RADAR - RAdio Detection And Ranging
This is the Part 2 of 2 of RADAR Introduction.
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2. Table of Content
SOLO
Radar Basics
Basic Radar Concepts
The Physics of Radio Waves
Maxwell’s Equations:
Properties of Electro-Magnetic Waves
Polarization
Energy and Momentum
The Electromagnetic Spectrum
Introduction to Radars
Dipole Antenna Radiation
Interaction of Electromagnetic Waves with Material
Absorption and Emission
Reflection and Refraction at a Boundary Interface
Diffraction
Atmospheric Effects
RADA
BASI
3. Table of Content (continue – 1)
SOLO
Radar Basics
Basic Radar Measurements
Radar Configurations
Range & Doppler Measurements in RADAR Systems
Waveform Hierarchy
Fourier Transform of a Signal
Continuous Wave Radar (CW Radar)
Basic CW Radar
Frequency Modulated Continuous Wave (FMCW)
Linear Sawtooth Frequency Modulated Continuous Wave
Linear Triangular Frequency Modulated Continuous Wave
Sinusoidal Frequency Modulated Continuous Wave
Multiple Frequency CW Radar (MFCW)
Phase Modulated Continuous Wave (PMCW)
RADA
BASI
4. Table of Content (continue – 2)
SOLO
Radar Basics
Non-Coherent Pulse Radar
Pulse Radars
Coherent Pulse-Doppler Radar
Range & Doppler Measurements in Pulse-Radar Systems
Range Measurements
Range Measurement Unambiguity
Doppler Frequency Shift
Resolving Doppler Measurement Ambiguity
Resolution
Doppler Resolution
Angle Resolution
Range Resolution
RADA
BASI
5. Table of Content (continue – 3)
SOLO
Radar Basics
Pulse Compression Waveforms
Linear FM Modulated Pulse (Chirp)
Phase Coding
Poly-Phase Codes
Bi-Phase Codes
Frank Codes
Pseudo-Random Codes
Stepped Frequency Waveform (SFWF)
RADA
BASI
6. Table of Content (continue – 4)
SOLO
Radar Basics
RF Section of a Generic Radar
Antenna
Antenna Gain, Aperture and Beam Angle
Mechanically/Electrically Scanned Antenna (MSA/ESA)
Mechanically Scanned Antenna (MSA)
Conical Scan Angular Measurement
Monopulse Antenna
Electronically Scanned Array (ESA)
RADAR
BASICS -
7. Table of Content (continue – 5)
SOLO
Radar Basics
RF Section of a Generic Radar
Transmitters
Types of Power Sources
Grid Pulsed Tube
Magnetron
Solid-State Oscillators
Crossed-Field amplifiers (CFA)
Traveling-Wave Tubes (TWT)
Klystrons
Microwave Power Modules (MPM)
Transmitter/Receiver (T/R) Modules
Transmitter Summary
8. Table of Content (continue – 6)
SOLO
Radar Basics
RF Section of a Generic Radar
Radar Receiver
Isolators/Circulators
Ferrite circulators
Branch- Duplexer
TR-Tubes
Balanced Duplexer
Wave Guides
Receiver Equivalent Noise
Receiver Intermediate Frequency (IF)
Mixer Technology
Coherent Pulse-RADAR Seeker Block Diagram
25. In 1921 Albert Wallace Hull invented the magnetron as a powerful microwawe tube.
resonant cavities anode
catode
Filament
leads
Fig. Cutaway view of a Magnetron
pickup loop
a) slot- type
b) vane- type
c) rising sun- type
d) hole-and-slot- type
Figure 3: forms of the plate of magnetrons
Albert Wallace Hull
(1880 – 1966)
Magnetron
26. Figure 1: the electron path under the
influence of the varying magnetic field.
1. Phase: Production and acceleration
of an electron beam
2. Phase: velocity-modulation
of the electron beam
Figure 2: The high-frequency
electrical field
3. Phase: Forming of a „Space-Charge Wheel”
Figure 3: Rotating space-charge
wheel in an eight-cavity magnetron
4. Phase: Giving up energy to the ac field
Figure 4: Path of an electron
Magnetron
27. Magnetron tuning
A tunable magnetron permits the system to be operated at a precise frequency
anywhere within a band of frequencies, as determined by magnetron characteristics.
The resonant frequency of a magnetron may be changed by varying the inductance or
capacitance of the resonant cavities.
inductive
tuning
elements
Tuner frame
anode block
Figure 12: Inductive magnetron tuning
28. Figure 13: Magnetron M5114B of the ATC-radar ASR-910
Figure 13: Magnetron VMX1090 of the ATC-radar PAR-80
This magnetron is even equipped with the permanent magnets
necessary for the work.
Magnetron
Return to Table of Content
31. SOLO
The Crossed-Field Amplifier (CFA), is a broadband microwave amplifier that can
also be used as an oscillator (Stabilotron). The CFA is similar in operation to the
magnetron and is capable of providing relatively large amounts of power with high
efficiency. The bandwidth of the cfa, at any given instant, is approximately plus or
minus 5 percent of the rated center frequency. Any incoming signals within this
bandwidth are amplified. Peak power levels of many megawatts and average power
levels of tens of kilowatts average are, with efficiency ratings in excess of 70 percent,
possible with crossed-field amplifiers.
Crossed-Field Amplifier (CFA)
Also other names are used for the Crossed-Field Amplifier
in the literature.
• Platinotron
• Amplitron
• Stabilotron
Figure 2: schematically view of a
Crossed-Field Amplifier
(1) cathode
(2) anode with resonant-cavities
(3) „Space-Charge Wheel”
(4) delaying strapping rings
Figure 1: water-cooled
Crossed-Field Amplifier
L-4756A in its transport case
32. SOLO
Crossed-Field Amplifier (CFA)
Because of the desirable characteristics of wide bandwidth, high efficiency, and the
ability to handle large amounts of power, the CFA is used in many applications in
microwave electronic systems. When used as the intermediate or final stage in high-
power radar systems, all of the advantages of the CFA are used.
The amplifiers in this type of power-amplifier transmitter must be broad-band
microwave amplifiers that amplify the input signals without frequency distortion.
Typically, the first stage and the second stage are traveling-wave tubes (TWT) and the
final stage is a crossed-field amplifier. Recent technological advances in the field of
solid-state microwave amplifiers have produced solid-state amplifiers with enough
output power to be used as the first stage in some systems. Transmitters with more than
three stages usually use crossed-field amplifiers in the third and any additional stages.
Both traveling-wave tubes and crossed-field amplifiers have a very flat amplification
response over a relatively wide frequency range.
Crossed-field amplifiers have another advantage when used as the final stages of a
transmitter; that is, the design of the crossed-field amplifier allows rf energy to pass
through the tube virtually unaffected when the tube is not pulsed. When no pulse is
present, the tube acts as a section of waveguide. Therefore, if less than maximum output
power is desired, the final and preceding cross-field amplifier stages can be shut off as
needed. This feature also allows a transmitter to operate at reduced power, even when
the final crossed-field amplifier is defective Return to Table of Content
34. SOLO
Travelling Wave Tube
Travelling wave tubes (TWT) are wideband
amplifiers. They take therefore a special position
under the velocity-modulated tubes. On reason of the
special low-noise characteristic often they are in use
as an active RF amplifier element in receivers
additional. There are two different groups of TWT:
• low-power TWT for receivers
occurs as a highly sensitive, low-noise and wideband amplifier in radar equipments
• high-power twt for transmitters
these are in use as a pre-amplifier for high-power transmitters.
collector
input
output
electron- beam bounching
Amplified Helix Signal
RF-Input
RF induced into Helix
The Travelling Wave Tube (twt) is a
high-gain, low-noise, wide-bandwidth
microwave amplifier. It is capable of
gains greater than 40 dB with
bandwidths exceeding an octave. (A
bandwidth of 1 octave is one in which
the upper frequency is twice the lower
frequency.) Traveling-wave tubes have
been designed for frequencies as low as
300 megahertz and as high as 50
gigahertz. The twt is primarily a voltage
amplifier. The wide-bandwidth and low-
noise characteristics make the twt ideal
for use as an rf amplifier in microwave
equipment.
35. SOLO
Travelling Wave Tube
collector
input
output
Figure 5. - electron- beam bounching and a detail-foto of a helix (Measure detail for 20 windings)
The following figure shows the electric fields that are parallel to the electron beam inside the
helical conductor.
The electron- beam bounching already starts at the beginning of the helix and reaches its highest
expression on the end of the helix. If the electrons of the beam were accelerated to travel faster than
the waves traveling on the wire, bunching would occur through the effect of velocity modulation.
Velocity modulation would be caused by the interaction between the traveling-wave fields and the
electron beam. Bunching would cause the electrons to give up energy to the traveling wave if the
fields were of the correct polarity to slow down the bunches. The energy from the bunches would
increase the amplitude of the traveling wave in a progressive action that would take place all along
the length of the TWT.
36. SOLO
Travelling Wave Tube
Characteristics of a TWT
The attainable power-amplification are essentially
dependent on the following factors:
• constructive details (e.g. length of the helix)
• electron beam diameter (adjustable by the
density of the focussing magnetic field)
• power input (see figure 6)
• voltage UA2 on the helix
As shown in the figure 6, the gain of the twt has got a linear characteristic of about 26 dB at small
input power. If you increase the input power, the output power doesn't increase for the same gain.
So you can prevent an oversteer of e.g the following mixer stage. The relatively low efficiency of
the twt partially offsets the advantages of high gain and wide bandwidth.
Given that the gain of an TWT effect by the electrons of the beam that interact with the electric
fields on the delay structure, the frequency behaviour of the helix is responsible for the gain.
The bandwidth of commonly used TWT can achieve values of many gigahertzes. The noise
figure of recently used TWT is 3 ... 10 dB.
Return to Table of Content
38. SOLO
Klystron amplifiers are high power microwave vacuum tubes. Klystrons are velocity-modulated
tubes that are used in some radar equipments as amplifiers. Klystrons make use of the transit-
time effect by varying the velocity of an electron beam. A klystron uses one or more special
cavities, which modulate the electric field around the axis the tube.
Klystron
On reason of the number of the cavities klystrons are divided up in:
• Multicavity Power Klystrons
• Reflex Klystron
Two-Cavity Klystron
A klystron uses special cavities which modulate the electric field around the axis the tube. In the
middle of these cavities, there is a grid allowing the electrons to pass. The first cavity together with
the first coupling device is called a „buncher”, while the second cavity with its coupling device is
called a „catcher”.
39. SOLO Klystron
• The electron gun produces a flow of electrons1
• The bunching cavities regulate the speed of
the electrons so that they arrive in bunches at the
output cavity.
2
• The bunches of electrons excite microwaves in the
output cavity of the klystron.3
• The microwaves flow into the waveguide , which
transports them to the accelerator.
4
• The electrons are absorbed in the beam stop 5
In a klystron:
http://www2.slac.stanford.edu/vvc/accelerators/klystron.html
40. SOLO Klystron
Reflex (Repeller) Klystron
Another tube based on velocity modulation, and used to generate
microwave energy, is the reflex klystron (repeller klystron). The reflex
klystron contains a reflector plate, referred to as the repeller, instead
of the output cavity used in other types of klystrons. The electron
beam is modulated as it was in the other types of klystrons by passing
it through an oscillating resonant cavity, but here the similarity ends.
The feedback required to maintain oscillations within the cavity is
obtained by reversing the beam and sending it back through the
cavity. The electrons in the beam are velocity-modulated before the
beam passes through the cavity the second time and will give up the
energy required to maintain oscillations. The electron beam is turned
around by a negatively charged electrode that repels the beam
(„repeller”). This type of klystron oscillator is called a reflex klystron
because of the reflex action of the electron beam.
Three power sources are required for reflex klystron operation:
1. filament power,
2. positive resonator voltage (often referred to as beam voltage) used to
accelerate the electrons through the grid gap of the resonant cavity, and
3. negative repeller voltage used to turn the electron beam around.
The electrons are focused into a beam by the electrostatic fields set up by
the resonator potential (U2) in the body of the tube.The
accompanying graphic shows a circuit diagram with a repeller
klystron using a so called „doghnut”-shaped cavity resonator.
Return to Table of Content
44. SOLO
Simplified Schematic of the T/R Module
http://www.abacusmicro.com/designs.asp?sub=Links9
http://www.microwaves101.com/encyclopedia/transmitreceivemodules.cfm
60. SOLO
Radar Receiver
Simplified Radar Receiver (Non-Coherent)
The received RF-signals must transformed in a video-signal to get the wanted
information from the echoes. This transformation is made by a super heterodyne
receiver.
• Circulator
• RF Waveguides
• TR Switches
• Low Noise Amplifier (LNA)
• RF Controllable Gain Amplifier
• Mixer
• IF Band-Pass Filter
• IF Controllable Gain Amplifier
Return to Table of Content
61. SOLO
Ferrite circulators are often used as a diplexer, generally in modules for active antennae. The
operation of a circulator can be compared to a revolving door with three entrances and one
mandatory rotating sense. This rotation is based on the interaction of the electromagnetic wave
with magnetised ferrite. A microwave signal entering via one specific entrance follows the
prescribed rotating sense and has to leave the circulator via the next exit. Energy from the
transmitter rotates anticlockwise to the antenna port. Virtually all circulators used in radar
applications contain ferrite.
Ferrite circulators
http://www.radartutorial.eu/01.basics/rb01.en.html Return to Table of Content
62. SOLO
Duplexer with quarter-wave co-axial stubs
ATR
Tube
TR
Tube
A B
C D
During the transmitting pulse, an arc appears across both the tr tube (at the point D) and the
atr tube (at the point C) and causes the tr and atr circuits to act as shorted (closed-end) quarter-
wave stubs. The circuits then reflect an open circuit to the tr (at the point B) and atr (at the point
A) circuit connections to the main transmission line. None of the transmitted energy can pass
through these reflected opens into the atr stub or into the receiver. Therefore, all of the transmitted
energy is directed to the antenna.
„Branch- Duplexer”
During reception the amplitude of the
received echo is not sufficient to cause an
arc across either tube. Under this
condition, the atr circuit now acts as a
half-wave transmission line terminated in
a short-circuit. This is reflected as an open
circuit at the receiver T-junction (at the
point B), three-quarter wavelengths away.
The received echo sees an open circuit in
the direction of the transmitter. However,
the receiver input impedance is matched to
the transmission line impedance so that
the entire received signal will go to the
receiver with a minimum amount of loss.
http://www.radartutorial.eu/01.basics/rb01.en.html
Return to Table of Content
63. SOLO
keep- alive electrode
main gap
DC ground
ATR-tube for waveguide-stubs with a keep-alive electrode
TR-Tubes
TR tubes are usually conventional spark gaps enclosed in partially evacuated, sealed glass envelopes, as shown in
figure 2. The arc is formed as electrons are conducted through the ionized gas or vapor. You may lower the
magnitude of voltage necessary to break down a gap by reducing the pressure of the gas that surrounds the
electrodes. Optimum pressure achieves the most efficient tr operation. You can reduce the recovery time, or
deionization time, of the gap by introducing water vapor into the tr tube. A tr tube containing water vapor at a
pressure of 1 millimeter of mercury will recover in 0.5 microseconds. It is important for a tr tube to have a short
recovery time to reduce the range at which targets near the radar can be detected. If, for example, echo signals
reflected from nearby objects return to the radar before the tr tube has recovered, those signals will be unable to
enter the receiver.
This TR tube used at microwave frequencies is built to fit into, and become a part of, a wave guide. The
transmitted pulse travels up the guide and moves into the tr tube through a slot. During the transmitting pulse, an
arc appears into the TR tube. One-quarter wavelength away, this action effectively closes the entrance to the
receiver and limits the amount of energy entering the receiver to a small value. The windows of Quartz-glass
(irises) are used to introduce an equivalent parallel-LC circuit across the waveguide for impedance matching.
Tube electron MD 80 S 2 of „Raytheon” Company.
http://www.radartutorial.eu/01.basics/rb01.en.html Return to Table of Content
64. SOLO
„Balanced Duplexer”
Output
• A -3 dB-hybride divides the transmitters power in two parts;
• this part passed the slot of the hybride take a phase-shift of 90°;
• both parts of power cause an arc across both spark gaps
• these arcs short-circuit the waveguide and the power would be reflected;
• the power divides in the -3 dB-hybride once again;
• this part passed the slot of the hybride again take a phase-shift of 90°;
among the parts in the direction of the transmitter occurs a phase-shift of 180° and
these parts of power compensates among each other;
• both parts in the direction of the antenna have the same phase and accumulate to the
full power.
During reception the amplitude of the
received echo is not sufficient to cause an
arc across either spark gap. both parts of
the received echo can pass the spark gaps.
The echoes recur both hybrides and
accumulate their parts in-phase. The loss
of this duplexer is about 0.5 to 1.5 dB.
„Balanced Duplexer” works in accordance with the following principle:
http://www.radartutorial.eu/01.basics/rb01.en.html Return to Table of Content
66. SOLO
Receiver Equivalent Noise
Boltzman’s constant
Gain = G1
Noise Figure = F1
Gain = G2
Noise Figure = F2
Gain = Gi
Noise Figure = Fi
The gain of the receiver is iGGGG 21 ⋅=
The noise figure of the receiver is
i
i
GGG
F
GG
F
G
F
FF
2121
3
1
2
1
111 −
++
−
+
−
+=
A radar receiver usually has a pre-amplifier (1) characterized by a low noise figure
(F1) and by a high gain (G1) such that the effect of the noise of other amplifiers is
negligible and This is the Low Noise Amplifier (LNA).1FF ≈
The noise energy (white noise) at the Receiver is [ ]jouleFTkEN 0=
where
Kjoulek
/1038.1 23−
×=
The receiver consists of a number of amplifiers in cascade.
KT
2900 = room temperature
F receiver noise figure
Receiver Noise Power [ ]wattBFTkN 0=
B - Receiver Bandwidth Return to Table of Content
67. SOLO
Transmitted RF signal (in phasor form) is ( ) ( )tpetS tj
Tr
RFω
=
p (t) - the pulse train function
At the front-end of the Antenna we receive a shifted and attenuated version of the
transmitted pulse:
( ) ( )
( )cRtpeVtS tj
cv
TRF
/2Re −= −ωω
ωRF - the RF angular velocity
ωT - the target’s Doppler shift
2 R/c time delay between transmission and reception
V – random complex voltage strength
c – velocity of light
We assume that from the Antenna emerge radar signal of the Sum S and
Difference D
( )
( )
( )
( ) ( )cRtpFeVD
cRtpeVS
tj
tj
TRF
TRF
/2
/2
−∆=
−=
−
−
ψωω
ωω
Receiver Intermediate Frequency (IF)
68. SOLO
The Superheterodyne Receiver translates the high RF frequency ωRF to a lower
frequency for a better processing.
This is done my mixing (nonlinear multiplication) the input frequency ωRF- ωT
with ωRF± ωIF to obtain ωIF - ωT
IF
Amp
IF
Amp
Band Pass
at IF
Band Pass
at IF
S
D
'D
'S
( ) tjst IFRF
eLO ωω ±
1
Mixer
Mixer
First Intemediate Frequaency (1st IF)
( )
( )
( )
( ) ( )cRtpFeVD
cRtpeVS
tj
tj
TRF
TRF
/2
/2
−∆=
−=
−
−
ψωω
ωω
The Receiver translates the high RF frequency ωRF to a lower frequency to a
better processing. This is done my mixing (nonlinear multiplication) the input
frequency ωRF- ωT with ωRF± ωIF to obtain ωIF - ωT .
The IF signal is amplified and bandpass filtered to produce an output at IF frequency
( )
( )
( )
( ) ( )cRtpFeVD
cRtpeVS
tj
tj
TIF
TIF
/2''
/2''
−∆=
−=
−
−
ψωω
ωω
If the mixing frequency is centered at ωRF± ωIF than the output is centered at
ωIF and at the image 2 ωRF± ωIF .
Receiver Intermediate Frequency (IF)
69. SOLO
A second mixing frequency is sometimes added to avoid potential problems with
image frequency.
IF
Amp
'S
''S
( ) tjnd IFIF
eLO ωω 2
2 ±
Mixer
Second Intemediate Frequaency (2nd IF)
IF
Amp
'D
''D
Mixer
Phase
Shifter
AGC
AGC
Band Pass
at 2nd IF
Band Pass
at 2nd IF
( )
( )
( )
( ) ( )cRtpFeVD
cRtpeVS
tj
tj
TIF
TIF
/2"
/2"
2
2
−∆=
−=
−
−
ψ
ωω
ωω
The output of the Second Intermediate Frequency (2nd
IF)
( )
( )
( )
( ) ( )cRtpFeVD
cRtpeVS
tj
tj
TIF
TIF
/2''
/2''
−∆=
−=
−
−
ψωω
ωω
Receiver Intermediate Frequency (IF)
Return to Table of Content
71. SOLO
Coherent Pulse-RADAR Block Diagram
Block Diagram of a Simple Coherent Radar
f0
Power
Amplifier
Signal
Generator
Coherent
Oscillator
(COHO)
fLO
fRF
fIF
fIF
f0 + fd
fIF + fd
fd
f0=fRF + fIF
IF BP &
Variable Gain
Amplifier
CYRCULATOR
SIGNAL
PROCESSOR
ANGLE
TRACKER
DOPPLER
TRACKER
RANGE
TRACKER
SEEKER
LOGIC
RADAR
CENTRAL
PROCESSOR
RADOME
LOW-PASS-
FILTER
ANTENNA
STABILIZATION
A/D
ANALOG DIGITAL
FREQUENCY
SOURCE
RFIF +
RECEIVER
ANTENNA
RF
Variable
gain
LNA
RF
Switch
AGC
Stable
Local
Oscillator
(STALO)
LNA
Run This
Return to Table of Content
72. Radar Equation
Radar Cross Section Definition
SOLO
- Target Radar Cross Section (RCS) [m2
]TGTσ
The incident Power Density (Irradiance) at the target is given by:
2 2 2
/i i i i iS E H H E watt m
µ ε
ε µ
= × = =
r r
The Power Density (Irradiance) intercepted and scattered
by the target is given by: [ ]i TGTS wattσ
The received Power Density (Irradiance) is defined as:
2 2 2
/r r r r rS E H H E watt m
µ ε
ε µ
= × = =
r r
Power scattered by the target in each steradian: ( ) [ ]/ 4 /i TGTS watt strσ π
Solid angle of receiver as seen from the target: [ ]2
/RCVRA R strΩ=
The received Power is given by:
[ ]2
4
i TGT RCVR
S A
watt
R
σ
π
The received Power is given also
by:
2
/r RCVRS A watt m
2
4
i TGT RCVR
r RCVR
S A
S A
R
σ
π
=
2
lim 4 r
TGT
R
i
S
R
S
σ π
→∞
=Since RCS is defined in the Far Field:
73. SOLO
Radar Cross Section σ of a Sphere of Radius r as a Function of the Wavelength λ
Radar Equation
75. Stealth aircraft are practically undetectable by sensors. They exploit the
diagram to minimize scattered and reflected signals, and to focus the
residuals in few directions, different from that of the sensors.
Stealth aircraft are practically undetectable by sensors. They exploit the
diagram to minimize scattered and reflected signals, and to focus the
residuals in few directions, different from that of the sensors.
Contributors to Target RCS
Radar Equation
84. fog (gr/cm3
)
rain (mm/hr)
air
Target
ECM Pod
Ground
A/C Radar
Missile, Target, Environment
fog (gr/cm3
)
rain (mm/hr)
air
Target
Transmitted
Mainlobe
Energy
ECM Pod
Ground
A/C Radar
Transmitted
Side-lobe
Energy
Missile RADAR Seeker Transmision
fog (gr/cm3
)
rain (mm/hr)
air
Target
Direct-path
Target Return
ECM Pod
Ground
A/C Radar
Target Reflected Energy Return
fog (gr/cm3
)
rain (mm/hr)
air
Multipath
Target Return
Target
ECM Pod
Ground
A/C Radar
Target Multipath Return
SOLO
Target Energy Return versus Return from Unwanted Factors
• A/C Radar, Target,
Environment (rain, fog, clutter)
• Radar Seeker Transmission
• Target Energy Return
• Target Multipath Return
• Target ECM Return
• Ground Clutter Return
fog (gr/cm3
)
rain (mm/hr)
air Electronic Counter
Measures (ECM)
Return
Target
ECM Pod
Ground
A/C Radar
Target ECM Return
fog (gr/cm3
)
rain (mm/hr)
air Electronic Counter
Measures (ECM)
Return
Target
Direct-path
Target Return
Received
Mainlobe
Clutter
Energy
ECM Pod
Ground
A/C Radar
Received
Side-lobe
Clutteer
Energy
Ground Clutter Return
fog (gr/cm3
)
rain (mm/hr)
air Electronic Counter
Measures (ECM)
Return
Multipath
Target Return
Target
Direct-path
Target Return
Transmitted
Mainlobe
Energy
ECM Pod
Ground
A/C Radar
Transmitted
Side-lobe
Energy
Target, Multipath, ECM, Clutter Returns
Run This
Radar Equation
Return to Table of Content
85. Far away from the source of radiation (far field)
the electromagnetic fields and are perpendicular
to each other and to the direction of propagation,
and their amplitudes drop off inversely with the Range R.
E
r
H
r
( ) ( ) ( ) 10202101 constRERRERRER =⇒=
( ) ( ) ( ) 20202101 constRHRRHRRHR =⇒=
That means that the electromagnetic field acts as a spherical wave.
Accordingly the irradiance at a range R from an isotropic radiator (radiating uniformly
in all directions) is:
[ ]2
2
/
4
mwatt
R
P
HES rad
r
π
=×=
rr
0
0
0
0 EH
µ
ε
=
where < > means the time average.
A non-isotropic radiator will radiate more in some direction than in others, and the
maximal irradiation will be:
[ ]2
2
/
4
mwattG
R
P
HES rad
MAXMAXr
π
=×=
rr
where G is the Antenna Gain, a measure of the maximum radiation capability of
the Antenna.
SOLO Radar EquationIrradiation
86. r
MAXr
S
S
G =:
Radar Equation
Bϕ
Bϑ
ϕD
ϑD
Antenna
Radiation
Beam
Assume for simplicity that the Antenna radiates all the power into the solid angle
defined by the product , where and are the angle from the
boresight at which the power is half the maximum (-3 db).
BB ϕϑ , 2/Bϕ± 2/Bϑ±
ϑϑ
λ
η
ϑ
D
B
1
=
ϕϕ
λ
η
ϕ
D
B
1
=
λ - wavelength
ϕϑ DD , - Antenna dimensions in directionsϕϑ,
ϕϑ ηη , - Antenna efficiency in directionsϕϑ,
then
( ) eff
BB
ADDG 22
444
λ
π
ηη
λ
π
ϕϑ
π
ϕϑϕϑ ==
⋅
=
where
ϕϑϕϑ ηη DDAeff =:
is the effective area of the Antenna.
2
4
λ
π
=
effA
G
SOLO
87. Radar Equation
Transmitter
IV
Receiver
R
1 2
Let see what is the received power on an
Antenna, with an effective area A2 and range R
from the transmitter, with an Antenna Gain G1
Transmitter
VI
Receiver
R
1 2
2122
4
AG
R
P
ASP dtransmitte
rreceived
π
==
Let change the previous transmitter into a receiver and the receiver into a
transmitter that transmits the same power as previous. The receiver has now an
Antenna with an effective area A1 . The Gain of the transmitter Antenna is now G2.
According to Lorentz Reciprocity Theorem the
same power will be received by the receiver; i.e.:
122
4
AG
R
P
P dtransmitte
received
π
=
therefore
1221 AGAG =
or
const
A
G
A
G
==
2
2
1
1
We already found the constant; i.e.: 2
4
λ
π
=
A
G
SOLO
88. Radar Equation
The Power Density (Irradiance) at the target is given by:
TRP
TRG
TRR
EV
Target
Transmitter
[ ]2
Pr
2
/
1
4
1
mW
LRL
GP
S
TGTXMTR
opagation
TGTTR
rTransmitte
TR
TRTR
r
→
→
=
π
- Transmitter Power [W]TRP
- Transmitter Antenna Gain in the Target directionTRG
- Transmitter Loss (XMTR+Antenna+Radome) ( > 1 )TRL
- Range Transmitter to Target [m2
]TRR
- Propagation Loss from Transmitter to Target ( > 1 )TGTTRL →
SOLO
89. Radar Equation
The Power reflected by the target in the receiver direction is:
[ ]WGA
LRL
GP
GASP
TGT
TGTTGT
TGTXMTR
opagation
TGTTRTR
rTransmitte
TR
TRTR
TGTTGTrTGT
σ
π
→
→
==
Pr
2
4
1
- Target Effective area in the Transmitter direction [m2
]TGTA
- Target Gain in the Receiver directionTGTG
- Propagation Loss from Target to Receiver ( > 1 )RCVRTGTL →
The Power Density [W/m2
] received at the Receiver is
[ ]2
Pr
2
/
1
4
1
mW
LR
Pp
RCVRTGT
opagation
RCVRTGTRCVR
TGTRCV
→
→
=
π
Target
Transmitter
Receiver
SOLO
- Target Radar Cross Section (RCS) [m2
]TGT TGT TGTA Gσ =
90. Radar Equation
[ ]2
Pr
2
Pr
2
/
1
4
11
4
1
mW
LR
GA
LRL
GP
p
RCVRTGT
opagation
RCVRTGTRCVR
TGTTGT
TGTXMTR
opagation
TGTTRTR
rTransmitte
TR
TRTR
RCVR
TGT
→
→
→
→
=
ππ σ
- Propagation Loss at the Receiver ( > 1 )RCVRL
The Power Density [W/m2
] received at the Receiver is
[ ]W
L
A
LR
GA
LRL
GP
LApP
ceiver
RCVR
RCVR
RCVRTGT
opagation
RCVRTGTRCVR
TGTTGT
TGTXMTR
opagation
TGTTRTR
rTransmitte
TR
TRTR
RCVRRCVRRCVRCVR
TGT
RePr
2
Pr
2
1
4
11
4
1
/
→
→
→
→
=
=
ππ σ
The Power [W/m2
] received at the Receiver is
- Effective area in the Receiver Antenna [m2
]RCVRA
SOLO
96. SOLO
Decibels
Radar Parameters Often Expressed in Decibels
• Antenna Gain
• dBi (gain relative to isotropic)
• Power Loss
• dB (power out/power in)
• Power
• dBW (power related to 1 watt)
• dBm (power related to 1 milliwatt)
• Radar Cross Section (RCS)
• dBsm (RCS related to 1 square meter)
Return to Table of Content
97. SOLO
Clutter is a return or group of returns that is undesirable for the radar performing
a certain task.
Clutter
Clutter returns are the vector summation (amplitude and phase) from all of the
Scattering centers within the radar resolution cell. Thus, the resultant Radar Cross
Section (RCS) of the clutter cell is given by:
( )
2
1
exp
= ∑=
scN
k
kk j φσσ
where
λ
ππφ kk
Radark
R
c
R
f 4
2
2 =
= relative phase
Resultant field
for
one polarization
1 2
3
4 5
6
7
98. SOLO
Mathematical Approaches to Characterize Clutter
Clutter
• Clutter Amplitude:
- Statistical quantities: mean, standard deviation
- Statistical distributions: probability amplitude (or power) density or
cumulative probability
• Time Varying Properties:
- Correlation function, power spectral density
• Spatially Varying Properties:
- Spatial distributions, correlations, spectra
99. SOLO
Characterizing Clutter Using Statistical Quantities
Clutter
• Statistical quantities are useful, but knowing the amplitude distribution is equaly
important
• Mean:
n
x
x
n
j
j∑=
=
1
• Standard deviation :
( )
1
1
2
−
−
=
∑=
n
xx
n
j
j
σ
Return to Table of Content
100. ah
MV
pθ
e
ψ
R
ψcosR
Ae
Aψ
Horizontal
Ground
Main Lobe
Beam
Transmitter
& Receiver
πθθπθ ≤+≤⇒−≤≤− ppp ee 0
Define a ray R from transmitter
to ground, defined by the angles
e,ψ, relative to Missile velocity
vector.
VM is the Missile (transmitter)
velocity vector, having an angle
θp with the horizontal plane.
( )
≤≤−
≤+≤
≥
+
=
2/2/
0
cossin
πψπ
πθ
ψθ
p
a
p
a
e
hR
e
h
R ( )
ψ
θ 22
cos
1cos
R
h
e a
p −±=+
The doppler frequency shift along the ray R is given by:
( ) ( ) ( )[ ]
ψ
θψθ
λ
ψθθθθ
λ
ψ
λ
cos
sincoscos
2
cossinsincoscos
2
coscos
2
2
2
_
aa
p
a
p
M
pppp
MM
clutterd
h
R
R
h
R
hV
ee
V
e
V
Rf
≥
+
−±=
+++==
SOLO
Ground Clutter
101. ( )
( ) ( )[ ]
+
−±=
+++=
=
R
h
R
hV
ee
V
e
V
Rf
a
p
a
p
M
pppp
M
M
clutterd
θψθ
λ
ψθθθθ
λ
ψ
λ
sincoscos
2
cossinsincoscos
2
coscos
2
2
2
_
( ) p
M
aclutterd
V
hRf θ
λ
ψ
sin
20
_
=
==
( ) ψθ
λ
θ
coscos
20
_ p
M
e
clutterd
V
Rf
p =+
=∞→
( ) ψθ
λ
πθ
coscos
2
_ p
M
e
clutterd
V
Rf
p
−=∞→
=+
Altitude Line
λ
ψ
θ
M
h
R
clutterd
V
ef
p
a
2
0,0
cos
_ =
==
=
clutterdf _
( )RangeR
( )RangeR
Clutter
No Clutter
Clutter
Power
Clutter
Power
Main Lobe
Clutter
(MLC)
Altitude
Return
λ
MV2
p
MV
θ
λ
cos
2
AA
M
e
V
coscos
2
ψ
λ
p
MV
θ
λ
sin
2
p
MV
θ
λ
cos
2
−
( ) ApA
a
e
h
ψθ cossin +
( )
( )
+
=
=
ApA
a
ML
AA
M
AAclutterd
e
h
R
e
V
ef
ψθ
ψ
λ
ψ
cossin
coscos
2
,_
Main Lobe
ah
MV
pθ
e
ψ
R
ψcosR
Ae
Aψ
Horizontal
Ground
Main Lobe
Beam
Transmitter
& Receiver
SOLO
Ground Clutter
102. ah
MV
e
ψ
R
ψcosR
Horizontal
Ground
Transmitter
& Receiver
Main Lobe
Beam
Ae
Aψ
0=pθ
( )
2
2
0
_
cos
2
coscos
2
−±=
=
=
R
hV
e
V
Rf
aM
M
clutterd
p
ψ
λ
ψ
λ
θ
( ) 0
0
_
=
==
ψ
aclutterd hRf
( ) ψ
λ
θ
cos
20
_
M
e
clutterd
V
Rf
p =+
=∞→
( ) ψ
λ
πθ
cos
2
_
M
e
clutterd
V
Rf
p
−=∞→
=+
Altitude Line
λ
ψ
θ
M
h
R
clutterd
V
ef
p
a
2
0,0
cos
_ =
==
=
clutterdf _
( )RangeR
( )RangeR
Clutter
No Clutter
Clutter
Power
Clutter
Power
Main Lobe
Clutter
(MLC)
Altitude
Return
λ
MV2
0=pθ
AA
M
e
V
coscos
2
ψ
λ
λ
MV2
−
AA
a
e
h
ψcossin
( )
=
=
AA
a
ML
AA
M
AAclutterd
e
h
R
e
V
ef
ψ
ψ
λ
ψ
cossin
coscos
2
,_
Main Lobe
0=pθ
SOLO
Ground Clutter
103. Ground
ah
MV
pθ
ψcosR
Ae
Aψ
Main Lobe
Beam
Transmitter
& Receiver
Cones of
Equi-Range
Rays
R
Projection of
Transmitter
& Receiver
on the Ground
Equi-range
Points
on the Ground
Projection on the Ground
M.L.B.
The Clutter energy from
a range R are obtained
for all points on the ground
that are at the range R from
the Transmitter/Receiver.
Assuming a flat ground,
the points on the ground
a a range R > ha are located
at the intersection of the
conical surface with the
apex at the Transmitter/
Receiver and its altitude line
as the conic axis..
The points on the flat
Ground having the same
range R from the
Transmitter/Receiver
are circles.
SOLO
Ground Clutter
104. Ground
ah
MV
pθ
ψcosR
Ae
Aψ
Main Lobe
Beam
Transmitter
& Receiver
Cones of
Equi-doppler
Rays
R
Intersection
of Missile
Velocity Vector
with the Ground
Ellipsee pθ<
Parabolee pθ=
Hyperbolee pθ>
Equi-doppler
Points
on the Ground
Projection on the Ground
M.L.B.
The points on the ground
that have the same doppler
shift are located on rays
started from Transmitter/
Receiver and are at the same
angle relative to the Missile
Velocity vector VM.
Therefore the points on the
Ground that have the same
doppler shift are located on
the intersection of the conus
with the apex at the
Transmitter/Receiver and
the conic axis the Missile
Velocity vector VM.
EllipseeFor p ⇒<θ
ParaboleeFor p ⇒=θ
HyperboleeFor p ⇒>θ
SOLO
Ground Clutter
105. Ground
ah
MV
pθ
ψcosR
Ae
Aψ
Main Lobe
Beam
Transmitter
& Receiver
Cones of
Equi-doppler
RaysCones of
Equi-Range
Rays
R
Projection of
Transmitter
& Receiver
on the Ground
Intersection
of Missile
Velocity Vector
with the Ground
Ellipsee pθ<
Parabolee pθ=
Hyperbolee pθ>
Equi-doppler
Points
on the Ground
Equi-range
Points
on the Ground
Projection on the Ground
M.L.B.
SOLO
Ground Clutter
106. SIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODESIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODE
SOLO Target in Ground Clutter
107. SIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODE MODE,
(a) A TYPICAL SITUATION: (b) MAP OF RETURNS ON THE RANGE/VELOCITY PLANE: (c) FOLDING OF
CLUTTER OVER THE RANGE AXIS (LOW PRE):
(d) CONCENTRATION OFRETURNS ON THE VELOCITY AXIS (HIGH PRF).
SIGNALS AND CLUTTER IN A PULSE DOPPLER RADAR, IN THE LOOK-HOTIZON MODE MODE,
(a) A TYPICAL SITUATION: (b) MAP OF RETURNS ON THE RANGE/VELOCITY PLANE: (c) FOLDING OF
CLUTTER OVER THE RANGE AXIS (LOW PRE):
(d) CONCENTRATION OFRETURNS ON THE VELOCITY AXIS (HIGH PRF).
SOLO
Target in Ground Clutter
108. SOLO
Ground Clutter
Illuminated Ground Area Resolution Cell : Beam Limitted Case
The Main Beam Clutter (Ground) Area in Range Resolution Cell when
is give (see Figure) by:
( ) ( ) pazcRA θϕτ cos/2/tan2/2Clutter =
Ground
Main Lobe
Beam
Transmitter
& Receiver
( ) ( )2//2/tan2tan τϕθ cR elp <
R – range to ground along beam center
φaz – angular beam width in azimuth
φel – angular beam width in elevation
θp –beam grazing angle
τ – pulse width [sec]
c – speed of light 3 108
m/sec
( )Clutter Clutter pAσ σ θ=
σ – ground reflectivity as function of
grazing angle
111. SOLO
Clutter
Illuminated Volume Resolution Cell (Pulse Limitted)
The Volume Clutter in Range Resolution Cell is give (see Figure) by:
( )2/
4
2
Clutter τϕϕ
π
cRV elaz=
R – range to ground along beam center
φaz – angular beam width in azimuth
φel – angular beam width in elevation
τ – pulse width [sec]
c – speed of light 3 108
m/sec
Main Lobe
Beam
Transmitter
& Receiver
Choose scatters on the main beam center Groundkk RRuntilkRkR ≥=∆= ,2,1
RADAR
I
k
f
c
where
sV
f =
⋅
= λ
λ
12
r
Their Doppler is given by
According to Range and Doppler of each scatter determine the Range-Doppler cell (i,j) for the
scatter.
112. Clutter returns are the vector summation (amplitude and phase) from all of the
scattering centers within the radar resolution cell.
SOLO Clutter
The Clutter is obtained by integration (summation) of the signals from the same
range-doppler cells:
where
Nsc – number of scatters in the volume VClutter
σk– Radar Cross Section of scatter k
Rk– Range to scatter k
The equivalent Radar Cross Section σClutter of the
clutter in the resolution cell of volume VClutter is:
( )2/
4
2
Clutter τϕϕ
π
cRV elaz=
g (0,0) ≈ 1 – antenna pattern
R – Range to the center of the volume VClutter
See Tildocs # 763310 v1
( )
( )
( )
∑=
+
−=Σ
jiN
k
k
kk
trver
Rcvr
Xmtr
sc
c
c
R
RR
j
L
GG
Pji
,
1
2
k
kscatter
3
2
0
2
ClutterVolume
2
2
2exp
R4
,
π
σ
π
λ
Illuminated Volume Resolution Cell (Pulse Limitted)
∑=
==
scN
k k
kscatter
ClutterClutter
R
RV
1
4
4
σ
ησ ∑=
=
scN
k k
kscatter
Clutter RV
R
1
4
4
σ
η
Since the Volume Clutter is on the Main-Beam the effect of it on angle errors is
like that of the radar noise.
Return to Table of Content
Main Lobe
Beam
Transmitter
& Receiver
113. Multipath
Target Return
Target
Ground
A/C
RADAR
Target Multipath Return
SOLO
Multipath Return
Target Multipath is the Received Signal
for the mirror reflection the target relative
to Earth surface.
The vector position of the Target relative
to earth is
LTLTLTT zhyYxXR 111 ++=
r
The vector position of the mirrored
Target relative to earth is
( ) LLTTLTLTLTMT zzRRzhyYxXR 112111_ ⋅−=−+=
rrr
The vector of the signal received by Seeker from the i Target scatter is
IT RRR
rrr
−=
The vector of the signal received by Seeker from the mirrored Target is
( ) ( ) LLTLLTITM zzRRzzRRRR 112112 ⋅−=⋅−−=
rrrrrr
Clutter
hT – altitude above ground surface
114. SOLO
Multipath Return – Range Discrimination
The Target Range to Seeker is
( )22
ITIT hhXR −+= −
Let compute
Clutter
The Range of the Mirror Target to Seeker is
( ) RhhXR ITITM ≥++= −
22
( )( ) ( ) ( ) ITITITMMM hhhhhhRRRRRR 4
2222
=−−+=−=+−
R
hh
RR
hh
RR
IT
RRR
M
IT
M
M 24 2≈+
≈
+
=−
..
2
GR
R
hh
RR IT
M ≤≈−If , for all Target scatters k, we cannot
distinguish between Target and Target’s Mirror
..
2
GR
R
hh
RR
IT
M >≈−If , for some Target scatters, we can
distinguish between Target and Target’s Mirror and we will
choose the echoes with the smallest range
Multipath
Target Return
Target
Ground
A/C
RADAR
Target Multipath Return
115. SOLO
Multipath Return – Doppler Discrimination
The Target Range-Rate to Seeker is
( )22
ITIT
IITTITIT
hhX
hhhhXX
R
−+
++
=
−
−−
Let compute
Clutter
The Range-Rate of the Mirror of Target to Seeker is
( )( ) ( )
( )
( )
( )
( )
( )[ ] ( )[ ] Mi
Mi
IT
ITITITIT
IITTITITIT
ITIT
IITTITIT
ITIT
IIiTTITIT
MMM
RR
RR
hh
hhXhhX
hhhhXXhh
HHX
HHHHXX
HHX
HHHHXX
RRRRRR
4
4
2222
2
22
2
22
2
22
=
++−+
++
=
=
++
++
−
−+
++
=−=+−
−−
−−
−
−−
−
−−
0
24
3
2
>≈
+
=−
≈+
M
IT
RRR
M
M
M
IT
Mi RR
R
hh
RR
RR
RR
hh
RR
M
..
2
3
GDRR
R
hh
RR M
IT
M ≤≈− If we cannot distinguish between
Target and Target’s Mirror
..
2
3
GDRR
R
hh
RR M
IT
M >≈−
If we can distinguish between
Target and Target’s Mirror and we don’t have a
Multipath problem.
( )22
ITIT
IITTITIT
M
hhX
hhhhXX
R
++
++
=
−
−−
Assume that Target & Mirror Target are in the same Range Gate.
Multipath
Target Return
Target
Ground
A/C
RADAR
Target Multipath Return
116. SOLO
Multipath Return – Angular Discrimination
We found:
( ) ( ) LLTLLTITM zzRRzzRRRR 112112 ⋅−=⋅−−=
rrrrrr
Clutter
The angular separation between Target Scatter k and Target Mirror Scatter k is:
( )
RR
RzzR
RR
RR
M
LLT
M
M
rrrr
×⋅
−=
× 11
2
Multipath Return – Range – Doppler Map
According to Range and Doppler of each scatter mirror:
determine the Range-Doppler cell (i,j) for the scatter mirror.
( ) kITkITMk RhhXR ≥++= −
22 ( )
( )22
ITkITk
IITkTkITkITk
Mk
HHX
hhhhXX
R
++
++
=
−
−−
integer=+= mRRmR kambiguoussunambiguouMk
RADAR
Mk
Mk
f
c
where
R
f == λ
λ
2
integer=+= nffnf kambiguoussunambiguouMk
( )RRIntegi kambiguousk ∆= /
( )ffIntegj kambiguousk ∆= /
Multipath
Target Return
Target
Ground
A/C
RADAR
Target Multipath Return
117. SOLO
Multipath Return – Signal Power
Assume that The Target and it’s Mirror can be represented each
by Nsc scatters ( k=1,Nsc)
Clutter
The Mirror signal received by the Seeker from scatter k passes
three paths:
TGTXMTR
opagation
TGTTRk
rTransmitte
TR
trXmtr
LRL
GP
→
→
Pr
2
1
4
1
π1. Transmitted power from Seeker to Target Scatter k at the distance Rk:
2. Reflected by the target scatter k and reaching the ground at the distance ( ) ( )[ ] 2/122
_1 TkIIT
TkI
Tk
k hhX
hh
h
R ++
+
=
GNDTGT
opagation
GNDTGTk
TGTTGT
LR
GA
TGT
→
→
Pr
2
1
1
4
1
πσ
3. Reflected by the ground and reaching the Seeker at the distance ( ) ( )[ ] 2/122
_2 TkIIT
TkI
I
k hhX
hh
h
R ++
+
=
ReceivernPropagatio
2
2
1
4
1
RCVR
RCVR
GNDTGT
RCVRGNDk
GND
L
A
LR
→
→π
σ
π
λ
4
2
RCVR
RCVR
G
A =
Multipath
Target Return
Target
Ground
A/C
RADAR
Target Multipath Return
118. SOLO
Multipath Return – Signal Power
Therefore the received power from the k scatter mirror is:
Receiver
2
nPropagatio
2
2
Pr
2
1
Pr
2
1
4
1
4
11
4
11
4
1
RCVR
RCVRant
GNDTGT
RCVRGNDk
GND
GNDTGT
opagation
GNDTGTk
kScatterkScatter
TGTXMTR
opagation
TGTTRk
rTransmitte
TR
antXmtr
M
L
GG
LRLR
GA
LRL
GP
P
kScatter
k
π
λ
π
σ
ππ
σ
→
→
→
→
→
→
=
Clutter
( ) ( )[ ] 2/122
_1 TkIIT
TkI
Tk
k hhX
hh
h
R ++
+
= ( ) ( )[ ] 2/122
_2 TkIIT
TkI
I
k hhX
hh
h
R ++
+
=
( )
( )
( )( ) ( )
++
+++++
−=Σ ∑=
Σ
c
cj
gG
L
GG
Pji
jiN
k
ClutterkElkAzproc
trver
Rcvr
Xmtr
k2k1k
k2k1kk2k1k,
1 k2k1k
kscatter
proc
Targ
3
2
0
2
TargetMultipath
RRR
RRRRRR
2exp
RRR
,
L4
,
π
σσεε
π
λ
( )
( )
2
2
2
1
2
2Targ
3
2
0
2
,
4 kkk
ClutterkScatterkElkAz
proc
proc
trver
Rcvr
XmtrM
RRR
g
L
G
L
GG
PP k
σσεε
π
λ Σ
=
or:
where: ( )kElkAzant gGG εε ,0 Σ=
RCVRRCVRGNDGNDTGTTGTTRTRtrver LLLLLL →→→=
proc
proc
RcvrRCVR
L
G
GG
Targ
=
The Target Multipath received signal is obtained by integration (summation) of the
signals from the same range-doppler cell (i,j):
in the same way:
( )
( )
( )( ) ( )
++
+++++
−=∆ ∑=
∆
c
cj
gG
L
GG
Pji
jiN
k
ClutterkElkAzElAzproc
trver
Rcvr
Xmtr
k2k1k
k2k1kk2k1k,
1 k2k1k
kscatter,
proc
Targ
3
2
0
2
Az/ElTargetMultipath
RRR
RRRRRR
2exp
RRR
,
L4
,
π
σσεε
π
λ
Return to Table of Content
135. SOLO Signal Processing
Collecting Pulsed Radar Data: 1 Pulse, Multiple Range-Gates Samples
• when using a coherent receiver, each range sample comprises one “I” sample and
one “Q” sample, forming one complex number I+j Q.
• Each range cells contains an echo from a different range interval.
• Also called Range-Bins, Range-Gates, Fast-Time Samples.
136. SOLO
Signal Processing
Collecting Pulsed Radar Data: Multiple Pulses
• when using a coherent receiver, each range sample comprises one “I” sample and
one “Q” sample, forming one complex number I+j Q.
• Repeat for multiple pulses in a “coherent processing interval” (CPI) or “dwell”
Sequence of samples for a fixed range bin represents echoes from same range interval
over a period of time.
137. SOLO Signal Processing
Perform FFT in Each Range Gate
After FFT a Range-Doppler
Map is obtained for Signal
Processing
FFT
Run This
138. SOLO Signal Processing
Perform FFT in Each Range Gate
Data-cube for Signal Processing
Repeat the Operation for each Receiver Channel (Σ,ΔAz,ΔEl,Γ for monopulse antenna
or Σi,j for each element in an Electronic Scanned Antenna)
Range – Doppler Cells in Σ and ΔAz, ΔEl
FFT
FFT
FFT
FFT
Run This
145. SOLO
Windowing (continue – 3)
Dolph-Chebyshev window
( ) ( )[ ]
( )
( )[ ]
( ) ( )4,3,2,10cosh
1
cosh
1,,2,1,0,
coshcosh
coscoscos
1
1
1
≈
=
−=
=
=
−
−
−
αβ
β
π
β
ω
ω
α
N
Nk
N
N
k
N
W
WIDFTnw
k
k
The α parameter controls the side-lobe level via the formula:
Side-Lobe Level in dB = - 20 α
The Dolph-Chebyshev Window (or Dolph window) minimizes the Chebyshev norm of
the side lobes for a given main lobe width 2 ωc:
( ) ( ){ }ωωω WWsidelobes cwwww >=∞= ∑
=
∑
maxmin:min 1,1,
The Chebyshev norm is also called the L - infinity norm, uniform norm, minimax
norm, or simply the maximum absolute value.
Signal Processing
157. SOLO Signal Processing
Generation of Σ , ΔAz, ΔEl Range – Doppler Maps (continue – 1)
The received signal from the scatter k is:
( ) ( )[ ] ( ) ( )ttTktttTkttfCts ddkdk
r
k
r
k ++≤≤++−= τθπ2cos
Ck
r
– amplitude of received signal
td (t) – round trip delay time given by ( )
2/c
tRR
tt kk
d
+
=
θk – relative phase
The received signal is down-converted to base-band in order to extract the quadrature
components. More precisely sk
r
(t) is mixed with: ( ) [ ] τθπ +≤≤+= TktTktfCty kkk 2cos
After Low-Pass filtering the quadrature components of Σk, ΔAz k or ΔEl k signals are:
( ) ( )
( ) ( )
=
=
tAtx
tAtx
kkQk
kkIk
ψ
ψ
sin
cos
( ) ( )
+−≅−=
c
tR
c
R
fttft kk
kdkk
22
22 ππψ
The quadrature samples are given by:
( ) ( )
+−≅=
c
tR
c
R
fjAjAtX kk
kkkkk
22
2expexp πψ
Ak - amplitude of Σk, ΔAz k or ΔEl k signals
ψk - phase of Σk, ΔAz k or ΔEl k signals
( )
+−
+≅+=
c
tR
c
R
fAj
c
tR
c
R
fAxjxtX kk
kk
kk
kkQkIkk
22
2sin
22
2cos ππ
159. Decision/Detection TheorySOLO
Hypotheses
H0 – target is not present
H1 – target is present
Binary Detection
( )0
Hp - probability that target is not present
( )1
Hp - probability that target is present
( )zHp |0 - probability that target is not present and not declared (correct decision)
( )zHp |1 - probability that target is present and declared (correct decision)
Using Bayes’ rule: ( ) ( ) ( )∫=
Z
dzzpzHpHp |00
( ) ( ) ( )∫=
Z
dzzpzHpHp |11
( )zp - probability of the event Zz ⊂
Since p (z) > 0 the Decision rules are:
( ) ( )zHpzHp || 01
< - target is not declared (H0)
( ) ( )zHpzHp || 01
> - target is declared (H1) ( ) ( )zHpzHp
H
H
|| 01
0
1
<
>
160. Decision/Detection TheorySOLO
Hypotheses H0 – target is not present H1 – target is present
Binary Detection
( )zHp |0 - probability that target is not present and not declared (correct decision)
( )zHp |1 - probability that target is present and declared (correct decision)
( )zp - probability of the event Zz ⊂
Decision rules are: ( ) ( )zHpzHp
H
H
|| 01
0
1
<
>
Using again Bayes’ rule:
( )
( ) ( )
( )
( )
( ) ( )
( )zp
HpHzp
zHp
zp
HpHzp
zHp
H
H
00
0
11
1
|
|
|
|
0
1
=
<
>
=
( )0
| Hzp - a priori probability that target is not present (H0)
( )1
| Hzp - a priori probability that target is present (H1)
Since all probabilities are
non-negative
( )
( )
( )
( )1
0
0
1
0
1
|
|
Hp
Hp
Hzp
Hzp
H
H
<
>
161. Decision/Detection TheorySOLO
Hypotheses
( )1
| Hzp - a priori probability density that target is present (likelihood of H1)
( )0
| Hzp - a priori probability density that target is absent (likelihood of H0)
Detection Probabilities
( ) M
z
D
PdzHzpP
T
−== ∫
∞
1| 1
( )∫
∞
=
Tz
FA
dzHzpP 0
|
( ) D
z
M
PdzHzpP
T
−== ∫∞−
1| 1
PD - probability of detection = probability that the target is present and declared
PFA - probability of false alarm = probability that the target is absent but declared
PM - probability of miss = probability that the target is present but not declared
T - detection threshold
D
P
FAP
( )1| Hzp( )0
| Hzp
M
P
z
Tz
( )
( )
T
Hzp
Hzp
T
T
=
0
1
|
|
H0 – target is not present H1 – target is present
Binary Detection
( )
( )
( )
( )
T
Hp
Hp
Hzp
Hzp
LR
H
H
=
<
>
=
1
0
0
1
0
1
|
|
:Likelihood Ratio Test (LTR)
162. Decision/Detection TheorySOLO
Hypotheses
Decision Criteria on Definition of the Threshold T
1. Bayes Criterion
D
P
FAP
( )1
| Hzp( )0
| Hzp
MP
z
T
z
( )
( )
T
Hzp
Hzp
T
T
=
0
1
|
|
H0 – target is not present H1 – target is present
Binary Detection
( )
( )
( )
( )
T
Hp
Hp
Hzp
Hzp
LR
H
H
=
<
>
=
1
0
0
1
0
1
|
|
:Likelihood Ratio Test (LTR)
The optimal choice that optimizes the Likelihood Ratio is
( )
( )1
0
Hp
Hp
TBayes
=
This choose assume knowledge of p (H0) and P (H1), that in general are not known a priori.
2. Maximum Likelihood Criterion
Since p (H0) and P (H1) are not known a priori, we choose TML = 1
( )1
| Hzp( )0
| Hzp
M
P z
Tz
( )
( )
1
|
|
0
1
== ML
T
T
T
Hzp
Hzp
D
P
FAP
163. Decision/Detection TheorySOLO
Hypotheses
Decision Criteria on Definition of the Threshold T (continue)
3. Neyman-Pearson Criterion
DP
γ=FAP
( )1
| Hzp( )0
| Hzp
M
P
z
T
z
( )
( ) PN
T
T
T
Hzp
Hzp
−
=
0
1
|
|
H0 – target is not present H1 – target is present
Binary Detection
( )
( )
( )
( )
T
Hp
Hp
Hzp
Hzp
LR
H
H
=
<
>
=
1
0
0
1
0
1
|
|
:Likelihood Ratio Test (LTR)
Neyman and Pearson choose to optimizes the probability of detection PD
keeping the probability of false alarm PFA constant.
Egon Sharpe Pearson
1895 - 1980
Jerzy Neyman
1894 - 1981
( )∫
∞
=
T
TT
z
z
D
z
dzHzpP 1
|maxmax ( ) γ== ∫
∞
Tz
FA
dzHzpP 0
|constrained to
Let use the Lagrange’s multiplier λ to add the constraint
( ) ( )
−+= ∫∫
∞∞
TT
TT
zz
zz
dzHzpdzHzpG 01 ||maxmax γλ
Maximum is obtained for:
( ) ( ) 0|| 01
=+−=
∂
∂
HzpHzp
z
G
TT
T
λ
( )
( ) PN
T
T
T
Hzp
Hzp
−
==
0
1
|
|
λ
zT is define by requiring that: ( ) γ== ∫
∞
Tz
FA
dzHzpP 0
|
169. SOLO SEARCH & DETECT MODE
Computation of the Σ Range-Doppler Map, chooses the Detection Threshold
and policy (continue – 2).
DOPPLER
WINDOW
R W
A I
N N
G D
E O
W
R G
A A
N T
G E
E S
DOPPLER
FILTERS
S cells
CFAR
Window
R∆
f∆
Target
Uncertainty
Window
( ) ( ) ( )[ ]∑
∗
+ Σ⋅Σ=
n
j Window
CFARNoiseClutter jiji
n
iC ,,
1
Guard
(Gap)
Window
• Computation of Clutter + Noise Threshold
• Coherent Detection:
( ) ( )
( ) ( ) ClutterThjiNiCIf
ClutternoThjiNiCIf
NoiseClutter
NoiseClutter
⇒+>
⇒+≤
+
+
1,
1,
( ) NoiseThNjiS +≥
Window
yUncertaint
Target,
( ) ( ) ( )[ ]∑
∗
+ Σ⋅Σ=
n
j Window
CFARNoiseClutter jiji
n
iC ,,
1
1. If no Clutter declare a Detection in the (i,j) cell of the Target Window if
ThNoise is chosen to assure a predefined
Probability of Detection pd and of False Alarm pFA
( ) NoiseClutterNoiseClutter ThCjiS ++ +≥
Window
yUncertaint
Target,
2. If Clutter declare a Detection in the (i,j) cell of the Target Window if
ThNoise is chosen to assure a predefined
Probability of Detection pd and of False Alarm pFA
193. SOLO Anti – Ballistic Missiles
AN/FPS-115 PAVE PAWS Radar
Peak Power 1,792 active elements at 325
watts = 582.4 kilowatts (kW)
Duty Factor 25% (11% search, 14%
track)
Average Power 145.6 kW
Effective Transmit
Gain
37.92 dB
Active Radar Diameter 22.1 m
Frequency 420 MHz – 450 MHz
Radar Detection Range 5,556 km (3,000 nmi)
Wavelength 0.69 m at 435 MHz
Sidelobs -20 dB (1st
), -30 dB (2nd
)
-- 38 dB (root mean square)
Face Tilt 20 degrees
Number of Faces 2
3 db Beam Width 2.2 degrees
Specifications
http://www.fas.org/spp/military/program/track/pavepaws.htm
Radars for Ballistic Missile Defense
197. SOLO Anti – Ballistic Missiles
Sea-Based X-Band Radar
Sea-Based X-Band Radar is a floating, self-propelled,
mobile radar station designed to operate in high winds
and heavy seas. It is part of the United States
Government's Ballistic Missile Defense System.
The Sea-Based X-Band Radar is mounted on a 5th
generation Norwegian-designed, Russian-built CS-50
semi-submersible twin-hulled oil-drilling platform.
Conversion of the platform was carried out at the
AMFELS yard in Brownsville, Texas; the radar mount
was built and mounted on the platform at the Kiewit
yard in Ingleside, Texas, near Corpus Christi. It will be
based at Adak Island in Alaska but can roam over the
Pacific Ocean to detect incoming ballistic missiles.
ST. LOUIS, Jan. 10, 2006 -- Boeing [NYSE: BA]
announced today the arrival in Hawaii of the Sea-
Based X-Band Radar (SBX) built for the U.S. Missile
Defense Agency. This marks an interim stop in the
vessel's transport operation, originating in the Gulf
of Mexico and maneuvering through the Straits of
Magellan, ultimately destined for Adak, Alaska.
http://cryptome.sabotage.org/sbx1-birdseye.htm
Radars for Ballistic Missile Defense
Return to Table of Content
208. Hovanessian, S.A.,“Radar Detection and Tracking Systems” , Artech House,1973
Hovanessian, S.A.,“Radar System Design and Analysis” , Artech House,1984
Levanon, N.,“Radar Principles” , John Wiley & Sons, 1988
Peebbles, P.Z., “Radar Principles “, John Wiley & Sons, 1998
References
RADAR Basics
209. Brookner, E.,“Tracking and the Kalman Filter Made Easy” , John Wiley & Sons, 1998
Brookner, E., Ed., “Radar Technology” , Artech House
Cook, C.C., Bernfeld, M., “Radar Signals: An Introduction to Theory and Application”,
Artech House, 1993
Schleher, D.C.,“MTI and Pulsed Doppler Radar”, Artech House, 1991
References
RADAR Basics
210. Galati, G., Ed.,“Advanced Radar Techniques and Systems”,
IEE Radar, Sonar, Navigation and Avionics Series 4, Peter Peregrinus Ltd., 1993
Sabatini, S., Tarantino, M., “Multifunction Array Radar: System Design and Analysis”,
Artech House, 1994
Ulaby, F.T., Fung, A.K., Moore, R.K., “Microwave Remote Sensing, Active and Passive:
Radar Remote Sensing and Surface Scattering and Emission Theory”, Vol. 2,
Artech House, 1982
Farina, A., “Antenna-Based Signal Processing Techniques for Radar Systems”,
Artech House, 1992
References
RADAR Basics
212. Zmuda, H., Touglian, E.N., “Photonic Aspects of Modern Radar ” , Artech House, 1994
Neri, F., “Introduction to Electronic Defense Systems”, SciTech Publishing, Incorporated,
2006
References
RADAR Basics
213. SOLO
References
RADAR Basics
1. S. Hermelin, “My RADAR Reference Books”,
2. S. Hermelin, “Electromagnetic Waves & Photons”,
3. S. Hermelin“Short History of Radar Beginnings”,
4. S. Hermelin “Airborne Radars1”,
. “Airborne Radars2”,
. “Airborne Radars Examples2”,
. “Airborne Radars Examples1”,
5. S .Hermelin, “Pulse Radar Doppler Seeker”,
214. SOLO
References
S. Hermelin, “Range & Doppler Measurements in RADAR Systems”,
RADAR Basics
S. Hermelin, “Clutter Models”,
Return to Table of Content
S. Hermelin, “Radar Signal Processing”,
S. Hermelin , “Fourier Transforms in Radar”,
S. Hermelin, “Matched Filters and Ambiguity Functions for Radar Signals”,
S. Hermelin, “Pulse Compression Waveforms”,
S. Hermelin, “Detection Decisions”,
Georgia Tech Lectures in RADAR
215. January 15, 2015 215
SOLO
Technion
Israeli Institute of Technology
1964 – 1968 BSc EE
1968 – 1971 MSc EE
Israeli Air Force
1970 – 1974
RAFAEL
Israeli Armament Development Authority
1974 –
Stanford University
1983 – 1986 PhD AA
218. SOLO
Formation of Standing Waves
Standing wave in a string (both ends clamped).
Formation of standing wave through reflection
of a sinusoidal wave at a fixed end.
226. Pulse Radar Parameters
Transmitted Signal
Tr
Tp
F0
Tr – Pulse Repetition Interval (PRI)
Tp – Transmitted Pulse Width
F0 – Transmitted RF frequency
Pp – RF peak power
D.C – Duty Cycle = Tp/Tr
Pav – RF average power = Pp*D.C
227. Pulse Doppler Radar – Clutter
Altitude
return
Antenna
Main Beam
Antenna
Side Lobes
Ground
Target
Power
Frequency
Altitude Side lobe
Main Lobe
Incoming TargetReceding Target
λ
Vc2
Doppler
Range
Radar Altitude
Vradar
Side lobe
Clutter
Main Lobe
Clutter
Incoming
Targets
Receding
Targets
Crossing
Targets
Noise limited
Clutter limited
228. Pulse Doppler Radar – Clutter
Clutter Cross Section in Doppler Cell
clutteratGainAntenna)G(
tcoefficienReflection
widthgateRangeR
cluttertodirectionflighbetweenAngle
VelocityRadarV
LengthWavedTransmitte
thfilter widFFTB
cluttertoRange
)()
sin2
(
a
0
g
0
=
=
=
=
=
=
=
=
=
θ
σ
θ
λ
θσ
θ
λ
σ
R
GR
V
RB ag
2 cos
D
V
f
θ
λ
=
2 cosD
B
B
f V
λ
θ
=
229. Detection of Radar Signals
Swerling Models
Case 1
The echo received from a target on any look is constant but are
independent (uncorrelated) from look to look
The probability-density function for the RCS:
nsfluctuatiotargetalloverRCSaveragetheis
)exp(
1
)(
av
avav
p
σ
σ
σ
σ
σ −=
Case 2
The probability-density function for the RCS is same as for Case 1, but
the fluctuations are more rapid
Cases 1 and Case 2 apply to a target consisting of many independent
scatterers equal in RCS - Aircrafts
231. Detection of Radar Signals
Swerling Models
Case 3
The fluctuation is assumed to independent from look to look as in Case
1, but the probability density function is given by
)
2
exp(
4
)( 2
avav
p
σ
σ
σ
σ
σ −=
Case 4
The probability-density function for the RCS is same as for Case 2, but
the fluctuations are more rapid
Case 3 and Case 4 apply to a target that can be represented as one large
reflector together with other small reflectors - Ships
In all the above cases the RCS value in the radar equation is the
average RCS.
The probability of detecting a given RCS can be calculated
233. Detection of Radar Signals
Noise and False Alarm
The noise is assumed to be Gaussian with probability density function
noisetheofvaluesquare-meantheis
dvvandvvalueebetween thvvoltagenoisethefindingofyprobabilittheis)(
)
2
exp(
2
1
)(
0
0
2
0
ψ
ψπψ
+
−=
dvvp
dv
v
dvvp
The probability that the noise envelope will exceed the voltage threshold VT is Pfa
)
2
exp(
0
2
ψ
T
fa
V
P −=
234. Detection of Radar Signals
Integration of pulse trains
The probability of detection for M-out-of-N:
∑=
−
−
−
=
N
Mj
jN
d
j
dd pp
jNj
N
P )1(
)!(!
!
Pd probability of single detection
And the probability of false alarm
∑=
−
−
−
=
N
Mj
jN
n
j
nn pp
jNj
N
P )1(
)!(!
!
Pn probability of false alarm in single detection
235. •Extraction of Information
• PRF selection guide lines:
– Incoming targets – High PRF
• No Doppler ambiguity
• Range ambiguity
– Receding targets – Medium PRF
• Range and Doppler ambiguity
– Crossing targets – low PRF given target and
main lobe clutter are not co-range – other wise
no detection
• No range ambiguity
• Doppler ambiguity
237. Extraction of Information
The Range coverage equals PRI – 2*Pulse_width + recovery time
The pulse width is defined by PRI and maximum available duty cycle
Example:
PRF = 100 KHz; Duty cycle 10%
PRI = 1/PRF = 10 µsec= 1500 meters
Maximum pulse width = 150 meters
Maximum range coverage 1500 – 300 = 1200 meters.
In this example if range uncertainty is smaller than 1200 meters, one PRF is suffice.
Otherwise a set of PRF’s must be selected to cover the uncertainty.
All targets ranges above PRI are folded within PRI – range ambiguity
238. Extraction of Information
Target range = N PRI + R1
Where R1 = Target Range within PRI
N = number of folds 0…N
)(
1
PRI
R
fixN
PRIRR
T
T
=
⊗=
Example
RT=12,300 m PRI = 1500 m
N = fix(12300/1500) = 8 R1= 12300-1500*8=300 meters
240. Extraction of Information
Resolving range ambiguity
Use at least 2 PRF’s so
RT = N PRI1+R1 = M PRI2 + R2
PRF1 and PRF2 are derived from basic clock so K1*clock= PRF1 and K2*clock=PRF2
Maximum unambiguous range is 1/ K1*K2*clock.
Where K1 and K2 are prime numbers.
Example
Clock = 20 KHz K1=6 K2=7
PRF1 = 120 KHz PRF2 = 140 KHz
PRI1= 1250 m PRI2~ 1070 m
R1= 950 m R2= 70 m
True range = 7*1250+950= 9*1070+70=9700 m
N= 7 M=9
Same applies for resolving the Doppler ambiguity.
241. Extraction of InformationRange Tracking
Target
Amplitude
Range Sampling
Range Gate
CFAR Threshold
E1
E2
E3
R11 R12 R13
∑
++
=
3,2,1
313212111
rangeTarget
E
ERERER
242. Extraction of Information
Range Tracking
The goal is to predict where the target range will be on following
detection
Based on current range using a tracking algorithm (KALMAN) the
following target range is predicated
The error between real position and actual position is calculated and the
tracking parameters are updated
Tracking algorithms implementing 2 integration will extract the range
and range rate for the target on line of sight.
Comp Int Int
True Range
Predicted Range
Closing Velocity
Range Error
243. Extraction of Information
Doppler Tracking
Target
Amplitude
Range Sampling
Doppler Gate
CFAR Threshold
E1
E2
E3
D11 D12 D13
∑
++
=
3,2,1
313212111
DopplerTarget
E
EDEDED
244. Doppler Tracking
The goal is to predict where the target Doppler will be on following
detection
Based on current Doppler using a tracking algorithm (KALMAN) the
following target Doppler is predicated
The error between real Doppler and actual Doppler is calculated and the
tracking parameters are updated
Tracking algorithms implementing 1 integration will extract the Doppler
on line of sight.
Comp Int
True Doppler Predicted DopplerDoppler Error
Extraction of Information
245. Extraction of Information
Angular Information
The Monopulse concept:
L
θ
θ
L sinθ
The path difference between the signals as received at each lobe is L sin θ
The phase difference φ for a wavelength λ:
λ
α
πφ
sin
2
l
=
The outputs from lobes are added and subtracted as vectors
)
2
sin(
)
2
cos(
φ
φ
∆
Σ
=∆
=Σ
K
KSUM
Difference
Editor's Notes
http://www.nndb.com/people/126/000099826/
“Principles of Modern Radar” Georgia Tech, 2004, Jim Scheer, “Advanced Radar Waveforms”
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
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Extraction of Information
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Extraction of Information
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Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
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Extraction of Information
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Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
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Extraction of Information
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Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
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Extraction of Information
Perry, B., “Clutter Characteristics and Effects”, Principlesof Modern Radar, 2003, GeorgiaTech
Perry, B., “Clutter Characteristics and Effects”, Principlesof Modern Radar, 2003, GeorgiaTech
Schleher, D. C., “MTI and Pulsed Doppler Radar”, Artech House, 1991, pg. 181
“Principles of Modern Radar” Georgia Tech, 2004, Samuel O.Piper
http://en.wikipedia.org/wiki/Hamming_window#Hamming_window
Oppenheim, A.V., Schafer, R.W., “Discrete Time Signal Processing”, Prentice Hall, 1989, pp.444-452
http://en.wikipedia.org/wiki/Hamming_window#Hamming_window
Oppenheim, A.V., Schafer, R.W., “Discrete Time Signal Processing”, Prentice Hall, 1989, pp.444-452
http://en.wikipedia.org/wiki/Hamming_window#Hamming_window
Oppenheim, A.V., Schafer, R.W., “Discrete Time Signal Processing”, Prentice Hall, 1989, pp.444-452
http://en.wikipedia.org/wiki/Hamming_window#Hamming_window
http://ccrma.stanford.edu/~jos/sasp/
Oppenheim, A.V., Schafer, R.W., “Discrete Time Signal Processing”, Prentice Hall, 1989, pp.444-452
http://ccrma.stanford.edu/~jos/sasp/
Oppenheim, A.V., Schafer, R.W., “Discrete Time Signal Processing”, Prentice Hall, 1989, pp.444-452
http://en.wikipedia.org/wiki/Hamming_window#Hamming_window
Oppenheim, A.V., Schafer, R.W., “Discrete Time Signal Processing”, Prentice Hall, 1989, pp.444-452
Oppenheim, A.V., Schafer, R.W., “Discrete Time Signal Processing”, Prentice Hall, 1989, pg. 450
http://ccrma.stanford.edu/~jos/sasp/
M.A. Richards, “Modern Radar Control”, GeorgiaTech Course, 2004
Morris, G. V.,”Pulsed Doppler Radar”, Artech House, 1988, pp. 204-209 and 396-397
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
PRF selection guide lines:
Incoming targets – High PRF
No Doppler ambiguity
Range ambiguity
Receding targets – Medium PRF
Range and Doppler ambiguity
Crossing targets – low PRF given target and main lobe clutter are not co-range – other wise no detection
No range ambiguity
Doppler ambiguity
Extraction of Information
Extraction of Information
Extraction of Information
Extraction of Information
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Pulsen, Rader, Mathew, “Improving Ground Moving Target Indication Performance”, MIT Lincoln Laboratory & DARPA, KASSPER 2003 Workshop
http://russinoff.com/papers/crt.html
http://www.cut-the-knot.org/blue/chinese.shtml
http://en.wikipedia.org/wiki/Chinese_remainder_theorem
D. Curtis Schleher, “MTI and Pulsed Doppler Radar”, Artech House, 1991, pp. 441-448
Y.H. Ku and Xiaoguang Sun, “The Chinese Remainder Theorem”, The Franklin Institute, vol. 329, No.1, pp. 93-97, 1992
http://russinoff.com/papers/crt.html
http://www.cut-the-knot.org/blue/chinese.shtml
http://en.wikipedia.org/wiki/Chinese_remainder_theorem
D. Curtis Schleher, “MTI and Pulsed Doppler Radar”, Artech House, 1991, pp. 441-448
http://en.wikipedia.org/wiki/Chinese_remainder_theorem
D. Curtis Schleher, “MTI and Pulsed Doppler Radar”, Artech House, 1991, pp. 441-448
Sheldon M.Ross, ”Introduction to Probability Models”
R.McDonough & A.D. Whalen, “Detection of Signals in Noise”, 2nd Ed., pg. 142
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Gosset.html
John Minkoff, “Signals, Noise, and Active Sensors - Radar, Sonar, Laser Radar”
John Minkoff, “Signals, Noise, and Active Sensors - Radar, Sonar, Laser Radar”
John Minkoff, “Signals, Noise, and Active Sensors - Radar, Sonar, Laser Radar”, pp. 46-47
John Minkoff, “Signals, Noise, and Active Sensors - Radar, Sonar, Laser Radar”, pp. 46-47
John Minkoff, “Signals, Noise, and Active Sensors - Radar, Sonar, Laser Radar”, pp. 46-47
John Minkoff, “Signals, Noise, and Active Sensors - Radar, Sonar, Laser Radar”, pp. 46-47