Clutter ModellingPresented By:

Armaghan Mohsin

Introduction•Clutter denote

unwanted echoes from land, sea, weather ,birds and insects that makes difficult the detection of wanted targets.

•Two types of clutter▫Area or Surface clutter

e.g. land and sea clutter

▫Volume Clutter e.g. weather, birds, insects and chaff

Why Clutter different from Noise? •Although clutter is also random

phenomenon but is differ from Noise in two major ways.▫Clutter power spectrum is not white (i.e., it

is correlated interference), while the noise power spectrum is WHITE (uncorrelated interference). In addition to temporal correlation, clutter is

also exhibit spatial correlation: reflectivity samples from adjacent resolution cells may be correlated.

▫Since clutter is the result of radar echo, the power is affected by such radar and scenario parameters e.g. antenna gain, transmitted power, signal processing gain and range from radar to the terrain

Correlation

•Temporal correlation▫If radar antenna is fixed and clutter data

are collected for fixed range bin, there is a correlation in different pulses for the specific range bin.

•Spatial correlation▫If radar antenna is rotating and clutter data

is collected from same range bins, the correlation present in the same range bin for different antenna positions.

Surface (Area) Clutter•Area Clutter RCS is dependant on clutter

characteristics and area of clutter which is illuminated by radar resolution cell.

Where σAC = RCS of area clutter

σo = RCS per unit area illuminatedAC = area of clutter illuminated within radar resolution cell

•Land and Sea are examples of Area Clutter.

Co

AC A

Factors effecting σo •Grazing Angle Ψ

▫It is the angle from horizontal axis at which radar beam strike the surface. For smooth surfaces, σo increases with increasing Ψ and, for rough surfaces, σo has lesser values at higher grazing angle than at lower angles.

•Vertical texture of Clutter▫Rough surfaces have larger σo than smooth at

low grazing angle, smooth surfaces have larger σo than rough surfaces at high grazing angle

•Wavelength of the radar’s beam▫σo have larger values at shorter wavelengths

Clutter Regions•Three distinct clutter regions are

recognized separated by the grazing angle.▫Low Grazing Angle Region.

Extends from zero to critical angle. Critical angle is the grazing angle below which a surface is smooth.

▫Plateau Region. Grazing angle dependence of Clutter RCS is

much less than in low grazing angle.▫High Grazing Angle Region.

It is characterized by the fact that, at angles near 90o, the surface acts as a specular “mirror” and area clutter coefficient is larger for smooth surface than for rough.

Clutter Regions

Radar resolution Cell(low grazing angle)

Radar resolution Cell(High grazing angle)

•Clutter Area viewed by the radar is determined by antenna beam widths θB and φB.

•The Area is defined as

)sin()4(

BBC RRA

Surface Clutter Radar equation for low grazing angle• Radar equation for detection of target in surface

clutter is different from radar equation is limited by receiver noise, and leads to different design guidelines.▫Radar equation for received echo from the

target is

▫Radar equation for received echo from the surface clutter

▫As σAC and AC are defined earlier so clutter radar equation is

42)4( R

GAPS tet

42)4( R

GAPC ACet

32)4(

sec)2(

R

cGAPC

Bo

et

Clutter Radar Equation Contd..•When clutter echo is large compared to

receiver noise, then the maximum range correspond to discernible signal to clutter ratio is defined as

Range appears as the first power means greater variations of Rmax of clutter dominated radar than a noise dominated

Transmitted power does not appear explicitly in clutter-radar equation

Narrower pulse width, the greater the range, opposite of conventional radar in noise case

Integeration of pulses is generally much less effective when detection is limited by clutter

System losses are not included explicitly in radar equation

sec)2()( minmax cCS

RB

ot

Volume Clutter•Volume Clutter RCS is also dependant on

clutter characteristics and Volume of clutter which is illuminated by radar resolution cell.

Where σVC = RCS of volume clutter

η = RCS per unit volume illuminated

VC = Volume of clutter illuminated within radar resolution cell

•Weather, Chaff, Birds and Insects are examples of Volume Clutter

CVC V

Radar resolution Cell(Volume Clutter)

•Clutter Volume viewed by the radar is determined by antenna beam widths θB and φB and in third dimension by pulse width τ.

•The Volume is defined as

2)4(

cRRV BBC

Clutter Modelling• A clutter model is a mathematical model of

clutter RCS coefficient and other parameters of clutter, as a function of grazing angle, frequency, polarization, and nature of the surface and environment.

• A good clutter model gives two advantages, in analysis it use to predict the performance of radar processors, secondly in design stage by using adaptation it allows optimum, or at least sub-optimum, receivers to be synthesized. In computer simulations they are also used as algorithms to generate clutter patterns. (David K. Barton, 1997)

Clutter Modeling Cont….• A clutter model describes the following

parameters of the clutter.▫The empirical formulas based on experimental

measurements and observations give mean RCS coefficient (σo), for given land or sea structure, grazing angle, frequency, and polarization. Similarly for Volume Clutter.

▫Probability density function to describe amplitude behavior of Clutter RCS (e.g. Rayleigh, Weibull distribution).

▫Velocity (or Doppler) spectrum behavior.▫Coherency in time domain (Temporal

Correlation). ▫Coherency in spatial domain (Spatial

Correlation).

Wheather Clutter Modelling•Radar is much less effected by weather

than are optical and infrared sensors, typically at microwaves and mm wavelength frequencies

•Mostly radar performance is effected by rain

•Rain RCS is model by rayleigh distribution .i.e many small scatteres and none of them is dominant the others.

•Rayleigh need one parameter to described clutter and is calculated by rain fall rate

3

2126.14 107m

mrfii

Continue…..•Generate rayleigh distributed data for a

single range bin centered at mean clutter cross section.

•Compute corresponding received power using Radar Range Equation for clutter.

•Compute corresponding voltage levels.•Apply this profile to signal to generate

echo.

2

2

)2(ln1024 R

cGPC t

Chaff

•Chaff is also describe by the rayleigh pdf and its mean clutter RCS coefficient is given as

▫Where total RCS of all resonantdipoles

within radar resolution volume (square meters)

number of dipoles in the resolution volume

radar operating wavelength

DipTotCh N215.0

TotCh

DipN

Rayleigh PDF

•The Rayleigh probability density function is

For

Mean

Variance

Surface Clutter Model•If there are many small land or sea

scatterers within resolution cell and none of them is dominant then rayleigh distribution describe land or sea clutter

•Mostly there are large values from the scatterers need distributions having long tails to caters these spikes or larger values

•Weibull and log-normal have long tails to accommodate these spikes.

•Two parameters need to specify these distributions

Clutter Models parameters continue…..•For log normal distribution the two

parameters mean and variance are required▫Mean is computed by empirical formulas

for Land and Sea clutter ▫Variance is selected according to nature of

clutter and grazing angle•For log normal distribution the two

parameters mean and skewness are required▫Mean is computed as given above ▫skewness is selected from the given tables

Surface Clutter Models parameters• Sea Clutter Model

▫The mean value for sea clutter RCS is defined as

Whereσ0

C = clutter coefficient at critical angle, taken zero above that angle

K = a constant from 1 to 4, Morchin suggests 1.9

SS = it defines sea statesλ = Radar operating wavelengthβo = clutter slope irregularity factor(radians),

for sea clutter

)(]}tan

)2/(tanexp[tan

]1.0)log(sinlog)1(6.04.6[10log{10

2

22 dB

SS

oo

oC

o

)log(10 CC

o K )180()1(44.2 08.1 SSo

Surface Clutter Models parameters•Land Clutter Model

▫The mean value for sea clutter RCS is defined as

▫Where he =RMS surface height irregularities A, B and βo are constants, these values are

given in tables for different terrains. u = high angle reflectivity of the clutter

surface, unity for sea

)()}10/(10]tan

)(tanexp[tan

]1.0)log(sinlog1.0[10log{10

2

22 dBu

B

A

oo

oC

o

)log(10 CC

o 2.23.9 oEh )/7.4log(10 fu

Log-Normal PDF•The log-normal distribution has the

probability density function

For x > 0

Mean

Variance

Weibull PDF•The probability density function of a

Weibull random variable x is.

• x= Clutter backscatter normalized.• b = Shape parameter(skewness).• σ = Mean Clutter Cross-Section

a

x

a

bxxP

bb

exp)(1

2ln

bma

)1(

)2(ln1

bbm

Clutter Doppler Spectrum•Sea Clutter Spectrum

▫Doppler spectrum is Gaussian in shape, whose clutter motion spread is defined by velocity standard deviation and zero mean velocity

Where σv is standard deviation of clutter motion in

velocity units Ws is wind velocity in same units SS is sea states B is 0.65 if σv and Ws in knots,0.36 if in m/sec

sv W101.0 )14.0(10101.0 SSBv

Clutter Doppler Spectrum•Land Clutter Doppler Spectrum

▫Some Land clutter spectra are Gaussian in shape, with zero mean Doppler and various standard deviation for different terrains

Where σv is standard deviation of clutter motion in

velocity units Ws is wind velocity in same units a = 0.007(vegetated terrain),

0.0045(woodlands) b = 1.28(vegetated terrain), 1.4 (woodlands)

bsv aW

Clutter spectrum Continue…….•Land Clutter Doppler Spectrum

▫Some clutter power spectrum is not fit the Gaussian an empirical formula is defined by Fishbein is

Where P(f) power spectrum of clutter as function of

frequency f, frequency of interest. fc, cutoff frequency. Ws is wind speed in knots

])(1[1)( 3cfffS )1356.0exp(33.1 sc Wf

Clutter spectrum Continue…….•Rain/Chaff Clutter Doppler Spectrum

▫Rain and chaff doppler spectra are gaussian in shape where doppler spread is define by standard deviation and is centered at some mean doppler velocity, standard deviation for rain and chaff is defined as

Where k = 4, R= range from clutter, Vo =wind velocity at beam center σturb = 1 m/sec (rain), 0.7 m/sec (chaff)

22222fallbeamturbshearv

elBshear kR 42.0 SinVazBobeam 42.0 sinshear

Clutter Doppler Spectra

Clutter Modeling