MS_9장 Clutter and MTI

RSP Lab Hankuk Aviation Univ.

Chapter 9.

Clutter and Moving Target

Indicator (MTI)


Ground Radar - Environment


Radar Environments

< Radar signals and Interference>

- Noise :

in the receiver, ant, tx line

outside from sun random.

Random motion at all temp.

above absolute zero.

- Clutter : Unwanted signal

echo from sea, land, weather

- ECM :

electromagnetic

countermeasures noise jamming

- EMI :

friendly sources such as other radar, comm. sys, friendly jammer

- Spillover : internal clutter


9.1 Clutter Definition Clutter Definition : Clutter is unwanted radar returns

that may interfere with normal radar operations.

Type : Mainloabe Clutter & Sidelobe Clutter

1) Surface clutter :

- Ground clutter : trees, vegetation, ground terrain, man-made structure

- Sea clutter : sea surface (sea clutter)

2) Volume clutter : chaff, rain, birds, insects

Notes: Individual clutter components : random phase and amplitude

Clutter signal level >> receiver noise level

Radars ability to detect targets signal-to-clutter ratio (SCR)


Radar Clutter Type

Clutter

OTHER VOLUME AREA

Land

-mountains

-woods

-vegetated

farmland

-desert

SEA

Weather

- rain

- snow

Chaff

Dust storm

Moving vehicles

Birds

Insects

Angles


Signal-to-Clutter Ratio (SCR)

areaclutter Ac

)/(tcoefficienscatteringclutterwhere

)1.9(

isClutterAverage

220

0

mm

A

RCS

cc

-Propagation factor :

- constructive/destructive interference of the electromagnetic waves diffracted

from an object (target or clutter)

-Target/clutter returns with different angles of arrival of different

propagation factors

2

22

cc

rtt

F

FFSCR

rtrt

c

FFFF

F

case,many in target.forfactorsnpropagatioRx/Tx/

factornpropagatioclutterwhere

)2.9(


9.2 Surface Clutter

- Surface clutter includes both land and sea clutter.

- Area clutter is concern for

1) Airborne radars in the look-down mode

2) ground-based radars when searching for targets at low grazing angle.

- Grazing angle ( ) : angle from the surface of the earth to the main axis of

the illuminating beam.

g

< Definition of grazing angle >


Grazing Angle vs. Scattering Coefficient

- Three factors affect the amount of clutter in the radar beam.

1) Grazing angle 2) Surface roughness 3) Radar wavelength

- Smaller wavelength larger scattering coefficient 0

< Dependency of on the grazing angle > 0


Critical Grazing Angle

- Low grazing angle region : from zero to the critical angle.

- Critical angle : angle below which a surface is considered to be smooth, and

above which a surface is considered to be rough.

- hrms = rms of a surface height irregularity

- According to the Rayleigh criteria the surface is considered to be smooth if

2sin

4

g

rmsh

- Due to surface height irregularity, the rough path is longer than the

smooth path

by a distance .

grmsh sin2

)3.9(


grmsh

sin2

2

Rough Surface

< Rough surface definition >

- When (first null), Grazing angle = critical angle g gc

- This path difference translates into a phase differential

)4.9(


Rough Surface

gc

rmsh sin4

or equivalently,

rms

gch

1sin

- In the case of sea clutter, the rms surface height irregularity is

)7.9(046.0025.0 72.1staterms Sh

- Clutter at low grazing angle diffuse clutter : large number of clutter

returns in the radar beam (non-coherent

reflections)

- Clutter in the high grazing angle region is more specular (coherent

reflections)

)5.9(

)6.9(


Radar Equation for Area Clutter

- Airborne radar in the look-down mode case.

Elliptical shape

- Footprint size =

- Footprint is divided into many ground range bins each size gc sec)2/(

),( 3dBgf


- 0

-

( 3% )

(A)

)sec()2//2)tan(2R(cA az

43

2

0

2

t

43

22

tc

)4(

P

)4(

PP

R

AG

R

G

Ground Clutter Model

: 3


sec)2/(c

)2/tan(2

az

R

R

2/

)2/tan(2tan

c

R el

RadarbeamwidthazimuthPowerHalfaz

2/

)2/tan(2tan sec)2/tan()2/(2

c

RwherecRA elaz

Ground Clutter Geometry


Radar Equation for Area Clutter

- Clutter area Ac is

)8.9(sec2

3 gdBc

cRA

- Power received by the radar from

a scatterer within Ac is

)9.9()4( 43

22

R

GPS ttt

RCSt targetwhere

< Footprint definition >

- Received power from clutter is

)10.9()4( 43

22

R

GPS ctAc

- SCR for area clutter is

)11.9(cos2

)(3

0

RcSCR

dB

gt

A c


Example 9.1

../0136.0

,1.20

,20,2,02.0

3.:1.9

22

2

3

SCRtheComputemm

tcoefficienreflectionclutterandmRCStargetAssume

anglegrazingandkmRrangeswidthpulsetheradbe

widthbeamdBantennatheLetradarairborneanConsiderExample

o

t

o

g

dB

.10,)36(

06.36)(

1048.2)102)(103)(20000)(02.0)(0136.0(

)20)(cos1)(2(cos2)( 4

68

3

0

betterordBofordertheonisXwheredBXleastat

bySCRitsincreasesomehowmustradarthedetectionrelibleforthus,

dBSCR

thatfollowsIt

RcSCR

c

c

A

dB

gt

A


- Sea State

WM v 8.0

105.0 WWv

)sec()2/ /2)tan(2R(cA az

43

2

0

2

t

43

22

tc

)4(

P

)4(

PP

R

AG

R

G

cP

Sea Clutter Model

R

-

-

(A)


9.3 Volume clutter

- Volume clutter includes rain, chaff, birds, insects the volume clutter

coefficient is expressed in squared meters

- Birds, insects and other flying particles are referred to as angel clutter

the average RCS as a function of the weight of the bird or insect is reported

as,

bdBsmb wlog8.546

where, wb is the individual weight in grams

- Bird and insect RCS are also function of frequency

ex) pigeons RCS is -26dBsm at S-band, -27dBsm at X-band

(9.12)


- Wind Shear, Beam Broadening, Turbulence

-

Az/El/(V)

43

22

t

43

22

tc

)4(

P

)4(

PP

R

VG

R

G v

cP

2/4/2 cRV azel

Volume Clutter Model

radar To

elR

azR

2/c

24

2 cRV azel


- Chaff is used as ECM technique by hostile forces.

It consist of a large number of dipole reflectors (large RCS values).

Maximum chaff RCS occurs when dipole length L is one half radar wavelength.

Average RCS for single dipole when broadside is,

2

1 88.0 chaff and for an average aspect angle, it drops to

2

1 15.0 chaff where, the subscript chaff1 indicate a single dipole

- The total chaff RCS within radar resolution volume is,

Dchaff N215.0

where, ND is total number of dipoles in the resolution volume

Chaff RCS

(9.13)

(9.14)

(9.15)


22222

0 cos

fallbeamturbshearv

v VM

sec)/( )sin(0.1

sec)/( sin42.0

sec)/( 0.1

sec)/( 42.0

0

m

mV

m

mkR

fall

azbeam

turb

elshear

Rain Clutter Model

ec)center(m/s beamat speed windV

angleelevation

center beamat direction wind torelativeazimuth

radians)beamwidth(azimuth

radians)beamwidth(elevation

)range(slant

))/(sec)((4gradient shear wind

0

az

el

KmR

Kmmk


- Weather or rain clutter is easier to suppress than chaff, since rain can be as

perfect small spheres.

- We can use the Rayleigh approximation of perfect sphere to rain droplets

RCS Rayleigh approximation is given as,

rkrr 429

where, and r is radius of a rain droplet /2k

- Electromagnetic wave when reflected from perfect sphere become strongly

co-polarized (same polarization as incident waves) .

Therefore backscatter energy from rain retains the same polarization as

incident waves, but reversed direction of propagation.

So, radar suppress rain clutter by co-polarizing the radar antenna.

Weather and rain clutter

(9.16)


- Defining as RCS per unit resolution volume VW, it computed as,

N

i

i

1

where, N is the total number of scatterers within the resolution volume

- Total RCS of a single resolution volume is,

N

i

WiW v1

- A resolution volume is in Fig 9.6, and is approximated by

cRV eaW2

8

where, a ,b are antenna beam width in az, el, is pulse width, R is range

(9.17)

(9.18)

(9.19)

Resolution volume


- Consider a propagation medium with an index of refraction m.

The ith rain droplet RCS approximation in this medium is,

62

4

5

ii DK

where, 2

2

22

2

1

m

mK

where, Di is the ith droplet diameter

(9.20)

(9.21)

Weather clutter coefficient


- For example, temperatures between 32F and 68F yield,

6

4

5

93.0 ii D

- and for ice (9.20) can be approximated by,

6

4

5

2.0 ii D

- Substituting (9.20) into (9.17) yields

ZK 24

5

where the weather clutter coefficient Z is defined as

N

i

iDZ1

6

- In general, the units of Z are often expressed in millimeter6/m3

(9.22)

(9.23)

(9.24)

(9.25)

Weather clutter coefficient


Radar equation for volume clutter

- The total power received by radar from t at R is

43

22

)4( R

GPS ttt

- The weather clutter power received by the radar is

43

22

)4( R

GPS WtW

- Using (9.18) and (9.19) into (9.27) and collecting terms yield,

N

i

ieat

W cRR

GPS

1

2

43

22

8)4(

- SCR for weather clutter is computed by dividing (9.26) by (9.28), more

precisely,

N

i

iea

t

W

tV

RcS

SSCR

1

2

8

where V is used to denote volume clutter.

(9.26)

(9.27)

(9.28)

(9.29)


9.4 Clutter statistical models

- Clutter is statistically described by a probability distribution function.

The type of distribution depends on the nature of clutter itself (sea, land,

volume), radar operating frequency and the grazing angle.

- If probability of receiving scatterer is statistically independent of another

scatterer, then, the clutter may be modeled using a Rayleigh distribution,

0;exp2

0

2

0

x

x

x

x

xxf

where x0 is the mean squared value of x

- The log-nomal distribution best describes land clutter at low grazing angles.

it also fits sea clutter in the plateau region. It given by,

(9.30)


Clutter statistical models

- Weibull distribution is used to model clutter at low grazing angles for 1 to 10

Ghz. Weibull probability density function is determined by the Weibull slope

parameter and a median scatter coefficient 0 and given by,

0;exp00

1

xxbx

xfbb

where, b=1/a is known as the shape prameter.

when b=2 the Weibull distribution becomes a Rayleigh distribution.

(9.32)

where xm is the median of the random variable x, is the standard deviation

of ln(x).

0;2

lnlnexp

2

12

2

x

xxxf m

(9.31)


9.5 Clutter Spectrum

- Clutter is not always stationary : wind speed, motion of the radar scanning

antenna Doppler frequency spread

- In Ground Radar

clutter spectrum : concentrated around 0f

rPRF f

and integer multiples of the radar

: some small spreading

- clutter power spectrum : fixed (stationary) + random (frequency spreading)

for most cases, Gaussian


Clutter Spectrum

parameter Weibull: component, spreadfrequency rms: ,2 00 of

frequency spreading stationary clutter

2

2

0

22

002

2

02

exp211

WW

WwSc (9.33)

- Clutter power :

concentrated around zero Doppler with some spreading

(typically less than 100Hz)

2W- denote the fixed to the random power ratio by

clutter spectrum


Ground Clutter - Environment


Clutter Radial Velocity Characteristics


Clutter PSD

Concentrated around DC and integer multiples PRF

2

2

0

2 2exp

2

cc

PwS (9.34)

mean : deviation, : clutter, total: 0cP

- Model clutter using a Gaussian-shaped power spectrum


clitterchaffandraingroundtoMTIcancellerdoubleaofeResponc ,,*

Clutter Spectrum Characteristics


9.6 Moving Target Indicator (MTI)

- In CW radar :

suppress clutter return by

ignoring the receiver output DC

- MTI filter :

deep stop-band at DC and

at integer multiples of the PRF

(a) Typical radar return PSD

(b) MTI filter frequency response

(c) Output from an MTI filter

- In Pulsed radar system:

suppress clutter return by using

special filter, MTI


Blind Speed

MTI Filter

- using delay line cancelers

- periodic frequency response (null at

Blind speed : target Doppler frequency=

0 ;2

nnf

v rblind

severely attenuate

- minimize the occurrence of blind speeds

PRF staggering : changing PRF between consecutive pulses

using high PRF

rnf )

rnf

(9.35)


Coherent MTI Radar Block Diagram


9.7 Single Delay Line Canceler

Ttxtxty

Tttth

11 zzH

f 2 TjeH 1

two-pulse canceler

rf T

thtxty

th

1 PRIdelay

output : *

response impulse :

< Single delay line canceler >

(9.36)

(9.37)

(9.38)

(9.39)

impulse response

Fourier transform

Z-domain


Power gain (Single Delay line Canceler)

TjTj eeHHH 11*2

TeeH TjTj cos12112

2sin42cos22

22 2sin4 TH

Power gain for the single delay line canceler response

wtjwte jwt sincos

(9.40)

(9.41)

(9.42)


MATLAB Function single_canceler.m

< Single canceler frequency response >

rrr nfffn fPRFf nulls ,212peak ),( periodcanceler single


9.8 Double Delay Line Canceler

- Two basic configurations of a double delay line canceler

Double canceler are often called three-pulse canceler

< Two configurations for a double delay line canceler. >


- The double line canceler impulse response is given by

)2()(2)()( TtTttth

- The power gain for the double delay line canceler is

2

1

2

1

2)()()( HHH

- It follows that

4

2

2sin16)(

TH

(9.43)

(9.44)

(9.45)

Double Delay Line Canceler

- In the z-domain

2121 21)1()( zzzzH (9.46)


MATLAB Function double_canceler.m

- MATLAB Function double_canceler.m

)(_][ fofrcancelerdoubleresp

is the number of periods desired.

Better response than the single canceler (deeper notch and flatter pass-band response)

fofr

< Normalized frequency response for single and double cancelers. >


9.9 Delay Line with Feedback(Recursive Filters)

- The advantage of a recursive filter

shape the frequency response of the filter

< MTI recursive filter >

- From the figure

)()1()()( twKtxty

- Applying the z-transform to the above three equation yields

)()()( twtytv

)()( Ttvtw

)()1()()( zWKzXzY

)()()( zWzYzV

)()( 1 zVzzW

(9.47)

(9.48)

(9.49)

(9.50)

(9.51)

(9.52)


Delay Line with Feedback(Recursive Filters)

- Solving for the transfer function yields

- The modulus square of is then equal to

1

1

1

1)(

Kz

zzH

- Using the transformation yields

)(zH

)()1(

)(2

)1)(1(

)1)(1()(

12

1

1

12

zzKK

zz

KzKz

zzzH

Tjez

Tzz cos21

)(/)()( zXzYzH

(9.53)

(9.54)

(9.55)

- Thus, Eq. (9.54) can now be rewritten as

)cos(2)1(

)cos1(2)(

2

2

TKK

TeH Tj

(9.56)



- When K=0, Eq. (9.56) collapses to Eq. (9.42)

22 2/sin4)( TH (9.42)

- By changing the gain factor K one can control of the filter response

< Frequency response corresponding to Eq.(9.56). >



- In order to avoid oscillation due to the positive feedback

the value of K should be less than unity

- The value is normally equal to the number of pulses received from

the target

ex) K=0.9 corresponds to ten pulses

1)1( K

K=0.98 corresponds to about fifty pulses


9.10 PRF Staggering

- Blind speeds can pose serious limitations

performance of MTI radars

ability to perform adequate target detection

- Using PRF agility by changing the pulse repetition interval consecutive pulse

extend the first blind speed to tolerable values

- In order to show how PRF staggering

assume that two radars with distinct PRFs are utilized for detection

using two radars to alleviate the problem of blind speed is a very costly

option

- A more practical solution

to use a single radar with two or more different PRFs


- Consider a radar system with two interpulse periods and

PRF Staggering

2

1

2

1

n

n

T

T (9.57)

Where, and are integer 1n 2n

2T1T

- The first true blind speed occurs when 2

2

1

1

T

n

T

n (9.58)

- The ratio (stagger ratio) 2

1

n

nks (9.59)


PRF Staggering

< Frequency responses of a single canceler. T1=4, T2=3, T1/T2=4/3 >

- Using staggering ratios closer to

unity the first true blind speed

farther out

- The dip in the vicinity of

becomes deeper 1/1 T


PRF Staggering

< MTI responses, staggering ratio 63/64 >

- In general, if there are N PRFs related by

N

N

T

n

T

n

T

n

2

2

1

1

- The first true blind speed for the staggered waveform is

121

blindN

blind vN

nnnv

- If the first blind speed to occur for any of the indiviual PRFs is 1blindv

(9.60)

(9.61)


9.11 MTI Improvement Factor

Performance of MTI systems - Clutter Attenuation (CA)

- MTI Improvement factor

(1) MTI Clutter attenuation

CA = Ci / Co Ci : MTI filter input clutter power

Co : Output clutter power

(2) MTI Improvement factor

CAS

S

C

C

S

S

C

S

C

SI

i

i

ii

i

0

0

0

0

0

So/Si = |H(w)|2 : average power gain for MTI filter

(9.62)

(9.63)

(9.64)


MTI Improvement Factor

Gaussian clutter power spectrum

2

22

8exp

22)(

v

fPfW

v

c

(9.65)

Pc : clutter power (constant) c : clutter rms frequency

/2 vc (9.66)

v : rms wind velocity => wind: main reason of clutter freq. spreading

)2exp(2

)( 22 cc

c fP

fW

(9.67)

Clutter power at the input of an MTI filter

dffP

Ccc

co

2

2

2exp

2 (9.68)



Factoring out

Clutter power at output of an MTI

dff

PCcc

ci

2

2

2exp

2

1

ci PC

(9.69)

(9.70)

dffHfWCo2

)()(

(9.71)

Analysis using a single delay line canceller

Single canceller power gain 2

2sin4)(

rf

ffH

(9.72)



Small f, then ratio f/ fr is very small. (ie c



Substituting eq.(9.76)&(9.70) into (9.62) 2

2

c

r

o

i f

C

CCA

(9.77)

(9.78)

(9.79)

(9.80)

Improvement factor for a single canceller 2

0

2

c

r

i

f

S

SI

Power gain ratio for a single canceller

22

cos221

)(

2/

2/

2

dff

f

ffH

r

r

f

f rr

Using the trigonometric identity 2)(sin4)2cos22(

dff

f

ffH

S

S

r

f

fri

o

r

r

22/

2/

2sin4

1)(



It follows that 2

22

c

rfI

(9.81) => Only c


9.12 Subclutter Visibility (SCV)

Phrase Subclutter Visibility (SCV)

- radars ability to detect non-stationary targets in a strong clutter background

- used as a measure of MTI performance


Subclutter Visibility (SCV)

SCV - expressed as the ratio of the improvement factor to the min.MTI output

SCR

Phrase Interclutter Visibility (ICV)

radars ability to detect non-stationary targets between strong clutter points

- > if radar system - resolve the area of strong and weak clutter

oSCRISCV )/(

SCV of two radars not compare their performance

-> target-to-clutter ratio : proportional to the size of the radar resolution

cell and may also be a function of frequency.

ex) Radar system with 10us pulse length & 10o beamwidth : need 20dB more

SCV than Radar system with 1us pulse length & 1o beamwidth.

(9.82)


9.13 Delay Line Cancellers with Optimal Weights

Delay line canceller transversal FIR filter (tapped delay line filter)

Weights : binomial coefficients -> N-stage cascaded single line cancellers

Binomial coefficient :

1,...,1;)!1()!1(

!)1( 1

Ni

iiN

Nw ii (9.83)


Delay Line Cancellers with Optimal Weights

Using the binomial coefficients produces an MTI filter (approximated optimal

filter) -> maximize the improvement factor

Two equivalent three delay line cancellers

(a) Tapped delay line (b)Three cascaded single line cancellers



For example, N=2 (delay line canceller)

N

i r

N

ii f

ffH

S

S

1

2

1

2

10 sin4)(

(9.85)

Average power gain for an N-stage delay line canceller

2

0 sin16

ri f

f

S

S

(9.84)

Rewritten N

r

NN

i f

ffH

S

S2

22

10 sin2)(

(9.86)

Blind speeds for N-stage delay canceller : identical to single cancellers blind speed

Blind speed : independent from the number of cancellers used

...!3

)2)(1(

!2

)1(1

22

20

NNNNNN

S

S

i

(9.87)



General expression by Nathanson

TT

I

23

1

3

41

1

(9.88)

wk & wj : weights of tapped delay line canceller

((k-j)/fr) : correlation coefficient between the kth and jth samples

For example, N = 2

N

k

N

j r

k

io

f

jkww

SSI

j

1 1

* )(

)/(

(9.89)

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MS_9장 Clutter and MTI