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SAR System and Signals Part 2 EE880 Synthetic Aperture Radar

SAR System and Signals Part 2 EE880 Synthetic Aperture Radar. M. A. Saville , PhD, PE Summer, 2012. Lesson Overview. Imaging radar requirements Array Basics SAR signal modeling Summary. Imaging Radar Requirements. Resolve scatterers in 1D,2D,3D Construct geospatial image

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SAR System and Signals Part 2 EE880 Synthetic Aperture Radar

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  1. SAR System and Signals Part 2EE880 Synthetic Aperture Radar M. A. Saville, PhD, PE Summer, 2012

  2. Lesson Overview • Imaging radar requirements • Array Basics • SAR signal modeling • Summary

  3. Imaging Radar Requirements • Resolve scatterers in 1D,2D,3D • Construct geospatial image • Estimate reflectivity function • Estimate RCS of scene scatterers • Estimate cross-section coefficient of clutter • Image one uncompressed range cell or voxel (3D case) • Achieve specified resolution in 1, 2 or 3D • Perform above within time and computational constraints

  4. Ideal 2D Radar Imaging Collection • Shown: ground plane imaging • Down-range resolution set by HRR waveform, i.e. bandwidth • Cross-range resolution set by narrow antenna beam • Each echo resolves both dimensions

  5. Realistic Down-range Reconstruction Ideal down-range target profile (infinite bandwidth) Time Domain Ideal receiver filtering (finite bandwidth) Spectral Domain Lost energy -2000 -1500 -1000 -500 0 500 1000 1500 2000 Reconstructed down-range target profile is IDFT of windowed Time Domain Profile distortion & spreading Note duality and reciprocity in Fourier Transforms. If we start with ideal S, transform to s, window by applying a range-gate and inverse transform, we still observe spread in sw

  6. Down-range Digital Signal Processing • Time/range domain • finite signal bandwidth B << W • sampling period ΔT • record length T • Frequency domain • Unambiguous spectrum fs/2 • spectral resolution f 2 D D-1 range results from scaling time

  7. Realistic Cross-range Reconstruction • Down-range resolved • Cross-range not resolvedbecause of antenna beam • Solution: apply discrete-time Fourier principles to form narrow antenna beam

  8. Cross-range Coordinates Start synthetic aperture Slant plane 1. Collection 4. Scene center reference Ground plane 2. Coordinate references End synthetic aperture Cross range scene extent is set by beamwidth of real aperture 3. Synthetic aperture reference

  9. SAR Coordinate Reference • SAR coordinates are different from detection and tracking radar applications • Coordinates are referenced to the scene center • Synthetic aperture elements (spacing d and length L) are referenced to scene center in angular coordinates • SAR is a receive array antenna Angle scene Angle scene Range radar Range radar Scene centric Radar centric

  10. Cross-range Digital Signal Processing • Array (angular) sampling: • array defined in linear coordinates • array spacing • array length • conceptually: spatial samples • Cross-range sampling • Unambiguous spectrum • cross-range extent • cross-range resolution B B-1 is based on arc-length, but resolution depends on the operator B and is subject of course Angles are scaled array length and spacing

  11. Antenna Array Basics • Array - collection of antenna elements • Each element is a single antenna • Typically, elements have identical radiation patterns • Isotropic elements used in analysis for convenience AN/SPY-1A

  12. Array Antenna (1/4) Received Power level (dB) Isotropic transmit antenna R0 P0 2R0 P0 - 6 4R0 P0 - 12 8R0 P0 - 18 R0 Observation angle ZL Receive antennas ZL Note: Antenna observation is defined in angle coordinates because pattern is range-invariant ZL

  13. Array Antenna (2/4) Array of Q isotropic transmit elements Spherical observation surface ZL ZL ZL Electric fields combine in a constructive or deconstructive manner at different points on the observation surface

  14. Array Antenna (3/4) GP0 Radiation pattern of array of isotropic elements Received Power level (dB) G R0 GP0 - 6 2R0 GP0 - 12 4R0 GP0 - 18 8R0 Observation angle ZL ZL ZL Null-to-null beamwidth Half-power beamwidth Note: transmit array radiation pattern is the same as the receive array pattern.

  15. Array Antenna (4/4) • Fields observed far from array • Array pattern looks like I/DFT of • Differential phase on elements steers array planar wave fronts Phase shift across dimension of array causes angular shift (translation) to angle , i.e. property of DFT.

  16. Synthetic Array • Synthetic aperture is a receive aperture • Fields caused by scatterers (targets, clutter) • Differential angle causes differential phase planar wave fronts target Synthetic array formed by correcting phases caused by differential ranges. For linear array, DFT along array dimension results in cross-range compression, i.e. resolution.

  17. Synthetic Aperture for Cross-range Resolution • SAR spatially samples along array dimension Incremental position Incremental angle Incremental path length differential phase shift across echoes Point target =, Cross-range resolution equals arc length

  18. SAR Signal Modeling Requirements • N-D images require N-D signal representation • Parameterize 2D signals (range,angle) with time • Time has two scales (PRI-, and CPI-) • System design must support stable collection method and accurate coherent measurement CPI (inter-pulse sampling) PRI (intra-pulse sampling) 0 0 slow time fast time

  19. SAR Radar System and Signals sTX(t) s(t) • SAR System differs from classic radar system • Collection method (transmit and store), receiver design to support imaging, signal processing TX TX Ant gc(t) Differences in receiver Env SAR Simple view sRX(t) r(t) Differences in CONOP RX RJ, sjam RT, σ RG, σ0 input yI(t) yQ(t) d[n] DB RSP Differences in RSP RX Ant output t, Tp, Fp, τ DM SYNC SAR is an inverse problem

  20. Detailed SAR Modeling • Signal development from signal processing perspective • Math development from inverse problem perspective • Algorithm processing from linear systems perspective • Outline: • Coordinate systems • Transmit “signal” • Scatterer response • Received signal • Operator representation

  21. Coordinate Systems (1/3) • Lower case letters: global coordinates • Primed lower case letters: local scene coordinates • Upper case letters: local antenna coordinates Antenna position + Scene center position + + ’+ Scene center position relative to antenna position

  22. Coordinate Systems (2/3) • Local coordinates show variation in position Antenna position Scene center position Scene center position relative to antenna position • Typically assume • Scene defined by • Position parameterized with slow time

  23. Coordinate System (3/3) • Waveform definition in fast time coordinates • Reference to scene center -- not antenna • Signal has dependency on both and complex envelope electromagnetic wave behavior sin Can be phase, frequency, or amplitude encoded Assumes Typically,

  24. Transmit Signal • Wideband signal (LFM or stepped frequency) • Directional (line-of-sight to scene) Cutaway view of a helix Traveling wave tube. (1) Electron gun; (2) RF input; (3) Magnets; (4) Attenuator; (5) Helix coil; (6) RF output; (7) Vacuum tube; (8) Collector. [wikipedia.com] Flight path Differential path length for arbitrary location in scene Scene

  25. Scattered Signal • Clutter & targets, atmospheric and space loss L • In SAR, heterogeneous clutter = “target” • Approximate target signal model is simple sum of isotropic point scatterers: amplitude scaled, time, frequency/phase shifted • EM physics (with typical approximations) SAR approximates scene’s reflectivity function

  26. Received Signal (1/2) • Signal comprises all echoes during synthetic aperture • Inertial navigation system provides motion compensation timing, i.e., compensates for aperture deviation from flight path compensation • Slow-time recorded in angle coordinates Flight path Scene

  27. Received Signal (2/2) • Fast-time signals sampled according to signal bandwidth • Signals recorded either with absolute time or relative to initial or middle pulse in collection with respect to scene center • LFM signal recovered using deramp and deskew receiver -- relates sample time to instantaneous frequency

  28. SAR Signal Processing Overview • Signal model after A/D • LFM transmit phase profile • LFM receive (deramp) phase profile Chirp [Hz/sec]

  29. Deramp & Deskew Receiver (1/5) • Recall LFM waveform with chirp Hz/sec [Sullivan, 7.2]: transmit receive x Reference to Scene Center(motion compensation point)

  30. Deramp & Deskew Receiver (2/5) • Mix reference signal with echo X fast time within PRI intermediate frequency Received pulse train from q-th target

  31. Deramp & Deskew Receiver (3/5) • Signal phase linear phase, easily compensated quadratic phase, not easily corrected, often dismissed as phase error term • For a fixed target range, the instantaneous received frequency is constant range-dependent frequency is dechirped or deramped

  32. Deramp & Deskew Receiver (4/5) Adapted from [SUL,7.2] frequency frequency SceneCenter Far Scene NearScene time time before deramp after Targets at different ranges have different frequencies Deramping also reduces A/D sampling speeds

  33. Deramp & Deskew Receiver (5/5) • Each echo contains multiple tones from scatterers at different ranges in the scene that occur at different times • SAR processing requires one-to-one mapping of frequency to sample time, i.e. no time-delay • Correct as • IFT each echo to recover frequencies frequency time Deramped and deskewed

  34. Operator Modeling PFA, CBP TX RX RSP ENV MF represents antenna radiation of signal from transmitter represents scattering from scatterer represents receiver front end (mixing, matched filtering, etc…) These operations can be approximated as a forward Fourier transform The approximation depends on simple linear superposition of scatterers and far field reception

  35. Summary of SAR Systems & Signals Part 2 • Imaging requirements • Antenna array • SAR signal modeling • Operator modeling

  36. 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.

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