aperture mean? (Courtesy of the Alaska SAR Facility)

Many people associate the word aperture with photography, where the term represents the diameter of the lens' opening. The camera's aperture then determines the area through which light is collected. Similarly, a radar antenna's length partially specifies the area through which it collects radar signals. The antenna's length is therefore also called its aperture.

Remember, light and radar just represent different wavelengths of electromagnetic radiation, so many terms and equations used in everyday optics also apply in radar theory.

So what does synthetic aperture mean?

In general the larger the antenna, the more unique information you can obtain about a particular viewed object. With more information, you can create a better image of that object (improved resolution). It's prohibitively expensive to place very large radar antennas in space, however, so researchers found another way to obtain fine resolution: they use the spacecraft's motion and advanced signal processing techniques to simulate a larger antenna.

A SAR antenna transmits radar pulses very rapidly. In fact, the SAR is generally able to transmit several hundred pulses while its parent spacecraft passes over a particular object. Many backscattered radar responses are therefore obtained for that object. After intensive signal processing, all of those responses can be manipulated such that the resulting image looks like the data were obtained from a big, stationary antenna. The synthetic aperture in this case, therefore, is the distance travelled by the spacecraft while the radar antenna collected information about the object.

The ERS-1 satellite's SAR sends out around 1700 pulses a second, collects about a thousand backscattered responses from a single object while passing overhead, and the resulting processed image has a resolution near 30 meters. The spacecraft travels around 4 kilometers while an object is "within sight" of the radar, implying that ERS-1's 10 meter x 1 meter radar antenna synthesizes a 4 kilometer-long stationary antenna!

Page 1 of 15Advanced Topics Notes - Radarsystems

This slide showing a SAR system operated from an aircraft illustrates the 2-dimensional nature of the SAR imaging mechanism.

One dimension is the aircraft flight direction, which is called azimuth. The other dimension is given by the radar beam, which is approximately perpendicular to the flight direction. This second dimension is called range, as it is proportional to the range R from the sensor to the reflectors on the ground.

Slide 8

In this group of slides, we will discuss the technical features of SAR systems which allow them to obtain their high resolution in azimuth. Key to this is the concept of coherence, and how the radar signals are timed and processed to maintain and take advantage of the coherence property.

Slide 9

If we can only observe the magnitude of a signal, the best that we can measure is the time of the signal’s reception. The accuracy of this measurement is given by the inverse of the bandwidth of the received signal, e.g. if the bandwidth is 18 MHz, then the time of arrival of a pulse can be measured to an accuracy of 56 nanoseconds. This corresponds to a distance of 8 m.

However, if we can observe the phase to an accuracy of 12o, then (at C-band) the time can be measured to an accuracy of 6 picoseconds, or 1 mm. A coherent radar, with precise control over the frequency of the coherent oscillator, and precise control over the timing of the transmitted pulses, can achieve this higher accuracy.

In the case of an airborne SAR, the platform may not fly in a straight line, because of atmospheric turbulence. When this happens, the received signal must be motion compensated so that the phase of the received signal is the same as it would be if the aircraft did fly in a straight line.

Slide 10

These are the main components of the analogue or radio frequency (RF) parts of a SAR system.

The coherent oscillator generates a very stable frequency, and counters are used to generate the discrete times of pulse generation and analogue-to-digital (A/D) conversion.

The pulse generator generates a chirp signal at low frequency with the desired bandwidth, say 20 MHz. Then the chirp is multiplied by the coherent oscillator to raise its centre frequency to the desired radar frequency, e.g. 5.3 GHz.

This weak RF signal is then amplified to a power of several kW, and fed to the antenna via the circulator. The circulator is a switch which cycles the path to the antenna between the transmit side (Tx) and the receiver side (Rx) of the radar system.

The transmit cycle lasts approximately 30 µsec, while the receive cycle lasts approximately 600 µsec. The circulator also plays the important function of protecting the sensitive receiver from the high power of the transmitter.

The antenna receives the weak echo from the Earth’s surface, and the Low Noise Amplifier (LNA) amplifies it by about 120 dB so that the subsequent analogue and digital electronics can deal with it. Because the LNA has to deal with such a weak received signal, it must have a very low thermal noise figure, to keep the received signal-to-noise ratio (SNR) at a reasonable level.

The demodulator down-converts the signal to baseband (or to an intermediate frequency) so that the sampler can operate at the Nyquist rate for the signal’s bandwidth.


The first step in the SAR signal generation process is to generate a chirp signal with the desired bandwidth, such as 20 MHz. The time of the beginning of the chirp is precisely controlled by a counter running off the coherent oscillator (coho). The beginning of the pulses are separated by the pulse repetition interval, or 1/PRF. Each pulse has exactly the same waveform including the same initial phase.

The pulse is then multiplied by the radar carrier frequency so that the resulting signal has the desired centre frequency, e.g. 5.3 GHz. The carrier is the same as the coho, or is derived from it.

The signal out of the multiplier is filtered so only the signal around the carrier frequency is kept. The signal remaining is then the pulse which is sent to the high power amplifier and transmitted.

The coho signal is a sine wave, and the transmitted pulse also looks like a sine wave, as its fractional bandwidth is very small, e.g. 0.3 %.

Slide 13

The coherent demodulator is essentially the reverse of the up-converter in the signal generator. If the received signal is the same as the transmitted signal (except for a gain change and a time delay), the demodulated signal is the baseband chirp originally generated.

However, the demodulated signal has two important properties:

• it has a time delay given by the return flight time of the signal, and

• it has a phase change proportional to the time delay.

Slide 14

This slide shows how the demodulation process imparts a phase change on the received pulse, proportional to the time delay of the pulse.

The received signal is shown along the top of the slide. In this case, we assume that it is the ideal signal from a point reflector, and the radar and reflector are moving away from each other slowly.

This is more clearly seen by the signals in the lower left panel, where the received signal is chopped up and stored in memory. The memory is 2-dimensional, with each new row of memory beginning at a precise time after the initiation of each transmitted pulse (referred to as range time). The time delay can be seen with respect to the vertical dashed line, which represents a fixed range time. Note that except for the time delay, the received signal has exactly the same shape (phase) in each row. The vertical dimension represents azimuth in this 2-D memory.

However, when the signal is demodulated, the phase of the pulse is changed by the time delay, because the phase of the demodulated signal equals the phase of the received signal minus the phase of the coho. But as the received signal is delayed with respect to the coho, a phase change proportional to delay is imparted on the signal.

The phase change can be observed in the lower right panel, where the circles represent samples taken at a common range time.

Slide 18

After demodulation, the signal is sampled and compressed in the range direction.

The compression is achieved by a matched filter, which is the complex conjugate of the ideal received signal. Weighting


is used to control the sidelobes of the compressed pulse.

The -3 dB width of the compressed pulse (in time units) is approximately equal to the inverse of the bandwidth of the pulse.

The phase of the compressed pulse is equal to the phase of the demodulated signal (at a certain reference point from its beginning).

Slide 19

This slide shows how a range-compressed target appears in signal memory (left panel), where 25 range lines are shown. In the memory, range runs horizontally, while azimuth runs vertically.

The range of the point target is increasing linearly with each pulse (with each range line), but each succeeding time delay increment is so small that the time delay is not obvious in the figure (the total time delay over the 25 pulses is only 93 nsec, representing a λ/2 change in range, or only 0.0019 of a sample).

If we then examine the stored signal at a fixed range R (at the peak of the compressed point target), and draw these 25 samples vs. azimuth time, we observe the sine wave shown in the right panel. This signal is the azimuth signal of the SAR system.

Slide 20

Let us observe the azimuth signal for two cases.

In case A, the target is stationary with respect to the radar. Then there is no differential time delay between the pulses, and the phase of each succeeding pulse is constant. In other words, the azimuth signal shown in the top panel has zero frequency.

Then consider case B, where the target is moving away from the radar at a constant rate, as in the previous slide. Every time the range to the target increases by λ/2 (the transmit plus receive range increases by λ), the azimuth phase changes by 360o, as seen in the lower panel.

The azimuth signal in case B is a sine wave. The frequency of this sine wave is

and is referred to as the Doppler frequency of the target.

Slide 21

This slide shows how the range to a target changes with time as the radar passes by, and the form of the resulting phase change.

Assuming constant-speed, straight-line motion, the zero-Doppler position of the radar, the current position of the radar and the target form a right-angled triangle. The zero-Doppler position is the point where the radar is closest to the target, a distance Ro away.

Then the range R varies with time as a hyperbola, but the hyperbola can be well approximated by a parabola, as the radar beamwidth is relatively narrow.

The change in range induces a phase change, discussed on the previous slide, which also has a parabolic form with time. Note that a signal with a parabolic phase or a linear frequency is a chirp. The form is much like the range chirp, but at a quite different time scale (the azimuth bandwidth is only a few hundred to a thousand Hz).


Note that we have used the units of cycles for phase, so when we differentiate phase relative to time on the next slide, we will get frequency in Hz.

Slide 22

The Doppler frequency is the rate of change of phase, which makes it a linear function of time for the rectilinear SAR motion shown in the previous slide.

The graph shows a typical plot of Doppler frequency vs. time in the linear FM SAR signal of a point target.

The most interesting property of this frequency is the slope of the graph, or the frequency modulation or FM rate, Ka. From the range equation developed on the last slide, we see that the azimuth FM rate is

Other interesting parameters of the signal are its bandwidth, centre frequency and duration or exposure time.

Slide 23

This slide shows the total Doppler bandwidth generated by the SAR system.

The SAR system design gives the fixed SAR parameters of antenna length D, radar wavelength λ and sensor velocity V. The length of the beam footprint and the associated azimuth exposure time are proportional to the range R.

The azimuth FM rate Ka is inversely proportional to range, with the interesting result that the total azimuth bandwidth generated 2V/D is independent of range and wavelength.

In order to make the bandwidth larger (and the resolution finer), the antenna length must be made shorter !

Slide 24

As in other instruments, the resolution, when expressed in time units, is approximately equal to the inverse of the bandwidth, or D/(2V) seconds in this case.

Then to get the resolution in space units, we multiply by the (azimuth) velocity of the sensor, or V. Thus the azimuth resolution is D/2 m.

Slide 25

Digital signal processing of received SAR data is the key to the higher performance of modern radar systems. Originally, SAR processing was performed with coherent laser optics, but in the 1980s, digital processing took over. Digital processing offered the advantage of higher dynamic range, better noise control and more precise focussing. Digital SAR processors were relatively slow at first, but now they can be built to operate in real time.

In this set of slides, we will review the mainstream algorithms in use today, and go through the steps of the most common algorithm, the Range/Doppler algorithm.

Slide 26

These are the main SAR processing algorithms in use for satellite SAR processing today. The Range/Doppler algorithm was developed in 1978, is the most general one, and is the one most widely used. It will handle most SAR cases efficiently, except those with very wide apertures, high squint and ScanSAR.


SPECAN is an algorithm developed in 1979 to use the minimum memory and computing operations for spaceborne use. It turns out to be very efficient for low resolution, multi-look processing, as well as ScanSAR processing. It is particularly efficient for ScanSAR because the time-frequency structure of the SAR processing algorithm can be exactly matched to the time-frequency structure of the ScanSAR data collection. It does not handle range cell migration correction (RCMC) easily.

The chirp scaling algorithm was developed in 1992. Its main advantage is that it obtains higher phase accuracy because it dispenses with the RCMC interpolator. Instead, it performs RCMC by scaling (expanding and shifting in range) the chirp in the range-time, azimuth-frequency domain.

The wave equation algorithm was originally developed for seismic processing, and was adapted to SAR processing in 1986. It is also called the Range Migration Algorithm (RMA), or the Wave Number algorithm. It operates in the 2-dimensional frequency (wave number) domain, and handles wide-aperture and high-squint SAR data accurately, as long as the radar velocity does not vary with range too much. It does not need an explicit Secondary Range Compression term, as this SRC term is implicit in the formulation, but it cannot adjust the SRC term with range.

The polar format algorithm was developed for squinted and spotlight aircraft SARs, and has limited use for satellite SARs. It can focus accurately at any squint angle, but has a limited depth of focus.

Slide 27

The signal is a linear FM pulse imposed upon a carrier frequency of f0 Hz. For ERS, Envisat and RADARSAT, the carrier frequency is C-band at 5.3 GHz.

The linear FM pulse or chirp has the properties of:

• duration τl usually 30 - 40 µs

• centre frequency, usually zero so that f0 is the centre frequency

• bandwidth BW, usually 10 - 30 MHz

• FM rate = BW / τl, often about 0.5 MHz/µs

The pulse is selected to be linear FM so that all frequencies within the selected bandwidth are used equally, a criteria for good pulse compression.

Slide 28

Here we assume that the ground is completely non-reflective except for a single, ideal point target or reflector. This is the easiest way to see how a SAR system works, and to derive the required signal processing operations to focus the image. In this way, we can observe the impulse response of the SAR, as the whole system is a linear system.

Slide 29

The range equation expressed the range from the antenna phase centre to the target scattering centre, as a function of pulse number or azimuth time. It is one of the most important equations in the SAR system, because the azimuth phase encoding, and the subsequent azimuth signal processing depend upon this change in range. It is the change in range which makes a SAR work, in the sense that it allows us to process the received data to get fine resolution in azimuth.

In both satellite and airborne SAR, it is common to use the straight line motion assumption illustrated in the sketch. The assumption is very accurate for airborne SARs; for satellite SARs it is also a good assumption with the proviso that Vr is allowed to change with range.


The received signal is demodulated because, in subsequent signal processing operations, we want to deal only with the information part of the signal, not the carrier.

However, the effect of the carrier frequency is very important, as the phase change 2πf0τd is a direct function of the radar carrier frequency or wavelength, λ = c / f0.

The demodulator multiplies the received signal by a coherent local oscillator. When the received signal is delayed, the phase of the local oscillator advances. In this way, the demodulation process changes the time delay τdinto the azimuth phase 2πf0τd .

Slide 31

This slides illustrates the flight geometry of a typical airborne SAR. The radar beam (not explicitly shown), begins illuminating the target while at point A, and finishes the illumination at point B.

During this interval, energy is received from the target. This energy is demodulated, sampled, and stored in SAR signal memory inside the signal processor. It could also be stored on tape or downlinked directly to the ground.

For each transmitted pulse, one line is stored in signal memory. As the range to the target R(η) changes, the energy shifts in signal memory, as illustrated on the next slide.

Slide 32

There are two significant azimuth times associated with this target, in addition to the exposure start and stop times. The first is the time when the centre of the beam crosses the target, and is denoted by ηc.

The second is the time that the target is closest to the radar, and is denoted by ηo. The latter time may not appear in the figure, if the beam squint is large enough that the target is not illuminated when it is closest to the radar system.

Slide 33

In order to illustrate the operation of the Range/Doppler algorithm, we have done a complete simulation using a single received point target.

We used parameters from the ERS satellite SAR, with the exception that we have shortened the range chirp length and the azimuth exposure time in order to fit the simulation into a 128 x 256 point array.

To achieve this shortening, we have increased the range and azimuth FM rates, to keep the bandwidths the same. Reducing the radar wavelength was one parameter changed to achieve this.

The simulation is still accurate, because the time-bandwidth products (TBP) are still over 100, a requirement for representative results.

Slide 34

This diagram shows the locus of energy in signal memory that would be received from a single point target on the ground.

This signal is important as it is used to define the SAR processing algorithms (the matched filters) and to define the impulse response of the end-to-end system, including the signal processor.


Note that the range migration is clearly seen. It appears step-like in this portrayal, because we have only plotted every 4th range cell (to keep the file size down).

Slide 35

Typical steps in the commonly-used Range/Doppler algorithm include:

• Unpack data from downlink format into complex (I,Q) words

• Balance the I & Q channels for gain and phase

• Range compression (fast convolution with weighting)

• Azimuth FFT (fast Fourier transform)

• Doppler centroid estimation

• Range cell migration correction (interpolation in range direction)

• Azimuth matched filter multiply (with weighting)

• Look extraction (select desired portion of Doppler spectrum)

• Azimuth IFFT (inverse fast Fourier transform)

• Detection*

• Look summation* * these operations are not done when complex images are desired

We will review the most important of these steps in the next group of slides. Note that Doppler Centroid Estimation is sometimes done before the azimuth FFT, depending upon the algorithm used.

Slide 36

In the next group of slides, we outline the main operations in range processing or compression.

Because the phase structure of the range signal is not significantly affected by range migration, range compression can be achieved by a 1-dimensional matched filtering operation along the range direction. If necessary, a secondary range compression can also be applied to improve range focussing.

The range compression operation is a conventional matched filtering operation, where the compression filter is applied in the frequency domain using FFTs. After the inverse FFT, only a portion of the output points is valid, because of the circular wraparound of the FFTs.

It is also useful to think of the matched filtering as a correlation between the received signal and a replica of the ideal received signal (with the latter conjugated, because the signals are complex). The matched filter will produce a strong, sharp output only when the phase structure of the received signal is well matched with the replica.

Slide 37

The first step is to find a replica of the transmitted range chirp. In some systems such as RADARSAT, a replica is embedded in the data stream of the received range lines. If not, the replica is generated knowing the duration, centre frequency and FM rate of the chirp.


To verify the correct matched filter, it is useful to look at the magnitude and phase spectrum of the replica and the matched filter.

In the left-hand plots, the magnitude spectrum is shown. In the top panel, the magnitude spectrum of the received datais shown. As this data contains only one point target with no noise, it can be used as the chirp replica. In the bottom panel, we show the magnitude of the spectrum of the matched filter, before weighting (in red) and after weighting (in green). Note that the shape of the spectrum of the matched filter before weighting is the same as the replica, and weighting tapers the matched filter energy at the edges of the spectrum.

The right-hand plots show the phase of the spectrum of the replica (top) and of the matched filter (bottom). They are designed to be equal and opposite to each other, as the main purpose of the matched filter is to match the phase of the signal.

Slide 38

This slide shows the result of compressing one range line containing a single point target. Before compression, the real part of the signal is shown, and after compression, the absolute value is shown.

The signal is a linear FM chirp centred at zero frequency after complex demodulation.

After compression, the width of the main lobe at the -3 dB level is shorter than the length of the uncompressed pulse by the ratio of the time-bandwidth product (TBP).

After compression, the point target looks like a sinc function. Compared to the usual sinc function, this pulse has a slightly wider main lobe, and lower side lobes, because of the smoothing action of the window.

Slide 39

A waterfall plot of the range compressed signal of a point target is shown in the left side of this slide (the absolute value of the complex number is shown). This time the whole azimuth exposure is shown, but for clarity, only every 15th line is shown.

The peaks have a wobbly appearance, as they are migrating through range cells, and no interpolator is used in this plot. However, an interpolator would show that the peaks are smooth.

On the right side, we show a mesh plot of the same data, but this time every 8th range line is shown. This subsampling in azimuth gives the peaks a rather spiky appearance, and the migration through range cells gives the side lobes a wavy appearance. However, the result is correct.

Slide 40

Finally we show a contour plot of range compressed energy. In this plot, the range migration is clearly seen, which will be corrected in a subsequent operation.

This time, every range line is contoured, but the migration through range cells still gives a wavy appearance to the plot.

Slide 41

The range resolution is a direct function of the processed range bandwidth, which is lowered a little by the weighting function.

The resolution can be expressed in a number of different units. The generic expression is given in seconds (or range cells), but it is also useful to express it in metres. This is done by multiplying by the effective propagation speed, which is one half the speed of light, or 150 m/µsec.


This gives the resolution in metres along the beam direction, referred to as the slant range resolution ρsr

To get the range resolution measured along the ground ρgr, the slant range resolution must be divided by the sine of the radar incident angle.

For ERS, ρsr= 9 m and ρgr= 23 to 30 m, depending upon the incident angle.

For RADARSAT, ρgr= 10 to 65 m, as it has a wide choice of range bandwidths and incident angles.

Slide 42

To examine the results in more detail, we use an interpolator to expand the sampling frequency in the range direction. Taking one range line, expanding by a factor of 16, and plotting the pulse magnitude on a dB scale, this plot is obtained.

Now we can measure detailed parameters of the compressed pulse, such as:

• -3 dB resolution

• the height of the maximum side lobe (MAXlobe)

• the 1-D integrated side lobe ratio (1-D ISLR)

• the phase at the peak of the pulse (Pkindex)

• the amplitude at the peak (Pkvalue) and

• the phase at the peak (Pkphase)

All parameters here have their ideal values in this example.

Slide 43

Next we plot the phase of the expanded pulse. Here we see that the phase is essentially zero everywhere. When the pulse amplitude is positive, as it is within the main lobe, the phase is almost exactly zero. When the amplitude changes sign, as it does for every second side lobe, the phase goes to either +180ο or - 180ο.

This excellent phase accuracy is due to the fact that the phase of the matched filter was carefully matched to the phase of the signal.

Slide 44

A required step before Range Cell Migration Correction (RCMC) is to get the data into the azimuth frequency domain, by taking an azimuth FFT.

This figure and the next one show the locus of target energy in the range-time, azimuth-frequency domain.

Because of the linearity of the frequency-time relationship of linear FM signals, the shape of the locus of target energy is the same as in the azimuth time domain, with the exception that the azimuth frequency axis is rotated with respect to the azimuth time axis to an arbitrary non-zero center frequency.

This centre frequency is directly proportional to the beam offset ηc and the azimuth FM rate Ka, and is given by:


This contour plot of azimuth frequency-domain energy illustrates the disjoint nature of the energy in the frequency domain, when compared with the azimuth time domain in slide 40.

However, it is not really disjoint --- the energy is simply circularly-rotated around the azimuth frequency axis. The rotation occurs because the actual azimuth frequency is many tens of KHz, but is aliased into the interval [ 0 : Fa ], where Fa is the azimuth sampling rate or PRF (pulse rate frequency).

Slide 47

In this slide, the Doppler energy is originally between M Fa and (M+1) Fa, where M is an integer. In this case, the complete Doppler centroid is at (M+1/2) Fa, and the observed Doppler centroid is at frequency Fa/2.

However, in general, the Doppler spectrum is not symmetrically placed between two integer multiples of Fa.

Slide 48

In this slide, the spectrum is not between integer Fa boundaries, but can lie anywhere along the azimuth frequency axis.

We want to estimate the complete, unaliased Doppler centroid, shown as Fcen.

From the observed spectrum, we can estimate Ffrac in a number of ways, which are relatively straightforward and reliable. But estimating the Doppler ambiguity number M is more difficult.

The earliest method of estimating Ffrac was to use a curve-fitting procedure on the blue curve. The earliest method of estimating M was to estimate the range shift in a multilook environment.

Recently, Doppler estimation methods based on signal phase were developed. One of these is illustrated on the next 2 slides.

Slide 49

In a method developed by Richard Bamler and Hartmut Runge of DLR (Deutsche Forschungsanstalt für Luft) in 1991, use is made of the fact that the Doppler centroid is directly proportional to the radar frequency (i.e. inversely proportional to the radar wavelength) to obtain both the fractional part of the Doppler centroid and the Doppler ambiguity.

As the radar pulse sweeps through its bandwidth (e.g. 17 MHz), the radar frequency changes by a small fraction (0.32 % in the ERS case). If we estimate the slope of Ffrac vs. range frequency, then the absolute Doppler centroid can be obtained. To do this, we perform the following steps on the range-compressed data in the range-time, azimuth-time domain:

• transform to the range frequency domain

• for each sample S(i) and the one following in the azimuth direction, compute conj(S(i)) * S(i+1)

• sum these terms over azimuth to obtain the average cross-correlation coefficient (ACCC)

• extract the phase angle of the sum (which is proportional of Ffrac)


• plot phase angle in radians vs. range frequency in Hz

• estimate the average value G1 and the slope G2 of this plot

• find the centroid by projecting the slope to the radar frequency

Steps 2 and 3 are illustrated in this slide. Each of the shorter lines radiating out from the centre represents the value of conj(S(i)) * S(i+1) at one azimuth time, all taken at the same range frequency. These complex vectors are then summed to obtain the longer vector with the circle on the end (shown scaled). The angle of this long vector is the ACCC angle at this range frequency.

Slide 50

These ACCC angles are then found for each range frequency, and are plotted in this slide. A straight line is then fitted to the central 75% of the range spectrum, and the average value G1 and the slope G2 is found.

We then compute the estimates of the fractional part, the ambiguity number and the absolute Doppler centroid using the formulae below. First, the fractional part is estimated by:

Then we project the slope G2 to the radar frequency to obtain the Doppler ambiguity number, M:

where Fintercept is the frequency where the plotted line intercepts the radar centre frequency. The projection of the slope is not very accurate, but M is obtained correctly if Fintercept is accurate to within +/- Fa / 2.

The estimated total Doppler centroid is then:

Slide 51

The total range cell migration depends mainly upon the synthetic aperture length, the range resolution, and upon the squint of the beam forward or aft of the zero Doppler. The synthetic aperture length and range resolution are fixed for a given radar system configuration (except for the linear increase of aperture with slant range), while the squint of the beam can vary with each data take.

The formula in the slide gives the range migration in range cells for the case where the squint angle is large enough that the zero Doppler point is not illuminated by the beam (if it is illuminated, the range migration is generally very small).

Vr = effective radar velocity (m/s)

Fr = range sampling rate (Hz)

c = speed of light (m/s)

R0= slant range (m)


If the RCM is greater than one range cell, then RCM correction (RCMC) should be performed.

In the graph, we draw the total RCM for our simulation parameters. These parameters use an exposure time somewhat less than the ERS satellite. In this case, ηc of 6.3 s corresponds to a squint angle of 3o. If ERS had the same squint angle, the RCM would be 34 range cells.

Slide 52

There are two steps in computing the required amount of RCMC for each azimuth frequency cell.

First, we must compute the absolute or unaliased frequency corresponding to each azimuth frequency cell. This is a linear relationship with a discontinuity of Fa. The discontinuity occurs at the azimuth frequency cell corresponding to frequency Ffrac + Fa / 2. The absolute frequency is then found by adding (M-1) Fa, M Fa or (M+1) Fa to the frequency of each cell, depending upon whether the DOPCEN is left or right of the discontinuity point.

Having obtained these frequencies, the range equation must be expressed as a function of azimuth frequency instead of azimuth time. This is done using the linear relationship

Then we obtain the RCM in cells vs. azimuth frequency. Strictly speaking, the RCM needed is a quadratic function of azimuth frequency. However, in C-band satellite SARs, the quadratic component is very small, so that the curve of RCM vs. frequency is almost linear. For this reason, we can annotate the right-hand axis in the figure with RCM, which closely portrays the correct RCM needed.

Slide 53

As the RCMC needed is usually some fraction of a range cell, we need an interpolator to move the data an arbitrary fraction of a cell.

Usually this fraction is quantized to 1/16 of a cell, so 15 different interpolators are needed to move the data by i /16 of a cell, where i = 1 : 15.

A simple interpolator is obtained from a truncated sinc function, as shown in blue. To avoid excessive frequency leakage in the interpolator, the coefficients are weighted by a Kaiser window with β = 3. After multiplying the coefficients by the window, the coefficients shown in red are obtained.

Slide 54

To get the 15 sets of coefficients, the red curve must be subsampled by 16, with the appropriate shift.

This slide shows 8 of the coefficient sets. Set 1 shifts by 1/16 of a cell, and set 8 shifts by 1/2 of a cell. Sets 9 to 15 are the mirror image of sets 7 to 1, while set 16 is the ``no-shift'' set = [ 0 0 0 1 0 0 0 0].

Slide 55

The RCMC operation is illustrated in this slide.

The amount of shift needed can be separated into an integer and a fractional number of range cells, as shown in panel (a). The integer cell shifts are performed simply by a shift of samples, while the fractional sample shift is performed by the interpolator.

Panel (b) shows the distribution of energy in every 16th range line prior to RCMC.


Panel (c) shows the distribution of energy after the integer shifts are performed. This shift corrects most of the RCM, but a significant amount of energy jitter remains.

Panel (d) shows the distribution of energy after the fractional shifts are performed with the interpolator.

We see that the energy is now well-aligned in azimuth, which is illustrated further in the next 3 slides.

Slide 56

This slide shows a mesh plot of signal energy, where every 12th line is shown.

Slide 57

To be sure that the energy does not appear elsewhere in the array, this slide gives the energy summed in the azimuth direction, including the energy from every range line.

Slide 58

This figure shows a contour plot of energy after RCMC.

Compare this plot with slide 44, which shows the contour plot of signal energy before RCMC. The alignment of energy along the azimuth direction is now complete, ready for azimuth compression.

Slide 60

The azimuth matched filter is generated and applied much the same as the range matched filter.

If multi-looking is done, only a fraction of the azimuth frequency data is used for each application of the matched filter.

Slide 61

To check the correct generation of the azimuth matched filter, the properties of the received data should be examined.

In this slide, we look at the magnitude (top) and phase (bottom) spectrum of the data in one range cell. As we have only a single point target in this simulation, we examine the range cell containing the majority of the target energy.

In the top plot, we note that the data has an appropriate oversampling ratio, i.e. the signal bandwidth is about 85% of the sampling frequency. We also note that the magnitude spectrum has a peak at about azimuth frequency cell number 33, which agrees with the DOPCEN frequency found by the estimators:

Note that in real data, the magnitude spectrum will be a noisy version of the top plot, but the phase spectrum will be random.

Slide 62

In this slide, we take a 30 x 30 point array centred on the largest value, and plot its magnitude with a mesh plot.

This gives an overview of the peak and its surrounding side lobes.


We see that the azimuth resolution is about 1.1 cells, a direct function of the weighting function and the oversampling ratio used. It is also due to the accurate definition of the azimuth matched filter, for if the azimuth FM rate were wrong, a coarser resolution would be obtained.

The first side lobe is down 18 dB, again a direct consequence of the weighting function used. The 1-dimensional integrated side lobe ratio (ISLR) is -16 dB, which is normal for the weighting function used.

The phase function is not quite perfect, with the answer being about 2 degrees off. This small error is a consequence of range migration, and the imperfect operation of the interpolator.

Note that the phase function has a distinct slope, because the Doppler centre frequency is not zero.


sar signal processing

Documents

advanced topics notes

natural resources canada

doppler centroid estimation

integer fa boundaries

real part part

linear fm signal

pulse repetition frequency

linear fm pulse