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826 SAR Basics-S09

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Synthetic Aperture Radar

Text of 826 SAR Basics-S09

1 Synthetic-Aperture Radar (SAR) Basics 2 Outline Spatial resolution Range resolution Short pulse system Pulse compression Chirp waveform Slant range vs. ground range Azimuth resolution Unfocused SAR Focused SAR Geometric distortion Foreshortening Layover Shadow Radiometric resolution Fading Radiometric calibration 3 Spatial discrimination Spatial discrimination relates to the ability to resolve signals from targets based on spatial position or velocity. angle, range, velocity Resolution is the measure of the ability to determine whether only one or more than one different targets are observed. Range resolution, r, is related to signal bandwidth, B Short pulse higher bandwidth Long pulse lower bandwidth Two targets at nearlythe same range 4 Spatial discrimination The ability to discriminate between targets is better when the resolution distance is said to be finer (not greater) Fine (and coarse) resolution are preferred to high (and low) resolutionVarious combinations of resolution can be used to discriminate targets 5 Range resolution 6 Range resolution Short pulse radar The received echo, Pr(t) is where Pt(t) is the pulse shape S(t) is the target impulse response - denotes convolution To resolve two closely spaced targets, r Example r = 1 m t s 6.7 ns r = 1 ft t s 2 ns ( ) ( ) ( ) t S t P t Pt r- =TxRxttTpoint target echoT= 2R/c2corc2rrt= s t7 Range resolution Clearly to obtain fine range resolution, a short pulse duration is needed. However the amount of energy (not power) illuminating the target is a key radar performance parameter. Energy, E, is related to the transmitted power, Pt by Therefore for a fixed transmit power, Pt, (e.g., 100 W), reducing the pulse duration, t, reduces the energy E. Pt = 100 W, t = 100 ns r = 50 ft, E = 10 J Pt = 100 W, t = 2 ns r = 1 ft, E = 0.2 J Consequently, to keep E constant, as t is reduced, Pt must increase. ( )}t=0tdt t P EtPt8 More Tx Power?? Why not just get a transmitter that outputs more power? High-power transmitters present problems Require high-voltage power supplies (kV) Reliability problems Safety issues (both from electrocution and irradiation) Bigger, heavier, costlier, 9 Simplified view of pulse compression Energy content of long-duration, low-power pulse will be comparable to that of the short-duration, high-power pulse t1 t2 and P1 P2 time t1 P1 P2 t2 2 2 1 1P P t ~ t Goal:10 Pulse compression Chirp waveforms represent one approach for pulse compression. Radar range resolution depends on the bandwidth of the received signal. The bandwidth of a time-gated sinusoid is inversely proportional to the pulse duration. So short pulses are better for range resolution Received signal strength is proportional to the pulse duration. So long pulses are better for signal reception B 2c2cr=t= c = speed of light, r = range resolution,t = pulse duration, B =signal bandwidth 11 Pulse compression, the compromise Transmit a long pulse that has a bandwidth corresponding to a short pulse Must modulate or code the transmitted pulse to have sufficient bandwidth, B can be processed to provide the desired range resolution, r Example: Desired resolution, r = 15 cm (~ 6) Required bandwidth, B = 1 GHz (109 Hz) Required pulse energy, E = 1 mJ E(J) = Pt(W)t(s)Brute force approach Raw pulse duration, t = 1 ns (10-9 s) Required transmitter power, P = 1 MW ! Pulse compression approach Pulse duration, t = 0.1 ms (10-4 s) Required transmitter power, P = 10 W 12 FM-CW radar Alternative radar schemes do not involve pulses, rather the transmitter runs in continuous-wave mode, i.e., CW. FM-CW radar block diagram 13 FM-CW radar Linear FM sweep Bandwidth: BRepetition period: TR= 1/fm Round-trip time to target: T = 2R/c AfR = Tx signal frequency Rx signal frequency If 2fm is the frequency resolution, then the range resolution r is Hz , fcR B 4T cR B 4T2 TBfmR RR= = = Am , B 2 cr = B 214 FM-CW radar The FM-CW radar has the advantage of constantly illuminating the target (complicating the radar design). It maps range into frequency and therefore requires additional signal processing to determine target range. Targets moving relative to the radar will produce a Doppler frequency shift further complicating the processing. 15 Chirp radar Blending the ideas of pulsed radar with linear frequency modulation results in a chirp (or linear FM) radar. Transmit a long-duration, FM pulse. Correlate the received signal with a linear FM waveform to produce range dependent target frequencies. Signal processing (pulse compression) converts frequency into range. Key parameters: B, chirp bandwidth t, Tx pulse duration 16 Chirp radar Linear frequency modulation (chirp) waveform for 0 s t s t fC is the starting frequency (Hz) k is the chirp rate (Hz/s) |C is the starting phase (rad) B is the chirp bandwidth, B = kt ( ) ( )C2Ct k 5 . 0 t f 2 cos A ) t ( s | + + t =17 Stretch chirp processing 18 Challenges with stretch processing time Tx BRx LO near far frequency time frequency near far Reference chirp Received signal (analog) Digitized signal Low-pass filter A/D converter Echoes from targets at various ranges have different start times with constant pulse duration.Makes signal processingmore difficult. To dechirp the signal from extended targets, a local oscillator (LO) chirp with a much greater bandwidth is required.Performing analog dechirp operation relaxes requirement on A/D converter. 19 Pulse compression example Key system parameters Pt = 10 W, t = 100 s, B = 1 GHz, E = 1 mJ , r = 15 cm Derived system parameters k = 1 GHz / 100 s = 10 MHz / s = 1013 s-2 Echo duration = t = 100 s Frequency resolution of = (observation time)-1 = 10 kHz Range to first target, R1 = 150 m T1 = 2 R1 / c = 1 s Beat frequency, fb = k T1 = 10 MHz Range to second target, R2 = 150.15 m T2 = 2 R2 / c = 1.001 s Beat frequency, fb = k T2 = 10.01 MHz fb2 fb1 = 10 kHz which is the resolution of the frequency measurement 20 Pulse compression example (cont.) With stretch processing a reduced video signal bandwidth is output from the analog portion of the radar receiver. video bandwidth, Bvid = k Tp (where Tp = 2 Wr /c is the swaths slant width) for Wr = 3 km, Tp = 20 s Bvid = 200 MHz This relaxes the requirements on the data acquisition system (i.e., analog-to-digital (A/D) converter and associated memory systems). Without stretch processing the data acquisition system must sample a 1-GHz signal bandwidth requiring a sampling frequency of 2 GHz and memory access times less than 500 ps. 21 Correlation processing of chirp signals Avoids problems associated with stretch processing Takes advantage of fact that convolution in time domain equivalent to multiplication in frequency domain Convert received signal to freq domain (FFT) Multiply with freq domain version of reference chirp function Convert product back to time domain (IFFT) FFTIFFT Freq-domainreference chirp Received signal (after digitization) Correlated signal 22 Signal correlation examples Input waveform #1 High-SNR gated sinusoid, no delay Input waveform #2 High-SNR gated sinusoid, ~800 count delay 23 Signal correlation examples Input waveform #1 High-SNR gated sinusoid, no delay Input waveform #2 Low-SNR gated sinusoid, ~800 count delay 24 Signal correlation examples Input waveform #1 High-SNR gated chirp, no delay Input waveform #2 High-SNR gated chirp, ~800 count delay 25 Signal correlation examples Input waveform #1 High-SNR gated chirp, no delay Input waveform #2 Low-SNR gated chirp, ~800 count delay 26 Chirp pulse compression and time sidelobes Peak sidelobe level can be controlled by introducing a weighting function -- however this has side effects. 27 Superposition and multiple targets Signals from multiple targets do not interfere with one another.(negligible coupling between scatterers) Free-space propagation, target interaction, radar receiver all have linear transfer functions superposition applies. Signal from each target adds linearly with signals from other targets. Ar = r range resolution 28 Why time sidelobes are a problem Sidelobes from large-RCS targets with can obscure signals from nearby smaller-RCS targets. Time sidelobes are related to pulse duration, t. Afb = 2 k AR/c Afb 29 Window functions and their effects Time sidelobes are a side effect of pulse compression. Windowing the signal prior to frequency analysis helps reduce the effect. Some common weighting functions and key characteristics Less common window functions used in radar applications and their key characteristics 30 Window functions Basic function: a and b are the 6-dB and - normalized bandwidths 31 Window functions 32 Detailed example of chirp pulse compression ( ) ( ) t s s | + + t = t 0 , t k 5 . 0 t f 2 cos a ) t ( sC2C( ) ( ) ( ) ( )C2C C2C) T t ( k 5 . 0 ) T t ( f 2 cos a t k 5 . 0 t f 2 cos a ) T t ( s ) t ( s | + + t | + + t = ( ) ( )(((

| + + t + t +t t + t= C C2C22C22 T f T k 5 . 0 t k t f 2 t k 2 cos) T k T t k 2 T f 2 ( cos2a) T t ( s ) t ( s( ) ( )2C2T k 5 . 0 t T k T f 2 cos2a) t ( q + t =after lowpass filtering to reject harmonicsdechirp analysiswhich simplifies to received signal quadratic frequency dependence linear frequency dependence phase terms chirp-squared term sinusoidal term sinusoidal term 33 Pulse compression effects on SNR and blind range SNR improvement due to pulse compression:Bt Case 1: Pt = 1 MW, t = 1 ns, B = 1 GHz, E = 1 mJ, r = 15 cm For a given R, Gt, Gr, , o:SNRvideo = 10 dB Bt = 1 or 0 dB SNRcompress = SNRvideo = 10 dB Blind range = ct/2 = 0.15 m Case 2: Pt = 10 W, t = 100 s, B = 1 GHz, E = 1 mJ , r = 15 cm For the same R, Gt, Gr, , o:SNRvideo = 40 dB Bt = 100,000 or 50 dB SNRcompress = 10 dB Blind range = ct/2 = 15 km ( )tto = BF B T k R 4G G PSNR432r t tcompress34 Pulse compression Pulse compression allows us to use a reduced transmitter power and still achieve the desired range resolution. The costs of applying pulse compression include: added tran