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IEEE New Hampshire Section
Radar Systems Course 1
Clutter 11/1/2009 IEEE AES Society
Radar Systems Engineering
Lecture 10 Part 2
Radar Clutter
Dr. Robert M. O’Donnell
IEEE New Hampshire Section
Guest Lecturer
Radar Systems Course 2
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Block Diagram of Radar System
Transmitter
Waveform
Generation
Power
Amplifier
T / R
Switch
Antenna
Propagation
Medium
Target Radar
Cross Section
Photo Image
Courtesy of US Air Force
Used with permission.
Pulse
Compression
Receiver
Clutter Rejection
(Doppler Filtering)
A / D
Converter
General Purpose Computer
Tracking
Data
Recording
Parameter
Estimation
Detection
Signal Processor Computer
Thresholding
User Displays and Radar Control
Buildings
(Radar Clutter)
Radar Systems Course 3
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Outline
• Motivation
• Backscatter from unwanted objects
– Ground
– Sea
– Rain
– Birds and Insects
Radar Systems Course 4
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Attributes of Rain Clutter
• Rain both attenuates and reflects radar signals
• Problems caused by rain lessen dramatically with longer
wavelengths (lower frequencies)
– Much less of a issue at L-Band than X-Band
• Rain is diffuse clutter (wide geographic extent)
– Travels horizontally with the wind
– Has mean Doppler velocity and spread
Transmitted Electromagnetic Wave
Reflected Electromagnetic Wave
Rain drop
Radar Systems Course 5
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
10 nmi Range Rings on PPI
Display
August 1975, FAA Test
Center
Atlantic City, New Jersey
PPI Display Radar Normal Video
Airport Surveillance Radar
S Band
Detection Range - 60 nmi on
a 1 m2 target
Clear Day (No Rain)
Courtesy of FAA
Radar Systems Course 6
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
10 nmi Range Rings on PPI
Display
August 1975, FAA Test
Center
Atlantic City, New Jersey
PPI Display Radar Normal Video
Airport Surveillance Radar
S Band
Detection Range - 60 nmi on
a 1 m2 target
Clear Day (No Rain)
10 nmi Range Rings on PPI
Display
August 1975, FAA Test
Center
Atlantic City, New Jersey
Day of Heavy Rain
Courtesy of FAA Courtesy of FAA
Radar Systems Course 7
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Reflectivity of Uniform Rain
(σ in dBm2/m3)
• Rain reflectivity increases as f 4 (or 1 / λ4)
– Rain clutter is an issue at S-Band and a significant one at
higher frequencies
Figure by MIT OCW.
Radar Systems Course 8
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Effect of Circular Polarization
on Rain Backscatter
• Assumption: Rain drops are spherical
• Circular polarization is transmitted (assume RHC),
– Reflected energy has opposite sense of circular polarization (LHC)
• Radar configured to receive only the sense of polarization that is
transmitted (RHC)
– Then, rain backscatter will be rejected (~ 15 dB)
• Most atmospheric targets are complex scatterers and return both
senses of polarization; equally (RHC & LHC)
– Target echo will be significantly attenuated
Transmitted Electromagnetic Wave
Right Handed Circular (RHC)
Reflected Electromagnetic Wave
Left Handed Circular (LHC)
Rain drop
Phase change
at reflection
point in
raindrop
Radar Systems Course 9
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Attenuation in Rain
Adapted from Skolnik, Reference 6
Rainfall Characterization
Drizzle – 0.25 mm/hr
Light Rain – 1 mm/hr
Moderate Rain – 4 mm/hr
Heavy Rain – 16 mm/hr
Excessive rain – 40 mm/hr
In Washington DC
0.25 mm/hr exceeded 450 hrs/yr
1 mm/hr exceeded 200 hrs/yr
4 mm/hr exceeded 60 hrs/yr
16 mm/hr exceeded 8 hrs/yr
40 mm/hr exceeded 2.2 hrs/yr0.25 mm/hr
1 mm/hr
16 mm/hr
4 mm/hr
40 mm/hr
Attenuationfromrain-dB/km(oneway)
10-4
10-3
10-2
10-1
1
10
Wavelength (cm)
0 1 2 3 4 5 6 7 8 9 10
Attenuation at 18° C
Radar Systems Course 10
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Reflectivity vs. Frequency
Reflectivity(mi-1)
10-16
10-14
10-12
10-10
10-8
10-6
10-4
100 1,000 10,000 100,000
Frequency (MHz)
Rain (15 mm/hr)
1 m2 on ASR radar
(10kft at 30 nmi)
Insects
(Maximum Observed)
Refractivity
Fluctuations
(Maximum Observed)
Radar Systems Course 11
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Reflectivity of Uniform Rain
(σ in dBm2/m3)
Heavy Stratus Clouds –100 –85 –69 –62
Drizzle, 0.25 mm/hr –102 –91 –81 –71 –58 –45* –50*
Light Rain, 1 mm/hr –92 –81.5 –72 –62 –49 –43* –39*
Moderate, 4 mm/hr –83 –72 –62 –53 –41 –38* –38*
Heavy Rain, 16 mm/hr –73 –62 –53 –45 –33 –35* –37*
Rain Type
S
3.0 GHz
C
5.6
X
9.3
Ku
15.0
Ka
35
W
95
mm
140
* Approximate
Frequency
=
=
+
−
=
=λ
λ
π
=σ ∑
D
93.0
1n
1n
K
DK
2
2
2
62
4
5
Reflectivity
Wavelength
Complex Index of Refraction
For Rain
Droplet Diameter Date Table Adapted from Nathanson,
Reference 3
Radar Systems Course 12
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Heavy Uniform Rain –
Backscatter Coefficient
* Theoretical Rainfall Rate
11,000 ft
Altitude
7 dB
21.5Slant Range, nmi
1.75 nmi
4.0
40 mm*/hr
10 mm*/hr
3 dB
9 dB
0.2 nmi
2.2 dB
Range of Altitude
11,500 ft to 12,800 ft
Altitude
11.5 k-ft 12.1 k-ft 12.8 k-ft
4.52.6 Slant Range, nmi
Amplitude(LinearUnits)
C Band
Azimuth 17°
Elevation 6°
Pulse Width
1.6 μsec
C Band
Azimuth 336°
Elevation 34°
Pulse Width
0.2 μsec
Adapted from Nathanson, Reference 3
Radar Systems Course 13
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Measured S-Band Doppler Spectra of Rain
– 60 Kt
Doppler Velocity
+ 60 Kt0
Azimuth = 320° Azimuth = 330°
0
– 10
– 20
– 30
– 40
– 50
– 60
– 70
– 80
– 90
dB
– 60 Kt
Doppler Velocity
+ 60 Kt0
Azimuth = 90°
0
– 10
– 20
– 30
– 40
– 50
– 60
– 70
– 80
– 90
0 + 60 Kt– 60 Kt
Doppler Velocity
0
– 10
– 20
– 30
– 40
– 50
– 60
– 70
– 80
– 90
• Rain is not Gaussian
• Mean velocity varies as storm moves
by radar
• In these examples the rainfall rate
was approximately 20 mm/hr
• Winds 30 kts on ground, 50 kts at
6000 ft dB – 60 Kt
Doppler Velocity
+ 60 Kt0
0
– 10
– 20
– 30
– 40
– 50
– 60
– 70
– 80
– 90
Velocity Spread
6 kts
Radar Systems Course 14
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Effects of Wind Shear on the
Doppler Spectrum
Adapted from Nathanson, Reference 3
0.5
Velocity Spectrum
Of Rain
Cross Sectional Sketch
of Radar Beam
With Wind Blown Rain
RvΔ
1Rv0Rv2Rv
Doppler Velocity
RelativePower
)h(vW
2Rv
1Rv
Wind Velocity
Vertical
Gradient
of Wind
(Wind Shear)
Radar Systems Course 15
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Nathanson Rain Spectrum Model
• Nathanson model for velocity spread of rain
( )( )
( )
( )
( )s/msin0.1
s/msinw42.0
s/m0.1
0.6s/mRk42.0
Fall
oBeam
Turb
ShearShear
2
Fall
2
Beam
2
Turb
2
Shearv
ψ=σ
βθ=σ
=σ
≤σφ=σ
σ+σ+σ+σ=σ
=
=
=
=
=
=
ow
,
R
k
ψ
β
φθ
Wind Shear Gradient (m/s/km)
(~4.0 averaged over 360°)
Slant range (km)
Horizontal and vertical two
way beam widths (radians)
Azimuth rel. to beam direction
at beam center
Elevation angle
Wind speed (m/s)
s/m0.1
s/m0.3
Turb
Shear
≈σ
≈σ
s/m0.1
s/m25.0
Fall
Beam
≈σ
≈σ
s/m3.3v ≈σ
• Typical Values:
Adapted from Nathanson, Reference 3
Radar Systems Course 16
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Outline
• Motivation
• Backscatter from unwanted objects
– Ground
– Sea
– Rain
– Birds and Insects
Radar Systems Course 17
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Clutter
• General properties
• Bird populations and density
– Migration / Localized travel
Land / Ocean
– Variations
Geography, Height, Diurnal, Seasonal etc
• Radar Cross Section
– Mean / Fluctuation properties
• Velocity / Doppler Distribution
• Effects of Birds on radar
– Sensitivity Time Control (STC)
Radar Systems Course 18
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
General Properties of Birds
• Good RCS model for bird
– Flask full of salt water
– Expanding and contracting body, at frequency of wing
beat, is the dominant contributor to individual bird radar
cross section fluctuations
• Since many birds are often in the same range-azimuth
cell, the net total backscatter is the sum of contribution
from each of the birds, each one moving in and out of
phase with respect to each other.
Erlenmeyer Flask Snow Goose Sea Gull
Courtesy of pbonenfant Courtesy of jurvetson
Courtesy of tk-link
Radar Systems Course 19
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
General Properties of Birds
• Since birds move at relatively low velocities, their speed, if
measured, can be used to preferentially threshold out the low
velocity birds.
– Direct measurement of Doppler velocity
– Velocity from successive measurement of spatial position
Range and angle
• Even though the radar echo of birds is relatively small, birds can
overload a radar with false targets because:
– Often bird densities are quite large, and
– Bird cross sections often fluctuate to large values.
• A huge amount of relevant research has been done over the last
20 years to quantify:
– The populations of bird species, their migration routes, and bird
densities, etc., using US Weather radar data (NEXRAD)
– Major Laboratory efforts over at least the last 20 years at Clemson
University and Cornell University
Radar Systems Course 20
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Clutter
• General properties
• Bird populations and density
– Migration / Localized travel
Land / Ocean
– Variations
Geography, Height, Diurnal, Seasonal etc
• Radar Cross Section
– Mean / Fluctuation properties
• Velocity / Doppler Distribution
• Effects of Birds on radar
– Sensitivity Time Control (STC)
Radar Systems Course 21
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Breeding Areas and Migration Routes
Virginia RailNorthern FlickerGadwall
Along the Gulf Coast, during the breeding season, wading and sea bird colonies exist
that have many tens of thousands of birds. Ten thousand birds are quite common.
These birds are large; weighing up to 2 lbs and having wingspreads from 1 to 6 feet.
Figure by MIT OCW.
Photos courtesy of vsmithuk, sbmontana, and khosla.
Radar Systems Course 22
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Breeding Areas and Migration Routes
Northern HarrierBlack TernSpotted Towhee
Figure by MIT OCW.
Photos courtesy amkhosla, Changhua Coast Conservation Action, and amkhosla.
In the lower Mississippi Valley, over 60 blackbird roosts have been identified with
greater than 1 million birds each. Many smaller roosts also exits. These birds disperse
several tens of miles for feeding each day.
Radar Systems Course 23
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Density of Migrating North American Birds
13%at0Density
75% 50% 25% 10% 1%
Number of birds per sq mi
1 10 100 1000
1
2
3
4
5
FrequencyofOccurrence(%/dB)
Adapted from Pollon, reference 7
Data Characteristics
286 Sites
1209 Observations
~3000 Count-hours
Count = #/mi2/hr
Evening of 3 - 4 October 1952
Radar Systems Course 24
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Migratory Bird Patterns
(Off the US New England Coast)
Bird migrations have been tracked by radars from the
Northeast United States to South America and the
Caribbean have on Bermuda at altitudes of 17 kft
Direction of Bird Migration
Circles note coverage
of 2 radars, one at tip
of Cape Cod, the
other, offshore on a
“Texas tower”
Adapted from Eastwood reference 8
Radar Systems Course 25
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Migration across the Mediterranean Sea
Spring
Autumn
45°
10°W 0° 10°E 20°E 30°E
35°
600 nmi.
For about 2 1/2 months in the Spring and Autumn,
there is heavy bird migration, to and from, Europe
and AfricaAdapted from Eastwood
reference 8
Radar Systems Course 26
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Altitude Distribution of Migrating Birds
1
2
3
4
5
6
7
0
Height(ftx1000)
0 2 4 6 8 10 12
Percent of Birds Detected
Nocturnal Migrating Birds
Bushy Hill, England
Spring 1966
Altitude distributions differ for
migrating and non-migrating
birds
The presence of cloud cover effects
the bird height distribution
Distance of their migration can
influence migration altitude (NE
United States to South America)
Over land vs. over sea migration
Day vs. night migration
Non-migrating birds stay closer to
the ground
Adapted from Eastwood, reference 8
Radar Systems Course 27
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Example of “Ring Roost” Phenomena
• Radar observations with C-Band, WSR-88 (NEXRAD) NOAA,
Pencil Beam Radar located at Green Bay, Wisconsin
“Ring Roosts” are flocks of birds
leaving their roosting location for
their daily foraging for food just
before sunrise
Data collected on August 10, 2006
5:25 to 6:15 AM
About 50 minutes of data is
compressed into ~1.5 sec duration
and replayed in a loop
Note intensity scale in dBZ
Courtesy of NOAA
Radar Systems Course 28
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Spring Bird Migration from Cuba to US
• Radar observations with C-Band, WSR-88 (NEXRAD) NOAA,
Pencil Beam Radar located at Key West, Florida
Data collected on April 28, 2002
~1 - 3 AM
About 2 hours of data is
compressed into ~3 sec duration
and replayed in a loop
Note intensity scale in dBZ
Radar Systems Course 29
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Clutter
• General properties
• Bird populations and density
– Migration / Localized travel
Land / Ocean
– Variations
Geography, Height, Diurnal, Seasonal etc
• Radar Cross Section
– Mean / Fluctuation properties
• Velocity / Doppler Distribution
• Effects of Birds on radar
– Sensitivity Time Control (STC)
Radar Systems Course 30
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird RCS Measurements
• In the late 1960s, Konrad, Hicks, and Dobson of JHU/APL
accurately measured the radar cross section (RCS) of
single birds and the RCS fluctuation properties.
– Bird RCS fit a log-normal quite well
– Like the Weibull distribution, it is a 2 parameter model that
fits data with long tails
Time (min)
RadarCrossSection(m2
)
10-3
10-4
10-2
0 1 2 3
SparrowS-Band
Radar Cross Section vs. TimeJoint Air Force NASA Radar Facility
Wallops Island, VA
UHF , S-Band and X-Band Radars
Adapted from Konrad, reference 12
Radar Systems Course 31
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Summary of Measured Bird Cross Section* Data
Grackle (male) 15.7 27 0.73
Grackle (female) 15.4 23.2 0.41
Sparrow 1.85 14.9 0.025
Pigeon 14.5 80.0 10.5
X-Band S-Band UHF
Adapted from Konrad, reference 12
Units of RCS measurement cm2
Radar Systems Course 32
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Distribution of Bird Radar Cross Section
0
NumberofBirdDetections
60
40
80
20
10-5 10-4
10-3 10-2 10-1 1 10
Radar Cross Section (m2) Adapted from Eastwood, reference 8
Radar Systems Course 33
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Radar Cross Section Model
• Wavelength dependence
• Fluctuation statistics of cross section (log normal)
Mean Standard Deviation of
Cross Section Log of Cross Section
Wavelength (dBsm) (dB)
X –33 6
S –27 6
L –28 7.5
UHF –47 15
VHF –57 17
Adapted from Pollon, Reference 7
Radar Systems Course 34
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Clutter
• General properties
• Bird populations and density
– Migration / Localized travel
Land / Ocean
– Variations
Geography, Height, Diurnal, Seasonal etc
• Radar Cross Section
– Mean / Fluctuation properties
• Velocity / Doppler Distribution
• Effects of Birds on radar
– Sensitivity Time Control (STC)
Radar Systems Course 35
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Distributions of the Radial Velocity of BirdsFrequencyofOccurrence
FrequencyofOccurrence
L-Band
X-Band
Radial Velocity (m/sec) Radial Velocity (m/sec)
0 5.7 11.4 17.1 22.8 28.5 0 5.7 11.4 17.1 22.8 28.5
0.05 0.05
0.15
0.10
0.10
0.15
0.20
0.20
00
0.25
0.30
Radar Systems Course 36
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Clutter
• General properties
• Bird populations and density
– Migration / Localized travel
Land / Ocean
– Variations
Geography, Height, Diurnal, Seasonal etc
• Radar cross section
– Mean / Fluctuation properties
• Velocity / Doppler distribution
• Effects of birds on radar
– Sensitivity Time Control (STC)
Radar Systems Course 37
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Why Birds Are an Issue for Radars
0 20 40 60 80 100 120 140 160
Birds
Insects
Clear Air Turbulance
DetectableCrossSection(m2)
1
101
10-2
10-1
10-3
10-4
10-1 m
2 at 70 km
10-2 m
2 at 70 km
10-3 m
2 at 70 km
Detection Curve
For an ASR
Range (km)
Radar Systems Course 38
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Sensitivity Time Control
• These two targets have the same detectability, because in
the radar equation:
• This false target issue can be mitigated by attenuating to
the received signal by a factor which varies as 1/R4
– Can also be accomplished by injecting 1/R4 noise to the
receive channel
• Radars that utilize range ambiguous waveforms, cannot
use STC, because long range targets which alias down in
range, would be adversely attenuated by the STC
– For these waveforms, other techniques are used to mitigate
the false target problem due to birds
Bird at 89 nmi, RCS = 0.0015 m2
Aircraft at 200 nmi, RCS = 1 m2
4
RN
S σ
∝
Radar Systems Course 39
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Example from Dallas-Fort Worth
Radar & Beacon
Beacon-Only
Radar Uncorrelated
Radar Correlated
Radar Systems Course 40
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Bird Clutter Issues - Summary
• Birds are actually moving point targets
– Velocity usually less than 60 knots
• Mean radar cross section is small, but a fraction of bird
returns fluctuate up to a high level (aircraft like)
– Cross section is resonant at S-Band and L-Band
• The density of birds varies a lot and can be quite large
– 10 to 1000 birds / square mile
• Birds cause a false target problem in many radars
– This can be a significant issue for when attempting to detect
targets with very low cross sections
Radar Systems Course 41
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Insects
• Insects can cause false
detections and prevent
detection of desired targets
• Density of insects can be many
orders of magnitude greater
than that of birds
• Insect flight path generally
follows that of the wind
• Cross section can be
represented as a spherical drop
of water of the same mass
• Insect echoes broad side are 10
to 1,000 times than when
viewed end on
Figure by MIT OCW. Adapted from Skolnik Reference 6
Radar Systems Course 42
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Mayfly Hatching
• Radar observations with C-Band, WSR-88 (NEXRAD) NOAA,
Pencil Beam Radar located at La Crosse, Wisconsin (SW WI)
Data collection - June 30, 2006
La Crosse is the breeding ground
of the mayfly population of the
world
~10s of billions of them hatch,
live, and die, over a 1 ½ day
period, each year in late June /
early July
Mississippi River
Ephemeroptera (mayfly)
Courtesy of National Weather Service
Courtesy of urtica
Radar Systems Course 43
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Summary
• A number of different types of radar clutter returns have
been described
– Ground, sea, rain, and birds
• These environmental and manmade phenomena will
produce a variety of discrete and diffuse, moving and
stationary false targets, unless they are dealt with
effectively
• A number of signal and data processing techniques can be
used to suppress the effect of these radar clutter returns.
Radar Systems Course 44
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
References
1. Billingsley, J. B. , Ground Clutter Measurements for Surface
Sited Radar, MIT Lincoln Laboratory, TR-916 Rev 1, (1991)
2. Billingsley, J. B., Low Angle Radar Land Clutter, Artech House,
Needham, MA, (2005)
3. Nathanson,F. , Radar Design Principles, McGraw Hill, New
York,2nd Ed., (1999)
4. Skolnik, M., Radar Handbook, McGraw Hill, New York,3rd Ed.,
(2008)
5. Barton, D., Radar System Analysis, McGraw Hill, Artech House,
Needham, MA, (1976)
6. Skolnik, M., Introduction to Radar Systems, McGraw Hill, New
York, 3rd Ed. (2000)
Radar Systems Course 45
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
References - Continued
7. Pollon, G., “Distributions of Radar Angels,” IEEE Trans.
AESS, Volume AES-8, No. 6, November 1972, pp. 721–726
8. Eastwood, E., Radar Ornithology, Methuen & Co, London,
(1967)
9. Riley,J. R., “Radar Cross Section of Insects,”
Proceedings of IEEE, February 1985, pp. 228–232
10. Vaughn, C. R., “Birds and Insects as Radar Targets:
A Review,” Proceedings of IEEE, February 1985, pp. 205–227
11. Billingsley, J. B. , Ground Clutter Measurements for Surface
Sited Radar, MIT Lincoln Laboratory, TR-786 Rev 1, (1993)
12. Konrad, et al, “Radar Characteristics of birds in Flight”,
Science, vol 159, January 19, 1968
Radar Systems Course 46
Clutter 11/1/2009
IEEE New Hampshire Section
IEEE AES Society
Homework Problems
• From Skolnik, Reference 6
– Problems 7-2, 7.4, 7.9, 7.11, 7.15, and 7.18

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Radar 2009 a 10 radar clutter.2pdf

  • 1. IEEE New Hampshire Section Radar Systems Course 1 Clutter 11/1/2009 IEEE AES Society Radar Systems Engineering Lecture 10 Part 2 Radar Clutter Dr. Robert M. O’Donnell IEEE New Hampshire Section Guest Lecturer
  • 2. Radar Systems Course 2 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Block Diagram of Radar System Transmitter Waveform Generation Power Amplifier T / R Switch Antenna Propagation Medium Target Radar Cross Section Photo Image Courtesy of US Air Force Used with permission. Pulse Compression Receiver Clutter Rejection (Doppler Filtering) A / D Converter General Purpose Computer Tracking Data Recording Parameter Estimation Detection Signal Processor Computer Thresholding User Displays and Radar Control Buildings (Radar Clutter)
  • 3. Radar Systems Course 3 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Outline • Motivation • Backscatter from unwanted objects – Ground – Sea – Rain – Birds and Insects
  • 4. Radar Systems Course 4 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Attributes of Rain Clutter • Rain both attenuates and reflects radar signals • Problems caused by rain lessen dramatically with longer wavelengths (lower frequencies) – Much less of a issue at L-Band than X-Band • Rain is diffuse clutter (wide geographic extent) – Travels horizontally with the wind – Has mean Doppler velocity and spread Transmitted Electromagnetic Wave Reflected Electromagnetic Wave Rain drop
  • 5. Radar Systems Course 5 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society 10 nmi Range Rings on PPI Display August 1975, FAA Test Center Atlantic City, New Jersey PPI Display Radar Normal Video Airport Surveillance Radar S Band Detection Range - 60 nmi on a 1 m2 target Clear Day (No Rain) Courtesy of FAA
  • 6. Radar Systems Course 6 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society 10 nmi Range Rings on PPI Display August 1975, FAA Test Center Atlantic City, New Jersey PPI Display Radar Normal Video Airport Surveillance Radar S Band Detection Range - 60 nmi on a 1 m2 target Clear Day (No Rain) 10 nmi Range Rings on PPI Display August 1975, FAA Test Center Atlantic City, New Jersey Day of Heavy Rain Courtesy of FAA Courtesy of FAA
  • 7. Radar Systems Course 7 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Reflectivity of Uniform Rain (σ in dBm2/m3) • Rain reflectivity increases as f 4 (or 1 / λ4) – Rain clutter is an issue at S-Band and a significant one at higher frequencies Figure by MIT OCW.
  • 8. Radar Systems Course 8 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Effect of Circular Polarization on Rain Backscatter • Assumption: Rain drops are spherical • Circular polarization is transmitted (assume RHC), – Reflected energy has opposite sense of circular polarization (LHC) • Radar configured to receive only the sense of polarization that is transmitted (RHC) – Then, rain backscatter will be rejected (~ 15 dB) • Most atmospheric targets are complex scatterers and return both senses of polarization; equally (RHC & LHC) – Target echo will be significantly attenuated Transmitted Electromagnetic Wave Right Handed Circular (RHC) Reflected Electromagnetic Wave Left Handed Circular (LHC) Rain drop Phase change at reflection point in raindrop
  • 9. Radar Systems Course 9 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Attenuation in Rain Adapted from Skolnik, Reference 6 Rainfall Characterization Drizzle – 0.25 mm/hr Light Rain – 1 mm/hr Moderate Rain – 4 mm/hr Heavy Rain – 16 mm/hr Excessive rain – 40 mm/hr In Washington DC 0.25 mm/hr exceeded 450 hrs/yr 1 mm/hr exceeded 200 hrs/yr 4 mm/hr exceeded 60 hrs/yr 16 mm/hr exceeded 8 hrs/yr 40 mm/hr exceeded 2.2 hrs/yr0.25 mm/hr 1 mm/hr 16 mm/hr 4 mm/hr 40 mm/hr Attenuationfromrain-dB/km(oneway) 10-4 10-3 10-2 10-1 1 10 Wavelength (cm) 0 1 2 3 4 5 6 7 8 9 10 Attenuation at 18° C
  • 10. Radar Systems Course 10 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Reflectivity vs. Frequency Reflectivity(mi-1) 10-16 10-14 10-12 10-10 10-8 10-6 10-4 100 1,000 10,000 100,000 Frequency (MHz) Rain (15 mm/hr) 1 m2 on ASR radar (10kft at 30 nmi) Insects (Maximum Observed) Refractivity Fluctuations (Maximum Observed)
  • 11. Radar Systems Course 11 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Reflectivity of Uniform Rain (σ in dBm2/m3) Heavy Stratus Clouds –100 –85 –69 –62 Drizzle, 0.25 mm/hr –102 –91 –81 –71 –58 –45* –50* Light Rain, 1 mm/hr –92 –81.5 –72 –62 –49 –43* –39* Moderate, 4 mm/hr –83 –72 –62 –53 –41 –38* –38* Heavy Rain, 16 mm/hr –73 –62 –53 –45 –33 –35* –37* Rain Type S 3.0 GHz C 5.6 X 9.3 Ku 15.0 Ka 35 W 95 mm 140 * Approximate Frequency = = + − = =λ λ π =σ ∑ D 93.0 1n 1n K DK 2 2 2 62 4 5 Reflectivity Wavelength Complex Index of Refraction For Rain Droplet Diameter Date Table Adapted from Nathanson, Reference 3
  • 12. Radar Systems Course 12 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Heavy Uniform Rain – Backscatter Coefficient * Theoretical Rainfall Rate 11,000 ft Altitude 7 dB 21.5Slant Range, nmi 1.75 nmi 4.0 40 mm*/hr 10 mm*/hr 3 dB 9 dB 0.2 nmi 2.2 dB Range of Altitude 11,500 ft to 12,800 ft Altitude 11.5 k-ft 12.1 k-ft 12.8 k-ft 4.52.6 Slant Range, nmi Amplitude(LinearUnits) C Band Azimuth 17° Elevation 6° Pulse Width 1.6 μsec C Band Azimuth 336° Elevation 34° Pulse Width 0.2 μsec Adapted from Nathanson, Reference 3
  • 13. Radar Systems Course 13 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Measured S-Band Doppler Spectra of Rain – 60 Kt Doppler Velocity + 60 Kt0 Azimuth = 320° Azimuth = 330° 0 – 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 dB – 60 Kt Doppler Velocity + 60 Kt0 Azimuth = 90° 0 – 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 0 + 60 Kt– 60 Kt Doppler Velocity 0 – 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 • Rain is not Gaussian • Mean velocity varies as storm moves by radar • In these examples the rainfall rate was approximately 20 mm/hr • Winds 30 kts on ground, 50 kts at 6000 ft dB – 60 Kt Doppler Velocity + 60 Kt0 0 – 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 Velocity Spread 6 kts
  • 14. Radar Systems Course 14 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Effects of Wind Shear on the Doppler Spectrum Adapted from Nathanson, Reference 3 0.5 Velocity Spectrum Of Rain Cross Sectional Sketch of Radar Beam With Wind Blown Rain RvΔ 1Rv0Rv2Rv Doppler Velocity RelativePower )h(vW 2Rv 1Rv Wind Velocity Vertical Gradient of Wind (Wind Shear)
  • 15. Radar Systems Course 15 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Nathanson Rain Spectrum Model • Nathanson model for velocity spread of rain ( )( ) ( ) ( ) ( )s/msin0.1 s/msinw42.0 s/m0.1 0.6s/mRk42.0 Fall oBeam Turb ShearShear 2 Fall 2 Beam 2 Turb 2 Shearv ψ=σ βθ=σ =σ ≤σφ=σ σ+σ+σ+σ=σ = = = = = = ow , R k ψ β φθ Wind Shear Gradient (m/s/km) (~4.0 averaged over 360°) Slant range (km) Horizontal and vertical two way beam widths (radians) Azimuth rel. to beam direction at beam center Elevation angle Wind speed (m/s) s/m0.1 s/m0.3 Turb Shear ≈σ ≈σ s/m0.1 s/m25.0 Fall Beam ≈σ ≈σ s/m3.3v ≈σ • Typical Values: Adapted from Nathanson, Reference 3
  • 16. Radar Systems Course 16 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Outline • Motivation • Backscatter from unwanted objects – Ground – Sea – Rain – Birds and Insects
  • 17. Radar Systems Course 17 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Clutter • General properties • Bird populations and density – Migration / Localized travel Land / Ocean – Variations Geography, Height, Diurnal, Seasonal etc • Radar Cross Section – Mean / Fluctuation properties • Velocity / Doppler Distribution • Effects of Birds on radar – Sensitivity Time Control (STC)
  • 18. Radar Systems Course 18 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society General Properties of Birds • Good RCS model for bird – Flask full of salt water – Expanding and contracting body, at frequency of wing beat, is the dominant contributor to individual bird radar cross section fluctuations • Since many birds are often in the same range-azimuth cell, the net total backscatter is the sum of contribution from each of the birds, each one moving in and out of phase with respect to each other. Erlenmeyer Flask Snow Goose Sea Gull Courtesy of pbonenfant Courtesy of jurvetson Courtesy of tk-link
  • 19. Radar Systems Course 19 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society General Properties of Birds • Since birds move at relatively low velocities, their speed, if measured, can be used to preferentially threshold out the low velocity birds. – Direct measurement of Doppler velocity – Velocity from successive measurement of spatial position Range and angle • Even though the radar echo of birds is relatively small, birds can overload a radar with false targets because: – Often bird densities are quite large, and – Bird cross sections often fluctuate to large values. • A huge amount of relevant research has been done over the last 20 years to quantify: – The populations of bird species, their migration routes, and bird densities, etc., using US Weather radar data (NEXRAD) – Major Laboratory efforts over at least the last 20 years at Clemson University and Cornell University
  • 20. Radar Systems Course 20 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Clutter • General properties • Bird populations and density – Migration / Localized travel Land / Ocean – Variations Geography, Height, Diurnal, Seasonal etc • Radar Cross Section – Mean / Fluctuation properties • Velocity / Doppler Distribution • Effects of Birds on radar – Sensitivity Time Control (STC)
  • 21. Radar Systems Course 21 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Breeding Areas and Migration Routes Virginia RailNorthern FlickerGadwall Along the Gulf Coast, during the breeding season, wading and sea bird colonies exist that have many tens of thousands of birds. Ten thousand birds are quite common. These birds are large; weighing up to 2 lbs and having wingspreads from 1 to 6 feet. Figure by MIT OCW. Photos courtesy of vsmithuk, sbmontana, and khosla.
  • 22. Radar Systems Course 22 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Breeding Areas and Migration Routes Northern HarrierBlack TernSpotted Towhee Figure by MIT OCW. Photos courtesy amkhosla, Changhua Coast Conservation Action, and amkhosla. In the lower Mississippi Valley, over 60 blackbird roosts have been identified with greater than 1 million birds each. Many smaller roosts also exits. These birds disperse several tens of miles for feeding each day.
  • 23. Radar Systems Course 23 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Density of Migrating North American Birds 13%at0Density 75% 50% 25% 10% 1% Number of birds per sq mi 1 10 100 1000 1 2 3 4 5 FrequencyofOccurrence(%/dB) Adapted from Pollon, reference 7 Data Characteristics 286 Sites 1209 Observations ~3000 Count-hours Count = #/mi2/hr Evening of 3 - 4 October 1952
  • 24. Radar Systems Course 24 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Migratory Bird Patterns (Off the US New England Coast) Bird migrations have been tracked by radars from the Northeast United States to South America and the Caribbean have on Bermuda at altitudes of 17 kft Direction of Bird Migration Circles note coverage of 2 radars, one at tip of Cape Cod, the other, offshore on a “Texas tower” Adapted from Eastwood reference 8
  • 25. Radar Systems Course 25 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Migration across the Mediterranean Sea Spring Autumn 45° 10°W 0° 10°E 20°E 30°E 35° 600 nmi. For about 2 1/2 months in the Spring and Autumn, there is heavy bird migration, to and from, Europe and AfricaAdapted from Eastwood reference 8
  • 26. Radar Systems Course 26 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Altitude Distribution of Migrating Birds 1 2 3 4 5 6 7 0 Height(ftx1000) 0 2 4 6 8 10 12 Percent of Birds Detected Nocturnal Migrating Birds Bushy Hill, England Spring 1966 Altitude distributions differ for migrating and non-migrating birds The presence of cloud cover effects the bird height distribution Distance of their migration can influence migration altitude (NE United States to South America) Over land vs. over sea migration Day vs. night migration Non-migrating birds stay closer to the ground Adapted from Eastwood, reference 8
  • 27. Radar Systems Course 27 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Example of “Ring Roost” Phenomena • Radar observations with C-Band, WSR-88 (NEXRAD) NOAA, Pencil Beam Radar located at Green Bay, Wisconsin “Ring Roosts” are flocks of birds leaving their roosting location for their daily foraging for food just before sunrise Data collected on August 10, 2006 5:25 to 6:15 AM About 50 minutes of data is compressed into ~1.5 sec duration and replayed in a loop Note intensity scale in dBZ Courtesy of NOAA
  • 28. Radar Systems Course 28 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Spring Bird Migration from Cuba to US • Radar observations with C-Band, WSR-88 (NEXRAD) NOAA, Pencil Beam Radar located at Key West, Florida Data collected on April 28, 2002 ~1 - 3 AM About 2 hours of data is compressed into ~3 sec duration and replayed in a loop Note intensity scale in dBZ
  • 29. Radar Systems Course 29 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Clutter • General properties • Bird populations and density – Migration / Localized travel Land / Ocean – Variations Geography, Height, Diurnal, Seasonal etc • Radar Cross Section – Mean / Fluctuation properties • Velocity / Doppler Distribution • Effects of Birds on radar – Sensitivity Time Control (STC)
  • 30. Radar Systems Course 30 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird RCS Measurements • In the late 1960s, Konrad, Hicks, and Dobson of JHU/APL accurately measured the radar cross section (RCS) of single birds and the RCS fluctuation properties. – Bird RCS fit a log-normal quite well – Like the Weibull distribution, it is a 2 parameter model that fits data with long tails Time (min) RadarCrossSection(m2 ) 10-3 10-4 10-2 0 1 2 3 SparrowS-Band Radar Cross Section vs. TimeJoint Air Force NASA Radar Facility Wallops Island, VA UHF , S-Band and X-Band Radars Adapted from Konrad, reference 12
  • 31. Radar Systems Course 31 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Summary of Measured Bird Cross Section* Data Grackle (male) 15.7 27 0.73 Grackle (female) 15.4 23.2 0.41 Sparrow 1.85 14.9 0.025 Pigeon 14.5 80.0 10.5 X-Band S-Band UHF Adapted from Konrad, reference 12 Units of RCS measurement cm2
  • 32. Radar Systems Course 32 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Distribution of Bird Radar Cross Section 0 NumberofBirdDetections 60 40 80 20 10-5 10-4 10-3 10-2 10-1 1 10 Radar Cross Section (m2) Adapted from Eastwood, reference 8
  • 33. Radar Systems Course 33 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Radar Cross Section Model • Wavelength dependence • Fluctuation statistics of cross section (log normal) Mean Standard Deviation of Cross Section Log of Cross Section Wavelength (dBsm) (dB) X –33 6 S –27 6 L –28 7.5 UHF –47 15 VHF –57 17 Adapted from Pollon, Reference 7
  • 34. Radar Systems Course 34 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Clutter • General properties • Bird populations and density – Migration / Localized travel Land / Ocean – Variations Geography, Height, Diurnal, Seasonal etc • Radar Cross Section – Mean / Fluctuation properties • Velocity / Doppler Distribution • Effects of Birds on radar – Sensitivity Time Control (STC)
  • 35. Radar Systems Course 35 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Distributions of the Radial Velocity of BirdsFrequencyofOccurrence FrequencyofOccurrence L-Band X-Band Radial Velocity (m/sec) Radial Velocity (m/sec) 0 5.7 11.4 17.1 22.8 28.5 0 5.7 11.4 17.1 22.8 28.5 0.05 0.05 0.15 0.10 0.10 0.15 0.20 0.20 00 0.25 0.30
  • 36. Radar Systems Course 36 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Clutter • General properties • Bird populations and density – Migration / Localized travel Land / Ocean – Variations Geography, Height, Diurnal, Seasonal etc • Radar cross section – Mean / Fluctuation properties • Velocity / Doppler distribution • Effects of birds on radar – Sensitivity Time Control (STC)
  • 37. Radar Systems Course 37 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Why Birds Are an Issue for Radars 0 20 40 60 80 100 120 140 160 Birds Insects Clear Air Turbulance DetectableCrossSection(m2) 1 101 10-2 10-1 10-3 10-4 10-1 m 2 at 70 km 10-2 m 2 at 70 km 10-3 m 2 at 70 km Detection Curve For an ASR Range (km)
  • 38. Radar Systems Course 38 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Sensitivity Time Control • These two targets have the same detectability, because in the radar equation: • This false target issue can be mitigated by attenuating to the received signal by a factor which varies as 1/R4 – Can also be accomplished by injecting 1/R4 noise to the receive channel • Radars that utilize range ambiguous waveforms, cannot use STC, because long range targets which alias down in range, would be adversely attenuated by the STC – For these waveforms, other techniques are used to mitigate the false target problem due to birds Bird at 89 nmi, RCS = 0.0015 m2 Aircraft at 200 nmi, RCS = 1 m2 4 RN S σ ∝
  • 39. Radar Systems Course 39 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Example from Dallas-Fort Worth Radar & Beacon Beacon-Only Radar Uncorrelated Radar Correlated
  • 40. Radar Systems Course 40 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Bird Clutter Issues - Summary • Birds are actually moving point targets – Velocity usually less than 60 knots • Mean radar cross section is small, but a fraction of bird returns fluctuate up to a high level (aircraft like) – Cross section is resonant at S-Band and L-Band • The density of birds varies a lot and can be quite large – 10 to 1000 birds / square mile • Birds cause a false target problem in many radars – This can be a significant issue for when attempting to detect targets with very low cross sections
  • 41. Radar Systems Course 41 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Insects • Insects can cause false detections and prevent detection of desired targets • Density of insects can be many orders of magnitude greater than that of birds • Insect flight path generally follows that of the wind • Cross section can be represented as a spherical drop of water of the same mass • Insect echoes broad side are 10 to 1,000 times than when viewed end on Figure by MIT OCW. Adapted from Skolnik Reference 6
  • 42. Radar Systems Course 42 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Mayfly Hatching • Radar observations with C-Band, WSR-88 (NEXRAD) NOAA, Pencil Beam Radar located at La Crosse, Wisconsin (SW WI) Data collection - June 30, 2006 La Crosse is the breeding ground of the mayfly population of the world ~10s of billions of them hatch, live, and die, over a 1 ½ day period, each year in late June / early July Mississippi River Ephemeroptera (mayfly) Courtesy of National Weather Service Courtesy of urtica
  • 43. Radar Systems Course 43 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Summary • A number of different types of radar clutter returns have been described – Ground, sea, rain, and birds • These environmental and manmade phenomena will produce a variety of discrete and diffuse, moving and stationary false targets, unless they are dealt with effectively • A number of signal and data processing techniques can be used to suppress the effect of these radar clutter returns.
  • 44. Radar Systems Course 44 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society References 1. Billingsley, J. B. , Ground Clutter Measurements for Surface Sited Radar, MIT Lincoln Laboratory, TR-916 Rev 1, (1991) 2. Billingsley, J. B., Low Angle Radar Land Clutter, Artech House, Needham, MA, (2005) 3. Nathanson,F. , Radar Design Principles, McGraw Hill, New York,2nd Ed., (1999) 4. Skolnik, M., Radar Handbook, McGraw Hill, New York,3rd Ed., (2008) 5. Barton, D., Radar System Analysis, McGraw Hill, Artech House, Needham, MA, (1976) 6. Skolnik, M., Introduction to Radar Systems, McGraw Hill, New York, 3rd Ed. (2000)
  • 45. Radar Systems Course 45 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society References - Continued 7. Pollon, G., “Distributions of Radar Angels,” IEEE Trans. AESS, Volume AES-8, No. 6, November 1972, pp. 721–726 8. Eastwood, E., Radar Ornithology, Methuen & Co, London, (1967) 9. Riley,J. R., “Radar Cross Section of Insects,” Proceedings of IEEE, February 1985, pp. 228–232 10. Vaughn, C. R., “Birds and Insects as Radar Targets: A Review,” Proceedings of IEEE, February 1985, pp. 205–227 11. Billingsley, J. B. , Ground Clutter Measurements for Surface Sited Radar, MIT Lincoln Laboratory, TR-786 Rev 1, (1993) 12. Konrad, et al, “Radar Characteristics of birds in Flight”, Science, vol 159, January 19, 1968
  • 46. Radar Systems Course 46 Clutter 11/1/2009 IEEE New Hampshire Section IEEE AES Society Homework Problems • From Skolnik, Reference 6 – Problems 7-2, 7.4, 7.9, 7.11, 7.15, and 7.18