1
Synthetic-Aperture Radar (SAR) Basics
2
OutlineSpatial resolution
Range resolution• Short pulse system
• Pulse compression
• Chirp waveform
• Slant range vs. ground range
Azimuth resolution• Unfocused SAR
• Focused SAR
Geometric distortionForeshortening
Layover
Shadow
Radiometric resolutionFading
Radiometric calibration
3
Spatial discriminationSpatial 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 nearly the same range
4
Spatial discriminationThe 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) resolution
Various combinations of resolution can be used to discriminate targets
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Range resolution
6
Range resolutionShort pulse radar
The received echo, Pr(t) is
wherePt(t) is the pulse shape
S(t) is the target impulse response
denotes convolution
To resolve two closely spaced targets, r
Exampler = 1 m 6.7 ns
r = 1 ft 2 ns
tStPtP tr
Tx
Rx
T
point target echo
T= 2R/c
2
cor
c
2r
r
7
Range resolutionClearly 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, , reduces the energy E.
Pt = 100 W, = 100 ns r = 50 ft, E = 10 J
Pt = 100 W, = 2 ns r = 1 ft, E = 0.2 J
Consequently, to keep E constant, as is reduced, Pt must increase.
0 t dttPE
Pt
8
More Tx Power??Why not just get a transmitter that outputs more power?
High-power transmitters present problemsRequire 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
1 « 2 and P1 » P2
time
1
Po
we r
P1
P2
2
2211 PP Goal:
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Pulse compressionChirp 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
B2
c
2
cr
c = speed of light, r = range resolution, = pulse duration, B = signal bandwidth
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Pulse compression, the compromiseTransmit a long pulse that has a bandwidth corresponding to a short pulse
Must modulate or code the transmitted pulseto 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)· (s)
Brute force approach
Raw pulse duration, = 1 ns (10-9 s) Required transmitter power, P = 1 MW !
Pulse compression approach
Pulse duration, = 0.1 ms (10-4 s) Required transmitter power, P = 10 W
12
FM-CW radarAlternative 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 radarLinear FM sweep
Bandwidth: B Repetition period: TR= 1/fm
Round-trip time to target: T = 2R/c
fR = Tx signal frequency – Rx signal frequency
If 2fm is the frequency resolution, then the range resolution r is
Hz,fc
RB4
Tc
RB4T
2T
Bf m
RRR
m,B2cr
B2
14
FM-CW radarThe 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 radarBlending 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
, Tx pulse duration
16
Chirp radar
Linear frequency modulation (chirp) waveform
for 0 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 = k
C2
C tk5.0tf2cosA)t(s
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Stretch chirp processing
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Challenges with stretch processing
time
TxB Rx
LO
near
farfreq
uen
cy
time
freq
uen
cy near
far
Reference chirp
Received signal (analog)
Digitized signalLow-pass filter
A/D converter
Echoes from targets at various ranges have different start times with constant pulse duration. Makes signal processing more 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 exampleKey system parametersPt = 10 W, = 100 s, B = 1 GHz, E = 1 mJ , r = 15 cm
Derived system parametersk = 1 GHz / 100 s = 10 MHz / s = 1013 s-2
Echo duration = = 100 sFrequency resolution f = (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 swath’s 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)
FFT IFFT
Freq-domain reference chirp
Received signal (after digitization)
Correlated signal
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Signal correlation examples
Input waveform #1High-SNR gated sinusoid, no delay
Input waveform #2High-SNR gated sinusoid, ~800 count delay
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Signal correlation examples
Input waveform #1High-SNR gated sinusoid, no delay
Input waveform #2Low-SNR gated sinusoid, ~800 count delay
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Signal correlation examples
Input waveform #1High-SNR gated chirp, no delay
Input waveform #2High-SNR gated chirp, ~800 count delay
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Signal correlation examples
Input waveform #1High-SNR gated chirp, no delay
Input waveform #2Low-SNR gated chirp, ~800 count delay
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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 targetsSignals 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.
r = r
range resolution
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Why time sidelobes are a problemSidelobes from large-RCS targets with can obscure signals from nearby smaller-RCS targets.
Time sidelobes are related to pulse duration, .
fb = 2 k R/c
fb
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Window functions and their effectsTime 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
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Window functionsBasic function:
a and b are the –6-dB and - normalized bandwidths
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Window functions
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Detailed example of chirp pulse compression
t0,tk5.0tf2cosa)t(s C2
C
C2
CC2
C )Tt(k5.0)Tt(f2cosatk5.0tf2cosa)Tt(s)t(s
CC2
C2
2C
2
2TfTk5.0tktf2tk2cos
)TkTtk2Tf2(cos
2
a)Tt(s)t(s
2C
2
Tk5.0tTkTf2cos2
a)t(q
after lowpass filtering to reject harmonics
dechirp analysis
which simplifies to
received signal
quadraticfrequency
dependence
linearfrequency
dependencephase terms
chirp-squaredterm
sinusoidal term
sinusoidal term
33
Pulse compression effects on SNR and blind range
SNR improvement due to pulse compression: B
Case 1: Pt = 1 MW, = 1 ns, B = 1 GHz, E = 1 mJ, r = 15 cm
For a given R, Gt, Gr, , : SNRvideo = 10 dBB = 1 or 0 dB
SNRcompress = SNRvideo = 10 dBBlind range = c/2 = 0.15 m
Case 2: Pt = 10 W, = 100 s, B = 1 GHz, E = 1 mJ , r = 15 cm
For the same R, Gt, Gr, , : SNRvideo = – 40 dBB = 100,000 or 50 dB
SNRcompress = 10 dBBlind range = c/2 = 15 km
B
FBTkR4
GGPSNR
43
2rtt
compress
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Pulse compressionPulse compression allows us to use a reduced transmitter power and still achieve the desired range resolution.
The costs of applying pulse compression include:added transmitter and receiver complexity
must contend with time sidelobes
increased blind range
The advantages generally outweigh the disadvantages so pulse compression is used widely.
Therefore we will be using chirp waveforms to provide the required range resolution for SAR applications.
35
Slant range vs. ground rangeCross-track resolution in the ground plane (x) is theprojection of the range resolution from the slant planeonto the ground plane.
At grazing angles ( 90°), r x
At steep angles ( 0°), x For = 5°, x = 11.5 r
For = 15°, x = 3.86 r
For = 25°, x = 2.37 r
For = 35°, x = 1.74 r
For = 45°, x = 1.41 r
For = 55°, x = 1.22 r
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Azimuth (along-track) resolutionDiscrimination of targets based on their along-track or azimuth position is possible due to the unique phase history associated with each azimuth position.
Note that phase variations and Doppler frequency shifts are analogous since f = d/dt where is phase.
Assuming the phase of the target’s echo is essentially constant over all observation angles, the phase variation is due entirely to range variations during the observation period.
Recall that /2 = 2R/ where R is the slant range, is the wavelength, and the factor of 2 is due to the round-trip path length.
37
Along-track resolutionConsider an airborne radar system flying at a constant speed along a straight and level trajectory as it views the terrain.
For a point on the ground the range to the radar and the radial velocity component can be determined as a function of time.Radar position = (0, vt, h), Target position = (xo, yo, 0), Range to target, R(t)
22o
2o 0hytvx0tR
22o
2o hyx0R
22
o2
o
o
hytvx
ytvvtR
td
dR
22
o2o
o
hyx
vy0R
22
o2o
oD
hyx
vy20R
2f
38
Along-track resolution
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Along-track resolutionExample
Airborne SAR
Altitude: 10,000 m
Velocity: 75 m/s
Five targets on ground
All cross-track offsets = 5 km
Along-track offsets of -1000, -500, 0, 500, and 1000 m
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Along-track resolutionAlt = 10 km
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
-15000 -10000 -5000 0 5000 10000 15000Along-track position (m)
Ra
ng
e (
m)
1000 m
500 m
0 m
-500 m
-1000 m
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Alt = 10 km, Vel = 75 m/s, = 10 cm
-1500
-1000
-500
0
500
1000
1500
-15000 -10000 -5000 0 5000 10000 15000Along-track position (m)
Do
pp
ler
fre
qu
en
cy
(H
z)
1000 m
500 m
0 m
-500 m
-1000 m
-300
-200
-100
0
100
200
300
-1000 -500 0 500 1000
c
Along-track resolution
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Along-track resolution
43
Along-track resolutionExample
Airborne SAR
Altitude: 10,000 m
Velocity: 75 m/s
Five targets on ground
All along-track offsets = 0 m
Cross-track offsets of 5, 7.5, 10, 12.5, and 15 km
44
Along-track resolution
Alt = 10 km
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
-15000 -10000 -5000 0 5000 10000 15000Along-track position (m)
Ra
ng
e (
m)
15 km
12.5 km
10 km
7.5 km
5 km
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Along-track resolutionAlt = 10 km, Vel = 75 m/s, = 10 cm
-1500
-1000
-500
0
500
1000
1500
-15000 -10000 -5000 0 5000 10000 15000Along-track position (m)
Do
pp
ler
fre
qu
en
cy
(H
z)
15 km
12.5 km
10 km
7.5 km
5 km
-100
-75
-50
-25
0
25
50
75
100
-750 0 750
c
46
Along-track resolution
47
Along-track resolutionNow solve for R and fD for all target locations and plot lines
of constant range (isorange) and lines of constant Doppler shift (isodops) on the surface.
48
Along-track resolution
Isorange and isodoppler lines for aircraft flying north at 10 m/s at a 1500-m altitude.r = 2 m, V = 0.002 m/s, fD = 0.13 Hz @ f = 10 GHz, = 3 cm
49
Along-track resolutionWithout the spatial filtering of the antenna, the azimuth chirp waveform covers a wide bandwidth.
50
Along-track resolutionSamples of phase variations due to a changing range throughout the aperture are provided with each pulse in the slow-time domain.Note that the range chirp has been frequency shifted to baseband.
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Along-track resolutionSquint-mode operation (or moving targets) will skew the Doppler spectrum. This skew can be detected and accommodated.
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Strip-map SAR signal example (no squint)
Single point target at center of scene.
53
Strip-map SAR signal example (no squint)Time domain characteristics of single point target.Magnitude of phase history mapped in azimuth and range.
• Constant amplitude in range axis indicates uniform pulse amplitude (no windowing).
• Variation in azimuth represents antenna beam pattern in azimuth plane.
54
Strip-map SAR signal example (no squint)Time domain characteristics of single point target.Real part of phase history mapped in azimuth and range.Can be shown that contour of constant phase follows:
Where K is the pulse chirp rate Ka is the azimuth chirp ratet is the fast time index is the slow time index is a constant
• Positive range chirp (K > 0), negative azimuth chirp (Ka < 0)
• Contours of constant phase map as hyperbolae
2a
2 KtK
55
Strip-map SAR signal example (no squint)
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Strip-map SAR signal example (no squint)Time domain characteristics of single point target.Real part of phase history mapped in azimuth and range.Can be shown that contour of constant phase follows:
Where K is the pulse chirp rateKa is the azimuth chirp ratet is the fast time index is the slow time index is a constant
• Negative range chirp (K < 0), negative azimuth chirp (Ka < 0)
• Contours of constant phase map as ellipses
2a
2 KtK
57
Unfocused SARProcessing SAR phase data to achieve a fine-resolution image requires elaborate signal processing.
In some cases trading off resolution for processing complexity is acceptable.
In these cases a simplified unfocused SAR processing is used wherein only a portion of the azimuth phase history is used resulting in a coarser azimuth resolution.
In unfocused SAR processing consecutive azimuth samples are added together (in the slow-time domain).Since addition a is simple operation for digital signal processors, the image formation processing is much easier (less time consuming) than fully-focused SAR processing.
58
Unfocused SARSumming consecutive samples, also known as a coherent integration or boxcar filtering, is useful so long as the signal’s phase is relatively constant over the integration interval.
ExampleFor a 20-sample interval the central portion of the chirp waveform (zero Doppler) is relatively constant.For the outer portions of the chirp the phase varies significantly and integrating produces a reduced output.
59
Unfocused SARExample (cont.)Over a 38-sample interval phase variations within the central portion of the chirp waveform results in a reduced output (0.8 peak vs. 1).The magnitude of the first sidelobe is also larger (0.4 vs. 0.3).The width of the main lobe is narrower.
60
Unfocused SARThe resolution improves with increased integration length up to a point when oscillations in the signal are included in the integral.
The maximum synthetic aperture length for unfocused SAR is Lu which
corresponds to a maximum phase shift across the aperture of 45º.
The azimuth resolution for L = Lu is
Notice the range- and frequency-dependencies of y.
)m(,2Ry
)m(,2RLu
61
Focused SARTo realize the full potential of SAR and achieve fine along-track (azimuth) resolution requires matched filtering of the azimuth chirp signal.
Stretch chirp processing, correlation processing, tracking Doppler filters, as well as other techniques can be used in a matched filter process.
However the range processing is not entirely separable from the azimuth processing as an intricate interaction between range and azimuth domains exists which must also be dealt with to achieve the desired image quality.
62
Focused SARConsider the phenomenon known as range walk or range-cell migration.
Variations in range to a target over the synthetic aperture not only introduce a quadratic phase change (resulting in the azimuth chirp) but may also displace echo in the range (fast-time) domain.
63
Focused SARIf the range to the target varies by an amount greater than the range resolution then the range-cell migration must be compensated during the image formation processing.
Details on the processing required to achieve fully-focused fine-resolution SAR images will be addressed later.
64
Focused SARIn SAR systems a very long antenna aperture is synthesized resulting in fine along-track resolution.For a synthesized-aperture length, L, the along-track resolution, y, is
L is determined by the system configuration.For a fully focused stripmap system, Lm = azR (m), where
az is the azimuthal or along-track beamwidth of the real antenna (az /ℓ)
R is the range to the target
For L = Lm, y = ℓ/2 (independent of range and wavelength)
L2Ry
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Radiometric resolution -- signal fadingFor extended targets (and targets composed of multiple scattering centers within a resolution cell) the return signal (the echo) is composed of many independent complex signals.
The overall signal is the vector sum of these signals.
Consequently the received voltage will fluctuate as the scatterers’ relative magnitudes and phases vary spatially.
Consider the simple case of only two scatters with equal RCSs separated by a distance d observed at a range Ro.
66
Signal fadingAs the observation point moves along the x direction, the observation angle will change the interference of the signals from the two targets.
The received voltage, V, at the radar receiver is
where
The measured voltage varies from 0 to 2, power from 0 to 4.Single measurement will not provide a good estimate of the scatterer’s .
ba Rk2j0
Rk2j0 eVeVV
sin2
dRR,sin
2
dRR 0b0a
sind2
cosV2V 0
Note: Same analysis used for antenna arrays.
67
Fading statisticsConsider the case of Ns independent scatterers (Ns is large) where the voltage due to each scatterer is
The vector sum of the voltage terms from each scatterer is
where Ve and are the envelope voltage and phase.
It is assumed that each voltage term, Vi and i are independent random variables and that i is uniformly distributed.
The magnitude component Vi can be decomposed into orthogonal components, Vx and Vy
where Vx and Vy are normally distributed.
iji eV
je
N
1i
ji eVeVV
s
i
iiyiix sinVVandcosVV
68
Fading statisticsThe fluctuation of the envelope voltage, Ve, is due to fading
although it is similar to that of noise.
The models for fading and noise are essentially the same.
Two common envelope detection schemes are considered, linear detection (where the magnitude of the envelope voltage is
output) and square-law detection (where the output is the square
of the envelope magnitute).
Linear detection, VOUT = |VIN| = Ve
It can be shown that Ve follows a Rayleigh distribution
0V,0
0V,e2
VVp
e
e2V
2e
e
22e where 2 is the variance
of the input signal
69
Fading statistics (linear detection)
For a Rayleigh distribution
the mean is
the variance is
The fluctuation about the meanis Vac which has a variance of
So the ratio of the square of the envelope mean to the variance of the fluctuating component represents a kind of inherent signal-to-noise ratio for Rayleigh fading.
22e 2V
2Ve
222
e2e
2ac 429.0
22VVV
dB6.5or66.3VV 2ac
2
e
70
Fading statistics (linear detection)
An equivalent SNR of 5.6 dB (due to fading) means that a single Ve measurement will have significant uncertainty.
For a good estimate of the target’s RCS, , multiple independent measurements are required.
By averaging several independent samples of Ve, we
improve our estimate, VL
where
N is the number of independent samples
Ve is the envelope voltage sample
N
1ieiL V
N
1V
71
Fading statistics (linear detection)
The mean value, VL, is unaffected by the averaging process
However the magnitude of the fluctuations are reduced
And the effective SNR due to fading improves as 1/N
As more Rayleigh distributed samples are averaged the distribution begins to resemble a normal or Gaussian distribution.
eL V2V
N429.0V 22ac
72
Fading statistics (square-law detection)
Square-law detection, Vs = Ve2
The output voltage is related to the power in the envelope. It can be shown that Vs follows an exponential distribution
Again the mean value is found
and the variance is found(note that )
Again for a single sample measurement yields a poor estimate of the mean.
0V,0
0V,e2
1Vp
s
s2V
2s
2s where 2 is the variance
of the input signal
2
s
2
s2s
2sac VVVV
22es 2VV
2
s2s V2V
dB0or1VV 2sac
2
s
73
Fading statistics (square-law detection)
An equivalent SNR of 0 dB (due to fading) means that a single Vs measurement will have significant uncertainty.
For a good estimate of the target’s RCS, , multiple independent measurements are required.
By averaging several independent samples of Vs, we
improve our estimate, VL
where
N is the number of independent samples
Vs is the envelope-squared voltage sample
N
1isiL V
N
1V
74
Fading statistics (square-law detection)
The mean value, VL, is unaffected by the averaging process
However the magnitude of the fluctuations are reduced
And the effective SNR due to fading improves as 1/N.
As more exponential distributed samples are averaged the distribution begins to resemble a 2(2N) distribution.For large N, (N > 10), the distribution becomes Gaussian.
2L 2V
NVV2
s2sac
75
Independent samplesFading is not a noise phenomenon, therefore multiple observations from a fixed radar position observing the same target geometry will not reduce the fading effects.
Two approaches exist for obtaining independent sampleschange the observation geometry
change the observation frequency (more bandwidth)
Both methods produce a change in which yields an independent sample.
Estimating the number of independent samples depends on the system parameters, the illuminated scene size, and on how the data are processed.
76
Independent samplesIn the range dimension, the number of independent samples (NS) is the ratio of the range of the illuminated
scene (Wr) to the range resolution (r)rS RN
77
Independent samplesWhen relative motion exists between the target and the radar, the frequency shift due to Doppler can be used to obtain independent samples.
The number of independent samples due to the Doppler shift, ND, is the product of the Doppler bandwidth, fD, and
the observation time, T
The total number of independent samples is
In both cases (range or Doppler) the result is that to reduce the effects of fading, the resolution is degraded.
TfN DD
DS NNN
78
Independent samples
N = 1 N = 10
N = 50 N = 250
79
Radiometric calibrationTranslating the received signal power into a target’s radar characteristics (cross section or attenuation) requires radiometric accuracy.
From the radar range equation for an extended target
we know that the factor affecting the received signal power include the transmitted signal power, the antenna gain, the range to the target, and the resolution cell area.
Uncertainty in these parameters will contribute to the overall uncertainty in the target’s radar characteristics.
43
2t
2
rR4
AGPP
80
Radiometric calibrationTransmit power, Pt
Addition of an RF coupler or power splitter at the transmitter output permits continuous monitoring of the transmitted signal power.
Antenna gain, GThe antenna’s radiation pattern must be well characterized. In many cases the antenna must be characterized on the platform (aircraft or spacecraft) as it’s immediate environment may affect the radiation characteristics. Furthermore the characterization may need to be performed in flight.
Target range, RRadar’s inherent ability to measure range accurately minimizes any contribution to radiometric uncertainty.
Resolution cell area, ADifficult to measure directly, requires measurement data from extended target with known .
81
Radiometric calibrationCalibration targets
Radiometric calibration of the entire radar system may require external reference targets such as spheres, dihedrals, trihedrals, Luneberg lens, or active calibrators.
82
Radiometric calibrationFlat plate
83
Radiometric calibrationDihedral and trihedral corner reflectors
84
Radiometric calibrationDihedral and trihedral corner reflectors
85
Radiometric calibrationLuneberg lens
86
Radiometric calibrationLuneberg lens
87
Radiometric calibration
88
Radiometric calibrationActive radar calibrator [Brunfeldt and Ulaby, IEEE Trans. Geosci. Rem. Sens., 22(2),
pp. 165-169, 1984.]
89
Radiometric calibrationActive radar calibrator
90
Radiometric calibration
91
Radiometric calibrationRCS of some common shapes
92
Radiometric calibration
93
Radiometric calibration