1. Introduction to Synthetic Aperture Radar (SAR)
Integrated Systems & Solutions – S & R Systems
Introduction to Synthetic Aperture Radar (SAR)
Floyd Millet
August 2005
Work was done under US Government contract.

2. RaDAR is an acronym for Radio Detection And Ranging
Radar Applications
Air Traffic Control
Air traffic and weather
Ground Control approach landing
Aircraft Navigation
Altimeter
Doppler navigation
Weather avoidance
Law Enforcement
Police speedometers
Intrusion alarms
Military
Surveillance and reconnaissance
Weapon guidance and control
Proximity fuzes for weapons
Bomb damage assessment
Remote Sensing the Earth
Flood monitoring
Crop and forest assessment
Location of archeological ruins
Remote Sensing the Solar System
Planetary rotation rates
Range to the moon and planets
Meteor tracking
Ship Safety
Collision avoidance
Piloting in restricted waters
Space
Rendezvousing of spacecraft
Spacecraft docking and landing
Satellite tracking
RaDAR is an acronym for Radio Detection And Ranging

3. Radar Imaging
Individual image points (pixels) must be discriminated in two dimensions, range and azimuth
Form a terrain image using a radar in a moving airborne vehicle
Problem
Simplest approach: Real-Beam Imaging Radar
Example: Plan Position Indicator (PPI)
PPI Display
Range
Azimuth

4. Cell Size: 1/5 Major Dimension
Target Not Identified When Coarse Resolution Used
Cell Size: 1/5 Major Dimension
Corresponding Map

5. Cell Size: 1/20 Major Dimension
Target Identified When Fine Resolution Used
Cell Size: 1/20 Major Dimension
Corresponding Map

6. Resolution Required for Various Mapping Applications
Features to be resolved
Coast lines, large cities, outlines of mountains
Major highways, variations in fields
“roadmap” details: city streets, large buildings, small air fields
Vehicles, houses, small buildings
Cell Size
150m
10-20 m
1-3 m
20-35 m
Resolution Cell da dr

7. High-Resolution Mapping Synthetic Aperture Radar (SAR)

8. What is High Resolution Radar Mapping?
HRM involves breaking up real antenna beam into fine resolution cells
Footprint of mainlobe on ground
The map is made by forming cells and measuring signal intensity in each cell
dAZ dr
Resolution Cell
dAZ = Azimuth Resolution
dr = Range Resolution

9. What Does a Radar Measure?
Amplitude versus Time
All other SAR parameters are derived:
Range (known time relationship)
Phase - coherent transmission plus demodulation
Doppler frequency
Range resolution (pulse compression)
Azimuth Resolution

10. Range Discrimination  2²d ²d
The transmitted pulse travels at the speed of light 300,000 km/second 3.3 nanoseconds/meter Round-trip “radar time” 6.7 nanoseconds/meter (²d = 2 meters ² = 13.3 nanoseconds) But target returns overlap if targets are separated by less than c/2

11. Short Pulse Range Resolution
R2 = R1 + ΔR R1
Transmitted Pulse O 
Time  
Received Pulses
2R1/c
2(R1 + ΔR/c)
2ΔR/c 
Pulses Just Resolvable
ΔR = c/2
2ΔR/c

12. Shorter Pulses
So for better resolution, just make the transmitted pulse SHORTER
However, the shorter pulses must somehow transmit the SAME ENERGY to the target
As the pulse gets SHORTER, the peak power gets HIGHER
Problem
Peak power gets MUCH to high before pulse length even approaches high resolution

13. Coded Pulses  f1 f2 Solution
Transmit a long coded pulse that can be decoded (compressed) after reception into a much shorter pulse
Solution  f1 f2
Linear Frequency Modulation (FM) Linear Swept Frequency “Chirp”
Note: A typical 200 microsecond pulse extends over 60 km resulting in a range resolution of 30 km

14. Pulse Compression Frequency Time  2 1
Transmitted/Received Pulse Resolution = c/2 f2 Δf
Variable Delay Line “Compression” Filter f1
Delay Time 
Time f1 f2 Δf
1/Δf
Decoded/”Compressed” Output Resolution = c/2Δf = (/2)(fo/ Δf) F number = fo/ 2Δf
Resolution varies as 1/ Δf , that is, it varies with transmitted bandwidth

15. Linear FM (Chirp) Waveform= c - B W t 2 + n , ( ) o S w e p r q u y h a v i g b d s l T m F P : S ( n , t ) = A c o s ( 2 p f t +
pαt2 ) x A - Ý t f c f t t f ( n , t ) = 2 p f t +
pαt2 , t t f ( ) f ( n , t ) = 1 d n , t =
fo + αt , t t t 2 p d t T r a n s m i t b a n d w i d t h g i v e n b y : B W = ατ t o L i n e a r F M h a s d e s i r a b l e p r o p e r t i e s o v e r o t h e r w a v e f o r m t y p e s : • E a s y t o g e n e r a t e •
" S t r e t c h m o d e
" d e m o d u l a t i o n

16. Pulse Compression o R e c i v d S g n a l G B y : C m p x ( f t r u /) * P • , S ( n , t ) = C ( n , t ) c o s [ 2 p f ( t - T ) + pα ( t - T ) 2 ] r R R S ( , t ) x S r , t ( ) P u l s e n = A - t 2 R 2 R + t t g t t g t c c R t g t = R a n g e - t o - T a r g e t S ( n , t ) = S ( n , t ) × e - j w t = [ C ( n , t ) × e - j w 2 T R ] × e x p { j pα ( t - T ) } = D ( n , t ) × e x p { j pα ( t - T ) 2 } v r R R w h i c h i s a n a l o g o u s t o : • M a x i m i z i n g t h e s i g n a l - t o - n o i s e r a t i o * d o e s n t a p l y
" S r c h M i g f I F m x - w v B U T : W q u z n t h e i m a g e ( G o o d s i d e l o b e c o n t r o l o n t h e i m p u l s e r e s p o n s e ( I P R ) )

17. Fine Range Resolution Requires Large Radar Bandwidth
Fourier Transform Pair
1/ 
Time
Frequency

18. Pulse Compression Advantages
Range resolution independent of transmit pulse length
Transmit long pulses
Keep peak power comfortably low
Set range resolution with transmitted bandwidth
Resolution inversely proportional to bandwidth
150 MHz 1 meter resolution
300 MHz 0.5 meter resolution
Resolution independent of slant range

19. Azimuth Resolution

20. Ability to Resolve Closely Spaced Targets is Beamwidth Dependent
The half-power (3dB) beamwidth is a measure of angular resolution of radar
(1/2)3dB
3dB
(3/2)3dB A B A B A B

21. Synthetic-Aperture Radar
Azimuth Considerations
SAR
Synthetic-Aperture Radar
Antenna beamwidth is inversely proportional to the number of wavelengths in its length (aperture) Rq L
= /L radians
= C/f R

22. Azimuth DiscriminationL
R/L Δd R
As the collection vehicle moves along the flight path, targets are detected as they move in and out of the antenna pattern
But target returns overlap if the targets are separated in azimuth by less than the antenna beamwidth
So achievable azimuth resolution degrades with range
Real-beam imaging radar
Flight Path

23. Azimuth Discrimination
So for better azimuth resolution, just make the antenna beam NARROWER!
Generate more wavelengths in the antenna aperture by lengthening the antenna or by shorting the wavelength (increasing the frequency)
However, very LONG antennas are difficult to carry and position and very HIGH frequencies limit performance in weather and at long ranges
Problem
Antennas get MUCH too long and frequencies MUCH to high before the beamwidth even approaches high resolution

24. Synthetic-Aperture Radar
Solution
Synthesize a long antenna aperture using a physically short antenna
SAR
Synthetic-Aperture Radar
Store the data collected sequentially and coherently across a long aperture and then process the data to synthesize a full aperture collection

25. Design Options for Improving Resolution Before SAR
Range Resolution
Decrease pulsewidth, at expense of power and range
Operate at short range/decrease power
Azimuth Resolution
Increase operating frequency to Ku and Ka-bands or higher, with increased atmospheric and weather attenuation, lower available power sources
Increase antenna aperture, with attendant installation and stabilization problems

26. The Resolution Breakthrough
Range -
Pulse Compression - Increased range resolution without loss of power
Azimuth -
Synthetic Aperture - Increased azimuth resolution without large antenna installation
Note: 1. Both use special waveforms
2. Both use signal processing techniques

27. Synthetic Aperture Radar

28. From Hovanessian, “Introduction to Synthetic Array and Imaging Radars”
Phase History of a Scatterer
From Hovanessian, “Introduction to Synthetic Array and Imaging Radars”

29. Anamorphic Hologram

30. SAR Collection Geometry

31. Resolution Limitation on Sidelooking SAR

32. Synthetic Aperture -Resolution limitation on sidelooking SAR:
Tgt 1 Ro
INT Ls
-Resolution limitation on sidelooking SAR:
Maximum θINT is limited by azimuth antenna beamwidth
, Lant is length of linear array
-This limitation does not apply to spotlight collection

33. Point-Target Phase History Compressed in Both Range and Azimuth

34. First SAR Imagery

35. ADTS Advanced Detection Technology Sensor
Ft. Devens, MA
35 GHZ
HH Polarization
± 20 Deg Depression Angle

36. Where Do You Fit in? Future Topics Implementation of Theory
September Algorithm Architecture for SAR Ground Processing
Creating an Image
September 20 Concepts in Image Processing
From Idealization to Realization
October PACE: An Autofocus Algorithm for SAR

37. Texts and Software Texts Software
Curlander, John and McDonough, Robert Synthetic-Aperture Radar - Systems and Signal Processing
Skolnik, Merrill Introduction to Radar Systems
Nathanson, Fred Radar Design Principles
Carrara, Walter et al Spotlight Synthetic-Aperture Radar
Oppenheim, Alan and Schafer, Ron Discrete Time Signal Processing
Skolnik, Merrill Radar Handbook
Software
Mathcad V6
Matlab