Download - MS_9장 Clutter and MTI
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Chapter 9.
Clutter and Moving Target
Indicator (MTI)
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RSP Lab Hankuk Aviation Univ.
Ground Radar - Environment
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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
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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)
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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
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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(
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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 >
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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
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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(
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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(
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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(
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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
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RSP Lab Hankuk Aviation Univ.
- 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
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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
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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
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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
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- 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)
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RSP Lab Hankuk Aviation Univ.
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)
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- 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
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- 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)
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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
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RSP Lab Hankuk Aviation Univ.
- 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)
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- 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
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- 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
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- 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
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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)
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RSP Lab Hankuk Aviation Univ.
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)
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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)
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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
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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
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Ground Clutter - Environment
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Clutter Radial Velocity Characteristics
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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
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clitterchaffandraingroundtoMTIcancellerdoubleaofeResponc ,,*
Clutter Spectrum Characteristics
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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
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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)
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Coherent MTI Radar Block Diagram
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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
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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)
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MATLAB Function single_canceler.m
< Single canceler frequency response >
rrr nfffn fPRFf nulls ,212peak ),( periodcanceler single
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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. >
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- 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)
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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. >
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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)
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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)
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Delay Line with Feedback(Recursive Filters)
- 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). >
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Delay Line with Feedback(Recursive Filters)
- 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
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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
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- 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)
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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
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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)
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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)
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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)
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MTI Improvement Factor
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)
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MTI Improvement Factor
Small f, then ratio f/ fr is very small. (ie c
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MTI Improvement Factor
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)(
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MTI Improvement Factor
It follows that 2
22
c
rfI
(9.81) => Only c
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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
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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)
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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)
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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
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Delay Line Cancellers with Optimal Weights
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)
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Delay Line Cancellers with Optimal Weights
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)