Radar systems
Some of this material is derived from
Microwave Remote Sensing—Vol II,
by Ulaby, Moore, and Fung
Chris Allen (callen@eecs.ku.edu)
Course website URL
people.eecs.ku.edu/~callen/823/EECS823.htm
1
Outline
Radar measurements
Radar equation
Range resolution
Doppler shift and velocity resolution
Signal fading
Spatial discrimination
Radar system types
Side-looking airborne radar (SLAR)
Synthetic-aperture radar (SAR)
Inverse SAR
Interferometers
Scatterometers
Scattering mechanisms and characteristics
2
Radar system
Like a radiometer, radar systems use very sensitive
receivers to output a voltage that contains information
about the target.
Unlike a radiometer, the signal that the radar receives does
not originate from the target (emission), rather it is a
scattered version of a signal transmitted by the radar.
Therefore the characteristics of the signal received by radar
may be fundamentally different from the radiometer signal.
3
Radar system
Radar is an acronym for radio detection and ranging.
Detection addresses the question of whether a target is
present or changing.
Ranging, the ability to measure the range to a target, is
possible as radar provides its own illumination (the
transmitter) unlike a radiometer that provides no range
information.
4
Radar system
The transmitted radar signal may be coherent, polarized,
and modulated in frequency, phase, amplitude, and
polarization. In addition, the transmit antenna determines
the spatial distribution of the transmitted signal.
While radar system measures only the received signal
voltage as a function of time, signal analysis enables the
extraction of new information about the target including
location, velocity, composition, structure, rotation, vibration,
etc.
Radar images of 3.5-km asteroid 1999 JM8 at a range of 8.5x106 km with ~ 30-m spatial resolution 5
Radar equation
Extraction of useful information using signal analysis requires
that the signal be discernable from noise, interference, and
clutter.
Noise usually originates inside the receiver itself (e.g.,
receiver noise figure) though may also come from external
sources (e.g., thermal emissions, lightning).
Interference is another coherent, spectrally-narrow emission
that impedes the reception of the desired signal (e.g., a
jammer). [May originate internal or external to radar]
Clutter is unwanted radar echoes that interfere with the
observation of signals from targets of interest.
6
Radar equation
Received signal power, Pr, is an essential radar parameter.
The radar range equation, used to determine Pr, involves
the geometry and system parameters.
Bistatic geometry
7
Radar equation
The power density incident on the
scatterer, Ss, is
 1 
2

Ss  Pt G t 
,
W
m
2 
4

R
t 

Pt is the transmit signal power (W)
Gt is the transmit antenna’s gain in the direction of the scatterer
Rt is the range from the transmitter to the scatterer (m)
The power intercepted by the scatterer, Prs, is
Prs  Ss A rs , W
Ars is the scatterer’s effective area (m2)
The power reradiated by the scatterer, Pts, is
Pts  Prs 1  f a  , W
fa is the fraction of intercepted power absorbed
8
Radar equation
The power density at the
receiver, Sr, is
 1 
2

Sr  Pts G ts 
,
W
m
2 
4

R
r 

Gts is the gain of the scatterer in the
direction of the receiver
Rr is the range from the receiver to the scatterer, (m)
The power intercepted by the receiver, Pr, is
Pr  Sr Ar , W
Ar is the effective area of the receiver aperture, (m2)
Combining the pieces together yields
Pt G t A r
Ars 1  f a  G ts  , W
Pr 
2
4  R t R r 
9
Radar equation
The terms associated with the scatterer may be combined
into a single variable, , the radar scattering cross section
(RCS).
  A rs 1  f a  G ts , m 2
The RCS value will depend on the scatterer’s shape and
composition as well as on the observation geometry.
For bistatic observations
q0 , f0 ; qs , fs ; p 0 , p s  , m 2
where
(q0, f0) = direction of incident power
(qs, fs) = direction of scattered power
(p0, ps) = polarization state of incident
and scattered fields
10
Radar equation
In monostatic radar systems the transmit and receive
antennas are collocated (placed together, side-by-side) such that
q0 = qs, f0 = fs, and Rt = Rr so that the RCS becomes
q, f; p 0 , p s  , m 2
The radar range equation for the monostatic case is
Pr 
Pt G t A r
4  R 
2 2
, W
Monostatic geometry
11
Radar equation
If the same antenna or identical antennas are used in a
monostatic radar system then
G t  G r  G and A t  A r  A
and recognizing the relationship between A and G
2 G
4A
A
and G  2
4

we can write
Monostatic geometry
Pt G 2 2 
Pt A 2 
Pr 

3
4
4  2 R 4
4  R
12
Radar equation
Receiver noise power, PN
PN  k T0 B F , W
k is Boltzmann’s constant (1.38  10-23 J K-1)
T0 is the absolute temperature (290 K)
B is receiver bandwidth (Hz)
F is receiver noise figure
Signal-to-noise ratio (SNR) is
Pt G 2 2 
SNR  Pr PN 
4  3 R 4 k T0 B F
may be expressed in decibels
SNRdB  10 log 10 SNR 
13
Radar range equation example
Example
Radar center frequency, f = 9.5 GHz
Transmit power, PT = 100 kW
Bandwidth, B = 100 MHz
Receiver noise figure, FREC = 2 (F = 3 dB)
Antenna dimensions, 1 m x 1 m (square aperture)
Range to target, R = 20 km (12.5 miles)
Target RCS,  = 1 m2 (small aircraft or boat)
Find the Pr , PN , and the SNR
First derive some related radar parameters
Wavelength, = 3.15 cm
Antenna gain, G = 4A/2 (assuming  = 1)
A = 1 m2
G = 12,600 or 41 dBi
14
Radar range equation example
Pt G 2 2 
Pr 
4  3 R 4
Find Pr
Solve in dB
Pr(dBm) = Pt(dBm) + 2G(dBi) + 2  (dB) + (dBsm) – 3  4(dB) – 4  R(dB)
Pt(dBm) = 80
G(dBi) = 41
(dB) = -15
(dBsm) = 0
4(dB) = 11
R(dB) = 43
Pr(dBm) = -76 dBm or 25 pW
PN  k T0 B F , W
Find PN
Solve in dB
PN(dBm) = kT0(dBm) + B(dB) + F(dB)
kT0(dBm) = -174
B(dB) = 80
PN(dBm) = -91 dBm or 0.8 pW
Find SNR
F(dB) = 3
SNR = – 76 – (– 91) = 15 dB or 31
15
Radar range equation example
Several options are available to improve the SNR.
Increase the transmitter power, Pt
Changing Pt from 100 kW to 200 kW improves the SNR by 3 dB
Increase the antenna aperture area, A, and gain, G
Changing A from 1 m2 to 2 m2 improves the SNR by 6 dB
Decrease the range, R, to the target
Changing R from 20 km to 10 km improves the SNR by 12 dB
Decrease the receiver noise figure, F
Changing F from 2 to 1 improves the SNR by 3 dB
Decrease the receiver bandwidth, B
Changing B from 100 MHz to 50 MHz improves the SNR by 3 dB
only if the received signal power remains constant
Change the operating frequency, f, and wavelength, 
Changing f from 9.5 GHz to 4.75 GHz degrades the SNR by 6 dB
Changing f from 9.5 GHz to 19 GHz improves SNR by 6 dB
16
Range resolution
The radar’s ability to discriminate between targets at different
ranges, its range resolution, rR or r or r, is inversely related
to the signal bandwidth, B.
c
rR 
, m
2B
where c is the speed of light in the medium.
The bandwidth of the received signal should match the
bandwidth of the transmitted signal.
A receiver bandwidth wider than the incoming signal bandwidth permits
additional noise with no additional signal, and SNR is reduced.
A receiver bandwidth narrower than the incoming signal bandwidth
reduces the noise and signal equally, and the radar’s range resolution
is reduced.
Therefore to achieve an rR of 1.5 m in free space requires a
100-MHz bandwidth in both the transmitted waveform and the
receiver bandwidth.
17
Velocity resolution
The signal from a target may be written as
Et   E 0 e jc t  2 k R 
and the relative phase of the received signal, f
f   2 k R  2
2R
, rad

A target moving relative to the radar produces a changing phase
(i.e., a frequency shift) known as the Doppler frequency, fD
1 df
2 
2 vr
fD 
 R
, Hz
2  dt


where vr is the radial component of the relative velocity.
The Doppler frequency can be positive or negative with a
positive shift corresponding to target moving toward the radar.
18
Velocity resolution
The received signal frequency will be
f  f c  f D  f c  2 R 
Example
Consider a police radar with a operating frequency, fo, of 10 GHz.
( = 0.03 m)
It observes an approaching car traveling at 70 mph (31.3 m/s) down the
highway. (v = -31.3 m/s)
The frequency of the received signal will be
fo – 2v/ = fo + 2.086 kHz or 10,000,002,086 Hz
Another car is moving away down the highway traveling at 55 mph
(+24.6 m/s). The frequency of the received signal will be
fo – 2v/ = fo – 1.64 kHz or 9,999,998,360 Hz
19
Velocity resolution
Given the position, P, and velocity, u, both the radar and the
target, the resulting Doppler frequency can be determined
uRadar
Radar path
uTarget
R
PTarget
PRadar
Target path
Instantaneous position and velocity
u
uTangential
u
=
q
^
^
uRadial = u  R
R (unit vector)
Radial velocity component
uRadar
uTarget
u = uRadar - uTarget
Relative velocity, u
^
uR = u cos(q)
fD = 2 u cos(q) / 
The ability to resolve targets based on their Doppler shifts
depends on the processed bandwidth, B, that is inversely
related to the observation (or integration) time, T
B  f D  1 T , Hz
20
Radar equation for extended targets
The preceding development considered point target with a
simple RCS, .
The point-target case enables simplifying assumptions in
the development.
Gain and range are treated as constants
Now consider the case of extended targets
including surfaces and volumes.
The backscattering characteristics of
a surface are represented by the
scattering coefficient, ,
   A
where A is the illuminated area.
q, f; p0 , ps  , unitless
21
Radar equation for extended targets
For an extended target there are multiple independent,
randomly located scatterers that each contribute to the
overall backscattered signal.
While the amplitude of the scatterers may be comparable,
the received phase of these scatterers are strongly
dependent on the observation geometry and the
observation wavelength (frequency).
Slight changes in observation geometry
or wavelength will produce a different
interference of the signals from these
scatterers.
22
Radar equation for extended targets
To analyze signal characteristics we first make some
simplifying assumptions
many point scatterers
randomly located
no single scatterer dominates the return
The received signal (E field) is the summation of the
individual fields from each scatterer
N 
N

E r   E r i   E r i e j fi e  j 2 k R i , V / m
where
i 1
i 1
fi is the phase associated with scatterer i
Ri is the exact distance from the radar to scatterer i
Since the scatterers are randomly located, the 2kRi term
represents a random phase thus producing noise-like
characteristics.
23
Radar equation for extended targets
As with noise, we can treat this as an incoherent process
and therefore we will focus on the average received power,
Pr
N
Pr   Pr i , W
i 1
where Pri is the average power from each scatterer, or
2 Pt N G i2 i
Pr 
4
R
4  3 
i 1
i
where i is the RCS of each individual scatterer.
In many cases Gi and Ri will be constant over the
illuminated area resulting in
2 G 2 Pt
Pr 
4  3 R 4
N

i 1
i
24
Radar equation for extended targets
The area of illumination to be used in the analysis is
dependent on the system characteristics.
Different illumination areas result depending on whether
the system is beam limited, pulse (or range) limited,
Doppler (or speed) limited, or a combination of these.
25
Radar equation for extended targets
26
Radar equation for extended targets
For homogeneous extended area targets (e.g., grass, bare soil,
forest, water, sand, snow, etc.)   constant (though still dependent on q,
f, and polarization).
Substituting this relationship leads to
Pr 
2 Pt G 2  A
4  3 R 4
where A is determined by the system’s spatial resolution.
The scattering coefficient, , contains target information.
Soil moisture
Surface wind speed and direction over water
Ground surface roughness
Water equivalent content of a snowpack
Therefore the accuracy and precision of  measurements
are important.
27
Accuracy and precision
As we saw earlier with radiometers, measurement accuracy
and precision are essential for effective remote sensing
applications.
In the context of measuring the target’s backscattering
coefficient, , accuracy will be achieved through calibration
and measurement uncertainty will determine the precision.
An understanding of the factors affecting measurement
uncertainty is required before steps to reduce the uncertainty
can be taken.
Assuming an acceptable signal-to-noise ratio is achieved
(and sources of interference and clutter have been reduced
to acceptable levels) the primary factor affecting uncertainty
in  measurement is signal fading.
28
Signal fading
For 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 s separated by
a distance d observed at a range Ro.
29
Signal fading
As the observation point moves along the x direction, the
observation angle q will change the interference of the
signals from the two targets.
The received voltage, V, at the radar receiver is
V  V0 e  j 2 k R a  V0 e  j 2 k R b
where
d
d
sin q , R b  R 0  sin q
2
2
 2d

V  2 V0 cos 
sin q 
 

Ra  R0 
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 .
Note: Same analysis used
for antenna arrays.
30
Fading statistics
Consider the case of Ns independent scatterers (Ns is large)
where the voltage due to each scatterer is Vi e jf
The vector sum of the
voltage terms from each scatterer is
N
i
V   Vi e jfi  Ve e jf
s
i 1
where Ve and f are the envelope voltage
and phase.
It is assumed that each voltage term,
Vi and fi are independent random variables and that fi is
uniformly distributed.
The magnitude component Vi can be decomposed into
orthogonal components, Vx and Vy
Vx  Vi cos fi and Vy  Vi sin fi
where Vx and Vy are normally distributed.
31
Fading statistics
The 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
 Ve Ve2
e

pVe    2  2

 0,
2 2
, Ve  0
Ve  0
where 2 is the variance
of the input signal
32
Fading statistics
(linear detection)
For a Rayleigh distribution
the mean is
Ve    2
the variance is
Ve2  2  2
The fluctuation about the mean
is Vac which has a variance of
2
ac
V
 V  Ve
2
e
2
 2

  2     0.429  2
2

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.
Ve
2
Vac2  3.66 or 5.6 dB
33
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
1 N
VL   Vei
N i 1
where
N is the number of independent samples
Ve is the envelope voltage sample
34
Fading statistics (linear detection)
The mean value, VL, is unaffected by the averaging process
VL    2  Ve
However the magnitude of the fluctuations are reduced
Vac2  0.429  2 N
And the effective SNR due
to fading improves as N
As more Rayleigh distributed
samples are averaged
the distribution begins to
resemble a normal
or Gaussian distribution.
35
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
 1 Vs
e

pVs    2  2

0 ,
2 2
, Vs  0
Vs  0
Again the mean value is found
where 2 is the variance
of the input signal
Vs  Ve2  2  2
2
2
and the variance is found Vsac  Vs  Vs
2
 Vs
2
(note that Vs2  2 Vs )
2
Again for a single sample measurement yields a poor
estimate of the mean.
2
2
Vs
Vsac
 1 or 0 dB
36
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
1 N
VL   Vsi
N i 1
where
N is the number of independent samples
Vs is the envelope-squared voltage sample
37
Fading statistics (square-law detection)
The mean value, VL, is unaffected by the averaging process
VL  2 2
However the magnitude of the fluctuations are reduced
2
Vsac
 Vs
2
N
And the effective SNR due
to fading improves as 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.
38
Independent samples
Fading 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 samples
change the observation geometry
change the observation frequency (more bandwidth)
Both methods produce a change in f 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.
39
Independent samples
In the range dimension, the number of independent
samples (NS) is the ratio of the range of the illuminated
scene (R) to the range resolution (rR)
NS  R rR
40
Independent samples
When 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
ND  f D T
The total number of independent samples is
N  NS N D
In both cases (range or Doppler) the result is that to reduce
the effects of fading, the resolution is degraded.
41
Independent samples
N=1
N = 10
N = 50
N = 250
42
Spatial discrimination
Consider an airborne radar system flying at a constant speed
along a straight and level trajectory as it views the surface
beneath.
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, vt, h), Target position = (xo, yo, 0), Range to target, R(t)
R t  
0  x o 2  v  t  yo 2  h  02
R 0  x o2  yo2  h 2
v v  t  yo 
dR 
 R t  
2
2
dt
x o  v  t  yo   h 2
R 0  
 yo v
x o2  y o2  h 2
2 yo v
2
f D   R 0 

 x o2  y o2  h 2
43
Example radar data
icebergs in open water
44
Spatial discrimination
Now 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.
45
Spatial discrimination
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
46
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, rR, is related to signal bandwidth, B
Two targets at nearly
the same range
Short pulse  higher bandwidth
Long pulse  lower bandwidth
47
Spatial discrimination
48
Spatial discrimination
Factors complicating target resolution include differing signal strength
(RCS), phase differences between targets, noise, and fading effects.
49
Spatial discrimination
The ability to resolve targets is somewhat subjective.
In microwave remote sensing a more objective definition of
resolution is: the distance (angle, range, speed) between
the half-peak-power response.
50
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) resolution
Various combinations of resolution can be used to
discriminate targets
51
Spatial discrimination
Ra nge S phe re
D opple r C one
Ba se line
Ve ctor
Aircra ft
Position
Ve locity
Ve ctor
Pha se C one
S ca tte re r is a t inte rse ction of Ra nge
S phe re , D opple r C one a nd Pha se
C one
52
Range resolution
Short pulse radar
The received echo, E(t) is
Et   pt St 
where

T= 2R/c
Tx

Rx
T
p(t) is the pulse shape
point target echo
S(t) is the target impulse response
 denotes convolution
To resolve two closely spaced targets, rR
2 rR

c
c
or rR 
2
Example
rR = 1 m    6.7 ns
rR = 1 ft    2 ns
53
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


E   Pt t  dt
0
Pt
Therefore for a fixed transmit power, Pt, (e.g., 100 W),
reducing the pulse duration, , reduces the energy E.
Pt = 100 W,  = 100 ns  rR = 50 ft, E = 10 J
Pt = 100 W,  = 2 ns  rR = 1 ft, E = 0.2 J
Consequently, to keep E constant, as  is reduced, Pt must
increase.
54
Range resolution
55
PRF and ambiguous ranges
Alternatively, a series of pulses are used to illuminate the
target and the pulse repetition frequency (PRF) is another
key radar parameter.
Tx
PRF  1 Tp , Hz
pulse period
Tp
So by increasing the PRF (i.e., reducing Tp) more pulses
can be used to illuminate the target in a given time interval
(thus overcoming the energy reduction associated with
shorter pulses).
However a new problem emerges, range ambiguity.
An ambiguous range implies uncertainty about which
transmit pulse the incoming target range is resulting from.
Uniquely identifying each pulse by “coding” is possible but adds
additional complexity and challenges.
56
PRF and ambiguous ranges
57
PRF and ambiguous ranges
Time domain
58
PRF and ambiguous ranges
The maximum unambiguous range, Ru is
R u  c Tp 2 , m
c
PRFmax 
, R u is the unambiguous range
2 Ru
Examples
PRF = 1 kHz, Tp = 1 ms  Ru = 150 km
PRF = 20 kHz, Tp = 50 s  Ru = 7.5 km
Combining received signal energy from multiple
consecutive transmitted pulses requires additional receiver
complexity and imposes new requirements on the
transmitter (i.e., coherence). But it can be done.
More on PRFs later.
59
PRF and ambiguous ranges
60
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
61
FM-CW radar
Linear FM sweep
Bandwidth: B
Repetition period: TR= 1/fm
Round-trip time to target: T = 2R/c
fR = Tx signal frequency – Rx signal frequency
f R 
B
TR 2
T
4BR 4BR

f m , Hz
c TR
c
If 2fm is the frequency resolution, then the range resolution rR is rR  c 2 B , m
The maximum unambiguous range, Ru is R u  c TR 2 , m
2B
62
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.
63
Blending the ideas of
pulsed radar with linear
frequency modulation
results in a chirp (or linear
FM) radar.
Chirp 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
64
Chirp radar
Linear frequency modulation (chirp) waveform
 

s( t )  A cos 2  f C t  0.5 k t 2  fC

for 0  t  
fC is the starting frequency (Hz)
k is the chirp rate (Hz/s)
fC is the starting phase (rad)
B is the chirp bandwidth, B = k
65
Stretch chirp processing
LO
66
Challenges with stretch processing
Low-pass
filter
Received signal
(analog)
Reference
chirp
Echos from targets at various
ranges have different start
times with constant pulse
duration. Makes signal
processing
more difficult.
A/D
converter
Digitized signal
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.
LO
B
Tx
frequency
frequency
near
Rx
far
near
time
far
time
67
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)
Received signal
(after digitization)
FFT
IFFT
Correlated signal
Freq-domain
reference chirp
68
Signal correlation examples
Input waveform #1
High-SNR gated sinusoid, no delay
Input waveform #2
High-SNR gated sinusoid, ~800 count delay
69
Signal correlation examples
Input waveform #1
High-SNR gated sinusoid, no delay
Input waveform #2
Low-SNR gated sinusoid, ~800 count delay
70
Signal correlation examples
Input waveform #1
High-SNR gated chirp, no delay
Input waveform #2
Low-SNR gated chirp, ~800 count delay
71
Analog chirp signal processing
chirp generation and compression
Dispersive
delay line is a
SAW device
SAW: surface
acoustic wave
72
Chirp pulse compression and sidelobes
Peak sidelobe level can be controlled by
introducing a weighting function -however this has side effects.
73
Window functions and their effects
Time sidelobes are an 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
74
Window functions
Basic function:
a and b are the –6-dB and - normalized bandwidths
75
Window functions
76
Detailed example of chirp pulse compression
received signal
 

s( t )  a cos 2  f C t  0.5 k t 2  fC

dechirp analysis
 


 

s( t ) s( t  )  a cos 2  f C t  0.5 k t 2  fC a cos 2  f C ( t  )  0.5 k ( t  ) 2  fC
which simplifies to
a2
s( t ) s( t  ) 
2
sinusoidal term

cos (2  f C   2  k t    k  2 )

2
2
  cos 2  k t  2 f C t  k  t  0.5 k   f C   2 fC
quadratic
frequency
dependence

 

linear
frequency
dependence




chirp-squared
term
phase terms
after lowpass filtering to reject harmonics
a2
q( t ) 
cos 2  f C   k  t  0.5 k  2 
2
77
Pulse compression
Chirp waveforms represent one approach for pulse
compression.
Radar range resolution depends on the bandwidth of the
received signal.
c
c
rR 

2 2B
c = speed of light, rR = range resolution,
 = pulse duration, B = signal bandwidth
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
78
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, …
79
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, rR
Example:
Desired resolution, rR = 15 cm (~ 6”)
Required bandwidth, B = 1 GHz (109 Hz)
Required pulse energy, E = 1 mJ
E(J) = P(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
80
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
P1
1
Goal: P1 1  P2 2
P2
2
time
81
Pulse coding
Long duration pulse is coded to have desired bandwidth.
Various ways to code pulse.

Linear frequency modulation (chirp)
 

s( t )  A cos 2  f C t  0.5 k t 2  fC
for 0  t  
fC is the starting frequency (Hz)
k is the chirp rate (Hz/s)
B = k = 1 GHz

1 ns
Phase code short segments
Each segment duration = 1 ns
Choice driven largely by required complexity of receiver
electronics
82
Phase coded waveform
83
Analog signal processing
84
Binary phase coding
85
Receiver signal processing
phase-coded pulse compression
time
Correlation process may be performed in analog or digital
domain. A disadvantage of this approach is that the data
acquisition system (A/D converter) must operate at the full
system bandwidth (e.g., 1 GHz in our example).
PSL: peak sidelobe level (refers to time sidelobes)
86
Binary phase coding
Various coding schemes
Barker codes
Low sidelobe level
Limited to modest lengths
Golay (complementary) codes
Code pairs – sidelobes cancel
Psuedo-random / maximal length sequential codes
Easily generated
Very long codes available
Doppler frequency shifts and imperfect modulation
(amplitude and phase) degrade performance
87
Pulse compression effects on SNR and blind range
SNR improvement due to pulse compression: B
SNR compress
Pt G t G r 2

B
3
4
4  R k T B F
Case 1: Pt = 1 MW,  = 1 ns, B = 1 GHz, E = 1 mJ
For a given R, Gt, Gr, , : SNRvideo = 10 dB
B = 1 or 0 dB
SNRcompress = SNRvideo = 10 dB
Blind range = c/2 = 0.15 m
Case 2: Pt = 10 W,  = 0.1 ms, B = 1 GHz, E = 1 mJ
For a same R, Gt, Gr, , : SNRvideo = -40 dB
B = 100,000 or 50 dB
SNRcompress = 10 dB
Blind range = c/2 = 15 km
88
Pulse compression effects on SNR and blind range
Okay, so that is what the math tells us, but what is really
going on?
Case 1: Pt = 1 MW,  = 1 ns, B = 1 GHz, E = 1 mJ
Pulse duration is 1 ns  B = 1 GHz
Find noise power using F = 4 dB and B = 1 GHz (90 dB)
PN = kT0BF = -174 + 90 + 4 dBm = -80 dBm
Case 2: Pt = 10 W,  = 0.1 ms, B = 1 GHz, E = 1 mJ
Pulse duration is 100 s but B = 1 GHz
Range is mapped into frequency, so my ability to resolve frequencies is
related to my range resolution
With 100 s echo duration, the frequency resolution is 10 kHz
Spectral analysis of the echo from a point target with 10-kHz frequency
resolution maximizes the SNR
Again find noise power using F = 4 dB but now B = 10 kHz (40 dB)
PN = kT0BF = -174 + 40 + 4 dBm = -130 dBm
89
Pulse compression effects on SNR and blind range
Okay, but what about the 15-km blind range?
The blind range issue concerns adverse impacts on radar
performance that result from transmissions while
receiving.
Issues include:
•
•
Dynamic range limitations
Saturation in the receiver chain
It is possible (though perhaps not trivial) to accommodate
transmission while receiving thus avoiding the blind range
constraint.
90
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 transmitter and receiver complexity
must contend with time sidelobes
increased blind range
The advantages generally outweigh the disadvantages so
pulse compression is used widely.
91
Short pulse vs. pulse compression
A comparison of short pulse (impulse) systems with
compressed pulse systems reveals several performance
benefits for the compressed pulse approach, including:
•
•
•
Noise rejection
Pulse energy
Electromagnetic interference (EMI)
The examples below were developed to compare a
compressed-pulse ground-penetrating radar (GPR) system
with an conventional impulse GPR.
Impulse GPR systems typically involve short-duration pulses
whose bandwidth ~ center frequency.
92
Short pulse vs. pulse compression
Noise rejection
Received broadband noise is dependent on bandwidth as noise is
present over the entire spectrum. The bandwidth of the compressed
pulse waveform is the inverse of the pulse duration, e.g., 100 s
yields 10-kHz bandwidth; the bandwidth of a conventional impulse
radar is the signal center frequency (e.g., 3.3 GHz). The noise
rejection advantage of the pulsed-chirp system is the ratio of these
bandwidths, 3.3 GHz/10 kHz = 3.3  105 or 55 dB.
Typical impulse radars have a transmit waveform bandwidth that is the
reciprocal of the impulse duration. The receiver bandwidth should
match the transmit waveform bandwidth. Therefore, a system with a
transmit pulse duration of about 300 ps will produce a waveform with
about 3.3 GHz of bandwidth (extending from 1.6 GHz to 4.9 GHz) and
the receiver bandwidth should likewise be 3.3 GHz and this figure is
used to compute received noise power.
93
Receive
Antenna
Short pulse vs. pulse compression
Noise rejection
Impulse
Signal Power (dB)
Reflectivity (dB)
Depth (m)
Weak Target Echo
Depth (m)
Depth (m)
Surface Echo
Illustration of theStrong
simple
operating
geometry showing response of impulse
and compressed pulse GPRs.
Compressed-Pulse
Signal Power (dB)
Noise
Signal power versus depth from surface and
shallow target for both impulse and
compressed-pulse systems.
Transmit
Antenna
Radar
Electronics
Receive
Antenna
Depth (m)
Strong Surface Echo
Compressed-Pulse
Signal Power (dB)
Compressed-Pulse
Signal Power (dB)
Depth (m)
Depth (m)
Impulse
Signal Power (dB)
Reflectivity (dB)
Depth (m)
Depth (m)
Depth (m)
Weak
Weak Target
Target Echo
Echo
Impulse
Signal Power (dB)
Reflectivity (dB)
Noise
Noise
Simple two-antenna geometry indicating echoes
from both surface and shallow buried target.
Signal power versus depth of surface and
deeper target, signal power from impulse and
compressed-pulse systems.
94
Short pulse vs. pulse compression
Pulse energy
The pulse energy of the pulsed-chirp system is the product of the
pulse duration (100 s) and the peak output power (1 W) yielding a
pulse energy of 10–4 J; the pulse energy for the impulse system is
the product of 300 ps and 1 kW or 3  10–7 J. Thus the pulse energy
of the compressed pulse system is more than 330 times (25 dB)
greater than that of the impulse system.
95
Short pulse vs. pulse compression
Electromagnetic interference (EMI)
The spectral energy content of the GPR waveform determines its
potential for adversely impacting susceptible electronic systems
nearby (e.g., radios, TV receivers, cell phones, etc.), termed
electromagnetic interference or EMI.
With digitally produced waveforms, the compressed pulse GPR can
readily modify its spectral content thereby avoiding sensitive
frequency bands to mitigate its impact on susceptible systems often
with minimal impact on GPR performance.
By their very nature impulse systems produce energy bursts with
broad spectral extent, thus producing significant EMI challenges.
96