Transcript Document

Chapter 1 Figure: Electronic Warfare Components
Electronic Warfare
Components
Electronic
Support
Electronic
Attack
Electronic
Protection
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1
Chapter 2 Figure: Radar Block Diagram
Antenna
Transmitter
Waveform
Generator
Control, Timing, Data Processing, & Storage
TransmitReceive
Switch
Receiver
Signal
Processor
Controls
& Displays
Plot Extractor
Threshold
Detection
Chapter 2 Figure: Radar Spherical Geometry
Radar Antenna Beam
R
Radar
4p steradians
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2
Chapter 2 Figure: Transmitted Pulsed Radar Waveform
sin(2pfct)
t
t
Amplitude
Amplitude
t
PRI
PRI
Time
Chapter 2 Figure: Incremental Buildup of the Received Target Signal Power
Target
3
2
4
Radar
1
5
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(1)
(2)
(3)
(4)
(5)
Radar effective radiated power (ERP)
Radar-to-target propagation
Reflected target signal power back to the radar
Target-to-radar propagation
Received target signal power out of the radar
receive antenna
3
Chapter 2 Figure: Polarization Of The Radar Waveform
E
H
Linear Polarization
Circular Polarization
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4
Chapter 2 Figure: Single Pulse Received Target Signal Power (S) And Receiver Thermal
Noise (N) vs. Radar-To-Target Range
 60
S
N
 70
 80
Power (dBW)
 90
 100
 110
 120
 130
 140
 150
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
Chapter 2 Figure: Single Pulse Target Signal-To-Noise Ratio vs. Radar-To-Target Range
80
70
Signal-To-Noise Ratio (dB)
60
50
40
30
20
10
0
 10
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
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5
Chapter 2 Figure: Multiple Pulse Signal-To-Noise Ratio (S/N)n, Detection Threshold (SNRdt),
and Single Pulse Signal-To-Noise Ratio (S/N), and as a Function of Radar-To-Target Range
80
(S/N)n
SNRdt
(S/N)
70
60
S/N (dB)
50
40
30
20
10
0
 10
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
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6
Chapter 2 Figure: A Basic Radar Receiver
Mixer
From
Antenna
RF
Amp
IF
Amp
Local
Oscillator
Matched
Filter
Signal
Processor
Envelop
Detector
Threshold
Detection
Video
Amp
Display
Plot
Extractor
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7
Chapter 2 Figure: Superheterodyne Receiver
Mixer
Received
Signal
Low
Noise
Amplifier
RF Signal
IF Signal
IF
Amplifier
Output
Signal
Local Oscillator Signal
100s MHz ~ 10s GHz
10s ~ 100s MHz
Chapter 2 Figure: Intermediate Frequency Amplifier And Bandpass Filter
Power
IF
Bandwidth
fIF
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fc
2fc+fIF
Frequency
8
Chapter 2 Figure: Digital Signal Processing Flow
I
From IF
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Quadrature
Detector
Q
AnalogTo-Digital
Converter
Digital
Signal
Processor
Output
9
Chapter 2 Figure: A Radar “A” Scope
To radar receiver
To timer
V
H
R 
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c t
2
10
Chapter 3 Figure: Target Signal Plus Noise Examples
S/N = 22 dB
S/N = 20 dB
S/N = 18 dB
S/N = 16 dB
S/N = 14 dB
S/N = 12 dB
S/N = 10 dB
S/N = 8 dB
S/N = 6 dB
Chapter 3 Figure: Threshold Detection of Target Signals
Target #2
Target #1
Receiver Output
Detection T hreshold
Mean Noise Level
False
Alarm
T ime
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11
Probability Density
Chapter 3. Probability Density Function For A Single Dice
1/6
1
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2
3
4
5
6
events
12
Chapter 3. Rayleigh Probability Density Function and Probability of False Alarm
pN(v)
P(v ≥ VT) = Pfa
N
v
VT
Chapter 3. Probability of False Alarm as a Function of Average Time Between False
Alarms and Radar Receiver Bandwidth
110
Probabi lity Of False Alarm
110
110
110
110
110
110
110
110
110
5
6
7
8
9
BR
(MHz)
0.1
 10
 11
0.5
1
5
10
50
100
 12
 13
 14
110
3
0.01
0.1
1
10
100
Average Time Between False Alarms (hours)
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Chapter 3. Impulse Probability Density Function Of A Constant Target Signal
1.0
pS(v)
S
v
Chapter 3. Rician Probability Density Function And Probability Of Detection
P(v ≥ VT) = Pd
pS+N(v)
VT
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S
v
14
Chapter 3. Probability Of False Alarm And Probability Of Detection
S/N
Noise
Signal + Noise
Pfa
Pd
v
VT
Chapter 3. Probability Of False Alarm And Probability Of Detection
110
(S/N)n
SNRdt
(S/N)
100
90
80
S/N (dB)
70
60
50
40
30
20
10
0
 10
0
25
50
75
100
125
150
175
200
225
250
275
300
Radar-To-Ta rget Range (km )
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Chapter 3. Pd As A Function Of S/N And Pfa – Constant Target Signal
Pfa = 10-4,10-6,10-8,10-10,10-12,10-14
1
0.9
Probability of Detection
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
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0
1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 17 18
S/N (dB)
16
Chapter 3 Figure: Additional Signal-To-Noise Ratio Required For Detection for Pfa = 10-6
Based On Swerling Case
Additio nal S/N Requi red For Detec tion (dB)
20.0
Swerling 1 & 2
Swerling 3 & 4
18.0
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
 2.0
 4.0
0.00
0.10
0.20
0.40
0.30
0.50
0.60
0.70
1.00
0.90
0.80
Probability Of Detection
Chapter 3 Figure: Change In Detection Range as a Function of the Change in the
Detection Threshold
Change In Detection Range
2
1.75
1.5
1.25
1
0.75
0.5
 12
 10
8
6
4
2
0
2
4
6
8
10
12
Change In Detection Threshold (dB)
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Chapter 3. Integration Gain – Coherent And Non-Coherent
100
Integratio n Gain
1.00
0.90
0.76
0.70
10
1
1
10
100
Number Of Pulses Integrated
Chapter 3. Non-Coherent Integration Gain: Pd = 50%, Pfa = 10-6
Non-Cohe rent Integratio n Gain
100
Case 0
Case 1
Case 2
Case 3
Case 4
Marcum
10
1
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1
10
Number Of Pulses Integrated
100
18
Chapter 3. Non-Coherent Integration Gain: Pd = 90%, Pfa = 10-8
1000
Non-Cohe rent Integratio n Gain
Case 0
Case 1
Case 2
Case 3
Case 4
Marcum
100
10
1
1
10
100
Number Of Pulses Integrated
Chapter 3. Constant False Alarm Rate Threshold And Receiver Output vs. Range
CFAR Threshold
Receiver Output
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Chapter 3. Cumulative Probability of Detection
Cummulati ve Probability O f Detection
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
2
3
5
6
8
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Attempts
Attempts
Attempts
Attempts
Attempts
0.9
1
Single Attempt Probability Of Detection
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Sequenti al Probability Of False Alarm
Chapter 3. Sequential Probability of False Alarm
110
110
110
110
110
110
110
110
110
110
110
110
110
110
110
4
2
3
5
6
8
5
6
7
8
Attempts
Attempts
Attempts
Attempts
Attempts
9
 10
 11
 12
 13
 14
 15
 16
 17
 18
110
6
110
5
110
4
110
3
110
2
Single Attempt Probability Of False Alarm
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Chapter 3. Binomial Probability of Detection for At Least M Detections Out Of N Attempts
1
Binomial Probability Of D etection
0.9
0.8
0.7
0.6
0.5
0.4
0.3
1-out-of-2
2-out-of-3
3-out-of-5
3-out-of-6
8-out-of-8
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Single Attempt Probability Of Detection
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Chapter 3 Figure: Simple Integrator And Delay Line Integrator
From IF
Range
Gate
Narrowband
Filter
Thresholding
Output
Simple Integrator
k<1
From IF
or Video
+
Delay
Line
Output
Delay Line Integrator
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Chapter 4 Figure: A Parabolic Antenna
Focus
E
l
e
c
t
r
o
m
a
g
n
e
t
i
c
W
a
v
e
Boresight
Axis
Parabola
Wavefront
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24
Chapter 4 Figure: Simple Line Antenna
z
A(y)
-D/2
x
q
y
D/2
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Line antenna
E(q)
25
Chapter 4 Figure: A Plane Wave
Wavefront
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Arriving
Wavelets
26
A zimu th P l ane
150
180
90
0
120
60
Chapter 4 Figure:
A Uniform
Current Distribution
10
20
z
30
30

40
A0
50
60
70
0
0
y
D/2
-D/2
210
330
240
300
270
Chapter 4 Figure: Antenna Gain Pattern, X-Y Plot And Polar Plot
0
 10
Antenna G ain (dBi)
 20
 30
 40
 50
 60
 70
 180
 135
 90
 45
0
45
90
135
180
El evat(degre
io n P es)
l an e
Angle
120
150
180
90
0
10
20
30
40
50
60
70
60
30
0
210
330
240
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300
270
27
Chapter 4 Figure: Antenna Pattern Characteristics
El evat io n P l an e
120
Backlobe
150
180
90
0
10
20
30
40
50
60
70
Nulls
60
Sidelobes
30
Mainbeam
or
0 Mainlobe
210
330
240
300
Sidelobes
270
Nulls
El evat io n P l an e
1
Antenna Gain (absolute)
0.8
0.6
Chapter 4 Figure: Antenna Half-Power Beamwidth
0.4
0.2
0 Antenna
 180
 135
Mainbeam
 90
 45
0
45
90
135
180
Angle (degrees)
q3dB
-3 dB
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Chapter 4 Figure: A Cosine Illumination
z
z = cos(y)
0
y
D/2
-D/2
Normaliz ed Antenna Gain (dBi)
Chapter 4 Figure: Antenna Patterns for Some Illumination Functions
0
Uniform
Cosine
Cosine Squared
5
 10
 15
 20
 25
 30
 35
 40
 45
0
5
10
15
20
25
30
Angle (degrees)
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29
Chapter 4 Figure: A Linear Array Antenna
Out Going or Incoming Signal
q
q
q
q
q
q
q
q
…
d
1
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d
2
d
3
d
4
d
5
d
6
7
N
30
Normali zed Antenna Ga in (dBi)
Chapter 4 Figure: Element Factor, Array Factor, And Resultant Antenna Gain
0
 10
 20
 30
 40
 90
Element Factor
Array Factor
Antenna Gain
 60
 30
0
30
60
90
Angle (deg)
Beam S teering
T he beam is steered in angle by changing the relative time delays (phase shifts) bet ween the individ
elements. We will comp ute and plot the array radiation pattern with beamq,steering,
d, q0) (noG(unit s) and
G_dB(q, d, q0). Whereq0 is the beam steering angle in degr T
ees.
his is Skolnik's equation 9.30 on page 56
the element radiation pattern included.
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Chapter 4 Figure: Time-Delay Steering
Far field
plane
wavefront
c T
q0
c t
q0
X
X
d
X
d
……..
X
X
X
d
d
D
X = Array element
Chapter 4 Figure: A Phase-Steered Array
Far field
plane
wavefront
B
q0
b1
q0
X
X
d
X
d
X = Array element
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……..
X
X
d
X
d
D
32
Normali zed Antenna Ga in (dBi)
Chapter 4 Figure: Element Factor, Array Factor, And Resultant Antenna Gain: Beam Steered
To 50°
0
 10
 20
 30
 40
 90
Element Factor
Array Factor
Antenna Gain
 60
 30
120
0
Angle (deg)
90
0
30
60
90
60
10
150
30
20
30
40
180
0
210
330
240
300
270
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Normali zed Antenna Ga in (dBi)
Chapter 4 Figure: Array Antenna Gain Pattern And Characteristics Change With Beam
Steering Angle
0
 10
 20
 30
 40
 90
 60
 30
0
30
60
90
Angle (deg)
120
90
0
60
10
150
30
20
30
40
180
0
210
330
240
300
270
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Normalized Antenna Gain (dBi )
Chapter 4 Figure: Array Factor Grating Lobes as A Function of Element Spacing
0
 10
 20
 30
 40
0.50 lamda
0.75 lamda
1.00 lamda
0
15
30
45
60
75
90
Angle (deg)
Normal ized Antenn a Gain (dBi )
Chapter 4 Figure: Array Factor Grating Lobes as A Function of Beam Steering Angle
0
 10
 20
 30
 40
 90
0 degees
30 degrees
60 degrees
 60
 30
0
30
60
90
Angle (deg)
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35
Chapter 4 Figure: Concept Of A Two Bit Phase Shift
Out
In
1
2
 = 180°
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1
2
 = 90°
36
Chapter 4 Figure: Array Configurations
Phase shifters
Amplifier-per-element
Amplifier
Element
Corporate Feed
Space Feed
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Amplifier-per-Subarray
Amplifier-per-Array
37
Chapter 5 Figure: A Simple Pulse – Time Domain, Voltage
f(t)  V sin(0 t)
0

t
2
t
2
0
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Time
38
Chapter 5 Figure: Spectral Plot Of Signal And Noise, Power – Log Scale
2
t 

sin   

V
t
 2 
G()  
t
 2p



2 

1
t
Noise

0
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Chapter 5 Figure: Range Gates
t
t
t
t
Range
gate 1
Range
gate 2
Range
gate 3
Range
gate 4
R
R
R
R
t
…
//
Range
gate n
Time
R
Range
0
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Chapter 5 Figure: Received Pulse In The Range Gates
Received
Pulse
t
Range
gate 1
Range
gate 2
Range
gate 3
Range
gate 4
…
//
Range
gate n
Range
R
Received
Pulse
t
Range
gate 1
Range
gate 2
Time
Range
gate 3
Range
gate 4
…
//
Range
gate n
Time
Range
R
Chapter 5 Figure: Resolving Range Ambiguous Using Multiple Pulse Repetition Intervals
Transmitted pulses
Received pulses
PRI 1
Apparent
Range 1
Apparent
Range 2
PRI 2
True Range
Time or Range
Time Reference
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Chapter 5 Figure: Convolution Of Simple Pulse
Transmitted
Pulse
f(t)

f(t+t)

t
2
t
2
0
0
t
2
t
2
Convolution
of pulse
with filter

 f(t)f(t  t)dt

Time
response
of filter
2t
Chapter 5 Figure: Half-Power Points

t
 f(t1)f(t1  t) dt 


 f(t2)f(t2  t) dt

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42
Chapter 5 Figure: Range Resolution As A Function Of Pulse Width
1500
Range Resolution (m)
1200
900
600
300
0
0
1
2
3
4
5
6
7
8
9
10
Pulsewidth (micro-sec)
Chapter 5 Figure: Unambiguous Range
t
PRI
Reflection
from pulse #1
Pulse #1
Pulse #2
0
Time
Range
Apparent
Range
True Range
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Chapter 5 Figure: Doppler Resolution – Simple Pulse
G()
G(+)

Frequency
Chapter 5 Figure: Linear Frequency Modulation Pulse Compression
df
dt
Bpc
t
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Time
t
Time
44
Chapter 5 Figure: Linear Frequency Modulation Pulse Compression Signal Processing
tc
t
Pulse
Compression
Filter
Time
Transit
Time
Frequency
Chapter 5 Figure: Phase Modulation And Pulse Compression Signal Processing Response
t
0°
0°
3
180°
2
1
2
3
Time
1
0
Time
0
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1
2
3
4
5
6
45
Chapter 5 Figure: Unambiguous Range As A Function Of Pulse Repetition Frequency
1500
Unambiguous Range (km)
1250
1000
750
500
250
0
100
1000
10000
Pulse Repetition Frequency (Hz)
Chapter 5 Figure: Eclipsing
Partial
Full
Time
Transmitted
Pulse
Received
Pulse
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Chapter 5 Figure: Range Resolution As A Function Of Modulation Bandwidth
Range Resolution (m)
1000
100
10
1
0.1
1
10
100
Modulation Bandwidth (MHz)
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47
Chapter 5 Figure: Split Gate Range Tracker Concept
Received Target Pulse
Time
Early
Gate
Late
Gate
Time
Early
Gate
Signal
Time
Late
Gate
Signal
Chapter 5 Figure: Split Gate Range Tracker
Range
Measurement
Early
Gate
Comparator
Late
Gate
Range
Track
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Error
Gate
Commands
48
Chapter 5 Figure: Split Gate Range Tracker Discriminator Curve
(-)
Err or Signal
(+)
High S/N
Medium S/N
Low S/N
(-)
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Range
(+)
49
Chapter 5 Figure: A Differentiating Circuit
Received Target Pulse
Output of
Differentiating Circuit
Chapter 5 Figure: Gun-Barrel Analogy
L
Prediction
errors
Trajectory
Prediction
point
Envelop of
possible trajectories
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l
Envelop of
measurement
uncertainties
R
q
50
Chapter 5 Figure: Range Rate for Stationary Radar and Moving Radar Systems
VT
Target
Range
Rate
Radar-to-target
range vector
VT
Target
Target
Range Rate
Stationary Radar
Radar-to-target
range vector
Radar
Range Rate
VR
Moving Radar
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51
Chapter 5 Figure: Doppler Shift Examples Based On Radar-Target Geometry
Only a part of this
target’s velocity produces
a Doppler shift
This target
produces no
Doppler shift
Target Doppler
shift negative with
respect to the ground
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Stationary Radar
Decreasing
Doppler shift
Target Doppler
shift similar to
that of the ground
Target Doppler shift
positive with respect
to the ground
This target
produces a
Doppler shift
Little or no
Doppler shift
Moving
Radar
Increasing
Doppler shift
Stationary
Radar
52
Chapter 5 Figure: Doppler Shift per Unit Range Rate (1 m/sec) As A Function of Carrier
Frequency
Per Unit Range Rate (1 m/sec)
1000
Doppler Shift (Hz)
100
10
1
0.1
0.1
1
10
100
Carrier Frequency (GHz)
Chapter 5 Figure: Range Rate per Unit Doppler Shift (1 Hz) As A Function of Carrier Frequency
Per Unit Doppler Shift (1 Hz)
10
Range Rate (m/sec)
1
0.1
0.01
0.001
0.1
1
10
100
Carrier Frequency (GHz)
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53
Chapter 5 Figure: A Coherent Pulse Burst Waveform And Its Spectrum
t
sin(2p fc t)
Time Domain
PRI
TI
1
t
Frequency Domain
fc+7PRF
fc+6PRF
fc+5PRF
fc+4PRF
fc+3PRF
fc+2PRF
fc+PRF
fc
fc-PRF
fc-2PRF
fc-3PRF
fc-4PRF
fc-5PRF
fc-6PRF
fc-7PRF
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1
t
54
Chapter 5 Figure: A Coherent Pulse Burst Waveform And Its Spectrum
Time Domain
Pulse Repetition
Frequency High
Frequency Domain
Pulse Repetition
Frequency Low
Time Domain
Frequency Domain
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55
Chapter 5 Figure: Doppler Filter Bank
Target Signal
Doppler Filters
fd
fIF
Negative Doppler Shift
Positive Doppler Shift
Frequency
Doppler Filter Bank
Chapter 5 Figure: Range Rate Resolution As A Function Of Carrier Frequency
Per Unit Doppler Filter Bandwidth (1 Hz)
Range Rate Resolution (m/sec)
10
1
0.1
0.01
0.001
0.1
1
10
100
Carrier Frequency (GHz)
7/15/2015
56
Chapter 5 Figure: Transmit And Receive Spectrums
Power
Transmit
Receive
Frequency
fd
fd
fd
fd
fd
fc+2PRF
fc+PRF+fd
fc+PRF
fc+fd
fc–PRF
fc-2PRF+fd
fc–2PRF
Chapter 5 Figure: Ambiguous Doppler Shift
PRF
Apparent Doppler
True Doppler
Reference
Receive
fd fd fd fd
fd
fd
fIF+PRF+fd
fIF+PRF
fIF+fd
fIF–PRF
7/15/2015
fd
57
Chapter 5 Figure: Unambiguous Range Rate As A Function Of Carrier Frequency
Per Unit PRF (1 Hz)
|Unambiguous Range Rate| (m/sec)
1
0.1
0.01
0.001
0.0001
0.1
1
10
100
Carrier Frequency (GHz)
Chapter 5 Figure: Average Power Over One Pulse Repetition Interval
Power
t
P
Pave
PRI
7/15/2015
Time
58
Chapter 5 Figure: Speed Gate Range Rate Tracker Concept
Target Signal
Voltage
Vhigh
Vlow
Low
Frequency
Filter
High
Frequency
Filter
Frequency
Chapter 5 Figure: Split Gate Range Rate Tracker
Mixer
Low
Filter
Doppler
Measurement
Comparator
High
Filter
Doppler
Track
7/15/2015
VCO
Error
Voltage Controlled
Oscillator Commands
59
Chapter 5 Figure: Range Rate Discriminator Curve
(-)
Err or Signal
(+)
High S/N
Medium S/N
Low S/N
(-)
7/15/2015
Doppler
(+)
60
Chapter 5. Cross Range Resolution
Cross Range
Target
q3dB
Radar
Chapter 5. Cross Range Resolution As A Function Of Radar-To-Target Range
Cross Range (m)
1000
100
10
0.25
0.50
0.75
1.00
1
1
10
deg
deg
deg
deg
100
Radar-To-Target Range (km)
7/15/2015
61
Chapter 5. Angle Tracking Using Offset Beams
Boresight Line
Beam
Position A
Target
Beam
Position B
Radar
Chapter 5. Angle Tracker
Angle
Measurements
Comparator
Angle
Track
7/15/2015
Angle
Commands
Error
62
Chapter 5. Angle Discriminator Curve
(-)
Err or Signal
(+)
High S/N
Medium S/N
Low S/N
(-)
Angle
(+)
Chapter 5. Far-Field Conical Scan (left) And Sequential Lobing (right) Patterns
Beam
Positions
over time
Beam
Rotation
7/15/2015
Boresight
Line
Beam Stepping
63
Normaliz ed Antenna Gain (dBi)
Chapter 5. Monopulse Tracking
0
5
 10
 15
Receive Beam 1
Receive Beam 2
 20
 10
5
0
5
10
Angle (degrees)
2
Response
Sum
Difference
1
0
1
 10
5
0
5
10
Angle (degrees)
7/15/2015
64
Chapter 5 Figure: Radar Resolution Cell
Range
Resolution (R)
Angular
Resolution (q)
Radar
Chapter 5 Figure: Target Altitude
RRT
fRT
hT
hR
RE
7/15/2015
RE
65
Chapter 5 Figure: Power Response Of Sidelobes
R
0
Range
Response (dB)
10
20
30
40
fd
Doppler
Chapter 5 Figure: Uniform (left) And Cosine (right) Weighting Functions
Time
7/15/2015
Time
66
Chapter 5 Figure: Ambiguity Diagram For A Simple Pulse
Scanned JPG file
7/15/2015
67
Chapter 5 Figure: Correlated Measurement Tracker
Range
Tracker
Range
Correlation
Tracker
Range Rate
Tracker
Range & Range Rate
Angle
Tracker
Angle
Tracker
Output
Range Rate
Chapter 5 Figure: Target State Tracker
Range
Range Rate
Angle
7/15/2015
Position
Target
Velocity
State
Tracker Acceleration
Tracker
Output
68
Chapter 6 Figure: Two Corner Reflector Designs
Dihedral
Trihedral
45°
45°
Note: Arrows indicated entry angle for maximum RCS
Chapter 6 Figure: Forward and Back Scattering from a Target
Forward Scatter
Forward Scatter
Target
Radar
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Backscatter
Forward
Scatter
Forward Scatter
69
Chapter 6 Figure: Radar Cross Section Of A Sphere
Mie or
Resonance
Region
Rayleigh
Region
Optical
Region
10
1
s
pr2
0.1
0.01
0.001
0.1
1
10
100
Circumference/Wavelength = 2pr/l
Chapter 6 Figure: Change In Radar Detection Range as a Function of the Change in the
Target Radar Cross Section
6
Change In Target Radar Detection Range
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
 30
 20
 10
0
10
20
30
Change In Radar Cross Section (dBsm)
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70
Chapter 6 Figure: Some RCS Patterns
l
2D
l
2D
Long Thin Rod
Sphere
D
D
D
l
2D
l
2D
D
Square Plate
l
2D
l
2W
D
D
Rectangular Plate
W
Note: Not to scale, approximately –90º to 90º aspect, D and W >> l
7/15/2015
71
Chapter 6 Figure: Area Of The Clutter Intercepted By The Radar Resolution Cell

h
R
ct
2
Elevation (Vertical) Plane

ct
2 cos 
q3dB
R q3dB
Azimuth (Horizontal) Plane
7/15/2015
72
Chapter 6 Figure: A 4p Corner Reflector And A Jack
7/15/2015
73
Chapter 7 Figure: Target, Clutter, and Noise Power Spectral Densities
Clutter
PSD
Target
PSD
Target
PSD
PRF
0
Receiver
Thermal
Noise PSD
2 PRF
Frequency
Chapter 7 Figure: Single Delay (Two Pulse) Canceller Power Frequency Response
Passbands
Response (dB)
20
Hd B( f )
d Bmi n
Rejection Notches
20
10
0
10
20
30
40
2500
2000
 f ma x
PRF = 500-Hz
7/15/2015
1500
1000
500
0
f
500
Frequency (Hz)
1000
1500
2000
2500
f ma x
74
Chapter 7 Figure: Clutter Rejection Due To Moving Target Indicator Frequency Response (a
close-up of Figure “x” at zero Doppler showing half the passband)
20
20
Input Clutter PSD
(f)
(f)
Response (dB)
10
d B( f )
0
MTI Response
10
20
Clutter PSD Residue
30
40
50
 60
60
0
0
7/15/2015
25
50
75
100
125
f
Frequency
150
(Hz)
175
200
225
250
f ma x
75
Chapter 7 Figure: Single- And Double-Delay Cancellers Power Frequency Response
Power Response (dB)
30
Clutter Spectra
Double-delay
10
Single-delay
10
30
50
200
150
100
50
0
50
100
150
200
Frequency (Hz)
7/15/2015
76
Chapter 7 Figure: Staggered PRF MTI
Rejection Notches
13.6
20
10
0
Hd B( f )
10
20
Passband
Passband
Passband
Passband
30
 40
40
4000
3000
3
2000
410Hz, PRF = 500 Hz
PRF1 = 400
2
7/15/2015
1000
0
f
1000
Frequency (Hz)
2000
3000
4000
410
3
77
Chapter 7 Figure: Frequency Response Of The Return Signals – Ground-based Radar
Amplitude
Ground clutter
Outgoing
targets
Low range
rate clutter
Incoming
targets
Receiver
Thermal Noise
-
7/15/2015
0
Doppler Frequency
+
78
Chapter 7 Figure: Airborne Pulse-Doppler Radar System
Scanned JPG File
7/15/2015
79
Chapter 7 Figure: Another View Of Pulse Doppler Clutter – Airborne Radar
Amplitude
Altitude
Return
Mainbeam Clutter
Sidelobe
Clutter
Outgoing
Targets
Incoming
Targets
-Vac
0
Vac cosq cosf
+Vac
Range Rate
Chapter 7 Figure: Moving Target Detection Signal Processing
Moving Target Detection Processor
20
Input
Signals
20
Output
Signals
10
0
HdB( f )
10
20
30
dBmi n 40
2500
 f max
7/15/2015
2000
1500
1000
500
0
f
500
1000
1500
2000
2500
f max
80
Chapter 7 Figure: Moving Target Indicator Improvement Factor As A Function of
the Clutter Spectral Width Over the Pulse Repetition Frequency
MTI Im provement Fa ctor (dB)
100
Triple Delay
Double Delay
Single Delay
90
80
70
60
50
40
30
20
10
0
0.001
0.01
0.1
(Clutter Spectral Width) / (Pulse Repetition Frequency)
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81
Chapter 7 Figure: Moving Radar Platform Produces A Synthetic Aperture And
Associated Geometry
VR
n
Sequential
Radar
Antenna
Positions
L
For Each
Transmitted
Pulse
...
5
Region
Being
Imaged
4
3
2
1
VR
Radar Antenna Mainbeam
Swath
Being Imaged
Range
Azimuth (Horizontal) Plane
Radar
Antenna
Mainbeam
Swath
Width
Swath
Width
Elevation (Vertical) Plane
Swath Being Imaged
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82
Chapter 7 Figure: Synthetic Aperture Radar Illuminating A Patch on the Ground
Leading Edge
Patch on
the ground
Trailing Edge
Lmax
q3dB
R q3dB
Rp
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83
Chapter 7 Figure: Synthetic Aperture Radar – Squint And Spotlight Modes
VR
Squint
Angle
Swath
Being Imaged
Swath
Width
Squint Mode
Spot
Being
Imaged
Spotlight Mode
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84
Cross R ange Resolut ion (meters)
Chapter 7 Figure: Doppler Beam Sharpening Cross Range Resolution As A Function
Of Azimuth Angle
100
15 km
30 km
90
80
70
60
50
40
30
20
10
0
0
15
30
45
60
75
90
Azimuth Angle To The Patch On The Ground (degrees)
7/15/2015
85
Chapter 7 Figure: Bistatic Radar Triangle
Target
b
R1
R2
g

R0
Receiver
Transmitter
Chapter 7 Figure: Bistatic Radar Detection Coverage – Ovals Of Cassini
Down Range (km)
40
R0 = 40-km
R0 = 50-km
R0 = 55-km
20
0
20
40
7/15/2015
R1R2 = 800-km2
40
20
0
20
Cross Range (km)
40
86
Chapter 7 Figure: Airborne Multi-Function Radar System
Cued Search
Track & ID
Weapon
Support
Wide
Area
Search
Search
While
Track
Surface Search, Ground Imaging,
Moving Target Indication, Ground Target Track
Chapter 7 Figure: Ground Based Multi-Function Radar System
Cued Search
Weapon Support
Identification
Track Update
Confirmation
Volume
Search
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87
Chapter 7 Figure: Concept Of OTH-B Radar
Ionosphere
OTH-B
Radar
Target
Area
Chapter 7 Figure: Frequency Modulated Continuous Wave Waveform
Frequency
Time
Bpc
t
7/15/2015
Time
88
Chapter 7 Figure: Radar Altimeter Ground Returns
~
~
q3dB
~
~
Area of
first return
R
7/15/2015
89
Chapter 7 Figure: Arecibo Spherical Antenna
305 meter
dish
Line
feed
7/15/2015
Feed arm
Plane
Wave
90
Chapter 8 Figure: Self Protection Jamming
Target
Onboard Jammer
Active
Expendables
Radar
Passive Expendables
Chapter 8 Figure: Support Jamming
Targets
Radar
Jammer Platform
Weapon System
Lethal Range
Targets
Standoff
Jamming
Weapon System
Lethal Range
Radar
Jammer Platform
Targets
Radar
Stand-In
Jamming
Weapon System
Lethal Range
Jammer
Platform
Escort
Jamming
7/15/2015
91
Chapter 8 Figure: Continuous Wave Jammer Noise Waveform
Amplitude
Amplitude
BJ
-3 dB
Frequency
Time
fJ
7/15/2015
92
Chapter 8 Figure: Repeater False Target Jammer
Radar
waveform
Receiver /
Processor
Antennas
Modulation
Amplitude,
Time, and
Frequency
Control
Transmitter
Jammer
waveform
Chapter 8 Figure: Repeater Response – Time/Range Domain
Jammer Pulses
Small
Delay
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Target Pulses
Increasing
Delay
Time
Range
93
Chapter 8 Figure: Transponder False Target Jammer
Radar
waveform
Receiver /
Processor
Control
Memory
Antennas
Modulation
Amplitude,
Time, and
Frequency
Jammer
waveform
Transmitter
Chapter 8 Figure: Transponder Response – Time/Range Domain
Shorter Range
Jammer Pulses
Cover
Longer Range
Time
Range
Target Pulse
7/15/2015
94
Chapter 9 Figure: Incremental Buildup of Received Radar Power
Target
3 Radar
Warning
Receiver
2
Radar
1
(1) Radar effective radiated power (ERP)
(2) Radar-to-target/RWR propagation
(3) Radar power out of the RWR antenna
Chapter 9 Figure Angular Coverage from Individual and Multiple EW Receiver Antennas
90
120
135°
60
45°
150
30
180
0
Individual antenna
pattern
210
225°
330
315°
240
300
Combined antenna
coverage
270
7/15/2015
95
Chapter 9 Figure Minimum Detectable Signal and Minimum Discernible Signal Sensitivities
Power
Minimum Detectable Signal
Detection Threshold
RWR Noise
Minimum Discernible Signal
Time
Chapter 9 Figure: Threshold Detection Of Radar Signals
Radar #2
Radar #1
Receiver Output
Detection T hreshold
Mean Noise Level
False
Alarm
T ime
7/15/2015
96
Chapter 9 Figure: Received Single Pulse Radar Signal Power (SRWR) and Receiver Thermal
Noise (NRWR) vs. Radar-To-Target/RWR Range
20
SRWR
NRWR
30
40
Power (dBW)
50
60
70
80
90
100
0
25
50
75
100
125
150
175
200
225
250
275
300
Radar-To-Target/RWR Range (km)
Chapter 9 Figure: Single Pulse Radar Signal-To-Noise Ratio vs. Radar-To-Target Range
70
(S/N)RWR
60
50
dB
40
30
20
10
0
0
25
50
75
100
125
150
175
200
225
250
275
300
Radar-To-Target/RWR Range (km)
7/15/2015
Detection Of The Received Radar Signal
97
Chapter 9 Figure: Relationship between Radio Frequency and Video Bandwidths
BRF
BV
Frequency
7/15/2015
98
Chapter 10 Figure: Self Protection Jamming
Target
Self Protection
Jammer
Radar
Chapter 10 Figure Incremental Buildup of Received Self Protection Jammer Power
Target
1
2
Radar
3
7/15/2015
Jammer
(1) Jammer effective radiated power (ERP)
(2) Jammer/target-to-radar propagation
(3) Jammer power out of the radar receive antenna
99
Chapter 10 Figure: Target Signal (S), Receiver Thermal Noise (N), And Jammer (J) Power
vs. Range
 60
S
N
J
 70
 80
Power (dBW)
 90
 100
 110
 120
 130
 140
 150
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
Compute the SPJ noise power out of the radar receiver as a function of radar-to-target
range,
(R_km)
J (dBW ). Add this SP J no
N_dBW
power to the plot of received target signal power an d receiver thermal noise power as a function of radar-to-target range
Received Jammer Power (dBW)
Chapter 10 Figure: Received Self Protection Jammer Power – Constant Power and Constant
Gain
Constant P ower
Constant Gain
1/R2
1/R4
Range at constant gain
jammer saturation
Radar-T o-T arget Range
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100
Chapter 10 Figure Constant Power and Constant Gain Jammers
Constant
Power
Jamming
Waveform
PJ
Radar
Waveform
Constant
Gain
Jamming
Waveform
Gs
Chapter 10 Figure Incremental Buildup of Constant Gain Self Protection Jammer Effective
Radiated Power
Constant
Gain
Jammer
2
1
3
4
(1) Incident radar power density
(3) Amplified radar power
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Radar
(2) Received radar power
(4) Jammer effective radiated power (ERP)
101
Chapter 10 Figure Constant Power and Constant Gain Regions
Target
Jammer
Radar
Constant
Power Region
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Constant
Gain Region
102
Chapter 10 Figure: Jammer Waveform Mismatch To The Radar Waveform And
Receiver Bandwidth
Radar
Amplitude
Jammer
BJ
BR
fJ
Frequency
fc
Chapter 10 Figure: Target Signal (S), Receiver Thermal Noise (N), Self Protection Jammer
Noise (JN), and Interference (I) vs. Range
 60
S
N
JN
I
 70
 80
Power (dBW)
 90
 100
 110
 120
 130
 140
 150
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
7/15/2015
103
Chapter 10 Figure: Multiple Pulse Signal-To-Noise Ratio (S/N)n, Detection Threshold, and
Signal-To-Interference Ratio (S/I)n vs. Range
90
(S/N)n
Detection Threshold
(S/I)n
80
70
60
dB
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
Chapter 10 Figure: Burnthrough Range and Detection Range
90
(S/N)n
Detection Threshold
(S/I)n
80
70
60
dB
50
Burnthrough
Range
40
Detection
Range
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
7/15/2015
104
Chapter 10 Figure: Sensitivity of Burnthrough Radar to Target Radar Cross Section
Normalized Burnthrough Range
100
10
1
0.1
0.01
30
20
10
0
10
20
30
Radar Cross Section (dBsm)
Chapter 10 Figure: Sensitivity of Burnthrough Radar to Jammer-Radar Bandwidth Mismatch
Normalized Burnthrough Ra nge
100
10
1
1
10
100
1000
Jamm er Bandwidth To Radar Bandwidth Ratio
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105
Chapter 10 Figure: Sensitivity of Burnthrough Radar to Jammer Antenna Gain in the
Direction of the Radar
Normalized Burnthrough Range
100
10
1
40
35
30
25
20
15
10
5
0
Jamm er Transm it Antenna Gain Relative To Mainbeam (dB)
Jam m in g-To-S ign al Ratio (J/S)
ming- to-signal r atio as a f unction of radar-to- target
range, J2S
(dB).
n_dB(R_km)
Chapter 10 Figure: Jamming-To-Signal Ratio as a Function of Radar-To-Target/Jammer
Range
0
Jamming-To-Signal Ratio (dB)
 10
 20
 30
 40
 50
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km )
7/15/2015
106
Chapter 10 Figure: Burnthrough and Detection Ranges with the Jamming-To-Signal Ratio
90
(S/N)n
Detection Thre shold
(S/I)n
(JN/S)n
80
70
60
50
Burnthrough
Range
40
Detection
Range
dB
30
20
10
0
 10
 20
 30
 40
 50
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km )
7/15/2015
107
Chapter 10 Figure: Multiple Pulse Signal-To-Noise Ratio (S/N)n, Detection Threshold, and
Jamming-To-Noise Ratio (J/N)n vs. Range
90
(S/N)n
Detection Threshold
(J/N)n
80
70
60
dB
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
1
Radar-to-Target Range (km)
7/15/2015
108
Chapter 10 Figure: False Target Jamming-To-Signal Ratio as a Function of Radar-ToTarget/Jammer Range
30
20
J/S (dB)
10
0
10
20
0
10
20
30
40
50
60
70
80
90
100
Radar-to-Target Range (km)
J/S (dB)
Chapter 10 Figure: Comparison of the Jamming-To-Signal Ratio from Constant Power and
Constant Gain Jammers
Range at constant gain
jammer saturation
Constant P ower
Constant Gain
Radar-T o-T arget Range
S e m iactive Miss ile Cas e
7/15/2015
109
Chapter 10 Figure Sensitivity of Jamming-To-Signal Ratio to Target Radar Cross Section
30
Normalized J/S (dB)
20
10
0
 10
 20
 30
 30
 20
 10
0
10
20
30
Radar Cross Section (dBsm)
Chapter 10 Figure: Sensitivity of Jamming-To-Signal Ratio to Jammer Antenna Gain in the
Direction of the Radar
0
5
Normalized J/S (dB)
 10
 15
 20
 25
 30
 35
 40
 40
 30
 20
 10
0
Jamm er Tra nsm it Antenna Gain Relative To Mainbeam (dB)
mum ef fective J/S as a function of minimumm in_km
effective
(J2SmJ/S,
) (km). Also
in_dBR
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110
mum ef fective J/S as a function of minimum effective J/S normalized to the range associated
Chapter 10 Figure: True Target and False Target Jamming Detection Ranges
90
(S/N)n
Detection Threshold
(J/N)n
80
70
60
False Target
Detection Range
dB
50
40
30
True Target
Detection Range
20
10
0
0
10
20
30
40
50
60
70
80
90
1
Radar-to-Target Range (km)
7/15/2015
111
Chapter 10Figure: Chaff Radar Cross Section Versus Time
Chaff Radar Cross Section (m^2)
Peak RCS
Bloom
Time
Time (seconds)
Chaff Rada r Cross Section (m^ 2)
Chapter 10 Figure: Multiple Chaff Drops Over Time
Protected
Target RCS
Time (seconds)
7/15/2015
112
Chapter 11 Figure: Support Jamming
Targets
Radar
Support Jammer
Chapter 11 Figure: Incremental Buildup of Received Support Jammer Power
Targets
1 Jammer
2
Radar
3
(1) Jammer effective radiated power (ERP)
(2) Jammer-to-radar propagation
(3) Jammer power out of the radar receive antenna
Chapter 11 Figure: Constant Power and Constant Gain Regions
Jammer
Radar
Constant
Power Region
Constant
Gain Region
Chapter 11 Figure: Target Signal (S), Receiver Thermal Noise (N), and Jammer (J) Power vs.
Radar-To-Jammer and Radar-To-Target Ranges
S
N
J
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115
Chapter 11 Figure: Target Signal (S), Receiver Thermal Noise (N), Support Jammer Noise
(JN), And Interference (I) vs. Radar-To-Jammer and Radar-To-Target Ranges
S
N
JN
I
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116
Chapter 11 Figure: Multiple Pulse Signal-To-Noise Ratio (S/N)n, Detection Threshold, and
Signal-To-Interference Ratio (S/I)n vs. Radar-To-Jammer and Radar-To-Target Ranges
(S/N)n
SNRdt
(S/I)n
7/15/2015
117
Chapter 11 Figure: Burnthrough Range and Detection Range
Burnthrough
(S/I)n ≥ SNRdt
Detection
(S/N)n ≥ SNRdt
(S/N)n
SNRdt
(S/I)n
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Chapter 11 Figure: Sensitivity of Burnthrough Range to Target Radar Cross Section
Normalized Burnthrough Ra nge
6
5
4
3
2
1
0
 30
 20
 10
0
10
20
30
Radar Cross Se ction (dBsm )
Chapter 11 Figure: Sensitivity of Burnthrough Range to Jammer-Radar Bandwidth Mismatch
(assumes JN >> N)
Normalized Burnthrough Ra nge
6
5
4
3
2
1
1
10
100
1000
Jamm er Bandwidth To Radar Bandwidth Ratio
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119
Chapter 11 Figure: Sensitivity of Burnthrough Range to Jammer Antenna Gain in the
Direction of the Radar (assumes JN >> N)
10
Normalized Burnthrough Range
8
6
4
2
0
 40
 30
 20
 10
0
Jamm er Tra nsm it Antenna Gain Relative To Mainbeam (dB)
Chapter 11 Figure: Sensitivity of Burnthrough Range to the Difference between the Radar
Antenna Gain in the Direction of the Target and the Direction of the Jammer (assumes J N >>
N)
10
Normalized Burnthrough Range
8
6
4
2
0
 40
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 30
 20
 10
Difference Between Rada r Antenna G ain In The Direction Of The Target A nd Jam mer (dB)
0
120
Chapter 11 Figure: Sensitivity of Burnthrough Range to Radar-To-Jammer Range Multiplier
(assumes JN >>N)
Normalized Burnthrough Range
10
8
6
4
2
0
1
10
100
Radar-To-Ja mm er Range Multiplier
Nois e Ja m m ing -To-Sig nal Ratio (J/S )
e jamming-to -signal r atio as a functio n of radar-to-target
J2Sn_dB(R_km)
range, (dB).
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121
Chapter 11 Figure: Jamming-To-Signal Ratio as a Function of Radar-To-Jammer and RadarTo-Target Ranges
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122
Chapter 11 Figure: Burnthrough and Detection Ranges with the Jamming-To-Signal Ratio
(S/N)n
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SNRdt
(S/I)n
(JN/S)n
123
Chapter 11 Figure: Support False Target Jamming
True
Targets
False Targets
False Targets
Radar
Support Jammer
False Targets
Chapter 11 Figure: Multiple Pulse Signal-To-Noise Ratio (S/N)n, Detection Threshold, and
Jamming-To-Noise Ratio (J/N)n vs. Radar-To-Jammer and Radar-To-Target Ranges
(S/N)n
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SNRdt
(J/N)n
125
Chapter 11 Figure: True Target and False Target Jamming Detection Ranges
True Target
Detection
(S/N)n ≥ SNRdt
False Target
Detection
(J/N)n ≥ SNRdt
(S/N)n
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SNRdt
(J/N)n
126
Chapter 11 Figure: False Target Jamming-To-Signal Ratio as a Function of Radar-To-Jammer
and Radar-To-Target Ranges
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127
Chapter 11 Figure: Comparison of the Jamming-To-Signal Ratio from Constant Power and
Constant Gain Jammers
Constant Power
Constant Gain
Range at constant
gain jammer saturation
M11
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128
Chapter 12 Figure: Radar System With A Sidelobe Canceller
Targets
Main
Antenna Pattern
Radar
Support Jammer
Auxiliary
Antenna Pattern
Chapter 12 Figure: Flow Diagram Of A Radar System With A Sidelobe Canceller
Main
Channel
Receiver
Main
Remaining
Radar
Processes
S
Phase
Cancellation
Algorithm
f
Gain
Auxiliary
Channel
Receiver
Aux
Chapter 12 Figure: Residual Noise Power-To-Receiver Thermal Noise Ratio As A Function
Of Noise Jamming-To-Receiver Thermal Noise Ratio For Various Ratios Of The Auxiliary
And Radar Antenna Gains In The Direction Of The Jammer
Residual Jamming-To-Noise Ratio (dB)
15
10
-10 dB
-5 dB
0 dB
5 dB
10 dB
5
0
 20
 10
0
10
20
30
Jamming-T o-Noise Ratio (dB)
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130
Chapter 12 Figure: Cancellation Ratio As A Function Of Noise Jamming-To-Receiver
Thermal Noise Ratio For Various Ratios Of The Auxiliary And Radar Antenna Gains In The
Direction Of The Jammer
30
Cancellation Ratio (dB)
25
20
-10 dB
-5 dB
0 dB
5 dB
10 dB
15
10
5
0
 20
 10
0
10
20
30
Jamming-T o-Noise Ratio (dB)
Chapter 12 Figure: Canceling A Sidelobe
Scanned JPG file
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131
Chapter 12 Figure: Flow Diagram Of A Radar System With A Sidelobe Blanker
Main
Channel
Receiver
Main

Auxiliary
Channel
Receiver
Range Gates
Aux
Main
Aux
Remaining
Radar
Processes
Blanking
Blanking Threshold
Chapter 12 Figure: Sidelobe Blanker Response
Ten Uniformly Spaced False Targets and One True Target
Receiver Output
Detection Threshold
SLB Off
Time
SLB On
True Target
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Blanked False Targets
Receiver Output
Detection Threshold
Blanked False Targets
132
Chapter 12 Figure: Correlated Measurement Tracker
Range
Tracker
Correlation
Tracker
Angle
Tracker
Target
Track
Range Rate
Tracker
Chapter 12 Figure: Target State Tracker
Range
Range Rate
Angle
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State
Tracker
Position
Velocity
Acceleration
Target
Track
133
Chapter 13 Figure: Radar Line-Of-Sight – Round Smooth Earth
Above
the horizon
Horizon
Below
the horizon
Round
Smooth Earth
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134
Chapter 13 Figure: Range To The Horizon
Rh
h
RE
RE
Round
Smooth Earth
Chapter 13 Figure: Radar Line Of Sight
RLOS
RhC
RhT
hR
hT
RE
RE
RE
Round
Smooth Earth
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135
Chapter 13 Figure: Refraction Geometry
Ray path
 
fi
sin(fi )
sin(fr )
fr
Chapter 13 Figure: Refracted Propagation
Straight line propagation
Atmospheric
Layers
Target
Refracted propagation
Radar
Round Smooth Earth
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136
Chapter 13 Figure: Atmospheric Attenuation – Overall with Oxygen and Water Vapor
Components
Atmosph eric Absorpt ion, dB/km
100
Overall
10
1
g(
go
gw
0.1
Oxygen
component
0.01
1 10
3
1 10
4
1 10
5
Water vapor component
0.1
1
10
100
Frequency, GHz
Chapter 13 Figure: Atmospheric Attenuation – As A Function Of Altitude
Atmosph eric Attenua tion (dB/km)
100
10
0 km
5 km
10 km
15 km
20 km
1
0.1
0.01
110
110
110
3
4
5
0.1
1
10
100
Frequency (GHz)
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137
Chapter 13 Figure: Atmospheric Attenuation – Rain and Clouds
Scanned JPG File
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138
Chapter 13 Figure: Far Field Calculation
R+e
D
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R
Far
Field
Point
139
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3
3
HF
Band 7
HF
30
30
30
A
VHF
Band 8
VHF
UHF
L
2
S
4
C
8
X KU
12 18
K
Frequency (GHz)
27
250
B
300
500
D
E
6 810
F G HI
3 4
Military Standard Bands
C
2
J
SHF
Band 10
International Standard Bands
UHF
Band 9
3
20
K
40
40
Ka
30
US Industry Standard Bands (IEEE Radar Designations)
300
Frequency (MHz)
L
W
60
M
100
EHF
Band 11
V
75 110
300
Appendix 2 Figure: The Radar Spectrum
140
Appendix 3 Figure: A Square Wave And Its Fourier Spectrum
4/p
+1
0
0 p 2p ...

2 3 4 5 6
t
Harmonics of fundamental
Appendix 3 Figure: Another Square Wave
T
+1
T
k
0
-p 
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p
p
0
2
2
p
x
141
Appendix 3 Figure: Another Spectrum Of A Square Wave
( )
sin np k
np
k
k = 4
1
k
-2
-1
1
n
k
2
Appendix 3 Figure: A Single Pulse And Its Fourier Transform
1
f(t)

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t
2
0
t
2
t
2p
g()

3p
t

2p
t

p
t
0
p
t
2p
t
3p
t
142