Report

SAR System and Signals Part 2 EE880 Synthetic Aperture Radar M. A. Saville, PhD, PE Summer, 2012 EE880 SAR System & Signals Part 2 Lesson Overview • • • • Imaging radar requirements Array Basics SAR signal modeling Summary EE880 SAR System & Signals Part 2 2 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 EE880 SAR System & Signals Part 2 3 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 EE880 SAR System & Signals Part 2 4 Realistic Down-range Reconstruction Ideal down-range target profile rect() (infinite bandwidth) Time Domain ∆ Spectral Domain -2000 -1500 -1000 Ideal receiver filtering rect() (finite bandwidth) Lost energy -500 0 Time Domain ∆ 500 1000 1500 2000 Profile distortion & spreading Reconstructed down-range target profile is IDFT of windowed rect() 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 EE880 SAR System & Signals Part 2 5 Down-range Digital Signal Processing • Time/range domain • Frequency domain – finite signal bandwidth B << W – sampling period ΔT – record length T Δ = 2 = D 1 Δ Δ = = = 2 2 4 – Unambiguous spectrum = fs/2 – spectral resolution Δf D-1 = = 2 2∆ Δ = Δ = 2 1 1 2 = ∆ range results from scaling time EE880 SAR System & Signals Part 2 6 Realistic Cross-range Reconstruction • Down-range resolved • Cross-range not resolved because of antenna beam • Solution: apply discrete-time Fourier principles to form narrow antenna beam EE880 SAR System & Signals Part 2 7 Cross-range Coordinates End synthetic aperture Θ 0 1. Collection 4. Scene center reference Start synthetic aperture 2. Coordinate references 3. Synthetic aperture reference Ground plane 0 Θ EE880 SAR System & Signals Part 2 Slant plane = 0 sin Θ Cross range scene extent is set by beamwidth of real aperture 8 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 EE880 SAR System & Signals Part 2 Radar centric Range radar Scene centric 9 Cross-range Digital Signal Processing • Array (angular) sampling: • Cross-range sampling – array defined in linear coordinates , – array spacing ← Δ – array length = ← Θ – conceptually: spatial samples = Angles are scaled array length and spacing EE880 SAR System & Signals Part 2 – Unambiguous spectrum Θ = 3dB – cross-range extent ≈ RΘ – cross-range resolution Δ = ℬ −1 Δ, Θ B B-1 Δ is based on arc-length, but resolution depends on the operator B and is subject of course 10 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 EE880 SAR System & Signals Part 2 AN/SPY-1A 11 Array Antenna (1/4) Isotropic transmit antenna Received P0 Power level (dB) P0 - 6 P0 - 12 P0 - 18 R0 R0 2R0 4R0 8R0 Observation angle ZL Receive antennas Note: Antenna observation is defined in angle coordinates because pattern is range-invariant EE880 SAR System & Signals Part 2 12 Array Antenna (2/4) Array of Q isotropic transmit elements 2 1 ≈ = Spherical observation surface 2 = 0 =1 ZL = , , , ∈ℂ Electric fields combine in a constructive or deconstructive manner at different points on the observation surface EE880 SAR System & Signals Part 2 13 Array Antenna (3/4) Radiation pattern of array of isotropic elements GP0 Received GP0 - 6 Power level (dB) GP0 - 12 GP0 - 18 G R0 2R0 4R0 8R0 Observation angle ZL cos , sin = −1 − =0 Δ Δ = sin = 0 −1 Δ 2 Δ 2 Δ sin 2 sin Null-to-null beamwidth ≈ − 2 Half-power beamwidth 3dB ≈ 0.866 Note: transmit array radiation pattern is the same as the receive array pattern. EE880 SAR System & Signals Part 2 14 Array Antenna (4/4) • Fields observed far from array • Array pattern looks like I/DFT of rect • Differential phase on elements steers array ≫ + = −1 = −1 =0 0 Δ Δ = sin + = planar wave fronts −1 2 0 EE880 SAR System & Signals Part 2 2 sin 2 sin Phase shift across dimension of array causes angular shift (translation) to angle , i.e. property of DFT. 15 Synthetic Array • Synthetic aperture is a receive aperture • Fields caused by scatterers (targets, clutter) • Differential angle causes differential phase ≫ + = −1 = −1 =0 0 Δ + Δ = 2 sin = planar wave fronts −1 2 0 = Δ + EE880 SAR System & Signals Part 2 2 sin 2 sin 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. 16 Synthetic Aperture for Cross-range Resolution • SAR spatially samples along array dimension Δ = 2 sin differential phase shift across echoes Incremental path length Point target 2 sin = DFT Δ =DFT{[]}, = 1, ⋯ , sin −Θ 2 ≤ sin ≤ sin Θ 2 EE880 SAR System & Signals Part 2 Incremental Incremental position angle Cross-range resolution equals arc length ∆ 17 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) 0 slow time [ms] EE880 SAR System & Signals Part 2 PRI (intra-pulse sampling) 0 Δ fast time [s] 18 SAR Radar System and Signals • SAR System differs from classic radar system • Collection method (transmit and store), receiver design to support imaging, signal processing TX Differences in CONOP sTX(t) s(t) SAR Simple view TX Ant gc(t) TX Env RT , σ RG, σ0 RJ, sjam Differences in receiver RX r(t) yI(t) yQ(t) , sRX(t) Differences in RSP RX d[n] DB output , t, Tp, Fp, τ EE880 SAR System & Signals Part 2 ℎ RX Ant RSP SYNC input DM ℎ−1 SAR is an inverse problem 19 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 EE880 SAR System & Signals Part 2 20 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 = + + ′ ′ ′ EE880 SAR System & Signals Part 2 Scene center position relative to antenna position = = − 21 Coordinate Systems (2/3) • Local coordinates show variation in position Antenna position Scene center position + ∆ + ′ Scene center position relative to antenna position = + ′ − + ∆ ∆ • Typically assume ∆ = 0 • Scene defined by ′ ′ ′ EE880 SAR System & Signals Part 2 ′ ′ = + ′ − = 0 + ′ • Position parameterized with slow time 22 Coordinate System (3/3) • Waveform definition in fast time coordinates • Reference to scene center -- not antenna • Signal has dependency on both and , = ℝ − complex envelope = cos = EE880 SAR System & Signals Part 2 electromagnetic wave behavior + sin = 0 + ′ Can be phase, frequency, or amplitude encoded Assumes ≪ Typically, ′ = 0 23 Transmit Signal • Wideband signal (LFM or stepped frequency) • Directional (line-of-sight to scene) , = ℝ − ∙ 0 = 0 = 0 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] ∙ = 0 ∙ ≈ 0 + ∆ 0 ∆ ≈ ∙ ′ Differential path length for arbitrary location in scene EE880 SAR System & Signals Part 2 Flight path ′ ′ ′ Scene ′ 24 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 − 20 , = −20 −2 0 +∆ • EM physics (with typical approximations) , = − 20 −20 −20 ′ = ′ − ′ −2 ∙ ′ ′ SAR approximates scene’s reflectivity function EE880 SAR System & Signals Part 2 25 Received Signal (1/2) • Signal comprises all echoes during synthetic aperture ′ , ; = 1, ⋯ , • Inertial navigation system provides motion compensation timing, i.e., compensates for aperture deviation from flight path compensation , = ′ , 2 ∙∆ = = 0 = 0, Flight path ∆ • Slow-time recorded in angle coordinates 0, ′ ′ , = , EE880 SAR System & Signals Part 2 Scene ′ 26 Received Signal (2/2) • Fast-time signals sampled according to signal bandwidth , ; = 1, ⋯ , • 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 EE880 SAR System & Signals Part 2 27 SAR Signal Processing Overview • Signal model after A/D , = − − 2 0, rect =0 −1 × Φ , ′ −2 ∙ ′ ′ • LFM transmit phase profile Φ , = 2 + − 2 Chirp [Hz/sec] • LFM receive (deramp) phase profile Φ , = − 4 20, + − − EE880 SAR System & Signals Part 2 − 0, + 4 − 0, 2 2 28 Deramp & Deskew Receiver (1/5) • Recall LFM waveform with chirp Hz/sec [Sullivan, 7.2]: transmit − 2 + = 0 rect , receive , − − − 2 = rect x 2 −2 + − −2 2 2 Reference to Scene Center (motion compensation point) , = EE880 SAR System & Signals Part 2 2 −20 + − −20 2 29 Deramp & Deskew Receiver (2/5) • Mix reference signal with echo , X = − , fast time within PRI conj , intermediate frequency , − 2 −4 = rect 20 + − −0 2 4 2 −0 Received pulse train from q-th target , = Φ , = − EE880 SAR System & Signals Part 2 −1 =0 rect − 2 Φ 4 20 +− , − 0 + 4 − 0 2 2 30 Deramp & Deskew Receiver (3/5) • Signal phase Φ , = − 4 20 +− − 0 + 4 − 0 2 linear phase, easily compensated 2 quadratic phase, not easily corrected, often dismissed as phase error term • For a fixed target range, the instantaneous received frequency is , 1 Φ 2 = =− − 0 2 constant range-dependent frequency is dechirped or deramped EE880 SAR System & Signals Part 2 31 Deramp & Deskew Receiver (4/5) Adapted from [SUL,7.2] frequency time Near Scene 2 Scene Center Far Scene before deramp frequency after Targets at different ranges have different frequencies < time Deramping also reduces A/D sampling speeds EE880 SAR System & Signals Part 2 32 Deramp & Deskew Receiver (5/5) • Each echo contains multiple tones from scatterers at different ranges in the scene that occur at different times 2 − 0 = =− • SAR processing requires one-to-one mapping of frequency to sample time, i.e. no time-delay • Correct as Φ ← Φ , 2 − • IFT each echo to recover frequencies EE880 SAR System & Signals Part 2 frequency Deramped and deskewed < time 33 Operator Modeling ℒ TX ENV ℳ1 ℒ RX RSP MF ℱ −1 ℳ2 ℒ PFA, CBP represents antenna radiation of signal from transmitter ℒ represents scattering from scatterer ℳ represents receiver front end (mixing, matched filtering, etc…) = ℳ1 ℒ These operations can be approximated as a forward Fourier transform EE880 SAR System & Signals Part 2 ≈ ℱℴ The approximation depends on simple linear superposition of scatterers and far field reception 34 Summary of SAR Systems & Signals Part 2 • • • • Imaging requirements Antenna array SAR signal modeling Operator modeling EE880 SAR System & Signals Part 2 35 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. EE880 SAR System & Signals Part 2 36