ch6-radar+detection+and+cfar

Korea Aerospace University

e-mail : [email protected]

2Radar Engineering Prof. Kwag@RSP-Lab

Lecture 6 : Target Echo Information Extraction

Objective- Detection- Coherent Detection- CFAR

- 6.1 Detection Introduction- 6.2 Detection in Noise- 6.3 Signal Integration and Fluctuations- 6.4 M of N Detection- 6.5 Threshold-Setting Concept CFAR - 6.6 Reference


6.1 Detection IntroductionRadar Environmental


6.1 Detection IntroductionThere are many sources and kinds of false alarms


6.1 Detection IntroductionDetection Criteria : Four Conditions

#1target

#2target

#3target

False alarmErrorYESNO

Miss detectionErrorNOYES

CorrectYESYES

CorrectNONO

RemarkResultDetection ?Target ?


6.1 Detection IntroductionDefinition : Probability of Detection- Ps : Probability of signal, for given single test of signal-plus-interference

and threshold, threshold crossing if a target was present single detection trial

- Pd : Probability of detection for given S+I and threshold, consecutivedetection if a target was present compound detection trial (M of N det.)

- Pn : Prob. of Noise; the prob. that interference & noise alone will cross the threshold for a single test

- Pfa : Prob. of false alarm; the prob. that interference alone will crossthe threshold for a look or compound


6.1 Detection Introduction- FAN : False Alarm Number

= number of test / false alarmFAN = 1 / Pfa = 1 / (false number / trial)

- FAT : False alarm time: mean time between noise threshold crossing

- FAR : False alarm Rate= average number of false alarm / sec.

( RDT = detection test ) Bandwidth of the system at the test point

FAR = 1/ FATFA DT FAP R P B =


6.1 Detection IntroductionGoal of Target Detection

low high FA dP P

Probability of Density functions- Noise : random phenomenon- Probability : measurement of the likelihood of the occurrence

of an event an event- Probability for continuous function, random noise

0

( / )represented by pdf. ( ) limx

N

x xP xN

=V

V

2

11 2( ) ( )

x

xx x x P x dx< < = pdf = ( ) 1P x dx

=


6.1 Detection Introduction- Uniform pdf

( )P x

x

1b

a a b+

phase of random sinewave A/D noise

2022

( )1( ) exp[ ]22

x xP x

=

- Gaussian pdf: noise thermal noise


6.1 Detection Introduction- Rayleigh pdf

envelope of narrow band filter when input noise voltage is Gaussian

- exponential pdf

x

( )P x2

2 2

2( ) exp( ) 0x xP x xm m

=

22 meanavm x= < >

0 0

1( ) exp( ) 0wP w ww w

=

2when replaced by in Rayleigh pdf.x w

( )P w

w


6.1 Detection Introduction- Others

Rice, Log-normal, Chi-square pdf

Probability Distribution Function

( )( ) ( ) or ( )x dP xP x P x dx P x

dx= =

- For Gaussian pdf2

22

1( ) exp( ) 22xP x dx

= 0 where 0 meanx x < < =


6.1 Detection IntroductionProbability of Detection & false alarm- Envelope Detector

From Mixer

IFAmplifier

2ndDetector

Video Amplifier

Thresholdvt

Decision

- The receiver noise at IF described by Gaussian prob densityfunction

2

00

1( ) exp( )22vP v

= 0 mean square of noise voltage =

- Rice showed that when Gaussian noise is passed throughthe IF filter pdf of the envelope is given by Rayleigh

2

0 0

( ) exp( )2

R RP R

=


6.1 Detection Introduction- Probability of False Alarm

2

0 02

0

( ) exp( )2

= exp( )2

TT V

TFA

R RV R dR

V P

< < =

=

- False Alarm time FAT1

1lim

1 where B= B/W of IF amp.

N

FA kN k

FAFA

T TN

PT B

=

=

=

- Prob. of detection for S + N2 2

00 0 0

( ) exp( ) ( )2s

R R A RAP R I

+=

0 ( ) 2

zeI zz

=


6.2 Detection in Noise

Target Detection in Noise

=

==

=

t

t

t

vfa

v

dmiss

vd

dnnPp

dvuPpp

dvuPp

)(

)(1

)(

0



Probability of false alarm

=

=

=

=

2

2

2

2

22

2

2log10/

)(2

exp

2exp)(

t

vFAt

fa

vnoisethreshold

dvvpPvp

vvvp

t



Detection in Noise- Signal & Noise model

Rayleigh prob. distribution for signal prob. in noise interferenceRicean (=modified Rayleigh) distribution for signal-plus-noise



Signal + Noise Probability

< Modified Rayleigh(Raeian Prob. Function and Distribution for Signal+Noise >



False Alarm Rate)/1(detectio soccurtestnwhichatrateRwhereRpFAR DTDTfa ==

- Pfa directly affected target detection probability ( Pd )since it is set by the detection threshold

Threshold vs False alarm rate


6.3 Signal Integration & Target FluctuationIn practical- Several echoes are integrated with the processed composite

applied to threshold- Real targets fluctuate- Signal-plus-interference other than threshold noise

Therefore, the pdf is to be modifiedActual design factors:- False alarm prob.- Detection prob.- S/I ratio- Interference type and statistics- Target fluctuations- Number of hits integrated into a look


6.3 Signal Integration & Target FluctuationSignal Integration


6.3 Signal Integration & Target Fluctuation

Coherent Integration

1/ ( / )( / ) ( / ) ( )N i i ii

S N S N N L S N NL

= =

1( / ) (1/ ) ( / ) ( / )

N

N k Nk

S N N S N N S N=

=

: Integrated S/N is N times the mean S/N



- signal phase error for rector sum process scalloping loss



Target Fluctuations and Coherent Integration- In Meyer & Mayers coherent integration model,- Case1: 8 pulses coherently integrated low PRF case

< Detection Probability for Eight Pulses Coherently Integrated >


(Ex) SW-3 case, S/N for 8 pulses hits of 9.0dB, 8.0dB, 12.4dB, 10dB, 9.8dB, 11.9dB, 8.9dB, 10.4dB

(Sol) - mean S/N = sum of power ratios= [7.94 + 6.31 + 17.38 + 10 + 9.55 + 15.49 + 7.76 + 10.96]/8= 85.40/8 = 10.67 10.28dB

- From Table11-1, integration loss for D-C window= 1.51 (1.79dB)= Equivalent Noise B/WScalloping loss (0.72dB=1.44 half)

Total loss = 2.51dB for S/N of 7.77dBFrom Fig5-7,

1910 , window ( =3.0) Dolph-Chebyshev half scalloping loss Table 11-1

FAP =

find for SW-3 targetdP

0.65 for 7.77dP SN dB=;

Example - Coherent Integration


6.3 Signal Integration & Target Fluctuation- Case2

64 pulses-Medium PRF8 pulses S/N Pd.several dwell (final decision ) M of N detection process

< Detection Probability for 64 Pulses Coherently Integrated >


6.3 Signal Integration & Target Fluctuation- Case3

1024 pulses- High PRF (pulse Doppler)

< Detection Probability for 1024 Pulses Coherently Integrated >


6.3 Signal Integration & Target FluctuationTarget Fluctuation- Slowly fluctuating targets are more difficult to detect than

those which are constant or rapidly fluctuating- The effect of fluctuation rapidity has more effect on

detection than the amount of fluctuation


6.3 Signal Integration & Target Fluctuation- Non-coherent integration & detection

Integration loss

< Detection after Non-Coherent Integration of Eight Hits >



< Detection after Non-Coherent Integration of 64 Hits >


6.4 M of N DetectionM of N Detection- To take several independent looks at the same target space, at different

PRF and/or frequencies. Because of range and Doppler ambiguities- Detection is enhanced by using multiple independent looks

look each on target the detecting ofy probabilitPtogether processed looks of number N

detection for successesof number requiredMwherePPJNJ

NP

S

JNS

JS

N

Mjd

==

=

= = )1()!(!

!

lookeachonceinterferenngdetectiofyprobabilitPwherePPJNJ

NP nJN

nJ

n

N

MJfa ==

= )1()!(!

!

Note :- improved false alarm probability

( Pfa is smaller than Pn ) ( Pfa < Pn )- detection probability is improved.( Pfa < Pn )- several looks must be made at the target

()


CFAR - Detection

CFAR Constant False Alarm Rate Detection


6.5 Threshold-Setting Concept-CFAR

Adaptive Mean Level Threshold DetectionMaintains Sensitivity



Mean Level Detector Control of False Alarms



Constant False Alarm Rate (CFAR)- Goal : Detection threshold setting so that the radar receiver

maintains a constant pre-determined prob. of false alarm- Given

=

=

2

2

2

2

2 2exp

2exp

T

VfaVdrrrP

T

- Threshold valueltheoreticaPV faT :1ln2 2 = Assuming the noise power is to be constant, then fixed threshold

satisfy it

2

TV

- To maintain a constant , the threshold value must becontinuously updated based on the estimates of the noisevariance

faP



Type of CFAR- Adaptive threshold CFAR

for known interference distribution

- Non-Parametic CFAR for unknown interference distribution

- Non- linear receiver technique for normalize the root meansquare amplitude of the interference

Reference : CFAR by G. Minkler & J. Minkler ,Magellan Book co.1990



Structure of CFAR

ZKYcriterionDetection

o 1

3Mcell Range Target +=

- used for the senses of range/Doppler binsAssuming that target of interest in CUT all reference cells=zero meanindependent Gaussian noise of variance

( )Mofa K

P+

=1

1



Threshold Setting- For fixed threshold

thresholdfixedawithDetection

thresholdadaptiveanwithDetection

thresholdadaptive

- For general scheme for threshold settingsensing the average interference level and set the threshold so that a relativelyconstant number of false alarms occursper unit of time = Adaptive ThresholdConstant False Alarm Rate = CFAR detection



Cell averaging CFAR (Range CFAR)

- each cell(bin) is tested against a threshold determined by theaverage signal level in a few bins on either side of it

- effective in clutter & jamming environment



- Threshold level

15...:

,:

11 12

12

=

+=

FignoiseoffunctionprobfrommultiplierthresholdM

testedbeingcelltheincludingcellsofnumberNwhere

VN

MV

TH

N

NnnTHTH

- Assuming the probability distribution of interference isknown, Rayleigh noise pdf.(ex)

- but, clutter and ECM type are not Rayleighin this case, sample the number of false alarm and modify the

threshold. parametric or distribution-free detector



Multiple Mean Levels are Required to Adapt toChanging Clutter



Guard band CFAR (Doppler CFAR)- effective in broadband interference (barrage jamming)- interference level examined by the freq. Bands adjacent to the

signal band

< Guard-Band CFAR >



Cell Averaging CFAR Using Greatest-Of


6.5 Threshold-Setting Concept-CFAR The Cell Averaging CFAR with Greatest-Of Selection


6.5 Threshold-Setting Concept-CFAR Clutter Map Design Considerations- Clutter amplitude or residue implementation- Clutter map cell size- CPI synchronization to map radials- Rejection of slow moving unwanted targets- Use of spreading in range and/or azimuth- Detection of low velocity targets- Map compensation for platform motion- Lin or log implementation and update algorithm- Normalization or thresholding algorithm- Clutter map CFAR loss


6.5 Threshold-Setting Concept-CFAR Typical Radar Clutter Map


6.5 Threshold-Setting Concept-CFAR Clutter-map CFAR- CA CFAR in azimuth dimension- radar space into range and azimuth bins- moving average of the clutter residue in each range-

azimuth cell over the several scan- signal on each scan is compared to threshold based on the

moving average

mapClutter


6.5 Threshold-Setting Concept-CFAR Limiting CFAR (analog)- signal and broadband interference to hard-limiting

rejects all amplitude information in both signal and interference

< Impulse Response >

< Analog Limiting CFAR (Dicke-fix) >



< Analog Limiting CFAR Waves and Spectra >


6.6 Reference[1] Radar Target Detection : Handbook of Theory and Practice by D. P. Meyer and

H. A. Mayer, Academic Press, 1973

[2] Introduction to Radar Systems, 2nd ed by M. I. Skolink, McGraw-Hill, 1980

[3] Radar Handbook by M. I. Skolink, McGraw-Hill, 1990

[4] A Statistical Theory of Detection by Pulsed Radar and Mathematical Appendixby J. I. Marcum, IRE Transactions, vol. IT-6, pp.59-267, 1960

[5] Probability of Detection for Fluctuating Targets by P. Swerling, IRETransactions, vol. IT-6, pp.269-308, 1960

ch6-radar+detection+and+cfar

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