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2 REPORT DOCUMENTATION PAGE Form Approved OMB No Public reporting burder for this collection of information is estibated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burder to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports ( ), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) REPORT TYPE 3. DATES COVERED (FROM - TO) xx-xx-2002 to xx-xx TITLE AND SUBTITLE 5a. CONTRACT NUMBER Development of a digital signal processor (DSP) based chaotic Communication System 5b. GRANT NUMBER with Emphasis on Military Applications 5c. PROGRAM ELEMENT NUMBER Unclassified 6. AUTHOR(S) Reddell, Noah F. ; 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME AND ADDRESS U.S. Naval Academy Annapolis, MD SPONSORING/MONITORING AGENCY NAME AND ADDRESS, 12. DISTRIBUTION/AVAILABILITY STATEMENT APUBLIC RELEASE, 13. SUPPLEMENTARY NOTES 14. ABSTRACT See report. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Public Release a. REPORT Unclassified b. ABSTRACT Unclassified c. THIS PAGE Unclassified 18. NUMBER OF PAGES PERFORMING ORGANIZATION REPORT NUMBER 10. SPONSOR/MONITOR'S ACRONYM(S) 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 19. NAME OF RESPONSIBLE PERSON from USNA, Annapolis, MD, (blank) lfenster@dtic.mil 19b. TELEPHONE NUMBER International Area Code Area Code Telephone Number DSN Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39.18

3 REPORT DOCUMENTATION PAGE Form Approved OMB No Public reporting burden for this collection of information is estimated to average 1 hour per response, including g the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of the collection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA , and to the Office of Management and Budget, Paperwork Reduction Project ( ), Washington, DC AGENCY USE ONLY (Leave blank) 2. REPORT DATE 7 May REPORT TYPE AND DATE COVERED 4. TITLE AND SUBTITLE Development of a digital signal processor (DSP) based chaotic communication system with emphasis on military applications 6. AUTHOR(S) Reddell, Noah F. (Noah Freeman), FUNDING NUMBERS 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING AGENCY REPORT NUMBER US Naval Academy Annapolis, MD Trident Scholar project report no. 300 (2002) 11. SUPPLEMENTARY NOTES 12a. DISTRIBUTION/AVAILABILITY STATEMENT This document has been approved for public release; its distribution is UNLIMITED. 12b. DISTRIBUTION CODE 13. ABSTRACT: Chaotic systems are aperiodic, deterministic, and sensitive to slight variations in initial condition. The latter property presents the problem that behavior of the system cannot be predicted for a significant period of time, even though for the next instant, it is completely predictable. The frequency domain and time domain properties of chaotic systems have generated interest in the military communications field. This paper explores the advantages of a communication system based on a chaotic carrier for military purposes. Digital signal processing techniques are used to implement the system, perform frequency domain analysis, and generate system performance curves. A series of computer simulations were used to enhance system performance. A digital transmitter was developed that is difficult to localize and detect by exploiting some of the natural properties of chaotic systems. A new dual synchronizing receiver scheme is demonstrated that works by storing samples over an entire bit period prior to estimation. Results show significantly better bit error probability performance in comparison to previously published methods. Research concentrated on developing a system that works effectively without a comspicuous signature in the frequency domain. Such a system should be extremely useful for cover wireless communications. 14. SUBJECT TERMS: Chaos communication, digital signal processing, Lyapunov exponent, dual synchronizing response system 15. NUMBER OF PAGES PRICE CODE 17. SECURITY CLASSIFICATION OF REPORT 18. SECURITY CLASSIFICATION OF THIS PAGE 19. SECURITY CLASSIFICATION OF ABSTRACT 20. LIMITATION OF ABSTRACT NSN Standard Form 298

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50 1U 7$tsj * jsk T qy R$tsj {sttb } B}ss $trstst BZRjk ej { B8st ${ R$tsjR } B}ss Y BZY s 8 I$Z8 s RB8 R} I j RR Yst Y R} I BP j$y 3B BZ RkR 8 by${y $R Zt$I$ {$Btsj sti JZ$ R tb P IAs{, P B8 Y { $% R$tsj I jsk $R tb R$t$h{st B BZ 8BI j nu _YsR * jsk T qy$r & { $R 8 st$tpzj Btjk B R$tsjR 8BIZjs I b$y {s $ R$tsjR 7B8 8BIZjs$Bt 8 YBIR JZ$ s {BY t { $% qy$r 8 str s R$tZRB$Isj BR{$jjsB $t Y { $% 8ZR Ys% ABY Y Rs8 P JZ t{k sti }YsR sr s {B R}BtI$t BR{$jjsB $t Y str8$ ;U pszrr$st WB$R T!P Y PBZ Y$R $R Y 8BR $8}B st & { Bt s b$ j RR str8$rr$bt RkR 8 y $R -} { I Ys Y { $% b$jj { $% t k BY Yst Ys by${y $R t s I Ak Y str8$ qy$r -{ RR t k $R Ztbst I sti {st {B8 $t 8stk PB 8R =RZsjjk tb$r $R 8BI j I sr st sii$$% } B{ RR b$y s pszrr$st I$R $AZ$Bt qy$r 8BI j $R P I B sr sii$$% by$ pszrr$st tb$r wvgpwd ]B88Zt${s$Bt {Ystt jr 8sk $t{jzi s {B8A$ts$Bt BP Y PBjjBb$t & {R Ys s 8B I$^{Zj B B% {B8 >dh!z AsR AstI str8$rr$bt RkR 8 $R RZA` { I B s P JZ t{k R j {$% {Ystt j xu WBtbY$ WBtTpsZRR$st sti WBtTsII$$% *$RZ Ast{ R T ]BjB I pszrr$st tb$r IB R tb Ys% {BtRst R} { sj I tr$k qy$r $R 8B sj$r${ Yst R$8}j VGpW sr tb sjj P JZ t{$ R {st }srr Y BZY s {Ystt j b$y {BtRst s tzst $Bt B s$t yt P t{ wzt$t t$btsjd sti `s88$t w$t t$btsjd {st A % k I$^{Zj B B% {B8 et k $R 8$ I Ak stby str8$ Ys B% js}r Y P JZ t{k AstI ZR I Ak Y {B88Zt${s$Bt RkR 8 WB$R {st sjrb A $8}ZjR$% $t tsz u B{{Z $t js$% jk $tp JZ tjk sti }BB jk 8BI j I Ak s pszrr$st } B{ RR EU 3 JZ t{k 7 j {$% ]Ystt jr T qy R {Ystt jr IB tb }srr sjj P JZ t{$ R b$y Y Rs8 j % j BP s tzs$bt G$ R s tb t sjjk s& { I Ak Y$R & { -{ } s % k Y$Y P JZ t{$ R 3B b$ j RR RkR 8R s8br}y ${ sti $BtBR}Y ${ & {R s R$t$h{st VjRB ts Bb AstI st ttsr 8sk tb R}BtI Zt$PB 8jk B Y PZjj AstIb$IY BP s str8$rr$bt 7 {Ys} d( PB s I R{ $}$Bt BP BZ I$^{Zj$ R t{bzt I b$y s P JZ t{k R j {$% {Ystt j $t BZ AsR AstI RkR 8 U q$8 Tzs k$t ]Ystt jr T qy R {Ystt j & {R s 8BR R$t$h{st PB 8BT A$j b$ j RR RkR 8R *B}}j RY$P {st A R$t$h{st PB s 8B%$t { $% B str8$ 3B R} IR 8Z{Y RjBb Yst Y R} I BP j$y *B}}j RY$P $R } BT }B $Btsj B Y js$% % jb{$k A b t Y str8$ sti { $% *B}}j $tiz{ I PsI$t $R BP {Bt{ t PB jbb Iss s RkR 8R!P t s str8$rr$bt s% jr B s { $% B% 8Zj$}j }syr qy R 8Zj$ }sy {Ystt jr s R} {$sjjk R$t$h{st $t Z Ast s sr by 4 {$BtR B& BP R Z{Z R {szr s R$tsj B A { $% I R % sj $8 R b$y I$& t $8 I jskr Zj$ }sy PsI$t $R BP Y$Y {Bt{ t PB Y$Y Iss s RkR 8R ;

51 Mn i RZjR BP $ e B _ BAsA$j$k 7$8Zjs$BtR ;M VR A$ B } BAsA$j$k $R R$t$h{st B stk {B88Zt${s$Bt RkR 8 b } R t RZjR P B8 R % sj I$& t R$8Zjs$BtR Vjj A$ B } BAsA$j$k R$8Zjs$BtR Zt $t VqNV b$y BZ IZsj Rkt{Y Bt$9$t { $% R{Y 8 qy h R R BP R$8Zjs$BtR Y$Yj$Y Y } PB 8st{ BP BZ IZsj Rkt{Y Bt$9$t { $% R{Y 8 b$y }s s8 R R Ys Ys% A t ZR I $t stby }ZAj$RY I bb, %$t ]ZB8B sj } R t s {B88Zt${s$Bt R{Y 8 AsR I Bt {YsBR $t >H qy $ {Bt$tZBZR RkR 8 $R AZ$j sr st stsjb {$ {Z$ yt Y $ R$tj }s s8 8BIZjs$Bt R{Y 8 Y # 8 $R Y Btjk }s s8 {Yst I AsR I Bt Y 8 RRs A$ B A str8$ I ]ZB8B sj I$I tb }B A$ B } BAsA$j$k } PB 8st{ PB Y $ RkR 8 qy B} t RJZs R $t 3$Z Md RYBb Y } PB 8st{ BP BZ RkR 8 by t 8BIZjs$t Btjk Y # }s s8 AsR I s 8 RRs A$ #w(d ) ;3( sti #wdd ) ;3; qy BY bb }s s8 R s {BtRstU ) de3( sti ' ) ;x3e G Z$j$9 Y 8 8B k BP BZ I$R{ } B{ RRB AsR I RkR 8 $t BZ IZsj Rkt{Y Bt$9$t { $% R{Y 8 qy$r sjjbbr PB s 8B RZARst$sj }s s8 R 8$R8s{Y A b t s Bt T A$ sti s 9 BTA$ k Ztt$t bb { $% R Bt PB s{y }s s8 R Y str8$ Rs sti { $% Rs b$jj sjbskr srbtsajk 8s{Y s Y ti BP stk A$ } $BI qy sr $R,R $t 3$Z Md RYBb Y } PB 8st{ BP BZ RkR 8 ZR$t s 8B RZARst$sj 8BIZjs$Bt BP # w#w(d ) ;3( sti #wdd ) ;3;D qy BY bb }s s8 R s {BtRstU ) de3( sti ' ) ;x3e qy B} t {$ {j R $t 3$Z Md RYBb Y A$ B } BAsA$j$k RZjR }ZAj$RY I $t s }s} Ak ]s Bj sti _ {B s PB {B8}s $RBt>d1H qy R b Y Btjk A$ B } BAsA$j$k RZjR b {BZjI hti PB s {YsB${ {B88Zt${s$Bt RkR 8 G s ZR$t s I$& t R{Y 8 Ys b -} { B A 8B {B% sti BZ RZjR RYBb A A$ B } BAsA$j$k } PB 8st{ qy A$ } $BI $R s { Z{$sj Ps{B PB A$ B } BAsA$j$k R$8Zjs$Bt A {szr $ s& {R YBb 8Z{Y $8 Y bb { $% R Ys% B Rkt{Y Bt$9 B B I$% P B8 Y $t4z t{ R$tsj qy$r sjrb I$ {jk & {R RkR 8 Iss s!z Rs8}j {BZt PB Y R R$8Zjs$BtR $R d(( Rs8}j R } A$ V ;M((( Rs8}j R } R {BtI Y A$ } $BI $R x ) 13(MEX3 3B {B8}s $RBt Y A$ } $BI PB Y B} t {$ {j R $R }B I B A 1(( R { Mnd =t -} { I 7BZ { BP e B R s <$Y G Ys% I$R{B% I by$j k$t B sr{ s$t Y {szr BP A$ B R st $t R$t RZj 3B js$% jk js s$br BP A$ t k B tb$r }Bb R} { sj I tr$k w8 srz I $t I D A$ B R s js jk IZ B {Ys s{ $R${R BP Y {YsB${ RkR 8 $tr si BP tb$r 3B AsR${ str8$rr$bt R{Y 8 R j$, _7 Y t k $t s A$ $R sjbskr Y Rs8 sti B R B{{Z by t Y tb$r t k $R js qy$r $R tb Z PB BZ {YsB${ R{Y 8 i {sjj Ys b ZR I s% s A$ t k o PB BZ {sj{zjs$btr BP tb$r }Bb R} { sj I tr$k y Z tr BZ Ys Y NB t9 RkR 8 B{{sR$Btsjjk B R $tb $BtR by Y t k BP `w0d $R R$t$h{stjk j RR Yst $R s% s GY t Y A$ b$tibb {B R}BtIR B Y R $BtR Y t k $t YBR A$R $R R8sjj Yst -} { I qy j % j BP pszrr$st tb$r $t4z t{ $R tb si`zr I $t BZ R$8Zjs$BtR B s{{bzt PB jbb R$tsj t k G I {$I I B 8BI j RkR 8 A Ys%$B $t Y$R bsk sr tb$r $R tb RB8 Y$t Ys {st ZRZsjjk A si`zr I $t s

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