Lecture on Radar measurement

1. 1
Radar Measurements II
Chris Allen (callen@eecs.ku.edu)
Course website URL
people.eecs.ku.edu/~callen/725/EECS725.htm

2. 2
Ground imaging radar
In a real-aperture system images of radar backscattering are mapped
into slant range, R, and along-track position.
The along-track resolution, y, is provided solely by the antenna.
Consequently the along-track resolution degrades as the distance
increases. (Antenna length, ℓ, directly affects along-track resolution.)
Cross-track ground range resolution, x, is incidence angle dependent
]
m
[
R
y az



]
m
[
sin
2
c
x
p



 where p is the compressed
pulse duration
y
x
x
along-track
direction
cross-track
direction
cross-track
direction
ground range
ground range
R

3. 3
Slant range vs. ground range
Cross-track resolution in
the ground plane (x) is the
projection of the range
resolution from the slant plane
onto 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

4. 4
Real-aperture, side-looking airborne
radar (SLAR) image of Puerto Rico
Mosaicked image composed of 48-km
(30-mile) wide strip map images
Radar parameters
modified Motorola APS-94D system
X-band (3-cm wavelength)
altitude: 8,230 m (above mean sea level)
azimuth resolution: 10 to 15 m
~ 40 x 100 miles
Digital Elevation Model of Puerto Rico

5. 5
Another SLAR image
SLAR operator’s console
5-m (18 feet) SLAR antenna
mounted beneath fuselage
X-band system
Civilian uses include:
• charting the extent of flood waters,
• mapping, locating lost vessels,
• charting ice floes,
• locating archaeological sites,
• seaborne pollution spill tracking,
• various geophysical surveying chores.
SLAR image of river valley

6. 6
Limitations of real-aperture systems
With real-aperture radar systems the azimuth resolution depends on the
antenna’s azimuth beamwidth (az) and the slant range, R
Consider the AN/APS 94 (X-band, 5-m antenna length) az = 6 mrad or 0.34
For a pressurized jet aircraft
altitude of 30 kft (9.1 km) and an incidence angle of 30 for a slant range of 10.5 km
R = h/cos  = 9100 / cos 30 = 10500 m
y = 63 m (coarse but useable)
Now consider a spaceborne X-band radar (15-m antenna length) az = 2 mrad or 0.11
500-km altitude and a 30 incidence angle (27.6 look angle) for a 570.5-km slant range
y = 1.1 km (very coarse)
The azimuth resolution of real-aperture radar systems is very coarse for
long-range applications
]
m
[
R
y az




7. 7
Radar equation for extended targets
Since A = x y we have
Substituting these terms into the range equation leads to
note the range dependence is now R-3 whereas for a point target it is R-4
This is due to the fact that a larger area is illuminated as R increases.
   
R
sin
2
c
R
4
G
P
R
4
A
G
P
P az
p
4
3
2
t
2
4
3
2
t
2
r 













 
R
sin
2
c
A az
p













  3
3
p
az
2
t
2
r
R
4
sin
2
c
G
P
P









8. 8
SNR and the radar equation
Now to consider the SNR we must use the noise power
PN = kT0BF
Assuming that terrain backscatter, , is the desired signal (and not
simply clutter), we get
Solving for the maximum range, Rmax, that will yield the minimum
acceptable SNR, SNRmin, gives
  F
B
T
k
R
4
sin
2
c
G
P
SNR
0
3
3
p
az
2
t
2








 
3
0
min
3
p
az
2
t
2
max
F
B
T
k
SNR
4
sin
2
c
G
P
R









9. 9
Radar altimetry
Altimeter – a nadir-looking radar that precisely measures the range to
the terrain below. The terrain height is derived from the radar’s
position.
c p/ 2
H

10. 10
Altimeter data
Radar map of the contiguous 48 states.

11. 11
Altimeter

12. 12
TOPEX/Poseidon
A - MMS multimission platform
B - Instrument module
1/Data transmission TDRS
2/Global positioning system antenna
3/Solar array
4/Microwave radiometer
5/Altimeter antenna
6/Laser retroreflectors
7/DORIS antenna
Dual frequency altimeter (5.3 and 13.6 GHz)
operating simultaneously.
Three-channel radiometer (18, 21, 37 GHz)
provides water vapor data beneath
satellite (removes ~ 1 cm uncertainty).
2-cm altimeter accuracy
100 million echoes each day
10 MB of data collected per day
French-American system
Launched in 1992
10-day revisit period (66 orbit inclination)
Altitude: 1336 km
Mass: ~ 2400 kg

13. 13
Altimeter data
Global topographic map of ocean surface produced with satellite altimeter.

14. 14
Altimeter data

15. 15
Mars Orbiter Laser Altimeter (MOLA)
Laser altimeter (not RF or microwave)
Launched November 7, 1996
Entered Mars orbit on September 12, 1997
Selected specifications
282-THz operating frequency (1064-nm wavelength)
10-Hz PRF
48-mJ pulse energy
50-cm diameter antenna aperture (mirror)
130-m spot diameter on surface
37.5-cm range measurement resolution

16. 16
Mars Orbiter Laser
Altimeter (MOLA)

17. 17
Radar altimetry
The echo shape, E(t), of altimetry data is affected by the radar’s point
target response, p(t), it’s flat surface response, S(t), which includes gain
and backscatter variations with incidence angle, and the rms surface
height variations, h(t).
Analysis of the echo shape, E(t), can provide insight
regarding the surface. From the echo’s leading we learn
about the surface height variations, h(t), and from its
trailing edge we learn about the backscattering
characteristics, ().

18. 18
Signal integration
Combining consecutive echo signals can improve the signal-to-noise
ratio (SNR) and hence improve the measurement accuracy, or it can
improve our estimate of the SNR and hence improve our measurement
precision.
Two basic schemes for combining echo signals in the slow-time
dimension will be addressed.
Coherent integration
Incoherent integration
Coherent integration (also called presumming or stacking)
involves working with signals containing magnitude and phase
information (complex or I & Q values, voltages, or simply signals that include
both positive and negative excursions)
Incoherent integration involves working with signals that have been
detected (absolute values, squared values, power, values that are always
positive)
Both schemes involve operations on values expressed in linear
formats and not expressed in dB.

19. 19
Coherent integration
Coherent integration involves the summation or averaging
of multiple echo signal records (Ncoh) along the slow-time
dimension.
Coherent integration is commonly performed in real time during radar
operation.
+ + +…+ =
Fast
time
Pulse
echo
#1
Pulse
echo
#2
Pulse
echo
#3
Pulse
echo
#Ncoh
Coherently
integrated
record
1 1 1 1 Ncoh
Coherent integration affects
multiple radar parameters.
It reduces the data volume
(or data rate) by Ncoh.
It improves the SNR of
in-band signals by Ncoh.
It acts as a low-pass filter
attenuating out-of-band
signals.

20. 20
Coherent integration

21. 21
Coherent integration

22. 22
Coherent integration
Signal power found using
where vs is the signal voltage vector
Noise power found using
where vs+n is the signal + noise voltage vector
SNR is then
note that [std_dev]2 is variance
 2
s
s )
v
(
dev
_
std
P 
  s
2
n
s
n P
)
v
(
dev
_
std
P 
 
n
s P
P
SNR 

23. 23
Coherent integration
Summing Ncoh noisy echoes has the following effect
Signal amplitude is increased by Ncoh
Signal power is increased by (Ncoh)2
Noise power is increased by Ncoh
Therefore the SNR is increased by Ncoh
Noise is uncorrelated and therefore only the noise power adds
whereas the signal is correlated and therefore it’s amplitude adds.
This is the power behind coherent integration.
Averaging Ncoh noisy echoes has the following effect
Signal amplitude is unchanged
Signal power is unchanged
Noise power is decreased by Ncoh
Therefore the SNR is increased by Ncoh
Noise is uncorrelated and has a zero mean value.
Averaging Ncoh samples of random noise reduces its variance by
Ncoh and hence the noise power is reduced.

24. 24
Coherent integration
Underlying assumptions essential to benefit from coherent
integration.
Noise must be uncorrelated pulse to pulse.
Coherent noise (such as interference) does not satisfy this requirement.
Signal must be correlated pulse to pulse.
That is, for maximum benefit the echo signal’s phase should vary by less
than 90 over the entire integration interval.
For a stationary target relative to the radar, this is readily achieved.
For a target moving relative to the radar, the maximum integration interval
is limited by the Doppler frequency. This requires a PRF much higher than
PRFmin, that is the Doppler signal is significantly oversampled.
Ncoh = 10
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
time (ms)
Signal
(V)
400-Hz 10-kHz samples
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
time (ms)
Signal
(V)
400-Hz 1-kHz samples

25. 25
Coherent integration
Coherent integration filters data in slow-time dimension.
Filter characterized by its transfer function.

26. 26
Coherent integration
Impact on SNR
Coherent integration improves the SNR by Ncoh.
For point targets
For extended targets
  vid
coh
0
3
3
coh
p
az
2
2
t
coh SNR
N
F
B
T
k
R
4
sin
2
N
c
G
P
SNR 








  vid
coh
0
4
3
coh
2
2
t
coh SNR
N
F
B
T
k
R
4
N
G
P
SNR 




SNRcoh
SNRvid

27. 27
Coherent integration
So what is going on to improve the SNR ?
Is the receiver bandwidth being reduced ? No
By coherently adding echo signal energy from consecutive pulses we
are effectively increasing the illumination energy.
This may be thought of as increasing the transmitted power, Pt.
Again returning to the ACR 430 airfield-control radar example
The transmitter has peak output power, Pt, of 55 kW and a pulse duration,
, of 100 ns, (i.e., B = 10 MHz).
Hence the transmit pulse energy is Pt  = 5.5 mJ
Coherently integrating echoes from 10 pulses (Ncoh = 10) produces an SNR
equivalent to the case where Pt is 10 times greater, i.e., 550 kW and the
total illumination energy is 55 mJ.
Alternatively, coherent integration permits a reduction of the transmit
pulse power, Pt, equivalent to the Ncoh while retaining a constant SNR.
Txn
S
n = 1
Ncoh
Pt

 Tx
NcohPt


28. 28
Incoherent integration
Incoherent detection is similar to coherent detection in that it involves
the summation or averaging of multiple echo signal records (Ninc) along
the slow-time dimension.
Prior to integration the signals are detected (absolute values, squared
values, power, values that are always positive).
Consequently the statistics describing the process is significantly more
complicated (and beyond the scope of this class).
The improvement in signal-to-noise ratio due to incoherent integration
varies between  Ninc and Ninc, depending on a variety of parameters
including detection process and Ninc.
How it works: For a stable target signal, the signal power is fairly
constant while the noise power fluctuates. Therefore integration
consistently builds up the signal return whereas the variability of the
noise power is reduced. Consequently the detectability of the signal is
improved.

29. 29
Incoherent integration
Example using square-law detection

30. 30
2200
2300
2400
2500
2600
2700
2800
2900
3000
-2000 -1500 -1000 -500 0 500 1000 1500 2000
X (m)
Range
(m)
5,280,000
5,480,000
5,680,000
5,880,000
6,080,000
6,280,000
6,480,000
6,680,000
6,880,000
7,080,000
Signal
phase
(deg)
More on coherent integration
Clearly coherent integration offers tremendous SNR improvement.
To realize the full benefits of coherent integration the underlying
assumptions must be satisfied
Noise must be uncorrelated pulse to pulse
Signal phase varies less than 90 over integration interval
The second assumption limits the integration interval for cases
involving targets moving relative to the radar.
Coherent integration can be used if phase variation is removed first.
Processes involved include range migration and focusing.
For a 2.25-kHz PRF, Ncoh = 100,000 or 50 dB of SNR improvement
[deg]
R
2
360



v
x
-y
z
H
flight path
ground track
target
offset
(0,0,0)
R
1 km
 = 30 cm
90 m/s

31. 31
Tracking radar
In this application the radar continuously monitors the
target’s range and angular position (angle-of-arrival – AOA).
Tracking requires fine angular position knowledge, unlike the search
radar application where the angular resolution was el and az.
Improved angle information requires additional information from the
antenna.
Monopulse radar
With monopulse radar, angular position measurements are
accomplished with a single pulse (hence the name monopulse).
This system relies on a more complicated antenna system that
employs multiple radiation patterns simultaneously.
There are two common monopulse varieties
• amplitude-comparison monopulse
• phase-comparison monopulse
Each variety requires two (or more) antennas and thus two (or more)
receive channels

32. 32
Amplitude-comparison monopulse
This concept involves two co-located antennas with slightly shifted
pointing directions.
The signals output from the two antennas are combined in two different
processes
S (sum) output is formed by summing the two antenna signals
 (difference) output is formed by subtracting signals from one another
These combinations of the antenna signals produce corresponding radiation
patterns (S and ) that have distinctly different characteristics
/S (computed in signal processor) provides an amplitude-independent
estimate of the variable related to the angle

33. 33
Phase-comparison monopulse
This concept involves two antennas separated by a small distance d
with parallel pointing directions.
The received signals are compared to produce a phase difference, ,
that yields angle-of-arrival information.
For small , sin   
]
rad
[
sin
d
2






]
rad
[
d
2
d
2














34. 34
Dual-axis monopulse
Both amplitude-comparison and phase-comparison
approaches provide angle-of-arrival estimates in one-axis.
For dual-axis angle-of-arrival estimation, duplicate monopulse
systems are required aligned on orthogonal axes.

35. 35
Dual-axis monopulse

36. 36
Monopulse
Conventional monopulse processing to obtain the angle-of-
arrival is valid for only one point target in the beam,
otherwise the angle estimation is corrupted.
Other more complex concepts exist for manipulating the
antenna’s spatial coverage.
These exploit the availability of signals from spatially diverse
antennas (phase centers).
Rather than combining these signals in the RF or analog domain,
these signals are preserved into the digital domain where various
antenna patterns can be realized via ‘digital beamforming.’

37. 37
Frequency agility
Frequency agility involves changing the radar’s operating
frequency on a pulse-to-pulse basis. (akin to frequency
hopping in some wireless communication schemes)
Advantages
Improved angle estimates (refer to text for details)
Reduced multipath effects
Less susceptibility to electronic countermeasures
Reduced probability detection, low probability of intercept (LPI)
Disadvantages
Scrambles the target phase information
Changing f changes 
To undo the effects of changes in f requires precise knowledge of R
Pulse-to-pulse frequency agility is typically not used in
coherent radar systems.
]
rad
[
c
f
R
4
R
2
2







38. 38
Pulse compression
Pulse compression is a very powerful concept or technique
permitting the transmission of long-duration pulses while
achieving fine range resolution.

39. 39
Pulse compression
Pulse compression is a very powerful concept or technique
permitting the transmission of long-duration pulses while
achieving fine range resolution.
Conventional wisdom says that to obtain fine range resolution, a short
pulse duration is needed.
However this limits the amount of energy (not power) illuminating the
target, 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 dt
t
P
E

Pt

40. 40
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, …

41. 41
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
P1
P2
2
2
2
1
1 P
P 


Goal:

42. 42
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
Solution: Transmit a long-duration pulse that has a
bandwidth corresponding to that of a short-duration pulse
c = speed of light, R = range resolution,
 = pulse duration, B = signal bandwidth
B
2
c
2
c
R 




43. 43
Pulse compression, the compromise
Transmitting a long-duration pulse with a wide bandwidth
requires modulation or coding 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)· (s)
Brute force approach
Raw pulse duration,  = 1 ns (10-9 s) Required transmitter power, Pt = 1 MW !
Pulse compression approach
Pulse duration,  = 0.1 ms (10-4 s) Required transmitter power, Pt = 10 W

44. 44
The long-duration pulse is coded to have desired bandwidth.
There are various ways to code pulse.
Phase code short segments
Each segment duration = 1 ns
Linear frequency modulation (chirp)
for 0  t  
fC is the starting frequency (Hz)
k is the chirp rate (Hz/s)
B = k = 1 GHz
Choice driven largely by required complexity of receiver electronics
Pulse coding
 
 
C
2
C t
k
5
.
0
t
f
2
cos
A
)
t
(
s 





1 ns

45. 45
Phase coded waveform

46. 46
Analog signal processing

47. 47
Binary phase coding

48. 48
Receiver signal processing
phase-coded pulse compression
Correlation process may be performed in the 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)
time

49. 49
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

50. 50
Chirp waveforms and FM-CW radar
To understand chirp waveforms and the associated signal processing,
it is useful to first introduce the FM-CW radar.
FM – frequency modulation
CW – continuous wave
This is not a pulsed radar, instead the transmitter operates continuously
requiring the receiver to operate during transmission.
Pulse radars are characterized by their duty factor, D
where  is the pulse duration and PRF is the pulse repetition frequency.
For pulsed radars D may range from 1% to 20%.
For CW radars D = 100%.
PRF
D 



51. 51
FM-CW radar
Simple FM-CW block diagram and associated signal
waveforms.
FM-CW radar block diagram

52. 52
FM-CW radar
Linear FM sweep
Bandwidth: B Repetition period: TR= 1/fm
Round-trip time to target: T = 2R/c
The beat frequency fb = fTx– fRx
The beat signal observation time is TR/2 providing a frequency resolution, f = 2 fm
Therefore the range resolution R = c/2B [m]
]
Hz
[
f
c
R
B
4
T
c
R
B
4
T
2
T
B
f m
R
R
b 


= k

53. 53
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.

54. 54
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
, Tx pulse duration

55. 55
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
 
 
C
2
C t
k
5
.
0
t
f
2
cos
A
)
t
(
s 





56. 56
Receiver signal processing
chirp generation and compression
Dispersive
delay line is a
SAW device
SAW: surface
acoustic wave

57. 57
Stretch chirp processing

58. 58
Challenges with stretch processing
time
Tx
B Rx
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 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.

59. 59
Pulse compression example
Key system parameters
Pt = 10 W,  = 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,  = 100 s
Frequency 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

60. 60
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 and Wr is the swath’s
slant range 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.

61. 61
Correlation processing of chirp signals
Avoids problems associated with stretch processing
Involves time-domain cross correlation of received signal with
reference signal. {Matlab command: [c,lag] = xcorr(a,b)}
Time-domain cross correlation can be a slow, compute-intensive
process.
Alternatively we can take 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

62. 62
Signal correlation examples
Input waveform #1
High-SNR gated sinusoid, no delay
Input waveform #2
High-SNR gated sinusoid, ~800 count delay

63. 63
Signal correlation examples
Input waveform #1
High-SNR gated sinusoid, no delay
Input waveform #2
Low-SNR gated sinusoid, ~800 count delay

64. 64
Signal correlation examples
Input waveform #1
High-SNR gated chirp, no delay
Input waveform #2
High-SNR gated chirp, ~800 count delay

65. 65
Signal correlation examples
Input waveform #1
High-SNR gated chirp, no delay
Input waveform #2
Low-SNR gated chirp, ~800 count delay

66. 66
Chirp pulse compression and time sidelobes
Peak sidelobe level can be controlled by
introducing a weighting function --
however this has side effects.

67. 67
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.
r is range resolution

68. 68
Why time sidelobes are a problem
Sidelobes from large-RCS targets with can obscure signals
from nearby smaller-RCS targets.
Related to pulse duration, , is the temporal extent of time sidelobes, 2.
Time sidelobe amplitude is related to the overall waveform shape.
fb = 2 k R/c
fb

69. 69
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

70. 70
Window functions
Basic function:
a and b are the –6-dB and - normalized bandwidths

71. 71
Window functions

72. 72
Detailed example of chirp pulse compression
 
  






 t
0
,
t
k
5
.
0
t
f
2
cos
a
)
t
(
s C
2
C
 
   
 
C
2
C
C
2
C )
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 











 
 























C
C
2
C
2
2
C
2
2
T
f
T
k
5
.
0
t
k
t
f
2
t
k
2
cos
)
T
k
T
t
k
2
T
f
2
(
cos
2
a
)
T
t
(
s
)
t
(
s
 
 
2
C
2
T
k
5
.
0
t
T
k
T
f
2
cos
2
a
)
t
(
q 



after lowpass filtering to reject harmonics
dechirp analysis
which simplifies to
received signal
quadratic
frequency
dependence
linear
frequency
dependence
phase terms
chirp-squared
term
sinusoidal term
sinusoidal
term

73. 73
Pulse compression effects on SNR and blind range
SNR improvement due to pulse compression is the
waveform’s time-bandwidth product: B (regardless of
pulse compression scheme used)
Case 1: Pt = 1 MW,  = 1 ns, B = 1 GHz, E = 1 mJ, R = 15 cm
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,  = 100 s, B = 1 GHz, E = 1 mJ , R = 15 cm
For the same R, Gt, Gr, , : SNRvideo = – 40 dB
B = 100,000 or 50 dB
SNRcompress = 10 dB
Blind range = c/2 = 15 km
 




 B
F
B
T
k
R
4
G
G
P
SNR 4
3
2
r
t
t
compress
(point target
range equation)

74. 74
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.

75. 75
Radar range equation (revisited)
We now integrate the signal-to-noise ratio improvement factors from
coherent and incoherent integration as well as pulse compression into
the radar range equation for point and distributed targets.
Point targets
Extended targets
    F
T
k
R
4
N
N
G
G
P
B
N
N
F
B
T
k
R
4
G
G
P
SNR 4
3
inc
coh
2
r
t
t
inc
coh
4
3
2
r
t
t










    F
B
T
k
R
4
sin
2
N
N
c
G
P
B
N
N
F
B
T
k
R
4
sin
2
c
G
P
SNR
0
3
3
inc
coh
az
2
t
2
inc
coh
0
3
3
p
az
2
t
2


















76. 76
Dynamic range example
The SNR improvements discussed (coherent and incoherent
integration, pulse compression) also expand the radar’s dynamic range.
In modern radars these SNR improvements occur in the digital domain.
Consequently the overall dynamic range is not limited by the ADC.
To illustrate this fact consider the following example.
A radar uses a Linear Technologies LT2255 ADC
Specs: 14-bit, 125 MS/s, 2-V full scale, 640-MHz analog bandwidth
It samples at 112 MHz (fs) a signal centered
at 195 MHz with 30 MHz of bandwidth.
At 200 MHz the ADC’s SNR is ~ 70 dB
(per the product specifications) indicating an
effective number of bits, ENOB = 11.7.
2 Vpp  10 dBm in a 50- system
To realize the SNR improvement offered
by coherent integration, the thermal noise
power must be 3 to 5 dB above the ADC’s
quantization noise floor.

77. 77
Dynamic range example
Radar center frequency is 195 MHz.
Radar bandwidth is 30 MHz.
Radar spectrum extends from 180 MHz to 210 MHz.
Sampling frequency is 112 MHz.
Satisfies the Nyquist-Shannon requirement since fs = 112 MHz > 60 MHz
Undersampling is used, therefore analysis is required to ensure signal is
centered within a Nyquist zone.
5th
Nyquist Zone
1st
Nyquist Zone 2nd
Nyquist Zone 3rd
Nyquist Zone 4th
Nyquist Zone
2 fS
180 190 200 210 220
160
90 100 110 120 130 140 150
80
30 40 50 60 70
20
10
0
180 to 210 MHz
10 µs
168
222
Frequency (MHz)
fS / 2 fS 3 fS / 2
170
112
56
224
0
DC
230 240 250 260 270 280
fs Available center frequencies (MHz) for a 30-MHz signal bandwidth w 40% guardbands
(MHz) 1st
Nyquist 2nd
Nyquist 3rd
Nyquist 4th
Nyquist 5th
Nyquist 6th
Nyquist 7th
Nyquist 8th
Nyquist 9th
Nyquist 10th
Nyquist 11th
Nyquist 12th Nyquist
108 27 81 135 189 243 297 351 405 459 513 567
109 27.25 81.75 136.25 190.75 245.25 299.75 354.25 408.75 463.25 517.75 572.25
110 27.5 82.5 137.5 192.5 247.5 302.5 357.5 412.5 467.5 522.5 577.5
111 27.75 83.25 138.75 194.25 249.75 305.25 360.75 416.25 471.75 527.25 582.75
112 28 84 140 196 252 308 364 420 476 532 588
113 28.25 84.75 141.25 197.75 254.25 310.75 367.25 423.75 480.25 536.75 593.25
114 28.5 85.5 142.5 199.5 256.5 313.5 370.5 427.5 484.5 541.5 598.5
115 28.75 86.25 143.75 201.25 258.75 316.25 373.75 431.25 488.75 546.25 603.75
116 29 87 145 203 261 319 377 435 493 551 609
117 29.25 87.75 146.25 204.75 263.25 321.75 380.25 438.75 497.25 555.75
118 29.5 88.5 147.5 206.5 265.5 324.5 383.5 442.5 501.5 560.5
119 29.75 89.25 148.75 208.25 267.75 327.25 386.75 446.25 505.75 565.25
120 30 90 150 210 270 330 390 450 510 570
121 30.25 90.75 151.25 211.75 272.25 332.75 393.25 453.75 514.25 574.75
122 30.5 91.5 152.5 213.5 274.5 335.5 396.5 457.5 518.5 579.5
123 30.75 92.25 153.75 215.25 276.75 338.25 399.75 461.25 522.75 584.25
124 31 93 155 217 279 341 403 465 527 589
125 31.25 93.75 156.25 218.75 281.25 343.75 406.25 468.75 531.25 593.75

78. 78
Dynamic range example
The radar system has a 10-kHz PRF, a 10-s  with 30-MHz bandwidth,
and performs 32 presums (coherent integrations) prior to data recording.
During post processing pulse compression is applied followed by an
additional 128 coherent integrations are performed (following phase
corrections or focusing).
These processing steps have the following effects
Signal Noise Dynamic
power power range
ADC 10 dBm -55 dBm 65 dB
presum: Ncoh = 32 30 dB 15 dB 15 dB
pulse compression, B = 300 25 dB 0 dB 25 dB
coherent integration: Ncoh = 128 42 dB 21 dB 21 dB
Overall 107 dBm -19 dBm 126 dB
Thus the radar system has an instantaneous dynamic range of 126 dB
despite the fact that the ADC has a 65-dB dynamic range.

79. LTC2255
ENOB
@
200
MHz:
11.7
bits
10 dBm
(FS: 2 V)
-58 dBm
(LSBeff: 400 μV)
A/D convert
12 effective bits
65 dB
12
Presum
N = 32
80 dB
17
Pulse compress
BT = 300
105 dB
21
Coherent integrate
NCOH = 128
126 dB
28
Thermal noise, -55 dBm →
FFFH
000H 00000H
1FFFFH
Thermal noise → Thermal noise →
000000H
← Thermal noise
Dynamic range:
Number of bits:
15 dB
21 dB
30 dB
25 dB
42 dB
1FFFFFH
FFFFFFFH
0000000H
126 dB
79
Dynamic range example
Level set by adjusting
receiver gain

80. 80
0/ modulation
Coherent noise limits the SNR improvement offered by coherent
integration.
Using interpulse binary phase modulation (which is removed by the
ADC), the SNR improvement range can be improved significantly.
On alternating transmit pulses, the phase of the Tx waveform is shifted
by 0 or  radians.
Once digitized by the ADC, the phase applied to the Tx waveform is
removed (by toggling the sign bit), effectively removing the interpulse
phase modulation and permitting presumming to proceed.
This scheme is particularly useful in suppressing coherent signals
originating within the radar.
Interpulse phase modulation can also be used to extend the ambiguous range.
+waveform waveform +waveform waveform

81. 81
0/ modulation
Graphical illustration of 0/ interpulse phase modulation to
suppress coherent interference signals.
+waveform waveform +waveform waveform
+int +int +int +int
+waveform +waveform +waveform +waveform
+int int +int int
Coherent integration produces
[+waveform +int] + [+waveform int] + [+waveform +int] + [+waveform int]
= 4 [+waveform]

82. 82
0/ modulation
Measured noise suppression as a function of the number of coherent
averages both with and without 0/ interpulse phase modulation.

83. 83
FM-CW radar
Now we revisit the FM-CW radar to better understand its
advantages and limitations.
CW  on continuously (never off)  Tx while Rx
Tx signal leaking into Rx limits the dynamic range
OR

84. 84
FM-CW radar
Circulator case (in on port 1  out on port 2, in on port 2  out on port 3)
• Leakage through circulator, port 1  port 3
isolation maybe as good as 40 dB
• Reflection of Tx signal from antenna back into Rx
“good antenna” has S11 < -10 dB
Separate antenna case
• Antenna coupling < - 50 dB
isolation enhancements (absorber material, geometry)
Leakage signal must not saturate Rx

85. 85
FM-CW radar
FM – frequency modulated
Frequency modulation required to provide range information
Unmodulated CW radar
No range information provided, only Doppler
Useful as a motion detector or speed monitor
Leakage signal will have no Doppler shift (0 Hz), easy to reject the
DC component by placing a high-pass filter after the mixer
FM-CW radar applications
Short-range sensing or probing
A pulsed system would require a very short pulse duration to avoid the
blind range
Altimeter systems
Nadir looking, only one large target of interest
FM-CW radar shortcomings
Signals from multiple targets may interact in the mixer producing
multiple false targets (if mixing process is not extremely linear)

86. 86
FM-CW radar
Design considerations
Range resolution, R = c/(2 B) [m]
Frequency resolution, f = 2/TR [Hz]
Noise power, PN = k T0 B F [W]
But the bandwidth is the frequency resolution, f, so
PN = k T0 f F [W]
Example – snow penetrating FM-CW radar

87. 87
FM-CW radar
Example – snow penetrating FM-CW radar
B = 2000 – 500 MHz = 1500 MHz  R = 10 cm
Frequency resolution, f = 1/sweep time = 1/4 ms = 250 Hz
PN = -140 dBm
Rx gain = 70 dB
PN out = -140 dBm + 70 dB = -70 dBm
ADC saturation power = + 4 dBm
Rx dynamic range, +4 dBm – (-70 dBm) = 74 dB
Consistent with the ADC’s 72-dB dynamic range
FM slope (like the chirp rate, k), 1500 MHz/4 ms = 375 MHz/ms
So for target #1 at 17-m range, t = 2R1/c = 113 ns
Beat frequency, fb = 113 ns  375 MHz/ms = 42.5 kHz
fb - f = 42.25 kHz  range to target #2, R2 = 16.9 m  R = 10 cm
Note: 1500-MHz bandwidth, 42-kHz beat frequency

88. 88
FM-CW radar block diagram
HPF
LPF

89. 89
FM-CW radar – RF circuitry
9” x 6.5” x 1” module

90. 90
Measured radar data
Measured radar data from
Summit, Greenland in July 2005
Laboratory test data

91. 91
Bistatic / multistatic radar
Bistatic radar
one transmitter, one receiver, separated by baseline L, and
bistatic angle, , is greater than either antenna’s beamwidth
OR
L/RT or L/RR > ~20%
The three points (Tx, Rx, target)
comprising the bistatic geometry
form the bistatic triangle that lies in
the bistatic plane.
Multistatic radar
more than one transmitter or receiver separated
bistatic
angle

Tx
antenna
Rx
antenna
L
baseline
RT
RR
target

92. 92
Bistatic / multistatic radar
Why use a bistatic or multistatic configuration?
Covert operation
• no Tx signal to give away position or activity
Exploit bistatic scattering characteristics
• forward scatter » backscatter
Passive radar or “hitchhiker”
• exploit transmitters of opportunity to save cost
• example transmitters include other radars, TV, radio, comm satellites, GPS,
lightning, the Sun
Counter ARM (ARM = anti-radiation missile)
• missile that targets transmit antennas by homing in on the source
Counter retrodirective jammers
• high-gain jamming antenna directing jamming signal toward the transmitter location
Counter stealth
• some stealth techniques optimized to reduce backscatter, not forward scatter
Homing missile
• transmitter on missile launcher, receiver on missile (simplifies missile system)
Unique spatial coverage
• received signal originates from intersection of Tx and Rx antenna beams

93. 93
Bistatic radar geometry
For a monostatic radar the range shell representing points at
equal range (isorange) at an instant forms a sphere centered
on the radar’s antenna.
For a bistatic radar the isorange surface forms an ellipse with
the Tx and Rx antennas at the foci.
That is, RT + RR = constant everywhere on the ellipse’s
surface.
Consequently, echoes from targets that lie on the ellipse
have the same time-of-arrival and cannot be resolved based
on range.

94. 94
Bistatic range resolution
The bistatic range resolution depends on the target’s position relative to
the bistatic triangle.
For targets on the bistatic
bisector the range resolution is RB
For targets not on the bisector
the range resolution is R
Therefore for target pairs on the ellipse,  = 90 and
R  , i.e., negligible range resolution.
Note: For the monostatic case,  = 0 and R = c/2.
 
2
cos
2
c
RB




  



 
cos
2
cos
2
c
R
R
RB
/2
Rx
RT
RR
target
Tx
/2

bistatic
bisector

95. 95
Bistatic Doppler
The Doppler frequency shift due to relative motion in the bistatic radar
geometry is found using
For the case where both the transmitter and receiver are stationary
while the target is moving, the Doppler frequency shift is
Note: For the monostatic case,  = 0 and fd = 2 VTGT cos ()/
  



















t
d
R
d
t
d
R
d
1
R
R
t
d
d
1
f R
T
R
T
B
 
2
cos
cos
V
2
f TGT
B 




Rx
TGT
Tx
VTGT
VRX
VTX
RT
RR
/2
Rx
RT
RR
Tx

bistatic
bisector
VTGT
TGT
VTX = 0
VRX = 0

96. 96
Bistatic Doppler
For the case where both the transmitter
and receiver are moving while the target
is stationary, the Doppler frequency shift is
Another way to determine the Doppler shift for the general case where the
transmitter, receiver, and target are moving is to numerically compute the ranges
(RT and RR) to the target position as a function of time. Use numerical
differentiation to find dRT/dt and dRR/dt that can then be used in
This approach can also be used to produce isodops (contours of constant
Doppler shift) on a surface by numerically computing fB to each point on the
surface. Matlab’s contour command is particularly useful here.
   
R
R
RX
T
T
TX
B cos
v
cos
v
f 










Rx
TGT
Tx
VTGT = 0
VRX
VTX
RT
RR
R
R
T
T










t
d
R
d
t
d
R
d
1
f R
T
B

97. 97
Example plots
Monostatic example
Aircraft flying straight and level
x = 0, y = 0, z = 2000 m
vx = 0, vy = 100 m/s, vz = 0
f = 200 MHz

98. 98
Example plots
Bistatic example
Tx (stationary atop mountain):
x = -6 km, y = -6 km, z = 500 m
vx = 0, vy = 0, vz = 0
Rx (aircraft flying straight and level):
x = 0, y = 0, z = 2 km
vx = 0, vy = 100 m/s, vz = 0
f = 200 MHz

99. 99