INTERNATIONAL JOURNAL OF COMPUTERS AND COMMUNICATIONS Issue 1, Volume 7, Theoretical Analysis of BER Performance of Optical ZCZ-CDMA System

Transcription

1 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, 3 Thortical Analysis of BER Prformanc of Optical ZCZ-CDMA Systm Takahiro MATSUMOTO, Hidyuki TORII and Shinya MATSUFUJI Abstract In this papr, w analyz th bit rror rat BER prformanc of optical cod division multipl accss CDMA systm basd on th optical zro-corrlation zon ZCZ cod with zrocorrlation zon n or which is calld th optical ZCZ-CDMA systm, by th lctrical and optical procssing ovr th optical fibr and spac by computr and thortical formula. In th optical fibr transmission of this systm, th ffct of th avalanch photodiod APD nois, thrmal nois and co-channl intrfrnc ar considrd. Additionally, th ffcts of th scintillation and background nois ar considrd in th optical spac transmission of this systm. Th optical ZCZ cod, which is a st of pairs of binary and biphas squncs consisting of or with zro-corrlation zon, may b abl to provid optical CDMA communication systm supprssd co-channl intrfrnc, and w hav proposd th compact construction of a cod gnrator and a bank of matchd filtrs for this cod. As a rsult, th BER prformanc of optical ZCZ-CDMA systm ovr th optical spac go down compard to that ovr th optical fibr, and th BER prformanc of this systm by th lctrical procssing go down compard to that by th optical procssing, and this systm can t rmov compltly co-channl intrfrnc. Kywords optical communication, optical cod division multipl accss CDMA, optical ZCZ cod, scintillation, avalanch photodiod APD nois, co-channl intrfrnc. provid optical CDMA communication systm supprssd cochannl intrfrnc [], [], [3], and w hav proposd th compact construction of a cod gnrator [] and a bank of matchd filtrs [5], [6] for this cod. In th low- and hi-spd optical communications, th rcivr is procssd by lctrical and optical signals, rspctivly. Th formr and lattr ar calld th lctrical and optical procssing, rspctivly. Th communication prformanc of this systm is influncd from ths procssing. In this papr, w analyz th bit rror rat BER prformanc of optical CDMA systm basd on th optical ZCZ cod with zro-corrlation zon n or which is calld th optical ZCZ-CDMA systm, by th lctrical and optical procssing ovr th optical fibr and spac by computr and thortical formula. In th optical fibr transmission of this systm, th ffct of th avalanch photodiod APD nois, thrmal nois and co-channl intrfrnc ar considrd. Additionally, in th optical spac transmission of this systm, th ffcts of th scintillation and background nois ar considrd. I. ITRODUCTIO THE optical cod division multipl accss CDMA communication systm can xpct a high spd communication bcaus this systm is abl to us a wid band [], [], [3]. In addition, this systm can giv th multipl accss without changing th wav lngth. In th optical CDMA systm, a psudo-nois P squnc usd to this systm dcids th communication prformanc [], [5], [6], [7], [8], and an optical orthogonal cod is oftn gnrally usd as a P squnc. Th optical orthogonal cod [9] is a st of binary squncs consisting of or, and its crosscorrlation proprty has low corrlation valu. Thrfor, th optical CDMA communication systm basd on optical orthogonal cod gos down th bit rror rat BER prformanc. On th othr hand, th optical zro-corrlation zon ZCZ cod [] is a st of pairs of a binary squnc consisting of or and a biphas squnc consisting of or with zro-corrlation zon. Thrfor, this cod may b abl to Manuscript rcivd Dcmbr 3,. T. Matsumoto is associat profssor with Univrsity Evaluat Dpartmnt, Yamaguchi Univrsity, Yamaguchi-shi, Yamaguchi, Japan -mail: matugn@yamaguchi-u.ac.p. H. Torii is associat profssor with Dpartmnt of Information twork and Communication, Kanagawa Institut of Tchnology, Atsugi-shi, Kanagawa, Japan -mail:torii@nw.kanagawa-it.ac.p. S. Matsufui is profssor with Graduat School of Scinc and Enginring, Yamaguchi Univrsity, Ub-shi, Yamaguchi, Japan -mail: s- matsu@yamaguchi-u.ac.p. 8 II. OPTICAL ZCZ CODE A. Dfinition of optical ZCZ cod Lt a b a biphas squnc of lngth whos lmnts tak or, writtn as a = a,, a,,, a,i,, a,, a,i {,. Similarly, lt â,d b a binary squnc of lngth whos lmnts tak or, writtn as â,d = â,d,, â,d,,, â,d,i,, â,d,, â,d,i {,, d {,, whr i dnots i mod. Lt A b a st of M pairs consisting of a biphas squnc a and a binary squnc â,d, writtn as A = {a, â,d, a, â,d,, a, â,d,, a M, â M,d, 3 whr M is th numbr of squncs in a squnc family and is calld family siz. A priodic corrlation function btwn squncs a and â,d at shift i is dfind by ρ a,â,d,i = a,iâ,d,i+i mod.

2 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, 3 In this papr, th abov corrlation function ρ a,â,d is,i calld th auto-corrlation function for = and th crosscorrlation function for. Th st is calld an optical ZCZ cod [] if th priodic auto- and cross-corrlation functions satisfy ρ a,â,d,i = w = w ; i =, =, d =, w ; i =, =, d =, ; i =,, ; i z, 5 â,d,i <, 6 whr w is th numbr of th nonzro lmnts in ach squnc and z is a zro-corrlation zon. Th optical ZCZ cods ar boundd by M z +. 7 B. Optical ZCZ cod with z = n Lt b b a Lgndr squnc [9] of lngth = n with positiv n or an M-squnc of lngth = n with n, whos lmnts tak valus of or, writtn as b = b,, b,,, b,i,, b,, 8 b,i {, with b,i =. A binary squnc ˆb,i {, of lngth is givn by ˆb,i = + b,i. 9 On th othr hand, lt H b an Hadamard matrix of ordr = n with n, writtn as H = [h, h,, h,, h ] T, h = h,, h,,, h,,,i h,, h,i {,, whr T dnots th matrix transposition, h is calld an Hadamard squnc and h =, i,i. A binary squnc ĥ,d,i {, of lngth is givn by Lt A b a st of M = pairs consisting of a biphas squnc a and a binary squnc â,d of lngth =, writtn as { A = a, â,d, a, â,d,, a, â,d,, a, â,d. 5 Th priodic corrlation function btwn a and,d â xcpt whn = = is givn by ρ a,â,d,i = + ; i =, =, d =, + ; i =, =, d =, ; i =,, ; i z =, 6 whr / < w = + / /3. Thrfor, th abov st of M = pairs consisting of a biphas squnc a and a binary squnc,d â is an optical ZCZ cod [] with z = = n and M = = /z +. As an xampl, w gnrat an optical ZCZ cod of = = 3 =, z = = and M = = 3. Lt and H = b 3 = +, +, h h h h 3 = , 7 whr H is a Sylvstr-typ Hadamard matrix, + and dnot + and, rspctivly. From Eq. 3, w can gnrat bi-phas squncs a, as follows, rspctivly. Similarly, lt a = +,,,, +, +, +,,,, +, +, a = +, +, +,, +,,,,, +,, +, a 3 = +,, +, +, +, +,, +,,,,. ˆb3 = +, +, ĥ,d,i = + d h,i. If and ar rlativly prim, i.., gcd, =, a biphas squnc a of lngth = is producd by a,i = b,i mod h,i mod. 3 Similarly, a binary squnc â,d of lngth = is producd by â,d,i = ˆb,i mod ĥ,d,i mod. 9 and ĥ, ĥ, ĥ, ĥ 3, ĥ, ĥ, ĥ, ĥ 3, = = ,,

3 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, 3 3 whr + dnots. From Eq., w can gnrat binary squncs â, as follows, rspctivly. â, = +,,,, +,, +,,,, +,, â, = +, +,,, +,,,,, +,,, â 3, = +,,, +, +,,, +,,,,, â, =, +,, +,,,, +,, +,,, â, =,,, +,,, +, +,,, +,, â 3, =, +,,,,, +,,, +, +,. A st consisting of a bi-phas squnc a and a binary squnc â,d, is an optical ZCZ cod with =, z = and M = 3. Its auto-corrlation functions ar givn by ρ a,â,,i =,,,,,,,,,,,, ρ a,â,,i =,,,,,,,,,,,, ρ a 3,â 3,,i =,,,,,,,,,,,, ρ a,â,,i =,,,,,,,,,,,, ρ a,â,,i =,,,,,,,,,,,, ρ a 3,â 3,,i =,,,,,,,,,,, and its cross-corrlation functions ρ a,â,,i =,,,,,,,,,,,, ρ a,â 3,,i =,,,,,,,,,,,, ρ a 3,â,,i =,,,,,,,,,,,, ρ a,â,,i =,,,,,,,,,,,, ρ a,â 3,,i =,,,,,,,,,,,, ρ a 3,â,,i =,,,,,,,,,,,. C. Optical ZCZ cod with z = Lt S b a Sylvstr-typ Hadamard matrix of ordr = n with n, writtn as S = [s, s,, s,, s ] T, 8 s = s,, s,,, s,,,i s,, 9 s,i {,, whr T dnots th matrix transposition. It can also b xprssd as S = S S, [ ] S =, whr th opration dnots th Kronckr product. Each row s is calld a Sylvstr-typ Hadamard squnc. A biphas squnc a with lngth = is givn by From Eqs. and 3, th man valu of this squnc a is givn by a,i = s,is,i s,is,i =, whr,. Thrfor, a biphas squnc a is calld a biphas balancd squnc. A binary squnc â,d of lngth is givn by â,d,i = + d a,i. 5 Lt A b a st of M = / pairs consisting of a biphas squnc a and a binary squnc â,d of lngth =, writtn as { A = a, â,d, a3, â 3,d,, a, â,d,, a, â,d. 6 Th priodic corrlation function btwn a and,d â xcpt whn, is givn by ρ a,â,d,i = ; i =, =, d =, ; i =, =, d =, ; i =,, ; i = ±z = ±, 7 whr w = /. Thrfor, th abov st of M = / pairs consisting of a biphas squnc a and a binary squnc â,d is an optical ZCZ cod with z = and M = / = /z +. As an xampl, w gnrat an optical ZCZ cod of = = = 8, z = and M = / =. From Eqs. 7, and 3, w can gnrat bi-phas squncs a 8, as follows, rspctivly. a 8 = +, +,,,, +, +,, a 3 8 = +,,, +,,, +, +. From Eq. 5, w can gnrat binary squncs â,d 8, as follows, rspctivly. â, 8 = +, +,,,, +, +,, â 3, 8 = +,,, +,,, +, +, â, 8 =,, +, +, +,,, +, â 3, 8 =, +, +,, +, +,,. A st of pairs consisting of a bi-phas squnc a 8 and a binary squnc â,d 8 is an optical ZCZ cod with = 8, z = and M =. Its auto-corrlation functions ar givn by ρ a 8,â, = ρ 8,i a 3 8,â 3, 8,i =,,,,,,,, ρ a 8,â, = ρ 8,i a 3 8,â 3, 8,i =,,,,,,, a,i = α,i s,i mod, and its cross-corrlation functions ar givn by { s α,i =,i mod = ; i, s,i mod = i+ ; i. ρ a 8,â 3, = ρ 8,i a 3 8,â, =,,,,,,,, 8,i ρ 3 a 8,â 3, = ρ 8,i a 3 8,â, =,,,,,,,. 8,i

4 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, 3 III. OPTICAL ZCZ-CDMA SYSTEM Th optical CDMA systm basd on th optical ZCZ cod is calld th optical ZCZ-CDMA systm. In th transmittr, th binary squnc is usd to snd optical signal corrsponding to a short puls and th absnc of light. A transmittr snds a binary squnc â,d in according to input data d {, as optical signal. On th othr hand, in th rcivr, th biphas squnc is usd as th rfrnc squnc. In a low-spd communication, th rcivr is procssd by an lctrical signal, which is calld th lctrical procssing. This systm nds on avalanch photodiod APD lmnt. Figur shows optical ZCZ-CDMA systm by th lctrical procssing. Th rcivd signal r i is passd through a filtr matchd to th biphas squnc, a, which is calld th lctrical corrlator, and is rcovrd to th bit data in th dtctor. From Eq., th input of a dtctor R is givn by R = a,i r i. 8 Similarly, in a high-spd communication, th rcivr is procssd by an optical signal, which is calld th optical procssing. This systm nds two avalanch photodiod APD lmnts bcaus th rfrnc squnc is th biphas squnc which taks as or. Figur shows optical ZCZ-CDMA systm by th optical procssing. In splittr, th rcivd signal is switchd to th optical corrlator and according to lmnt valus and of th rfrnc squnc a, rspctivly, and is addd as ˆR and ˆR in th optical corrlator and, rspctivly. Th diffrnc output signal of APD and APD is rcovrd to th bit data in th dtctor. From Eq. 8, th input of a dtctor R is givn by + a,i a,i R = r i r i = ˆR ˆR. 9 ot that if z = thn + a,i / and a,i / ar from Eq. 5, rspctivly. â,,i and â,,i IV. THEORETICAL AALYSIS OF BER PERFORMACE W thortically analys th BER prformanc of optical ZCZ-CDMA systms by th lctrical and optical procssing, and valuat it by computr. Tabl I shows spcifications of thortical analysis and computr. A. BER prformanc in optical fibr transmission Th thortical formula of BER charactristics of th optical ZCZ-CDMA systm by th lctrical procssing ovr th optical fibr is givn by p BER = πσ m = rfc { a µ xp σ da m, 3 µ σ m M µ = wgt c λ s, 3 M TABLE I SPECIFICATIOS OF THEORETICAL AALYSIS AD COMPUTER SIMULATIO. Sprading squnc optical ZCZ cod Squnc lngth 6 Family siz M 7 6 Zro corrlation zon z um. of th nonzro lmnts w um. of trials 6 Bit rat 56Mbps 3Mbps Chip rat 3,7Mcps Lasr wavlngth λ 83nm APD quantum fficincy η.6 APD gain G APD ffctiv ionization ratio K ff. Bulk lakag currnt I b.na Surfac lakag currnt I s na Modulation xtinction ratio M Rcivr nois tmpratur T r,k Rcivr load rsistor R L,3 Ω Background nois P b -5 dbm Scintillation logarithm varianc σs. { σ m = G F T c λ s w + w m + I b M + I st c + σ th, 3 λ s = ηp w hf, 33 P w = w P bit, 3 G F = K ff G + K ff, 35 G σ th = k BT r T c R L, 36 f = c λ, 37 w = { z+ z+ ; z = n, ; z =, 38 whr µ and σ m ar th avrag and varianc of th corrlation output, m is th numbr of usrs, G is th APD gain, T c is th chip duration, is th squnc lngth, M is th modulation xtinction ratio, λ s is th avrag numbr of absorbd photons ovr T c, w is th numbr of th nonzro lmnts in ach squnc, F is th xcss nois factor, I b is th bulk lakag currnt, I s is th surfac lakag currnt, is th lmntary lctric charg, σth is th varianc of thrmal nois, η is th APD quantum fficincy, P w is th rcivd lasr powr pr chip without scintillation, P bit is th avrag rcivd lasr powr pr bit without scintillation, P b is th background nois pr chip duration T c, h is Planck s constant, f is th optical frquncy, K ff is th APD ffctiv ionization ratio, k B is Boltzmann constant, T r is th rcivr nois tmpratur, R L is th rcivr load rsistor, c is vlocity of light, and λ is th lasr wavlngth. ot that th background nois isn t considrd ovr th optical fibr. Figurs 3 and show BER prformanc of optical ZCZ- CDMA systm with z = and by th lctrical procssing

5 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, 3 Transmittr d Cod Gnrator â, â, â,d d Cod Gnrator â, â, â,d Optical fibr or spac APD A/D channl Rcivr r i R Elctrical corrlator Data d m Cod Gnrator â m, â m, â m,dm a â, â, Fig.. Optical ZCZ-CDMA systm by th lctrical procssing. Transmittr d Cod Gnrator â, â, â,d Rcivr d Cod Gnrator â, â, â,d Optical fibr or spac channl ˆR r i Optical corrlator APD A/D Splittr + R Optical - APD A/D corrlator ˆR Data d m Cod Gnrator â m, â m, â m,dm â, â, Fig.. Optical ZCZ-CDMA systm by th optical procssing. ovr th optical fibr, rspctivly. Similarly, th thortical formula of BER charactristics of th optical ZCZ-CDMA systm by th optical procssing ovr th optical fibr is givn by p BER = rfc µ, 39 σ m M µ = wgt c λ s M σ m = G F T c { + I st c λ s w + w M = µ, m + I b + σ th. Figurs 5 and 6 show BER prformanc of optical ZCZ- CDMA systm with z = and by th optical procssing ovr th optical fibr, rspctivly. From Figs. 3,, 5 and 6, th optical ZCZ-CDMA systm by th lctrical and optical procssing ovr th optical fibr can t rmov compltly co-channl intrfrnc, and th BER prformanc of this systm by th lctrical procssing ovr th optical fibr go down compard to that by th optical procssing. B. BER prformanc in optical spac transmission Th thortical formula of BER charactristics of th optical ZCZ-CDMA systm by th lctrical procssing ovr th

6 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, Avrag rcivd lasr powr pr a bit Pbit [dbm] Fig. 3. BER prformanc of optical ZCZ-CDMA systm with z = by th lctrical procssing ovr th optical fibr Avrag rcivd lasr powr pr a bit Pbit [dbm] Fig. 5. BER prformanc of optical ZCZ-CDMA systm with z = by th optical procssing ovr th optical fibr Avrag rcivd lasr powr pr a bit Pbit [dbm] -3 Fig.. BER prformanc of optical ZCZ-CDMA systm with z = by th lctrical procssing ovr th optical fibr Avrag rcivd lasr powr pr a bit Pbit [dbm] -3 Fig. 6. BER prformanc of optical ZCZ-CDMA systm with z = by th optical procssing ovr th optical fibr. optical spac is givn by P BER = pa pa pa m µa rfc da σ A, A,, A m da da m = pa pa µa rfc da da, σ A, A m A = A, 3 pa = = { ln A + σ s xp πσ s A σ s, pa = pa pa m, 5 M µa = wgt c λ s A, 6 M 3 { σ A, A = G F T c λ s w + w A + A +λ b + I b M + I st c + σ th, 7 whr pa is th probability dnsity function of th scintillation A for th m usr, σ s is th scintillation logarithm varianc, µa and σ A, A ar th avrag and varianc of th corrlation output, rspctivly and dnots th convolution as pa pa = pa pa a. 8 a = Figurs 7 and 8 show BER prformanc of optical ZCZ- CDMA systm with z = and by th lctrical procssing ovr th optical spac, rspctivly. Similarly, th thortical formula of BER charactristics of th optical ZCZ-CDMA systm by th optical procssing ovr

7 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, Avrag rcivd lasr powr pr a bit without scintillation Pbit [dbm] Fig. 7. BER prformanc of optical ZCZ-CDMA systm with z = by th lctrical procssing ovr th optical spac. ovr th optical spac, rspctivly Avrag rcivd lasr powr pr a bit without scintillation Pbit [dbm] Fig. 9. BER prformanc of optical ZCZ-CDMA systm with z = by th optical procssing ovr th optical spac Avrag rcivd lasr powr pr a bit without scintillation Pbit [dbm] Fig. 8. BER prformanc of optical ZCZ-CDMA systm with z = by th lctrical procssing ovr th optical spac Avrag rcivd lasr powr pr a bit without scintillation Pbit [dbm]. th optical spac is givn by P BER = pa pa pa m µa rfc da σ A, A,, A m da da m = pa pa µa rfc da da, 9 σ A, A M µa = wgt c λ s A = µa, 5 M { σ A, A = G F T c λ s w + w A + A +λ b + I b M + I st c + σ th. 5 Figurs 9 and show BER prformanc of optical ZCZ- CDMA systm with z = and by th optical procssing Fig.. BER prformanc of optical ZCZ-CDMA systm with z = by th optical procssing ovr th optical spac. From Figs. 7, 8, 9 and, th optical ZCZ-CDMA systm by th lctrical and optical procssing ovr th optical spac can t rmov compltly co-channl intrfrnc, and th BER prformanc of this systm by th lctrical procssing ovr th optical spac go down compard to that by th optical procssing. From Figs. 3,, 5, 6, 7, 8, 9 and, th BER prformanc of this systm ovr th optical spac go down compard to that ovr th optical fibr. V. COCLUSIOS In this papr, w analyz th BER prformanc of optical ZCZ-CDMA systm with zro-corrlation zon n or by th lctrical and optical procssing ovr th optical fibr and spac with considring th ffcts of th scintillation, APD nois, thrmal nois and co-channl intrfrnc by computr and thortical formula. As a rsult, th BER prformanc of this systm ovr th optical spac go down compard to that ovr th optical fibr, and th BER prformanc of this systm by th lctrical procssing go down compard to that by th optical procssing.

8 ITERATIOAL JOURAL OF COMPUTERS AD COMMUICATIOS Issu, Volum 7, 3 8 Th optical ZCZ-CDMA systm by th lctrical and optical procssing can t rmov compltly co-channl intrfrnc. ACKOWLEDGMET This rsarch was supportd by th Ministry of Education,Cultur, Sports, Scinc and Tchnology MEXT, Grantin-Aids for Young Scintists B769 and challnging Exploratory Rsarch REFERECES [] J. G. Zhang and G. Picchi, Tunabl prim-cod ncodr/dcodr for all-optical CDMA applications, IEE Elctron. Ltt., vol. 9, no. 3, 993, pp.. [] J. A. Salhi, A. M. Winr and J. P. Hritag, Cohrnt ultrashort light puls cod-division multipl accss communication systms, IEEE J. Lightwav Tchnol., vol. 8, no. 3, 99, pp [3] H. Fathallah, L. A. Rusch and S. LaRochll, Passiv optical fast frquncy-hop CDMA communications systm, IEEE J. Lightwav Tchnol., vol. 7, no. 3, 999, pp [] T. Otsuki, Prformanc analysis of atmosphric optical PPM CDMA systms, IEEE J. Lightwav Tchnol., vol., no., 99, pp [5] Y. Kozawa and H. Habuchi, Thortical analysis of optical wirlss CDMA with modifid psudo orthogonal M-squnc sts, Proc. of IEEE Global Communications Confrnc, Exhibition and Industry Forum Co-locatd with WTCGLOBECOM9, 9. [6] Y. Kozawa and H. Habuchi, A comparison of wirlss optical CDMA systms using chip-lvl dtction, IEICE Trans. Fundam., vol. E93-A, no.,, pp [7] A. T. Pham and H. Yashima, Prformanc Analysis of Rd-Solomon Codd Spctral Amplitud Encoding OCDMA Systm, WSEAS Trans. on Elctronics, Issu, vol.,, pp [8] Y. Mizuno and H. Yashima, Optical CDMA systms using xtndd chaotic binary cods, J. Signal Procssing, vol., no.,, pp [9] P. Z. Fan and M. Darnll, Squnc dsign for communications applications, Rsarch Studis Prss, 996. [] S. Matsufui, T. Matsumoto, Y. Tanada and. Kuroyanagi, ZCZ cods for ASK-CDMA systm, IEICE Trans. Fundam., vol. E89-A, no. 9, 6, pp [] T. Matsumoto, M. Inou, H. Torii and S. Matsufui, Study on BER Prformanc of Atmosphric Optical CDMA Systm Using Optical ZCZ Cod, Proc. of th RISP Intrnational Workshop on onlinar Circuits, Communications and Signal Procssing,, pp [] T. Matsumoto, H. Torii and S. Matsufui, Thortical Analysis of BER Prformanc of Optical ZCZ-CDMA Systm With Smallst Zro Corrlation Zon Using Optical Corrlator, Proc. of th IEEE Intrnational Symposium on Intllignt Signal Procssing and Communication Systms,, pp [3] T. Matsumoto, H. Torii and S. Matsufui, Comparison of Optical ZCZ-CDMA Systm with Zro Corrlation Zon n by Elctrical and Optical Procssing, Proc. of th 3rd Europan Confrnc of Communications, pp [] T. Matsumoto and S. Matsufui, Optical ZCZ cod gnrators using Sylvstr-typ Hadamard matrix, Intrnational J. of Communications, Issu, vol.,, pp. 9. [5] T. Matsumoto, S. Tsukiashi, S. Matsufui and Y. Tanada, Th bank of matchd filtrs for an optical ZCZ cod using a Sylvstr typ Hadamard matrix, IEICE Trans. Fundam., vol. E89-A, no. 9, 6, pp [6] T. Matsumoto and S. Matsufui, Compact matchd filtr banks of optical ZCZ cods using fast algorithm for M-squnc typ Hadamard matrix, J. Signal Procssing, vol., no. 6,, pp Takahiro Matsumoto rcivd his B. Eng. and M. Eng. dgrs in Information and Computr Scinc from Kagoshima Univrsity, Japan, in 996 and 998, rspctivly, and his Ph. D. dgr in Enginring from Yamaguchi Univrsity, Japan, in 7. H was a Rsarch Associat from 998 to 7 and an Assistant Profssor from 7 to at Yamaguchi Univrsity, Japan. Sinc, h has bn an Associat Profssor of th Univrsity Evaluation Dpartmnt at Yamaguchi Univrsity. From to, h was a visiting rsarchr at th Univrsity of Mlbourn, Australia. His currnt rsarch intrsts includ sprad spctrum systms and thir applications. H rcivd th Bst Papr Award in th th WSEAS Intnational Confrnc on Applid Informatics and Communications in. H is a mmbr of IEEE and IEICE. Hidyuki Torii rcivd th B. Eng., M. Eng., and Ph. D. dgrs from th Univrsity of Tsukuba, Tsukuba, Japan in 995, 997, and rspctivly. In, h oind th Dpartmnt of twork Enginring, Kanagawa Institut of Tchnology as a Rsarch Associat. H is currntly an Associat Profssor in th Dpartmnt of Information twork and Communication at th sam univrsity. His rsarch intrsts includ sprading squncs, CDMA systms, and mobil communication systms. H is a mmbr of IEEE and IEICE. Shinya Matsufui graduatd from th Dpartmnt of Elctronic Enginring at Fukuoka Univrsity in 977. H rcivd th Dr. Eng. in Computr Scinc and Communication Enginring from Kyushu Univrsity, Fukuoka, Japan in 993. From 977 to 98, h was a tchnical official at Saga Univrsity, Saga, Japan. From 98 to, h was a rsarch associat in th Dpartmnt of Information Scinc at Saga Univrsity. From to, h was an associat profssor of th Dpartmnt of Computr Scinc and Systms Enginring at Yamaguchi Univrsity. Sinc, h has bn a profssor of th Graduat School of Scinc and Enginring at Yamaguchi Univrsity. His currnt rsarch intrsts includ squnc dsign and sprad spctrum systms. H rcivd th Excllnt Papr Award in IET Intrnational Communication Confrnc on Wirlss Mobil and Computing, and th Bst Papr Award in th th WSEAS Intnational Confrnc on Applid Informatics and Communications in 9 and, rspctivly. H is a mmbr of IEEE, IEICE and IEEJ. 5