New Binary Complementary Codes Compressing a Pulse to a Width of Several Sub-pulses

Transcription

1 Nw Biary Complmtary Cods Comprssig a Puls to a Width of Svral Sub-pulss Hiroshi TAKASE ad Masaori SHINRIKI Dpartmt of Computr ad Iformatio Egirig, Nippo Istitut of Tchology 4- Gakudai, Miyashiro, Saitama-k, Japa -mail: takas@it.ac.jp, shiriki@it.ac.jp Abstract I this papr, w propos w biary complmtary cods, which comprss a puls to a width of svral sub-pulss, ad survy all combiatios of th biary complmtary cods with svral cod lgths. W ar abl to fid a larg umbr of biary complmtary cods ad complt complmtary cods. Furthrmor, w show that logr such complmtary cods ca b acquird usig th xpasio mthod show by Golay. I additio, w show that th auto-corrlatio sidlob of a idividual cod for th proposd biary complmtary cod pair is smallr tha that of th covtioal. Idx Trms radar, puls comprssio, complmtary cod, complt complmtary cod, cross corrlatio I. INTRODUCTION To improv th rag rsolutio of radar whil maitaiig a good sigal-to-ois ratio (S/N, it is cssary to dcras th puls width ad to icras th pak powr. Thr ar cass, howvr, i which th pak powr caot b icrasd, such as i phasd array radars usig smicoductor dvics, ad millimtr-wav radar. Th puls comprssio tchiqu has b ivstigatd as a rmdy i such cass. Howvr, ucssary sidlobs ar prst bfor ad aftr th comprssd puls, ad thr hav b fforts to rduc thos sidlobs. Applyig th complmtary cod is o of th most ffctiv mthods to limiat sidlobs wh th Dopplr ffct is gligibl []. Th complmtary cod cosists of a pair of cods, which hav th proprty that th sum of auto-corrlatio fuctios has a sidlob lvl of zro. I a actual radar systm, ach of th codd pulss ar trasmittd sparatly i tim or frqucy, ad thy ar addd aftr ach is auto-corrlatd at th rcivr. Th first applicatio of th complmtary cod was to ifrard multislit spctromtry. Followig that, thr wr attmpts to apply it to th radar; i fact, th complmtary cod has b utilizd for th msosphr-stratosphrtroposphr (MST radar [0],[]. Nowadays, thr ar may attmpts to apply it to commuicatio tchology [3]. I this study, w biary complmtary cods ar proposd, ad thir applicatios ar cosidrd, maily focusig o radar. Golay firstly proposd th biary complmtary cod [] i additio to itroducig th xpasio mthods, by which aothr complmtary cod of lgth N m (m is itgr is costructd by a complmtary cod of lgth N. Th biary complmtary cods ar availabl i lgths of,, 4, 8, 0, 6, 0, 6, 3, 40, 5, 64, 80, 00 (up to 00. Howvr, availabl cod lgths ar limitd, ad th umbr of availabl cods i ach lgth is also limitd [],[5]. Sivaswamy ad Frak proposd th multi-phas complmtary cod [4],[5], which hav mor cod pairs tha th biary complmtary cod. Howvr, th multi-phas cod has th problm of th complxity of th hardwar for th digital dcodr. It should b otd, howvr, that all of thos studis cosidr th codd puls that comprsss th puls to a sigl subpuls width. O th othr had, it has b show by authors that th cod comprssig a puls to a width of svral subpulss could hav som mrits as a stadard puls comprssio cod [8]. Furthrmor, it has b show that th 4-phas complmtary cod comprssd to a width of svral sub-pulss has far mor cod pairs tha a puls comprssd to th width of a sigl sub-puls. Morovr, by usig such 4-phas complmtary cods, it is possibl to rduc th sidlob producd by th Dopplr frqucy; howvr, th biary complmtary cod that comprsss a puls to a width of svral sub-pulss has ot yt b ivstigatd. This study itroducs w biary complmtary cods that comprss a puls to th width of svral sub-pulss. W th show that mor cod pairs xist i such biary complmtary cods tha i covtioal biary complmtary cods, ad also idicat that ths cod pairs ca compos logr complmtary cods of th proposd typ usig th xpasio mthod proposd by Golay. As a rsult, w fid that thr ar mor biary complmtary cods of th proposd typ tha of th covtioal typ. Aothr importat advatag of th proposd biary complmtary cods itroducd i this papr is that thr ar mor complt complmtary cods [6], which cosist of a pair of complmtary cods ad th sum of two cross-corrlatio fuctios btw th mat cods that ar always zro for ay tim shift, tha i th covtioal typ. It is also show that, i th proposd complmtary cods, thr ar tworks coctd by th rlatioship btw two complmtary cods that joitly costruct a complt complmtary cod. This fact mas that it is possibl to limiat or supprss th mutual itrfrc v o th sam frqucy by usig such proposd complmtary cods o svral adjoiig radars ad sychroizig th puls trasmissio. Namly, th ffctiv us of th frqucy rsourc is possibl.

2 Rport Documtatio Pag Form Approvd OMB No Public rportig burd for th collctio of iformatio is stimatd to avrag hour pr rspos, icludig th tim for rviwig istructios, sarchig xistig data sourcs, gathrig ad maitaiig th data dd, ad compltig ad rviwig th collctio of iformatio. Sd commts rgardig this burd stimat or ay othr aspct of this collctio of iformatio, icludig suggstios for rducig this burd, to Washigto Hadquartrs Srvics, Dirctorat for Iformatio Opratios ad Rports, 5 Jffrso Davis Highway, Suit 04, Arligto VA Rspodts should b awar that otwithstadig ay othr provisio of law, o prso shall b subjct to a palty for failig to comply with a collctio of iformatio if it dos ot display a currtly valid OMB cotrol umbr.. REPORT DATE 4 APR 005. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Nw Biary Com plmtary Cods Comprssig a Puls to a Width of Svral Sub-pulss 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S 5d. PROJECT NUMBER 5. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S AND ADDRESS(ES Dpartmt of Computr ad Iformatio Egirig, Nippo Istitut of Tchology 4- Gakudai, Miyashiro, Saitama-k, Japa 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S AND ADDRESS(ES 0. SPONSOR/MONITOR S ACRONYM(S. DISTRIBUTION/AVAILABILITY STATEMENT Approvd for public rlas, distributio ulimitd. SPONSOR/MONITOR S REPORT NUMBER(S 3. SUPPLEMENTARY NOTES S also ADM00798, Procdigs of th Itratioal Cofrc o Radar (RADAR 003 Hld i Adlaid, Australia o 3-5 Sptmbr 003., Th origial documt cotais color imags. 4. ABSTRACT 5. SUBJECT TERMS 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT UU a. REPORT uclassifid b. ABSTRACT uclassifid c. THIS PAGE uclassifid 8. NUMBER OF PAGES 6 9a. NAME OF RESPONSIBLE PERSON Stadard Form 98 (Rv Prscribd by ANSI Std Z39-8

3 χ(τ+ψ(τ Sub-puls width τ (a Covtioal cod χ(τ+ψ(τ Fig. Comprssd puls wavform. Sub-puls width τ k (b Proposd cod III. PROPOSED BINARY COMPLEMENTARY CODE This papr cosidrs biary complmtary cods. Th biary sts ar (0,, ad th total umbr of two-cod combiatios is ( - /. Th biary complmtary cods that comprss a puls to a width of svral sub-pulss, amly satisfyig Eq.(4, ar ivstigatd. First of all, such biary complmtary cods of short cod lgth ar survyd for all cod combiatios. A pair of biary cods whos lgth is 3 ca b writt by Eqs.(5 ad (6, jφ 0 j( φ0+ φ φ0+ φ+ φ A = {,, } (5 0 j( θ0+ θ j( θ0+ θ+ θ B = {,, } (6 Furthrmor, w show that th auto-corrlatio sidlob of a idividual cod for th proposd complmtary cod pair is smallr tha that for th covtioal typ. Usig such proposd complmtary cods, it is possibl to rduc th sidlob producd by th Dopplr frqucy. II. PRINCIPLE Th auto-corrlatio fuctios of two cods, A =(a,a,,a ad B =(b,b,,b, ar dfid as Eq.( ad Eq.( rspctivly. χ ( τ = A i A* i+ τ τ 0 ( ψ ( τ = B i B * i+ τ τ 0 ( Th covtioal biary complmtary cod is dfid by Eq.(3. Namly, th sum of two auto-corrlatio fuctios is zro for ay tim shift xcpt =0: 0, χ( τ + ψ ( τ =, for all τ > 0 for τ = 0 whr is th tim shift ad * is a complx cojugatio. This papr proposs w biary complmtary cods that comprss a puls to a width of svral sub-pulss. Th w biary complmtary cods is dfid by Eq.(4. zro, χ ( τ + ψ ( τ = ozro,, for all for all τ > k for τ = 0 k τ > 0 Th spctrum badwidth of th proposd biary complmtary cod is arrowr tha that of th covtioal biary complmtary cod, bcaus th comprssd puls width is widr. Figur (b shows th puls shap comprssd by th proposd cod (that by th covtioal cod is show i Fig.(a, whr k is th umbr of subpulss as idicatd i Fig.(b, ad if m is th umbr of subpuls, th k=(m-/. (3 (4 whr φ 0, φ, φ ar th phas diffrcs btw ighbor sub-pulss of cods A, whil 0,, ad ar thos of cod B. Thir auto-corrlatio fuctios, (, (, ca b writt by Eqs.(7 ad (8, rspctivly. j χ( = χ( 0 j ψ ( = ψ ( 0 φ θ jφ j( φ + φ j( θ+ θ Coditio (4 ca th b writt as Eqs.(9 ad (0. (7 (8 jφ ( ( jφ χ + ψ = (9 j( φ + φ θ+ θ χ( + ψ ( = + = 0 (0 Equatio (9 mas that th comprssd puls is composd of thr sub-pulss. I that cas, th valu of k is. A pair of biary cods whos lgth quals 4 is similarly xprssd as Eqs.( ad (. jφ 0 j( φ0+ φ φ0 + φ + φ φ0+ φ + φ+ φ3 A = {,,, } ( 0 j( θ0+ θ θ0+ θ+ θ θ0+ θ+ θ+ θ3 B = {,,, } ( Thr ar two cass satisfyig Eq.(4. O is giv by Eqs.(3, (4, ad (5. jφ 3 3 ( ( jφ jφ χ + ψ = (3 j( φ + φ φ + φ3 θ + θ θ + θ3 χ( + ψ ( = = 0 (4 j( φ + φ + φ3 θ + θ + θ 3 χ(3 + ψ (3 = + = 0 (5 I this cas, th umbr of th o-sid ighbors is, amly k=. Th cas of k= is giv by Eqs.(6, (7, ad (8. jφ jφ jφ3 3 χ ( + ψ ( = (6 j( φ + φ φ+ φ3 θ+ θ θ+ θ3 χ( + ψ ( = (7 j( φ + φ + φ3 θ + θ + θ 3 χ(3 + ψ (3 = + = 0 (8 Similarly, it is possibl to obtai th coditios for a logr complmtary cod of th proposd typ.

4 Tabl Numbr of biary complmtary cods ad complt complmtary cods. Cod lgth Covtioal cods Proposd cods k =0 k= k= k=3 k=4 k= ( ( ( 4 ( ( 4 ( (8 ( 0 ( * 4 ( (54 6 (8 6 (8 8 4 ( 8 (8 * 3 (6 50 (5 50 (4 80 ( (0 8 (4 0 6 (8 8 (4 0 (60 3 (6 58 (9 46 (84 * ( (64 8 (8 * 44 (88 * 4 ( 36 (8 m ( : m-valu ad -valu ar th umbr of complmtary cods ad complt complmtary cods, rspctivly. * : icluds coctio of complt complmtary cods. k : icluds th umbr of o-sidd sub-pulss. Tabl shows th umbr of cod pairs satisfyig thos coditios, which ar obtaid usig a computr. Th valu i parthss idicats th umbr of complt complmtary cods, which ar dscribd furthr i Sctio 5-A. Th covtioal biary complmtary cod is th idicatd at th cas of k=0, which is comprssd to a sigl sub-puls. If k=, th th umbr of sub-pulss for a mailob is 3, ad similarly, if k= ad k=3, it is 5 ad 7, rspctivly. This papr ivstigats biary complmtary cods whos cod lgths rag from 3 to ad hav a k of lss tha 5. It should b otd that thr xist mor biary complmtary cods of th proposd typ tha do thos of th covtioal typ. Cosqutly, th icras i cod cssary for slctig appropriat jammig ad mutual itrfrc btw ighborig radars is actually rducd [5]. A xampl of th proposd biary complmtary cod is show as follows. [Cod lgth= ( k=] A=(0, 0, 0, 0, 0, 0, 0,,,, 0, 0 B=(0, 0, 0, 0,, 0,,, 0, 0,, Th comprssd puls wavform is show i Fig.. Fig. Output wavform for proposd complmtary cod with cod lgth (k=. IV. EXPANSION OF CODE LENGTH I sctio 3, w ivstigatd th biary complmtary cods of th proposd typ of which lgth is from 3 to, ad foud that th os of logr cod lgth ar cssary for th actual applicatio. It may b possibl to acquir v logr biary complmtary cods by a xhaustiv computr sarch as usd i sctio 3. Howvr, th calculatio tim will b xcssiv wh th cod lgth is logr tha 0. Thrfor, i this sctio, w discuss whthr it is possibl to obtai log biary complmtary cods of th proposd typ usig th xpasio mthod itroducd by Golay. Wh a complmtary cod of lgth, A =(a,a,,a ad B =(b,b,,b, is giv, a complmtary cod of lgth, {C, D }, which is show i Eqs.(9 ad (0, or Eqs.( ad (, will b obtaid by th Golay's mthod []. C = (a, a,, a, b, b,, b (9 D = (a, a,, a, (-b, (-b,, (-b (0 or C = (a, a,, a, b, b,, b ( D = (a, (-b, a, (-b,, a, (-b ( Howvr, this is th mthod for covtioal biary complmtary cods. It should thrfor b cofirmd whthr th Golay's mthod could b also applicabl for th proposd biary complmtary cod by which a puls is comprssd to a width of svral sub-pulss. Howvr, it is asily foud that th xpasio mthod giv by Eqs.(9 ad (0 ca b applid to th proposd biary complmtary cod, whras that giv by Eqs.( ad ( caot, bcaus i th cas of th mthod giv i Eqs.( ad (, th mailob of th comprssd puls is dividd with som sparatd paks. Th comprssd puls width is scarcly chagd by usig th xpasio mthod of Eqs.(9 ad (0, bcaus thr is barly ay chag to th spctrum badwidth of th cod. This mthod ca b applid rpatdly. Th cod lgth will b about m if th xpasio mthod is applid m tims. Sic th umbr of biary complmtary cods obtaid by th xpasio dpds o th umbr of th cod pairs, it is th foud that mor log biary complmtary cods xist for th proposd typ tha for that of th covtioal typ,

5 {m, } Complmtary cod Complt complmtary cod {, f} {g, h} {a, b} {c, d} {, f} {g, h} {a, b} {c, d} a Covtioal cod b Proposd cod Fig. 3 Output wavform for proposd complmtary cod with cod lgth 4 (k=. which is a vry importat advatag of th proposd biary complmtary cod. A xampl cod for which th xpasio mthod is applid is as show blow, whr {A, B} is th bas cod pairs ad {C, D} is th xpadd cod. Th cod lgth of A ad B is (k=, ad th cod lgth of C ad D is 4 (k=. A = (0, 0, 0, 0, 0, 0, 0, π, π, π, 0, 0 B = (0, 0, 0, 0, π, 0, π, π, 0, 0, π, π C = (0, 0, 0, 0, 0, 0, 0, π, π, π, 0, 0, 0, 0, 0, 0, π, 0, π, π, 0, 0, π, π D = (0, 0, 0, 0, 0, 0, 0, π, π, π, 0, 0, π, π, π, π, 0, π, 0, 0, π, π, 0, 0 Figur 3 shows th puls wavform comprssd by th xpadd xampl cod. V. CHARACTERISTICS OF PROPOSED BINARY COMPLEMENTARY CODES A. Complt Complmtary Cods A complt complmtary cod cosists of a pair of complmtary cods ad icluds th fatur that th sum of two cross-corrlatio fuctios btw th mat cods is always zro for ay tim shift [6]. A pair of complmtary cods, {A, B } ad {A', B' }, is th calld complt complmtary cod if it satisfis Eqs.(3 ad (4. A = (a, a,, a B = (b, b,, b A' = (a', a',, a' B' = (b', b',, b' ( = A + + i A * i τ Bi B * i+ τ C τ (3 C( τ = 0 for τ = 0 ~ (4 It is possibl to rduc mutual itrfrc by usig complt complmtary cods [5]. Th umbr of complt complmtary cods amog all cod pairs coutd i Sctio 3 is show i parthss i Tabl. Th covtioal biary complmtary cods hav lgths of 4, 8 ad 0, wh survyd up to a lgth of. Fig. 4 Coctio structur of complt complmtary cods. Th lgths of complt complmtary cods ar also 4, 8 ad 0, rspctivly. O th othr had, th proposd biary complt complmtary cods ar foud i all cod lgths ragig from 3 to, ad thr xist may complt complmtary cod pairs. As show i Tabl, it should b otd that thr ar actually mor complt complmtary cods of th proposd typ tha of th covtioal typ, which is aothr importat advatag of th proposd biary complmtary cod. A xampl of a complt complmtary cod of th proposd typ is show as follows: [Cod lgth=6 (k=] A = (0, 0, 0, 0, 0, π B = (0, π, π, 0, 0, 0 A' = (0, 0, 0, π, π, 0 B' = (0, π, π, π, π, π It is clar that th cod xpadd by Eqs.(9 ad (0 has th charactristics of a complt complmtary cod, that is to say, th complt complmtary cod xpadd by Eqs.(9 ad (0 also bcoms a complt complmtary cod with a logr cod lgth. Furthrmor, th proposd biary complmtary cods hav a uiqu fatur i that thy costruct a twork coctd by th rlatioship btw complt complmtary cods. Figur 4(a shows th structur coctd by th complt complmtary cods i th covtioal typ, whil Fig.4(b shows th structur coctd by th proposd biary complt complmtary cods. Th symbol {m, } rprsts a complmtary cod, ad th symbols m ad rprst ach compot cod. Th symbol rprsts th rlatioship btw two complmtary cods that joitly costruct a complt complmtary cod. It is otd that th twork is costructd by th proposd biary complt complmtary cod, oly o th cod lgths of 6 (k=3, 8 (k=, 0 (k=5, (k=, ad (k=3. (Th symbol * dots th rlatioship show i Tabl. Th symbol show i Fig.4(b idicats th complt complmtary cods of which th cross-corrlatio is zro for all tim shifts. It is th possibl to limiat or supprss th mutual itrfrc v o radars with th sam trasmittd frqucy by usig th proposd complt complmtary cods. This rsults i th ffctiv us of th frqucy rsourcs.

6 Tabl Sp/Mp ratio of idividual cod of biary complmtary cod pair for comprssio ratio ad cod lgth. Complmtary cods Comprssio ratio Sp/Mp ratio of auto-corrlatio of idividual cod Proposd cod Lgth, k= db (=.0/ Covtioal cod Lgth db (=.0/8 Proposd cod Lgth 4, k= db (=4.0/4 Covtioal cod Lgth db (=3.0/6 B. Charactristics of Dopplr frqucy Pak-sidlob to pak-mailob ratio Usig a complmtary cod, it is possibl to limiat sidlobs wh th Dopplr frqucy is vry small. Howvr, wh th Dopplr frqucy is fairly larg, thr is a problm that sidlobs appar du to th Dopplr frqucy. This ffct ca b rducd, howvr, by usig a complmtary cod with a smallr auto-corrlatio sidlob of idividual cod [5]. Figur 5 shows th auto-corrlatio of idividual cod for th proposd biary complmtary cod giv i Sctio 3. Tabl shows th comprssio ratios ad th miimum S p /M p ratio (pak-sidlob to pak-mailob ratio survyd for th comprssd wavform of th idividual cod. Th comprssio ratio is dfid as th ratio of th trasmittd puls width to th comprssd puls width, ad th comprssd puls width is dfid as th width btw two poits whr th valu of th auto-corrlatio fuctio is half th ctr pak valu [7],[8],[9]. Th S p /M p ratio of th idividual cod i Tabl for th proposd cod is th smallst amog all th proposd biary complmtary cods with cod lgth ad cod lgth 4 xpadd from th complmtary cods of cod lgth i Tabl by applyig Golay s mthod oc. Similarly, th S p /M p ratios for th covtioal cods ar also th smallst amog all th covtioal biary complmtary cods of cod lgth 8 ad cod lgth 6 xpadd from th complmtary cods of cod lgth 8 by Golay s mthod. Th comprssio ratio of th proposd complmtary cod is 8.0, whos cod lgth is at k=. Tabl idicats that th miimum S p /M p ratio for th proposd complmtary cod is 5.6 db, ad th miimum S p /M p ratio for th covtioal complmtary cod is.0 db, suggstig that th charactristic for th Dopplr frqucy shift is improvd by usig th proposd complmtary cods. Th proposd biary complmtary cods i Tabl ar show i th followig. [Proposd complmtary cod, cod lgth= (k=] A = (0, 0, 0, 0, 0, 0, 0, π, π, π, 0, 0 B = (0, 0, 0, 0, π, 0, π, π, 0, 0, π, π [Covtioal complmtary cod, cod lgth=8] A = (0, 0, 0, π, 0, π, 0, 0 B = (0, 0, 0, π, π, 0, π, π [Proposd complmtary cod, cod lgth=4 (k=] A = (0, 0, 0, 0, π, 0, π, π, 0, 0, π, 0, π, π, π, 0, 0, 0, 0, 0, 0, 0 B = (0, 0, 0, 0, π, 0, π, π, 0, 0, π, π, π, π, 0, 0, 0, π, π, π, π, π, π, π [Covtioal complmtary cod, cod lgth=6] A = (0, 0, π, 0, 0, 0, 0, π, 0, 0, π, 0, π, π, π, 0 B = (0, 0, π, 0, 0, 0, 0, π, π, π, 0, π, 0, 0, 0, π Total sidlob powr to mailob powr ratio Hr, w coduct a quatitativ valuatio to xami th ffct of th actual us for th Dopplr frqucy. Th mailob powr P m ad th total sidlob powr P S of th proposd biary complmtary cods ar dfid by Eqs.(5 ad (6, rspctivly [9]. P m ( k+ Ts = 0 S( ω ω cos + χ ( τ,0 + χ ( τ,0 B S( ω ω si NTs χ ( τ,0 + χ ( τ,0 d d A A ( ωt ( ωt / dωdτ PS 4 χ A ( τ,0 S( ω ω d (6 ( k + Ts si ( ωt / dωdτ Hr, χ A, χ B ar th ambiguity fuctios of th complmtary cod, which cosists of ach cod A ad B (S Appdix-, whil S(ω ad ω d ar th powr spctrum of th cho from th targt ad th Dopplr frqucy, rspctivly. Th itrpuls priod is rprstd by T, T S is th sub-puls duratio, N is th umbr of sub-pulss, ad k is th umbr of o-sid ighbor sub-pulss. Th covtioal biary complmtary cod is prst i th cas of k=0 [0]. Th rlatio btw th P S /P m ratio ad th Dopplr frqucy is show i Fig.6, whr S( ω = / πσ xp( ω / σ, σ=0, ad tim ad frqucy ar ormalizd by th sub-puls duratio Ts ad th rciprocal of th sub-puls duratio /Ts, rspctivly. It should b otd that th P S /P m ratio of th proposd biary complmtary cods improvs by 6.7 db wh th comprssio ratio is 8. = VI. DISCUSSION Th proposd biary complmtary cods whos cod lgths rag from 3 to ar ivstigatd i this papr. W foud that th proposd biary complmtary cods hav mor cod pairs tha th covtioal biary complmtary cods, ad is thought that this occurs by rlaxig th coditios for th comprssd pulss. Th coditio is to comprss a puls to svral sub-pulss. Furthrmor, th coditio carris th advatag that mor complt complmtary cods ar foud ad that complmtary cods with smallr auto-corrlatio sidlobs of a idividual cod ar acquird. W also ot that th proposd biary complmtary cods improvs th S P /M P ratio ad th charactristics for th Dopplr frqucy shift. B / (5

7 two complmtary cods ca b costructd. This fact mas that, by usig such proposd biary complmtary cods i svral adjoiig radars with plus trasmissio sychroizd with ach othr, it is possibl to limiat or supprss th mutual itrfrc, v i th radars opratig o th sam frqucy. W also show that th autocorrlatio sidlob of idividual cod for th proposd biary complmtary cod is smallr tha that for th covtioal. As a rsult, w cofirmd that th ffct of sidlob suprssio for th Dopplr frqucy shift is improvd by usig th proposd complmtary cod. SIDELOBE SUPPRESSION FACTOR (db Fig.5 Auto-corrlatio for o cod of complmtary pair with cod lgth (k= NORMALIZED DOPPLER SHIFT FREQUENCY VII. CONCLUSIONS proposd IPP=000 proposd IPP=0000 covtioal IPP=000 covtioal IPP=0000 3bit Barkr Fig.6 Ps/Pm ratio vrsus th Dopplr shift frqucy for th itrpuls priod IPP of,000 ad 0,000. (Comprssio ratio=8 W itroducd w biary complmtary cods that ca comprss a puls to th width of svral sub-pulss. Such biary complmtary cods of cod lgths ragig from 3 to wr survryd, ad w foud that mor of th proposd biary complmtary cods xist tha do covtioal biary complmtary cods. Aothr importat rsult itroducd i this papr was that thr ar also a larg umbr of complt complmtary cods i th proposd biary complmtary cods. Cosqutly, th availabl cod choics for itrfrc ad jammig icras. Furthrmor, w also cofirmd that logr complmtary cods ca b acquird by usig th mthod show by Golay. It was also show that, with th proposd biary complmtary cods, a twork coctd by th rlatioship of th complt complmtary cod btw APPENDIX. Ambiguity fuctio Th ambiguity fuctio χ(ω is dfid by Eq.(A. [3]. jωt χ ( τ, ω = A( t A*( t + τ dt (A. whr A is cod squc, ω is th Dopplr frqucy, ad τ is th tim shift. Th ambiguity fuctio cosistig of two cods, A ad B, ca b xprssd as follows: χ( τ, ω jωt / jωt / = χ A( τ, ω + χ B ( τ, ω (A. whr T is th sub-puls duratio [0]. REFERENCES [] M.I.Skolik, Radar hadbook, scod ditio, McGraw-Hill, Nw York, 990. [] M.J.E.Golay, Complmtary sris, IRE Tras. Iformatio Thory, vol.it-7, pp.8-87, April 96. [3] Richard va N, OFDM cods for pak-to-avrag powr rductio ad rror corrctio, Proc. IEEE Globcom, pp , Nov [4] R.Sivaswamy, Multiphas complmtary cods, IEEE Tras. Iformatio Thory, vol.it-4, o.5, pp , 978. [5] R.L.Frak, Polyphas complmtary cods, IEEE Tras. Iformatio Thory, vol.it-6, o.6, pp , 980. [6] N.Suhiro, Complt complmtary cod composd of N-multiplshift orthogoal squcs, Tras. IECE of Japa (i Japas, vol.j65-a, o., pp.47-53, 98. [7] W.S.Burdic, Radar sigal aalysis, Prtic-Hall, Eglwood Cliffs, 968. [8] R.Sato, M.Shiriki, Tim sidlob rductio tchiqu for biary phas codd puls comprssio, Tras. IEICE of Japa (i Japas, vol.j83- B, o.3, pp , March 003. [9] H.Takas, M.Shiriki, R.Sato, 4-phas complmtary cods comprssd to svral sub-pulss, Tras. IEICE of Japa (i Japas, vol.j85-b, o.8, pp , Aug. 00. [0] K.Wakasugi ad S.Fukao, Sidlob proprtis of a complmtary cod usd i MST radar obsrvatios, IEEE Tras.Gosci.Rmot Ssig, vol.grs-3, o., pp.57-59, Ja [] T.Takao, T.Sato, M.Kashimoto, M.Murada, Radio istrumtatio ad avigatio i spac (i Japas, pp.6-7, Coroa publishig, Tokyo, 000. [] M.I.Skolik, Itroductio to radar systms, third ditio, McGraw-Hill, Nw York, 00.