synthetic high range resolution radar

7/25/2019 Synthetic high range resolution radar

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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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)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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) 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.



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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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( ) ( ) ( ){ }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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!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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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

= =


'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

=


'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"




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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



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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


'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.;(



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!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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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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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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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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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


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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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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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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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

synthetic high range resolution radar

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