Generation of the ambiguity function for ultra wideband radar waveforms

100 Pages·4.3 MB·en_US

by  Leon, Efrain.

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GENERATION OF THE AMBIGUITY FUNCTION FOR ULTRAWIDEBAND
RADAR WAVEFORMS
by
EfrainLeon
Lieutenant Commande(r/, Venezuelan Navy
B.S., Venezuelan Naval Academy, 1982
Submitted in partial fulfillment
ofthe requirements for the degree of
MASTER OF SCIENCE IN ELECTRICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOL
December, 1993
fi
Dr. Michael Morgan, Chairman
Department of Electrical and Computer Engineering
. )
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Master's Thesis
December 17, 1993
4. TITLEANDSUBTITLE 5. FUNDINGNUMBERS
GENERATIONOFTHEAMBIGUITYFUNCTIONFORULTRA
WIDEBAND RADARWAVEFORMS
6. AUTHOR(S)
Leon, Efrain
7. PERFORMINGORGANIZATIONNAMES(S)ANDADDRESS(ES) 8. PERFORMINGORGANIZATION
Naval Postgraduate School
Monterey, CA 93943-5000
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AGENCYREPORTNUMBER
Naval Postgraduate School
Monterey. CA 93943-5000
11. supplementarynotes The views expressed in this thesis care those of the author and do
not reflect the official policy or position of the Department of Defense or the U.S.
Government-
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13. ABSTRACT(Maximum200words
TheAmbiguityFunctionisone ofthetoolsusedto studythe suitability ofwaveforms forradarapplications. Anunderstanding ofthis
functiongivestheradarengineeraninsight into differentradarwaveformsandpermitshim to selectthebest design foraparticular
system application. Thisthesis investigatestheAmbiguity Functionforultrawidebandradarwaveforms generatedbythe Fourier
SynthesisMethod,whichprovidesthe capability toproduceverynarrowpulsesinacoherent andcontrollable form. Since, forultra
widebandradarwaveforms, thetransmitted signal isabaseband signalwithout sinusoidal carrier, theAmbiguityFunctionforthiskinc
ofwaveform shouldbegeneratedby Dopplerprocessing inthetimedomainratherthaninthefrequency domain, as isdone for
conventional radarwaveforms. Inthisthesis,theAmbiguity Functionhasbeengeneratedandanalyzedfortwo differentultra
widebandradarwaveformsby means ofcomputersimulationofaradarreceiverwhichincorporatestime-Dopplerprocessing.
14. SUBJECT TERMS 16. PRICECODE
15. NUMBEROFPAGES
84
17. SECURITYCLASSIFICATION 18. SECURITYCLASSIFICATION 19. SECURITYCLASSIFICATION 20. LIMITATIONOFABSTRACT
OFREPORT OFTHISPAGE OFABSTRACT
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NSN7540-01-280-5500 StandardForm298(Rev,2-89)
PrescribedbyANSIStd.239-18,298-1C
ABSTRACT
The Ambiguity Function is one of the tools used to study the suitability of
waveforms for radar applications. An understanding of this function gives the radar
engineer an insight into different radar waveforms and permits him to select the best
design for a particular system application. This thesis investigates the Ambiguity
Function for ultra wideband radar waveforms generated by the Fourier Synthesis Method,
which provides the capability to produce very narrow pulses in a coherent and
controllable form. Since, for ultra wideband radar waveforms, the transmitted signal is a
baseband signal without sinusoidal carrier, the Ambiguity Function for this kind of
waveform should be generated by Doppler processing in the time domain rather than in
the frequency domain, as is done for conventional radar waveforms. In this thesis, the
Ambiguity Function has been generated and analyzed for two different ultra wideband
radar waveforms by means ofcomputer simulation ofa radar receiver which incorporates
time-Doppler processing.
in
..
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CONTENTS
INTRODUCTION
I. 1
OVERVIEW
A.
1
ULTRA WIDEBAND RADAR
B. 2
THE AMBIGUITY FUNCTION
II. 6
AMBIGUITY FUNCTION
A. 6
MATHEMATICAL EXPRESSION FOR NARROWBAND AMBIGUITY
B.
FUNCTION
7
THE WIDEBAND AMBIGUITY FUNCTION
C. 11
D. MATHEMATICAL EXPRESSION FOR WIDEBAND AMBIGUITY
FUNCTION
12
AMBIGUITY FUNCTION OF A UWB RADAR WAVEFORM
E. 13
Doppler Effect 14
1
2. Matched Filtering 16
3. Doppler Processing Technique 17
UWB
4. Ambiguity Function of Processor 20
F. IMPORTANT PROPERTIES OF THE AMBIGUITY FUNCTION 24
Property 24
1 I
2. Property II 24
3. Property III 24
4. Property IV 25
IV
..
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G. IDEAL AMBIGUITY FUNCTION 25
AMBIGUITY FUNCTION OF UWB RADAR WAVEFORMS GENERATED BY
III.
THE FOURIER SYNTHESIS METHOD
27
A. AMBIGUITY FUNCTION OF A TRAIN OF UWB RADAR PULSES 27
UWB
Transmitted Waveform 27
1
UWB
2. Processing ofthe Received Signal 29
3. Ambiguity Function 30
4. Cuts Through the Ambiguity Function 36
5. Analysis ofthe Ambiguity Function Along the Velocity Axis Avj//t 36
AMBIGUITY FUNCTION OF A UWB PULSE TRAIN OF BARKER CODE OF
B.
LENGTH
13 41
UWB
Transmitted Waveform 42
1
UWB
2. Processing ofthe Received Signal 42
3. Ambiguity Function 46
4. Cuts Through the Ambiguity Function 48
5. Analysis ofthe Ambiguity Function Along the Velocity Axis A\|//x 52
CONCLUSIONS AND RECOMMENDATIONS
IV. 55
CONCLUSIONS
A. 55
RECOMMENDATIONS
B. 56
APPENDIX A. THE FOURIER SYNTHESIS METHOD 57
APPENDIX B. PROGRAM CODES 59
LIST OF REFERENCES 70
INITIAL DISTRIBUTION LIST 72
VI