Radar 2009 a 6 detection of signals in noise

IEEE New Hampshire Section
Radar Systems Course 1
Detection 1/1/2010 IEEE AES Society
Radar Systems Engineering
Lecture 6
Detection of Signals in Noise
Dr. Robert M. O’Donnell
Guest Lecturer

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Block Diagram of Radar System
Transmitter
Waveform
Generation
Power
Amplifier
T / R
Switch
Antenna
Propagation
Medium
Target
Radar
Cross
Section
Photo Image
Courtesy of US Air Force
Used with permission.
Pulse
Compression
Receiver
Clutter Rejection
(Doppler Filtering)
A / D
Converter
General Purpose Computer
Tracking
Data
Recording
Parameter
Estimation
Detection
Signal Processor Computer
Thresholding
User Displays and Radar Control
This Lecture

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Outline
• Basic concepts
– Probabilities of detection and false alarm
– Signal-to-noise ratio
• Integration of pulses
• Fluctuating targets
• Constant false alarm rate (CFAR) thresholding
• Summary

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Radar Detection – “The Big Picture”
• Mission – Detect and
track all aircraft within
60 nmi of radar
• S-band λ ~ 10 cm
Example – Typical Aircraft Surveillance Radar
ASR-9
Courtesy of MIT Lincoln Laboratory
Used with permission
Rotation
Rate
12. rpm
Range
60 nmi.
Transmits
Pulses at
~ 1250 Hz

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Range-Azimuth-Doppler Cells to Be
Thresholded
Rotation
Rate
12.7 rpm
10 Pulses / Half BW
Processed into
10 Doppler Filters
Example – Typical Aircraft Surveillance Radar
ASR-9
Range - Azimuth - Doppler Cells
~1000 Range cells
~500 Azimuth cells
~8-10 Doppler cells
5,000,000 Range-Az-Doppler Cells
to be threshold every 4.7 sec.
0 50 100
-25
-50
0
Radial Velocity (kts)
Magnitude(dB)
Doppler Filter Bank
Az
Beamwidth
~1.2 °
As Antenna Rotates
~22 pulses / Beamwidth
Is There a Target Present
in Each Cell?
Range
Resolution
1/16 nmi
Radar
Transmits
Pulses at
~ 1250 Hz
Range
60 nmi.

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Target Detection in Noise
• Received background noise fluctuates randomly up and down
• The target echo also fluctuates…. Both are random variables!
• To decide if a target is present, at a given range, we need to set a
threshold (constant or variable)
• Detection performance (Probability of Detection) depends of the
strength of the target relative to that of the noise and the threshold
setting
– Signal-To Noise Ratio and Probability of False Alarm
ReceivedBackscatterPower(dB)
20
40
30
10
Noise
Threshold
False
Alarm
Detected
Strong
Target
Weak target (not detected)
0
0 25 50 100 125 150 175
Range (nmi.)

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The Radar Detection Problem
Radar
Receiver
Detection
Processing
Measurement Decision
x
10 HH or
nx =
Measurement
Probability
Density
Target absent hypothesis,
Noise only
Target present hypothesis,
Signal plus noise
nax +=
)Hx(p 0
1H
)Hx(p 1
For each measurement
There are two possibilities:
For each measurement
There are four decisions:
0H
0H 1H
1H
Don’t
Report
False
Alarm
Detection
Missed
Detection
Truth
Decision
0H

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Maximize subject to no greater than specifiedFAPDP
( )α≤FAP
Threshold Test is Optimum
0H
0H 1H
1H
Don’t
Report
False
Alarm
Detection
Missed
Detection
Truth
Decision
Probability of Detection:
Probability of False Alarm:
DP
FAP
The probability we choose
when is true
The probability we choose
when is true
1H 1H
1H 0H
Likelihood Ratio Test
> η=
)Hx(p
)Hx(p
)x(L
0
1
<
1H
0H
Likelihood
Ratio Threshold
Objective:
Neyman-Pearson
criterion

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Basic Target Detection Test
0 2 4 6 8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Voltage
ProbabilityDensity
Detection
Threshold
Noise Probability Density
Noise Only
Target Absent
Probability of False Alarm ( PFA )
PFA = Prob{ threshold exceeded given target absent }
i.e. the chance that noise is called a (false) target
We want PFA to be very, very low!
Probability of False Alarm ( PFA )
PFA = Prob{ threshold exceeded given target absent }
i.e. the chance that noise is called a (false) target
We want PFA to be very, very low!

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Basic Target Detection Test
0 2 4 6 8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Voltage
ProbabilityDensity
Detection
Threshold
Noise
Probability Density
Signal-Plus-Noise
Probability Density
Probability of
False Alarm ( PFA )
Probability of
False Alarm ( PFA )
Signal + Noise
Target Present
Probability of Detection ( PD )
PD = Prob{ threshold exceeded given target present }
I.e. the chance that target is correctly detected
We want PD to be near 1 (perfect)!
Probability of Detection ( PD )
PD = Prob{ threshold exceeded given target present }
I.e. the chance that target is correctly detected
We want PD to be near 1 (perfect)!
)Hx(p 1

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Signal Plus Noise
SNR = 10 dB
PD = 0.61
Signal Plus Noise
SNR = 20 dB
PD ~ 1
Detection Examples with Different SNR
• PD increases with target SNR for a fixed threshold (PFA)
• Raising threshold reduces false alarm rate and increases
SNR required for a specified Probability of Detection
• PD increases with target SNR for a fixed threshold (PFA)
• Raising threshold reduces false alarm rate and increases
SNR required for a specified Probability of Detection
0 5 10 15
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Voltage
ProbabilityDensity
Noise Only
Detection Threshold
PFA = 0.01

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Non-Fluctuating Target Distributions
0 2 4 6 80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Voltage
Probability
Threshold
Noise pdf
Signal-Plus-Noise pdf
Set threshold rT based
on desired false-alarm probability
Compute detection probability for
given SNR and false-alarm probability
Is Marcum’s Q-Function
(and I0(x) is a modified Bessel function)
where
Rayleigh Rician
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
2
r
exprHrp
2
o ( ) ( )RrI
2
Rr
exprHrp o
2
1 ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ +
−=
2
R
SNR =
FAeT Plog2r −=
( ) ( )( )FAe
r
1D Plog2,SNR2QdrHrpP
T
−== ∫
∞
( ) ( )drraI
2
ar
exprb,aQ o
b
22
∫
∞
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ +
−=

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Probability of Detection vs. SNRProbabilityofDetection(PD)
Signal-to-Noise Ratio (dB)
PFA=10-4
PFA=10-6
PFA=10-10
PFA=10-12
PFA=10-8
4 6 8 10 12 14 16 18
0.6
1.0
0.4
0.0
0.2
0.8
SNR = 13.2 dB
needed for
PD = 0.9 and
PFA = 10-6
Steady Target
Remember
This!

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Probability of Detection vs. SNR
SNR = 13.2 dB
needed for
PD = 0.9 and
PFA = 10-6
Steady Target
Remember
This!
ProbabilityofDetection(PD)
4 6 8 10 12 14 16 18 20
0.7
0.9999
0.1
0.3
0.5
0.05
0.9
0.2
0.999
0.99
0.8
0.95
0.98
PFA=10-4
PFA=10-6
PFA=10-10
PFA=10-12
PFA=10-8

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Tree of Detection Issues
Detection
Non-Fluctuating
Multiple pulses
Swerling I
Fluctuating
Fluctuating
Single Pulse
Square Law Detector
Coherent
Integration
Single Pulse
Decision
Binary
Integration
Non-Coherent
Integration
Linear Detector
Non-Fluctuating
Uncorrelated
Swerling IISwerling III Swerling IV
Fully Correlated Partially Correlated

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Detection Calculation Methodology
Probability of Detection vs. Probability of False Alarm and Signal-to-Noise Ratio
Determine PDF at
Detector Output
• Single pulse
• Fixed S/N
Integrate N fixed
target pulses
Scan to Scan Fluctuations
(Swerling Case I and III)
Pulse to Pulse Fluctuations
(Swerling Case II and IV)
Average over
signal fluctuations
Integrate over N
pulses
Average over
target fluctuations
Integrate from
threshold, T, to ∞
PD vs. PFA, S/N, &
Number of pulses, N

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Outline
• Basic concepts
• Summary

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Integration of Radar Pulses
Detection performance can be improved by integrating
multiple pulses
Calculate
Threshold
Calculate
Coherent Integration Noncoherent Integration
• Adds ‘voltages’ , then square
• Phase is preserved
• pulse-to-pulse phase coherence required
• SNR Improvement = 10 log10 N
• Adds ‘powers’ not voltages
• Phase neither preserved nor required
• Easier to implement, not as efficient
…
Pulses
Tx
N
1
2N
1n
n >∑=
Tx
N
1 N
1n
2
n >∑=
Sum Calculate
Threshold
Pulses
…
2N
1n
nx∑=
nx
Nx
2x
1x 1x
Nx
2
1x
Calculate
2
2x
Calculate
2
Nx
2x
∑=
N
1n
2
nx
Target Detection
Declared if Target Detection
Declared if

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Integration of Pulses
Signal to Noise Ratio per Pulse (dB)
0 5 10 15
ProbabilityofDetection
0.6
1.0
0.4
For Most Cases, Coherent Integration is More Efficient
than Non-Coherent Integration
0.2
0.8
Steady
Target
PFA=10-6
One Pulse
Ten Pulses
Coherent
Integration
Ten Pulses
Non-Coherent
Integration
Coherent
Integration
Gain
Non-Coherent
Integration
Gain

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Different Types of Non-Coherent Integration
• Non-Coherent Integration – Also called (“video integration”)
– Generate magnitude for each of N pulses
– Add magnitudes and then threshold
• Binary Integration (M-of-N Detection)
– Separately threshold each pulse
1 if signal > threshold; 0 otherwise
– Count number of threshold crossings (the # of 1s)
– Threshold this sum of threshold crossings
Simpler to implement than coherent and non-coherent
• Cumulative Detection (1-of-N Detection)
– Similar to Binary Integration
– Require at least 1 threshold crossing for N pulses

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Calculate
Binary (M-of-N) Integration
Threshold
T
Calculate
Sum…
Pulse 1
Pulse 2
Pulse
Threshold
T
Threshold
T
2nd Threshold
M
Individual pulse detectors:
Target present if at least M detections in N pulses
1x
1i
Nx
2x
1i,Tx n
2
n =≥
∑=
=
N
1n
nim
N
2nd thresholding:
2i
Ni
0i,Tx n
2
n =<
Mm ≥
Mm <
, target present
, target absent
At Least
M of N
Detections
At Least
1 of N
( )
( ) kNk
N
Mk
N/M p1p
!kN!k
!N
P
−
=
−
−
= ∑ ( )N
C p11P −−=
2
1x
Calculate
2
2x
Calculate
2
Nx
Binary Integration Cumulative Detection

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Detection Statistics for Binary Integration
Signal to Noise Ratio per Pulse (dB)
2 4 6 8 10 12 14
0.01
0.10
0.50
0.90
0.99
0.999
1/4
2/4
3/4
4/4
“1/4”
= 1 Detection
Out of 4
Pulses
Steady
(Non-Fluctuating )
Target
PFA=10-6

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Optimum M for Binary Integration
OptimumM
1
10
100
1 10 100
Number of Pulses
Steady
(Non-Fluctuating )
Target
PD=0.95
PFA=10-6
For each binary Integrator, M/N,
there exists an optimum M
M (optimum) ≈ 0.9 N0.8

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Optimum M for Binary Integration
• Optimum M varies somewhat with target fluctuation model,
PD and PFA
• Parameters for Estimating MOPT = Na 10b
Adapted from Shnidman in Richards, reference 7
Target Fluctuations a b Range of N
No Fluctuations 0.8 - 0.02 5 – 700
Swerling I 0.8 - 0.02 6 – 500
Swerling II 0.91 - 0.38 9 – 700
Swerling III 0.8 - 0.02 6 – 700
Swerling IV 0.873 - 0.27 10 – 700

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Detection Statistics for Different Types
of Integration
PFA=10-6
Coherent and Non-Coherent Integration
2 4 6 8 10 12 14 16
0.10
0.50
0.90
0.95
0.99
0.999
0.01
Coherent
Integration
4 Pulses
Non-Coherent
Integration
4 Pulses
Binary
Integration
3 of 4 Pulses
Single Pulse
Signal to Noise Ratio (dB)

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of Integration
0.10
0.50
0.90
0.95
0.99
0.999
0.01
2 4 6 8 10 12 14 16
PFA=10-6
Non-Coherent
Integration
4 Pulses
Coherent
Integration
4 Pulses
Binary
Integration
3 of 4 Pulses
Single Pulse

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Signal to Noise Gain / Loss vs. # of Pulses
Number of Pulses Number of Pulses
1 10 100 1 10 100
SignaltoNoiseRatioGain(dB)
SignaltoNoiseRatioLoss(dB)
0
5
15
10
20
2
4
10
6
0
8
Steady
Target
PD=0.95
PFA=10-6
• Coherent Integration yields the greatest gain
• Non-Coherent Integration a small loss
• Binary integration has a slightly larger loss than regular
Non-coherent integration
Coherent
Binary
(Optimum M)
Binary N1/2
Non-Coherent
Binary N1/2
Binary
(Optimum M)
Non-Coherent
Relative
To Coherent
Integration

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Effect of Pulse to Pulse Correlation on
Non-Coherent Integration Gain
• Non-coherent Integration Can Be Very Inefficient
in Correlated Clutter
EquivalentNumberofIndependentPulses
N
=300
50
30
20
10
3
100
0.001 0.01 0.1 1
1
5
2
50
10
100
20
rv f/ λσ
Independent
Sampling
Region
Dependent
Sampling
Region
vσ
T
1
fr =
Velocity
Spread
Of
Clutter
Pulse
Repetition
Rate

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Effect of Pulse to Pulse Correlation on
Non-Coherent Integration Gain
• Non-coherent Integration Can Be Very Inefficient
in Correlated Clutter
)T(ρ .99 0.9 0.1 0.02
EquivalentNumberofIndependentPulses
N
=300
50
30
20
10
3
100
0.001 0.01 0.1 1
1
5
2
50
10
100
20
rv f/ λσ
Independent
Sampling
Region
Dependent
Sampling
Region
vσ
T
1
fr =
Velocity
Spread
Of
Clutter
Pulse
Repetition
Rate
Adapted from nathanson, Reference 8

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Albersheim Empirical Formula for SNR
(Steady Target - Good Method for Approximate Calculations)
• Single pulse:
– Where:
– Less than .2 dB error for:
– Target assumed to be non-fluctuating
• For n independent integrated samples:
– Less than .2 dB error for:
– For more details, see References 1 or 5
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
++=
D
D
e
FA
e
P1
P
logB
P
62.0
logA
B7.1BA12.0A)unitsnatural(SNR
( )B7.1BA12.0Alog
44.0n
54.4
2.6nlog5)dB(SNR 1010n ++⎟
⎠
⎞
⎜
⎝
⎛
+
++−=
1.0P9.010P10 D
7
FA
3
>>>> −−
1.0P9.010P101n8096 D
7
FA
3
>>>>>> −−
SNR
Per
Sample

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Outline
• Basic concepts
• Summary

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Fluctuating Target Models
• For many types of targets, the
received radar backscatter
amplitude of the target will vary a
lot from pulse-to-pulse:
– Different scattering centers on
complex targets can interfere
constructively and destructively
– Small aspect angle changes or
frequency diversity of the
radar’s waveform can cause this
effect
• Fluctuating target models are
used to more accurately predict
detection statistics (PD vs., PFA,
and S/N) in the presence of target
amplitude fluctuationsRCS versus Azimuth
B-26, 3 GHz
RCS vs. Azimuth for a Typical Complex Target

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Swerling Target Models
=σ Average RCS (m2)
RCS
Model
Nature of
Scattering Fast Fluctuation
“Pulse-to-Pulse”
Slow Fluctuation
“Scan-to-Scan”
Fluctuation Rate
Swerling I
Swerling IVSwerling III
Swerling II
Similar amplitudes
One scatterer much
Larger than others
Exponential
(Chi-Squared DOF=2)
(Chi-Squared DOF=4)
( ) ⎟
⎠
⎞
⎜
⎝
⎛
σ
σ
−
σ
=σ exp
1
p
( ) ⎟
⎠
⎞
⎜
⎝
⎛
σ
σ
−
σ
σ
=σ
2
exp
4
p 2

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Swerling Target Models
Amplitude
Model
Nature of
Scattering Fast Fluctuation
“Pulse-to-Pulse”
Slow Fluctuation
“Scan-to-Scan”
Fluctuation Rate
Swerling I
Swerling IVSwerling III
Swerling II
Similar amplitudes
One scatterer much
Larger than others
=σ Average RCS (m2)
Central Rayleigh,
DOF=4
Rayleigh
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
σ
−
σ
=
2
a
exp
a2
ap
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
σ
−
σ
=
2
2
3
a2
exp
a8
ap

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Other Fluctuation Models
• Detection Statistics Calculations
– Steady and Swerling 1,2,3,4 Targets in Gaussian Noise
– Chi- Square Targets in Gaussian Noise
– Log Normal Targets in Gaussian Noise
– Steady Targets in Log Normal Noise
– Log Normal Targets in Log Normal Noise
– Weibel Targets in Gaussian Noise
• Chi Square, Log Normal and Weibel Distributions have
long tails
– One more parameter to specify distribution
Mean to median ratio for log normal distribution
• When used
– Ground clutter Weibel
– Sea Clutter Log Normal
– HF noise Log Normal
– Birds Log Normal
– Rotating Cylinder Log Normal

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RCS Variability for Different
Target Models
0
5
10
15
20
0
5
10
15
20
RCS(dBsm)
0 20 40 60 80 100
0
5
10
15
20
Sample #
Non-fluctuating Target
Swerling I/II
Swerling III/IV
Constant
High
Fluctuation
Medium
Fluctuation

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Fluctuating Target Single Pulse
Detection : Rayleigh Amplitude
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
σ
−
σ
=
2
a
exp
a2
)a(p
2
Nσ
σ
=ξ0
1
HTx
HTxz
<
>=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
σ
−= 2
N
2
FA
T
expP
∫ >= dzda)a(p)a,HTz(pP 1D
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ξ+σ
−=
1
1T
expP 2
N
2
D
naex:H j
1 += φ
Detection Test
Probability of
False Alarm
(same as for
non-fluctuating)
Average
SNR per
pulse
Rayleigh
amplitude
model
Probability of
Detection Test
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ξ+= 1
1
FAD PP
nx:H0 =

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Fluctuating Target Single Pulse DetectionProbabilityofDetection(PD)
0.6
1.0
0.4
0.0
0.2
0.8
0 5 10 15 20 25
Non-Fluctuating
Swerling Case 3,4
Swerling Case 1,2
Fluctuation Loss
For high detection probabilities, more signal-to-noise is required for
fluctuating targets.
The fluctuation loss depends on the target fluctuations, probability of
detection, and probability of false alarm.
PFA=10-6

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Fluctuating Target Multiple Pulse Detection
0.6
1.0
0.4
0.0
0.2
0.8
Signal-to-Noise Ratio per Pulse (dB)
0 4 8 12 16 20
Steady Target
Coherent Integration
Swerling 2 Fluctuations
Non-Coherent Integration, Frequency
Diversity
Swerling 1 Fluctuations
Coherent Integration, Single Frequency
PFA=10-6
N=4 Pulses
• In some fluctuating target cases, non-coherent integration with
frequency diversity (pulse to pulse) can outperform coherent
integration

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Detection Statistics for Different Target
Fluctuation Models
Steady Target
Swerling Case I
Swerling Case II
Swerling Case III
Swerling Case IV
Signal-to-Noise Ratio (SNR) (dB)
-2 0 2 4 6 8 10 12 14
0.0
0.4
0.6
0.8
1.0
0.2
10 pulses
Non-coherently
Integrated
PFA=10-8
Adapted from Richards, Reference 7

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Shnidman Empirical Formulae for SNR
(for Steady and Swerling Targets)
• Analytical forms of SNR vs. PD, PFA, and Number of pulses
are quite complex and not amenable to BOTE* calculations
• Shnidman has developed a set of empirical formulae that
are quite accurate for most 1st order radar systems
calculations:
* Back of the Envelope
( )( ) ( ) ( )( )DDDFAFA P1P4ln8.05.0PsignP1P4ln8.0 −−−+−−=η
=α
40N0 ≤
40N
4
1
>
N2
,2
,NK
,1
=
∞ Non-fluctuating target (“Swerling 0 / 5”)
Swerling Case 1
Swerling Case 2
Swerling Case 3
Swerling Case 4
Adapted from Shnidman in Richards, Reference 7

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Shnidman Empirical Formulae for SNR
(for Steady and Swerling Targets)
( )( )( )
( ) ( )
( ) )SNR(log10dBSNR
N
XC
)unitsnatural(SNR
10CC
80
20N2
P
10
ln7.08.0Pe
K
1
C
K/525.3P5339.14P4496.18P7006.17C
4
1
2
N
2X
10
10
C
dB
FA
5
D
)14.25P31.27
2
DDD1
dB
D
==
==
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ −
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+=
−+−=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
−α++ηη=
∞
−
−
∞
99.0P872.0CC
872.0P1.0C
D21
D1
≤≤+
≤≤

Detection 11/1/2010
IEEE AES Society
Shnidman’s Equation
• Error in SNR < 0.5 dB within these bounds
– 0.1 ≤ PD ≤ 0.99 10-9 ≤ PFA ≤ 10-3 1 ≤ N ≤ 100
Steady Target
Swerling I
Swerling II
Swerling III
Swerling IV
SNRCalculationError(dB)
Probability of Detection
0.0 0.2 0.4 0.6 0.8 1.0
0.0
-0.5
1.0
0.5
-1.0
SNR Error vs. Probability of Detection
N = 10 pulses
PFA= 10-6

Detection 11/1/2010
IEEE AES Society
Outline
• Basic concepts
• Summary

Detection 11/1/2010
IEEE AES Society
Practical Setting of Thresholds
• Need to develop a methodology to set target detection
threshold that will adapt to:
– Temporal and spatial changes in the background noise
– Clutter residue from rain, other diffuse wind blown clutter,
– Sharp edges due to spatial transitions from one type of
background (e.g. noise) to another (e.g. rain) can suppress
targets
– Background estimation distortions due to nearby targets
Display, NEXRAD Radar, of Rain Clouds
Range (nmi)
Rain
Cloud
Receiver
Noise
0 1 2
S-Band Data
0
20
40
Rain Backscatter Data
Ideal Case- Little variation in Noise
Power
Power
Courtesy of NOAA

Detection 11/1/2010
IEEE AES Society
Constant False Alarm Rate (CFAR)
Thresholding
• Estimate background (noise, etc.) from data
– Use range, or range and Doppler filter data
– Set threshold as constant times the mean value of background
• Mean Background Estimate =
CFAR Window – Range Cells CFAR Window – Range and Doppler Cells
Range
Range cells
DopplerVelocitycells
Cell to be
Thresholded
“Guard”
Cells
Data Cells Used
to Determine
Mean Level of
Background
∑=
N
1n
nx
N
1

Detection 11/1/2010
IEEE AES Society
Effect of Rain on CFAR Thresholding
Cell Under Test
“Guard” Cells
Data Cells for Mean Level Computation
Window Slides Through Data
2.2 dB
9 dB
4.52.6 Slant Range, nmi
RadarBackscatter(LinearUnits)
Rain Cloud
C Band
5500 MHz
Receiver Noise
Receiver Noise
Range Cells
Mean Level Threshold CFAR

Detection 11/1/2010
IEEE AES Society
Effect of Rain on CFAR Thresholding
2.2 dB
9 dB
4.52.6 Slant Range, nmi
Rain Cloud
C Band
5500 MHz
Range Cells
Cell Under Test
“Guard” Cells
Data Cells for Mean Level Computation
Receiver Noise
Receiver Noise
Sharp Clutter or Interference Boundaries
Can Lead to Excessive False Alarms
RadarBackscatter(LinearUnits) Mean Level Threshold CFAR

Detection 11/1/2010
IEEE AES Society
Greatest-of Mean Level CFAR
• Find mean value of N/2 cells before and after test cell
separately
• Use larger noise estimate to determine threshold
• Helps reduce false alarms near sharp clutter or interference
boundaries
• Nearby targets still raise threshold and suppress detection
Cell Under Test
“Guard” Cells
Data Cells for Mean Level 1
Use Larger Value

Detection 11/1/2010
IEEE AES Society
Censored Greatest-of CFAR
• Compute and use noise estimates as in Greatest-of, but
remove the largest M samples before computing each
average
• Up to M nearby targets can be in each window without
affecting threshold
• Ordering the samples from each window is computationally
expensive
Cell Under Test
“Guard” Cells
Use Larger Value
“Censored” Data (Not Used
in Computation of Average)

Detection 11/1/2010
IEEE AES Society
Mean Level CFAR Performance
PFA=10-6
1 PulseMatched Filter
Mean Level CFAR – 10 Samples
CFAR
Loss
Signal-to-Noise Ratio per Pulse (dB)
4 6 8 10 12 14 16 18
0.01
0.999
0.99
0.90
0.50
0.10
0.9999

Detection 11/1/2010
IEEE AES Society
CFAR Loss vs. Number of Reference Cells
PFA=10-8
10-6
10-4
Number of Reference Cells
0 10 20 30 40 50
CFARLoss(dB)
2
1
0
3
4
5
6
PD= 0.9
The greater the number of reference cells in the CFAR, the better is
the estimate of clutter or noise and the less will be the loss in
detectability. (Signal to Noise Ratio)
Adapted from Richards, Reference 7

Detection 11/1/2010
IEEE AES Society
CFAR Loss vs Number of Reference Cells
For Single Pulse Detection
Approximation
CFAR Loss (dB) =
- (5/N) log PFA
Dotted Curve PFA = 10-4
Dashed Curve PFA = 10-6
Solid Curve PFA = 10-8
N = 15 to 20 (typically)
Since a finite number of
cells are used, the estimate
of the clutter or noise is
not precise.
Number of Reference Cells, N
CFARLoss,dB
N=100
N=3
N=10
N=30
N=1
PFA
10-8
10-6
10-4
2 5 7 10 20 50 70 100
4
0.4
1
0.5
0.2
0.3
0.7
3
2
5
Adapted from Skolnik, Reference 1

Detection 11/1/2010
IEEE AES Society
Summary
• Both target properties and radar design features affect the
ability to detect signals in noise
– Fluctuating targets vs. non-fluctuating targets
– Allowable false alarm rate and integration scheme (if any)
• Integration of multiple pulses improves target detection
– Coherent integration is best when phase information is available
– Noncoherent integration and frequency diversity can improve
detection performance, but usually not as efficient
• An adaptive detection threshold scheme is needed in real
environments
– Many different CFAR (Constant False Alarm Rate) algorithms exist
to solve various problems
– All CFARs algorithms introduce some loss and additional
processing

Detection 11/1/2010
IEEE AES Society
References
1. Skolnik, M., Introduction to Radar Systems, McGraw-Hill,
New York,3rd Ed., 2001.
2. Skolnik, M., Radar Handbook, McGraw-Hill, New York, 3rd
Ed., 2008.
3. DiFranco, J. V. and Rubin, W. L., Radar Detection, Artech
House, Norwood, MA, 1994.
4. Whalen, A. D. and McDonough, R. N., Detection of Signals in
Noise, Academic Press, New York, 1995.
5. Levanon, N., Radar Principles, Wiley, New York, 1988
6. Van Trees, H., Detection, Estimation, and Modulation
Theory, Vols. I and III, Wiley, New York, 2001
7. Richards, M., Fundamentals of Radar Signal Processing,
McGraw-Hill, New York, 2005
8. Nathanson, F., Radar Design Principles, McGraw-Hill, New
York, 2rd Ed., 1999.

Detection 11/1/2010
IEEE AES Society
Homework Problems
• From Skolnik, Reference 1
– Problems 2.5, 2.6, 2.15, 2.17, 2.18, 2.28, and 2.29
– Problems 5.13 , 5.14, and 5-18

Radar 2009 a 6 detection of signals in noise

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