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Synthetic high range resolution
radar achieved by using pulse to
pulse stepped frequency signals.
Radar target range profile
Course 3
4 hours
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Synthetic high range resolution
radar. Radar target range profile
Frequency-Doain !arget Signatures
"ulse to pulse stepped frequency signals
Synthetic Range "rofile #eneration
$ffect of !arget %elocity
Range- "rofile Distortion "roduced byFrequency $rror
$&aples 'on synthetic data and realdata(
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Frequency-Doain !arget Signatures
)ny signal can be described as either a function of time
or a function of frequency. !he echo signal fro a range-e&tended target
illuinated by a short RF pulse usually is observed in the
tie doain. *ts aplitude and phase versus frequency
is the echo signal spectru+ ,hich is a frequency-
doain description of the signal.
easureents of a targets echo signal in the tie and
frequency doains provide equivalent data for
deterining target reflectivity.
!he targets reflectivity profile in range delay can be
defined as its echo signal aplitude and phase versus
delay easured ,ith respect to the carrier signal of the
transitted pulse.
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Frequency-Doain !arget Signatures
) continuous series of short RF pulses transitted at a
fi&ed pulse repetition frequency can be defined as aFourier series of steady-state frequency coponents,ith a frequency spacing equal to the radars "RF.
Reflectivity equivalent to that easured fro the train ofshort pulses could be obtained fro easureents of
the aplitude and phase of the received Fourier seriesfrequency coponents relative to the respectivetransitted coponent.
!his set of frequency-doain easureents ofreflectivity is the spectru of the tie-doain echo pulse
train. *n practice+ ,hat ,e ,ant is the /RR reflectivity profile of
a target+ not the periodic echo response. Frequency spacing can be the reciprocal of the target0s
range-delay e&tent+ instead of the reciprocal of the
radar0s "R*.
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!he tie duration of each transitted frequencycoponent need only be sufficient to produce anappro&iation to the steady-state echo response.
!he pulse duration have to be greater than the target
range-delay e&tent. *f a series of RF pulses ,ere transitted stepped in
frequency fro pulse to pulse over a band,idth 1+ theset of echo aplitude and phase easureents ade
relative to each transitted pulse can be transfored byusing the DF! into the range-profile equivalent of echoaplitude and phase easureents obtained relative toa short RF pulse of band,idth 1.
Frequency-Doain !arget Signatures
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"ulse to pulse stepped frequency
signals1
0 0
0
( ) ( . ).cos[2 .( . ).( . )]Ne
r r
k
x t X t k T f k f t k T
=
= + [ ]0 0( ) , ( ) otherwiser r iX t A if t kT kT t and X t A= + =
'3.2(
Fig. 3.1 Signal SFS
0
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"ulse to pulse stepped frequency signals
( ) ( ) ( ){ }1
0 0
0
sin c exp2
Ni
i r
k
tX At k j k k T
=
= + + +
( ) ( ){ }1
0 0
0
sin c exp +2
N ii r
k
tAt k j k kT
=
+ + + '3.(
Fig. 3.2 SFS Spectrum.
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"ulse to pulse stepped frequency signals
!he abiguity function odule of the signal SFS is given by
sin[ . .( . . )]1( , ) 1 .sin [ . .( ].
sin[ .( . . )]
rc i
i r
N F T fF F t
N t F T f
+ = +
'3.3(
Fig.3.3 The SFS signal ambiguity function
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"ulse to pulse stepped frequency signals !he section of the abiguity function are
1 sin[ . . . ]( ,0) 1sin[ . . ]i
N fN t f
= '3.4(
Fig. 3.4 Section of the SFS signal ambiguity function for F=
1
N f =
( ) ( ) ( )( )
0 1, sin
sin
sinF
Nc Ft
NFT
FTi r
r=
1
r
FNT
=
'3.5(
'3.6(
'3.7(
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"ulse to pulse stepped frequency signals
Fig. 3.! SFS "atche# filter
ii
tQ t B N
= = =
'3.8(
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Synthetic Range "rofile #eneration
- !ransit a series of 9 e&ploring pulses ,ith carrier frequencyfors
fk = f0 + kf, k=0, 1, , N-1
- Set a range-delayed sapling gate to collect Iand Qsaples of
the targets base band echo response for each transitted pulse.
- Store the quadrate coponents for each of the 9 pulses.
- )pply frequency ,eighting to each data and corrections for target
velocity+ phase and aplitude ripple of echo signals+ etc.
- !a:e a inverse discrete Fourier transfor 'DFT-1( of each record
to obtain the synthetic range-profile ,ith Neleents.
S th ti R P fi! " ti
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Synthetic Range Prfi!e "eneratin
STORAGE
DFT-1PROCESSOR
RECEIVED
SIGNAL
yk(t)
REFERENCE
SIGNAL
GENERATOR
RANGESELECTION
CIRCUIT
SAMPLINGCIRCUIT 1
ADC 1
MIXER 1
ADC 2
SAMPLINGCIRCUIT 2
MIXER 2
H(k)
h(t)
Fig.3.6 Functional block diagram of signal processor
( )
( )cos 2 ,
for
0 , otherwise
k k k
k r r i
f t
x t kT t kT t
+
= +
( )
{ } ( ) ( )cos 2 [ ( )] , for
0 , otherwise
k r k k r r i
k
f t t kT t t kT t t
! t
+ + + +
=
( ) 2 t" # tt c =
( ) [ ]0 cos 2k k k$ t f t = +
The ree!"e# $!%&' r*+ '& !#e' $'tter!&% ,*!&t t'r%et '$$+e# 't r'&%e R. /!th r'#!'
"e*!ty t*/'r# r'#'r "r. !$0
A ,$e r*+ '& N
,$e$ $er!e$ !$ #e$r!e# y the
**/!&% re't!*&0
The reere&e $!%&' k(t) !$0
+k(t) +
k(t)
/here
'3.;(
'3.2
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!he difference bet,een the phases of the transitted signal and the received one is
( ) 222 tk k # t"t fc c
=
!he signal at i&ers output is sapled at
where k = 0, 1, ..., N-
1
2
2
ik r
t "% kT
c= + +
Replacing tie ,ith S:results the e&pression for total sapled difference of phases
22 22
2
t ik k r
# t" "f kT
c c c
= + +
!herefore+ after sapling the signal at i&ers output is
( ) 0 cosk k k k m % =
)fter i&ing the quadrature coponents results
( ) ( )0 0cos sin exp( )k k k k k & k j j = + =
*f applying inverse discrete Fourier transfor for all 9 cople& saples it ,ill be obtained
the target synthetic range-profile ,hich appro&iates the target ,eighting function h'n(
( ) ( )1
0
1 2exp , for 0 1N
k
' n & k j kn n N N N
= =
Synthetic Range Prfi!e "eneratin
'3.23(
'3.24(
'3.25(
'3.26(
'3.27(
'3.28(
( )
( ) ( ) ( )0 cos 2 , for
0 , otherwise
k k r r i
k
f t kT t t kT t t
m t
+ + + =
'3.2(
!he signal at the
i&ers output is
S th ti R P fi! " ti
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Since f:= f
?f results0
( )1
00
1 2R 2 2exp(-j2 f ) exp[ ( )], for 0 1
c
N
k
N" f' n j k n n N
N N c
=
=
@sing substitution2N" f
! nc
=
results1
0
0
1 2 2( ) exp( 2 ) exp( )
N
k
"' n j f j !k
N c N
=
=
*n the above relation it is recogniAed the su of a geoetric progression eleents+
therefore this relation can be re,ritten as
( ) ( )01 exp 21 2
exp 22
1 exp
j !' n j f
!N cj
N
=
0
1 sin 1 2( ) exp exp 2
sin
! N "' n j ! j f
!N N c
N
= or
!he agnitude of the synthetic range-profile is
( )
sin
sin
!
' n !N
N
=
Synthetic Range Prfi!e "eneratin
'3.
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Responses fro a point target ,ill be a&iiAed ,hen y=
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f [ MHz] "max [m] N = 16r
s[m]
B [ MHz] N=32
rs[m]
B [ MHz] N =256
rs[m]
B [ MHz]
0,5 1500 9,!5 1," #",$! ,2 5,$5 25,"
0,2 !50 #",$! ,2 2,#$ ",# 2,92 51,2
0, 500 1,25 #,$ 15,"2 9," 1,95 !",$
0,# !5 2,# ",# 11,!1 12,$ 1,#" 102,#
0,5 00 1$,!5 $ 9,! 1" 1,1! 12$
0," 250 15,"2 9," !,$1 19,2 0,9! 15,"
0,! 21#,2$ 1,9 11,2 ","9 22,# 0,$ 1!9,2
0,$ 1$!,50 11,!1 12,$ 5,$5 25," 0,! 20#,$
0,9 1"","" 10,#1 1#,# 5,20 2$,$ 0,"5 20,#
1 150 9,! 1" #,"$ 2 0,5$ 25"2 !5 #,"$ 2 2,# "# 0,29 512
50 ,125 #$ 1,5" 9" 0,19 !"$
# !,5 2,# "# 1,1 12$ 0,1# 102#
5 0 1,$! $0 0,9 1"0 0,11 12$0
" 25 1,5" 9" 0,!$ 192 0,09! 15"
Synthetic Range Prfi!e "eneratin
Synthetic Range Prfi!e "eneratin
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Synthetic Range Prfi!e "eneratin
f [ %&'] Rmax [m] 1"
rs[m]
* [ %&'] 2
rs[m]*[ %&']
25"
rs[m]
* [ %&']
! 21,#2 1, 112 0,"" 22# 0,0$ 1!92
$ 1$,!5 1,1! 12$ 0,5$ 25" 0,0! 20#$
9 1","" 1,0# 1## 0,5 22$ 0,0"5 20#
10 15 0,9 1"0 0,#" 20 0,05$ 25"0
11 1," 0,$5 1!" 0,#2 52 0,05 2$1"
12 12,5 0,!$ 19$ 0,9 $# 0,0#$ 0!2
1 11,5 0,!2 20$ 0," #1" 0,0#5 2$
1# 10,!1 0,"" 22# 0, ##$ 0,0#1 5$#
15 10 0,"2 2#0 0,1 #$0 0,09 $#0
1" 9,! 0,5$ 25" 0,29 512 0,0" #09"
1! $,$2 0,55 2!2 0,2! 5## 0,0# #52
1$ $, 0,52 2$$ 0,2" 5!" 0,02 #"0$
19 !,$9 0,#9 0# 0,2# "0$ 0,00 #$"#
20 !,5 0,#" 20 0,2 "#0 0,029 5120
Synthetic Range Prfi!e "eneratin
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y analyAing the previous table+ one can see that the ,ider the
signal band is+ respectively the larger stepped frequency and pulses nuberare+ the better range resolution is.
/o,ever by increasing the frequency step value the unabiguous
range length becoes saller.
ic
a
tm N
T= =
!his ratio has the sae value as if obtained by analogical
processing. !herefore ,e can deduce that the synthetic range-profile
generation diagra is a digital atched filter for stepped frequency fro
pulse to pulse signal.
Fro general e&pression of range resolution one can deduce that
signal duration at signal procesor output is !a=2E9?f. *f input signal duration
is tiit results that the copression ratio for one pulse inside the pac:age is
given by
Synthetic Range Prfi!e "eneratin
'3.7(
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Synthetic Range Prfi!e# $ffect %f Target &e!city
!he synthetic range-profile of the oving target is given by
( )1
0
21 2 2 2exp 2
2
Nt i
k r
k
# t" "' n j kn f kT
N N c c c
=
= + +
Fig. 3.& The synthetic range'profile #epen#ing on t(o variables vtan# n.
!he Doppler frequency for a oving target is
02 2t t# # fF
c= =
'3.8(
'3.;(
Synthetic Range Prfi!e "eneratin
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Synthetic Range Prfi!e "eneratin
!he a&iu response shifts as the ratio signalEnoise decreases and
distortions of the response eerge+ for velocities higher than 3
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Synthetic Range Prfi!e "eneratin Fre'(ency F!(ct(atin)
Inf!(ence#
( )& k ej k= k kf " c= 2 2
!he cople& saples+ in frequency doain+ for a ideal target are
,here '3.3
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Synthetic Range Prfi!e "eneratin Fre'(ency F!(ct(atin)
Inf!(ence#
!he position of the detected scattering point corresponds ,ell to the delay associated to the target. !he average value of the aplitude of the principal
pea: is given by
( )[ ]( ' n x e, = 2 2 2 '3.35(
'3.36(
*f ,e consider that the only source of error is the frequency
synthesiAer results
= 22
"
c
ne can consider as acceptable value for .G2 H ,hat is equivalent toan pea: attenuation of the pea: of less than 4 d. !hen for the detection
to 3
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Synthetic Range Prfi!e "eneratin Fre'(ency F!(ct(atin)
Inf!(ence#
Fig. 3.11 A scattering point rangeprofile for 1+,
Fig. 3.1 A scattering point rangeprofile for +,
Fig. 3.12 A scattering point rangeprofile for 4+,
Fig.3.13 for #ifferent values of the - 2+, 4 +, an# & +,
( ),( ' n x
S th ti R P fi! $ t T t
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Synthetic Range Prfi!e# $*tene Target)
!he range-profile of ulti scattering points target is
( )1 1
0 0
21 2exp 2 exp , for 0 1
( Ni
k
i k
"' n j f j kn n N
N c N
= =
=
Fig. 3.14 /0ample of a synthetic range profile in high resolution
'3.37(
S th ti R P fi! $ t T t
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Synthetic Range Prfi!e# $*tene Target)
Fig.3.1! Synthetic range profile for arelative ban# of 3!
Fig.3.1 Synthetic range profile for arelative ban# of !
Fig.3.1$ Synthetic range profile for arelative ban# of &
Fig.3.1& Synthetic range profile for arelative ban# of 1
S th ti R P fi! $*tene Target)
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Synthetic Range Prfi!e# $*tene Target)
Fig.3.1& Synthetic range profile
for an e0ten#e# target four
scattering points at #ifferent
ban#(i#th of the signal
S nthetic Range Prfi!e $*tene Target)
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Sy&thet! r'&%e re$*t!*& e0 3456 +
Re' r'&%e re$*t!*& e0 153 +
Ste,,e#
re7e&y
r'#'r
Synthetic Range Prfi!e# $*tene Target)
Fig.3.1& Synthetic range profile
for an e0ten#e# target four
scattering points at #ifferentban#(i#th of the signal
) stepped-frequency radar is sho,n e&ploring a target using a pulse
,idth of 2 Is+ equivalent to 25< eters in range delay. Radar resolution ,hen56 frequency steps of 2/A are used is
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Synthetic Range Prfi!e# $*tene Target)
Fig.3.1) A'&5 +A%%6/% aircraft. The high resolution range profilefor #ifferent sight angle- o
3o
o
an# )o
.
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Synthetic Range Prfi!e# $*erienta! Re)(!t)
Fig. 3.2 7onfiguration of
measurement system-
2.Frequency synthesiAer
.9et vectorial analyAer
3.)ngle reote coand
4.Jo, noise aplifier
5.!arget
!he atri& has 28 lines and
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Synthetic Range Prfi!e# $*erienta! Re)(!t)
Fig. 3.22 7omparison of range profile of a F11$ a "6%A8/ 2 an# a 973 face
Synthetic Range Prfi!e $*erienta! Re)(!t)
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Synthetic Range Prfi!e# $*erienta! Re)(!t)
Fig.3.24 ariation of the
correlation coefficient for
a "6%A8/ 2
Fig.3.23 7omparison of
range profile of a
"6%A8/ 2 seen to
face continuous curve
an# un#er an angle of
: pointillist curve
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Concluding rear:s