1. EE880 SAR System & Signals Part I SAR System and Signals Part 1 EE880 Synthetic Aperture Radar M. A. Saville, PhD Summer, 2012

2. EE880 SAR System & Signals Part I Lesson Overview Review radar concept & range equation Develop signal models for pulse-Doppler radar Review discrete time & bandwidth relations 2

3. EE880 SAR System & Signals Part I Radar Concept Illustration Transmitter (ASR-9) Transmit Line of sight Scatterer Receiver Receive Line of sight Measure time it takes pulse to reach object and return to receiver (implies detection of the echo) 3

4. EE880 SAR System & Signals Part I Radar Concept RAdio Detection And Ranging (RADAR) Send energy burst into environment – Transmit pulses of pulsewidth τ seconds – Periodically transmit a pulse every T p seconds Recover echoes (indicating presence of an object) – Threshold received energy and declare detection – Measure time to receive pulse since last transmission – Derive range R meters to object using speed of light Radar range equation describes amount of energy returned – enables hardware trade studies 4

5. EE880 SAR System & Signals Part I Radar Concepts – Timing & Sampling 5 Signal Amplitude Time (seconds) Signal Amplitude Time (milli-seconds) Signal Amplitude Time (micro-seconds) Diagram to be completed during lecture R un = ΔR =

6. EE880 SAR System & Signals Part I Radar Range Equation (RRE) (Conservation of power equation) P tx – transmit power G tx – transmit antenna gain G rx – receive antenna gain λ – wavelength R – range to object σ – radar cross section P rx – receive power 6 Speed of light in free space is c 0 = 3.0x10 8 m/s. Equations to be completed during lecture. P rx = > P min R max =

7. EE880 SAR System & Signals Part I Basic Radar System Transmitter (TX) Receiver (RX) Synchronizer (SYNC) RX Antenna TX Antenna Environment Targets Interference Clutter Receiver Signal Processor (RSP) Display or Decision Maker (DM) Concept of Operation Database (DB) 7 See [Stimson] or [Sullivan] for more detail or alternate schematics

8. EE880 SAR System & Signals Part I Example of Parametric Modeling Using RRE Use the range equation to: – Design a monostatic air traffic control radar system to detect 1-m 2 aircraft up to 80 nmi – Determine the “best” cost-performance solution ComponentValueCost ($K) Transmitter 1 ( P t )10.0 KW < P t < 100.0 KW 15 + 5/KW Transmitter 2 ( P t )250.0 KW < P t < 1.0 MW 50 + 3/KW Receiver 1 ( P min ) 1.0 μW < P min < 10.0 μW 360 Receiver 2 ( P min ) 10.0 μW < P min < 100.0 μW 150 – 12/μW Antenna 1 ( G ) 24.0 dB < G < 27.0 dB50 + 0.6/dB Antenna 2 ( G ) 30.0 dB < G < 36.0 dB150 + 0.2/dB Duty Cycle ( δ ) 0.0110 +200δ Example worked during lecture 8

9. EE880 SAR System & Signals Part I Pulse Generator Coherent Oscillator Modulator Power Amplifier Pre- Amplifier Basic Transmitter & Signals Synchronizer TX Ant t, T p, F p, τ p(t)p(t) gc(t)gc(t)a ∙ p(t) ∙ g c (t) s(t)s(t) Signals to be developed in lecture. Transmitter RX gc(t)gc(t) Env Display or Decision Maker Database Receiver Signal Processor (RSP) 9

10. EE880 SAR System & Signals Part I Basic Transmitter Signals p(t) = g c (t) = s(t) = Signals to be developed in lecture. 10

11. EE880 SAR System & Signals Part I Basic Radar Antenna Properties Antenna D G ≈ θ HPBW ≈ Signals to be developed in lecture [Stimson, Sullivan]. 11

12. EE880 SAR System & Signals Part I Example – Range and Angle Discrimination Determine the minimum separation distance needed to discriminate each case below Antenna Case 1 Case 2 ΔR = R, Δθ s = Signals to be developed in lecture. 12

13. EE880 SAR System & Signals Part I Basic TX Antenna & “Signals” TX Ant s TX (t) = s(t) = 13

14. EE880 SAR System & Signals Part I Basic Environment & “Signals” TX RX SYNC TX Ant TargetsInterferenceClutter RSP DM Concept of Operation DB RX Ant Environment Space Loss Atmospheric Loss Space Loss s TX (t) s RX (t) s(t)s(t) r(t)r(t) R T, σ R G, σ 0 R J, s jam 14

15. EE880 SAR System & Signals Part I Environment Basic Radar Physics in Environment Electromagnetic (EM) Plane Waves Spherical wavefront appears locally planar far from antenna (called the far field) Antenna D Planar means δβ < δS TX < δR δβ = Signals to be developed in lecture. 15

16. EE880 SAR System & Signals Part I Basic Radar Physics in Environment EM Scattering EM waves are reflected (scattered), transmitted, or absorbed by objects (scatterers) in the environment Scattering coefficient determines scattered power Objects are assumed to be points in the basic system Received power determined with radar range equation Incident Power Scattered Power Transmitted Power Absorbed Power 16

17. EE880 SAR System & Signals Part I Basic Radar Physics in Environment Doppler Frequency (1/2) Relative motion between transmit (and receive) antenna and scatterers cause a frequency shift known as the Doppler Shift f Instantaneous = f i = f Doppler = f D = Ant β =β = Speed of light in free space is c 0 = 3.0x10 8 m/s. Equations to be completed during lecture. 17

18. EE880 SAR System & Signals Part I Basic Radar Physics in Environment Doppler Frequency (2/2) Alternative view is time dilation / compression c 0 >> v Time dilation – compression factor κ = F 0 ’ is the apparent frequency which is simply F 0 ’ = 1/ T 0 ’ Speed of light in free space is c 0 = 3.0x10 8 m/s. Equations to be completed during lecture. 18

19. EE880 SAR System & Signals Part I Basic Environment “Signals” s TX (t) = s RX (t) = s(t) = r(t) = Signals to be developed in lecture. 19

20. EE880 SAR System & Signals Part I Basic RX Antenna & “Signals” RX Ant s RX (t) = r(t) = 20

21. EE880 SAR System & Signals Part I Basic Receiver & Signals Low-noise Amplifier Band-pass Filter Synchronous Detector Synchronizer RX Ant Env Amplifier Matched Filter Receiver Transmitter (TX) t, T p, F p, τ gc(t)gc(t) r(t)r(t) rI(t)rQ(t)rI(t)rQ(t) yI(t)yQ(t)yI(t)yQ(t) Display or Decision Maker Database Receiver Signal Processor (RSP) 21

22. EE880 SAR System & Signals Part I Basic Receiver Signals r I (t) = y I (t) = r Q (t) = y Q (t) = Signals to be developed in lecture. 22

23. EE880 SAR System & Signals Part I Basic Radar Signal Processing TX RX SYNC TX Ant DM Concept of Operation DB RX Ant s TX (t) s RX (t) s(t)s(t) r(t)r(t) Env Receiver Signal Processor (analog & digital shown) yI(t)yQ(t)yI(t)yQ(t) A/D Digital Matched Filter MTD, STAP MTI d[n]d[n] d[n]d[n] Doppler Filter Bank v(t)v(t) Hypothesis Test A/D 23

24. EE880 SAR System & Signals Part I Basic Digital Radar Signal Processing Signals 24 d[n] = v(t) = Signals to be developed in lecture.

25. EE880 SAR System & Signals Part I Basic Displays & Decision Making B-Scope (Planned Position Indicator ) Range Amplitude A-Scope (range versus amplitude) Range versus Angle Information is displayed Decision can be made by a human interpreter of data or automatically by a computer algorithm 25

26. EE880 SAR System & Signals Part I Basic Radar System and Signals TX RX SYNC RX AntTX Ant Env R T, σR J, s jam R G, σ 0 RSP DM Concept of Operation DB s TX (t) s RX (t) s(t)s(t) r(t)r(t) yI(t)yQ(t)yI(t)yQ(t) d[n]d[n] gc(t)gc(t) t, T p, F p, τ 26

27. EE880 SAR System & Signals Part I Topics in Radar Signal Processing Detection – High range resolution (HRR) – Moving target detection – Airborne moving target indication – Adaptive clutter suppression Tracking – HRR – Velocity (high velocity discrimination) – Angle Radar imaging 27

28. EE880 SAR System & Signals Part I Detection of Signals in Noise Assuming a matched filter precedes the ADC s(t) = Output of matched filter and sampling ΔT = τ Time Amplitude y(t) = y[n] = 28

29. EE880 SAR System & Signals Part I Radar Ambiguity Function Determines the energy in a range cell Accounts for mismatch in time and Doppler 29 Ambiguity function of unmodulated rectangular pulse Time Delay Frequency mismatch Graphics made with MATLAB code from [Levanon]

30. EE880 SAR System & Signals Part I Wide Band Signals Commonly used pulses have frequency or phase variation within the pulse – Chirp or Costas code s chirp (t) = – Barker code Signals to be developed in lecture. 30

31. EE880 SAR System & Signals Part I High Range Resolution Range bins (or cells) Radar can resolve very closely spaced objects Depends on bandwidth: B ≈ 2/τ (unmodulated pulse) Common compressed pulse has bandwidth B c and pulse compression ratio ρ = B c /B Uncompressed pulse τ Compressed pulse τ/ρτ/ρ Time Amplitude 31

32. EE880 SAR System & Signals Part I Radar Ambiguity Function 32 Graphics made with MATLAB code from [Levanon]

33. EE880 SAR System & Signals Part I Velocity Detection and Discrimination Doppler filter banks ΔFΔF Frequency Amplitude (M-1)ΔF -ΔF-ΔF 0 ΔFΔF … ΔF = Δv = 33

34. EE880 SAR System & Signals Part I Topics in Modern Radar Phased array and multi-channel radar Waveform diversity Networked, distributed, layered sensors Object detection and classification Imaging with synthetic aperture radar 34 Preponderance of topics involve advanced radar signal processing.

35. EE880 SAR System & Signals Part I Digital Processing Discrete Fourier Transform – Transform fast-time (intra-pulse sampling) or slow-time (inter-pulse sampling) samples to frequency domain Often implemented with Fast Fourier Transform t nΔTnΔT F qΔFqΔF F F -1 D D -1 35

36. EE880 SAR System & Signals Part I Range-Frequency Transforms Following matched filter – Range is time scaled by speed of light r = ct/2 – Discrete time samples ΔT are same as range bins ΔR – Range bin size is inversely proportional to signal bandwidth 36 Discrete Time (nΔT) Record length NΔT Discrete Range (nΔR) Range extent NΔR

37. EE880 SAR System & Signals Part I Range-Frequency Transforms Transforming real-valued time samples – Results in sampled frequency spectrum with unambiguous region F s /2, where F s = 1/ΔT – Frequency spacing is inversely proportional to range extent 37 Discrete Spectrum (nΔF) Unambiguous spectrum NΔF=F s /2 Discrete Spectrum (nΔF) Spreading of single tone

38. EE880 SAR System & Signals Part I Detection and Ranging Range cell & Doppler bin thresholding Matched filter every range cell Doppler process the CPI for every range cell 38 L range cells M Doppler bins Uncompressed range cell Compressed range cell

39. EE880 SAR System & Signals Part I HRR in SAR Imaging Antenna beam and pulse width determine scene extent 39 Image one uncompressed range cell HRR waveform provides range resolution Azimuth resolution in next lesson

40. EE880 SAR System & Signals Part I Summary of SAR Systems & Signals Part 1 Radar Concept Radar Range Equation Radar System – Concept of Operation – Transmitter – Receiver – Environment – Receiver Signal Processor – Antennas – Displays – Syncronization Radar Signal Modeling Signal processing for detection and estimation Doppler processing for velocity detection and estimation Discrete Fourier Transform relationships 40

41. EE880 SAR System & Signals Part I Lesson References [Levanon] N. Levanon, Radar Signals, Wiley-IEEE Press, 2004. [Stimson] G. Stimson, Introduction to Airborne Radar, SciTech Publishing Inc., 1998. [Sullivan] R. Sullivan, Foundations for Imaging and Advanced Concepts, SciTech Publishing Inc., 2004. 41