Zero Vectors Combinatorial Code Family for Spectral Amplitude Coding (SAC-OCDMA)

Transcription

1 0 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.8 No.3, March 008 Zro Vctors Combinatorial Cod Family for Spctral Amplitud Coding (SAC-OCDMA) Hassan Yousif Ahmd, Ibrahima Fay, and N.M.Saad, Elctrical & Elctronic Enginring Dpartmnt, Univrsiti Tknologi PETRONAS, Bandar Sri Iskandar, Tronoh, Prak, MALAYSIA Summary Although multipl accss intrfrnc (MAI) problms xisting in optical cod division multipl accss (OCDMA) systms can b solvd by lctrical subtraction, phas inducd intnsity nois (PIIN) rsulting from th phas incohrnt of ovrlapping still rmains and compltly dtriorats th systm prformanc. It is thrfor dsirabl to allviat MAI and PIIN ffcts in dsigning OCDMA systm. W propos a nw mthod to construct cods with zro in-phas cross corrlation namly Zro Vctor Combinatorial Cod (ZVCC) basd on combination of spcific vctors with combinatorial thoris. Simplicity of cod construction, flxibility of choosing th numbr of usrs and wights, mak our proposd systm strong candidat for futur ntworks. In addition, transmittr sid and rcivr sid ar proposd. Dtaild xampls ar givn on how to pick th bst cod among diffrnt options basd on spcific paramtrs. Th rsults show that th proposd cod is ffctiv to rduc th MAI, PIIN and cost, whil maintaining a good signal to nois ratio and bit rror probability. A comparison study btwn th proposd cod and th xisting cods such as Hadamard and MDW has bn carrid out. Ky words: Optical Cod Division Multipl Accss (OCDMA), Multipl Accss Intrfrnc (MAI), Zro Vctor Combinatorial Cod (ZVCC), Optical Communication, Dirct Rcovry Schm (DRS) 1. Introduction A major challng in dvising optical communication systms is to fully xploit th vast bandwidth providd by optical fibr channls. Th succssful of long-span fibr optic communication systms has shiftd th focus of optical ntwork to shortr-span mtropolitan and local ara domains [1]. Thr is not much diffrnc btwn multipl accss and multiplxing tchniqus. Multipl accss allows communication mdia to b shard btwn diffrnt usrs. It rprsnts on of th most ssntial functions of accss ntworks, whil multiplxing is combination of signals into singl transmission signal. Th thr basic multipl accss tchniqus ar Wav Division Multipl Accss (WDMA), Tim Division Multipl Accss (TDMA) and Cod Division Multipl Accss (CDMA). TDMA is a tchnology that allows multipl usrs to accss a channl by allocating tim slots to ach usr within ach channl. WDMA is a tchnology allowing multipl usrs to accss a channl by allocating wavlngth or frquncy to ach usr within ach channl.tdma and WDMA hav a limitd bandwidth for vry usr. Optical Cod Division Multipl Accsss (OCDMA) [1-4] has gaind mor attntion in rcnt yars du to its succss in wirlss communication systms. This is bcaus it allows multipl usrs to accss th channl simultanously with low latncy through assignmnt of uniqu cod squnc [3]. An OCDMA systm suffrs from diffrnt noiss such as shot nois, thrmal nois, dark currnt and multipl accss intrfrnc (MAI) from othr usrs. Among ths noiss, MAI is considrd as th dominat sourc. Thrfor, intllignt dsign of cod squnc is important to rduc th contribution of MAI to th total rcivd powr [4]. Although MAI can b canclld by balanc dtction schm, a phas inducd intnsity nois (PIIN) arising from spontanous mission of broad band sourc, inhrntly rmains. It is thn important to dsign codword such that th ffct of MAI and PIIN of th total rcivd powr is rducd. In OCDMA systms, minimization of cross corrlation to a vry small valu is an advantag. Systms using Cods with zro cross corrlation hav lss nois, which rsults in rducing th hardwar complxity. In this work, Zro Vctor Combinatorial cods (ZVCC) is proposd. This papr is organizd as it follows. In sction II, optical spctral cod division multipl accss is rviwd. In sction III, cods construction and dvlopmnt of all thortical studis is prsntd. Th advantags of ZVCC compard to othr OSCDMA cods, is rportd in sction IV. In sction V, th prformanc analysis of th nw proposd systm is don, and finally, conclusions ar givn in sction VI

2 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.8 No.3, March Optical Spctrum Cod Division Multipl Accss (OSCDMA) Optical CDMA systms can b dividd into major catgoris. Th first is cohrnt systms, whr knowldg of th phas and amplitud is ndd in ordr to achiv succssful dtction. Th scond is incohrnt systms, whr th prformanc of th systm dpnds mainly on th amplitud. OSCDMA is an incohrnt broadband light sourc which contains N usr with optical transmittrs and rcivrs as shown in Fig. 1 [5][6]. OSCDMA systm contains ncodrs and dcodrs which can b dsignd by using any kind of optical filtring tchnology. Spctral Amplitud Coding (SAC) was introducd to liminat th MAI xisting in convntional OCDMA systms. SAC systms us complmntary dtction tchniqu to rcovr th original signals. This balanc rcivr is usd as a part of rcivr which filtrs th incoming signals. For unmatchd transmittrs half of transmittr spctral componnts will match th dirct filtr and th othr half will match th complmntary filtr. Th output of th balanc rcivr rprsnts th diffrnc btwn th two parts, with unmatchd channls bing canclld, whil th matchd channl is dmodulatd. It is possibl to dsign cods with th full orthogonality in th incohrnt spctral intnsity OCDMA systm, sinc thr is a subtraction btwn two photo dtctors. In this systm, th signatur squnc is sprad across diffrnt wavlngth with ach chip occupying diffrnt wavlngth [5][6].Th advantag of OSCDMA is it dos not nd synchronization as th chip sprads in frquncy and not in tim. 3. CODE CONSTRUCTION Lt V b a vctor spac of dimnsion n. Th st {v 1, v,.., v n } is a basis of V if th st spans {v i } whr i=1,.., n ar linarly indpndnt and if any lmnt of V can b writtn as a combination of th v i, i= 1,,,n Lt R dnots th fild of ral numbrs. Th spac of all n-tupls of ral numbrs forms an n-dimnsional vctor spac ovr R dnotd by R n. An lmnt x of R n can b writtn as a column vctor: x1 x x = (1) M xn Lt i dnot th lmnt of R n having 0 at all lins xcpt th i th lin. {,,, } n 1 K is a basis of R n calld th standard basis. For n = =, = () 0 1 x1 Lt x = an lmnt of R x x1 x1 0 x= = + (3) x 0 x Thrfor, w hav x1 1 x1 0 x = + x 0 x 1 = x 1 1 +x (4) For n= = 0, = 1, 3 = 0 (5) Whr { 1,, 3} is a basis of R 3. Fig. 1: OCDMA Ntwork

3 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.8 No.3, March 008 Lt x1 x = x an lmnt of R 3 x3 Thrfor, w obtain x x x = x 1 1 +x + x 3 3 (6) Lt N b th numbr of usrs and L th cod lngth. W can writ th cod in a matrix form corrsponding to th cod word of N usrs. W obtain N L matrix with two dimnsions as shown in Fig.. Start Entr th wight W and numbr of usr N Comput th lngth L Matrix (N usrs L lngth) Usr1# Usr# Cod pattrns possibilitis UsrN# Fig.: Matrix of ZVCC Th construction of ZVCC is basd on th following mntiond: to hav (shortst) Zro Cross Corrlation (ZCC), w hav to hav on 1 in ach column. This mans for ZCC any column is an lmnt of th standard basis of R n. Givn N and th wight W, w can gnrat all possibilitis of ZVCC having lngth L=N W by gtting all th prmutations of th vctors 1,,, n with rptitions of ach vctor W-tims Any rdundant No All possibilitis Ys Elimination rdundant pattrns of A. Elimination of rdundant pattrns Prmutation has bn don for th first vctor to produc pattrns of ths vctors. Symmtric pattrns appard for th sam wight and numbr of usrs i.., swapping btwn th locations of usrs, th first usr bcom scond usr or th last usr and so on, whil for asymmtric no such duplicat, so w hav to find way to rmov th symmtric pattrns. Fig. 3 shows th flowchart stp to construct cod pattrn for both cass. End Fig.3: Flow chart of cod construction Th cod lngth L for numbr of usrs N with wight W is givn by: L = N W (7) To calculat th cod possibilitis (Cpos) of givn N and W by quation appar blow as prmutation opration

4 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.8 No.3, March Cpos = ( W N )! ( W! W!) whr W rprsnt th invrt of W (i.., th numbr of zro). By applying this quation, it is clar that it dpnds on th wight to gt bttr Signal to Nois Ratio (SNR), nvrthlss, its dcras th numbr of possibilitis and th lngth rmain th sam. Lt us invstigat th following xampl. N= W= L= N W= = 4. W = L-W= 4-= Thrfor ( ) ( ) W N!! Cpos = ( W! W!) = (!! ) = 6 W obtain th cods pattrns possibilitis as shown in (9), (10), (11), (1), (13), and (14). Hz 1 = Hz = Hz 3 = Hz 4 = Hz 5 = Hz 6 = (8) (9) (10) (11) (1) (13) (14) From th abov cods pattrns possibilitis, w obsrv that thr is a symmtric btwn (9) and (1), (10) and (14), (11) and (13). Combination of any two symmtric quations produc on pattrn, hnc, whn w swap th position of usr1# and usr#, to rduc th numbrs of symmtric pattrns w us th following quation: ( W N )! Nc = N!( W!) N (15) Whr Nc is numbr of pattrns aftr modification. For th xampl of (N=, W=) aftr applying Eq. (15) w obtain: ( W N )! Nc = N! W! ( ) N = ( )!!(!) = 3 Cpos bcam 3 instad of 6 aftr applying th nw quation, hnc, w obtain Hz 1, Hz, and Hz COMPARSION AND EVALUATION In rcnt yar, many cods hav bn proposd such as modifid doubl wight (MDW) cod [5], modifid frquncy hopping (MFH) [10] and zro cross corrlation (ZCC) [11]. All ths cods suffr from various limitations on way or anothr, th cod construction is complicatd (.g., MFH and ZCC) or th cross corrlation is not idal. Howvr, th cod construction not only dpnds on a cross corrlation proprtis, th lngth plays an important rol w hav to considr as wll. Long lngth is a disadvantag sinc th cod is subjct to ithr vry wid band sourc or narrow filtr bandwidths ar rquird. ZVCC has long lngth and this is considrd as disadvantag, w hav to mak a tradoff btwn th lngth and multipl accss intrfrnc (MAI), bcaus a MAI is a dominant sourc of th noiss. In MFH cod, although th cod lngth is shortr compard to ZVCC, th cross corrlation always qual to unity and this contributs to phas induc intnsity nois (PIIN), whil in ZVCC always th cross corrlation quals to zro which liminats th ffct of PIIN. In tabl.i ZVCC shows flxibility in trms of choosing th numbr of usrs and th wight du to th us of a novl mthod in cod construction which gnrats many possibilitis from a givn numbr of usrs and wights. Tabl 1: SAC-OCDMA cods comparaison cod xistnc wigh Cross Cod lngth t corrlatio n MFH K=Q Q+1 λ=1 N= Q +Q MDW K=n Evn λ=1 N=3n+8/3[sin ( Nii/3)] ZCC K= m m -1 λ=0 C= m Hadamar K= M -1 M-1 λ= M- N= M d M ZVCC Any numbr option λ=0 L=W N

5 4 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.8 No.3, March 008 Fig.4: Dirct rcovry schm (ncodr and dcodr using ZVCC) 5. DIRECT RECOVERY SCHEME In OCDMA systm, intllignt cod dsign is dsird to rduc th MAI contribution. Thrfor, a rcivr sid which plays an important rol should b addrssd as wll. In convntional SAC-OCDMA, balanc dtction schm is us to diffrntiat btwn th wantd and th unwantd cod squncs. Hnc, in Dirct Rcovry Schm (DRS), no subtractors ar ndd. At th rcivr sid, dirct filtrs ar using and this significantly liminat th ffct of MAI sinc only th wantd signal will b filtrd out. DRS hav bn proposd as structur of transmittr and rcivr for ZVCC cod family. Fig. 4, shows th procdur of ncoding th signal in transmittr sid thn coupld to th fibr mdia, at th rcivr sid, th rcivr signals ar splitting into qually part followd by filtr and photodiod, finally th signals ar rcovrd by th intndd usrs. Du to all ths, phas induc intnsity nois (PIIN) could b liminatd which provids a possibl way of achiving gratr prformanc. Fig.5: Ey diagram of ZVCC at 10 km 6. CODE SELECTION FROM Cpos Sinc w hav larg numbrs of Cpos in cod construction, in ordr to diffrntiat btwn ths possibilitis, simulation rsults ar acquird by using a softwar tool namd VPI transmission makr. For Hz 1, Hz, Hz 3, Hz 4, Hz 5, and Hz 6, th numbr of usrs is, th wight is, th lngth is 4 and Cpos is 6. Aftr liminats th symmtric pattrns bcam 3. To choos on family among six familis, a simulation work has bn don rspctivly for ach family startd from Hz 1 up to Hz 6 using dirct rcovry schm (transmittr part and rcivr part) to rproduc th signal for intndd usr and th rsults can b show as follows: Fig.6: Ey diagram of ZVCC at 50 km

6 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.8 No.3, March SNR BER= P = rfc ( ) (17) 8 Whr L is th cod lngth, W is th cod wight, N th of usrs, R is photodiod rsponsivly, P sr is th ffctiv powr of a broad-band sourc at th rcivr, is an lctronic charg, B is th lctrical quivalnt nois band-width of th rcivr, K B is th Boltizmann s constant, Tr th absolut tmpratur of rcivr nois, R L th load rsistanc and ΔV th optical sourc bandwidth. rfc is a complmntary rror function xprss as follows Fig.7: Ey diagram of ZVCC at 70 km In Fig.5, Fig.6, and Fig.7, a diffrnt fibr lngth has bn chosn to obsrv th incrasing lngth in systm prformanc in trms of y diagram pattrns. In Figs 5, and Fig.6, ZVCC is adoptd with th following paramtrs: lngth of fibr varis from 10 up 50 and data rat is.5gbps. It is shown that, th systm improvs and th ffct of MAI is liminatd whil in Fig 7 th ffct of disprsion in optical fibr is unavoidabl bcaus th distanc is quit long. Th simulation rsults obtaind from Hz and Hz 3 is similar as compard to Hz 1 whn using th sam paramtrs, thrfor, w can tak any cod randomly from Cpos. Furthr improvmnt could b achivd by incrasing th data rat up to 10Gbps. 7. SYSTEM PERFORMANCE In communication systm maximum Signal to Nois Ratio (SNR) yilds bttr Bit Error Rat (BER), ths two compltly affct th systm prformanc. In SAC- OCDMA systm good dsign of th cod plays an important rol by kping up th valu of intrfrnc from simultanous usrs as small as possibl. In ZVCC, in ordr to comput th SNR, w usd th sam mthod dscribd in [7]. Sinc th valu of cross corrlation is zro w compnsat this valu in th SNR [7], th SNR of ZVCC can b xprssd as follows SNR= P sr BR L (16) R P sr W L P [ ] sr BR N 4 ( N 1) + W + [( N 1) + W ] + L ΔV L K b T n B R rfc ( x) = π x u du (18) In litratur rviws, thr hav bn many cods proposd for SAC-OCDMA such as Hadamard [8] and modifid doubl wight (MDW) cod [9] and zro cross corrlation (ZCC) [11]. Howvr, our proposd cod familis hav mor flxibility of gnrating trmndous option of cod pattrns. In this work, th cod prformanc has bn don, th systm paramtrs ar: ΔV=3.75 THz; B=80 MHz; Tr = 300; R L = 1030 Ω ; bitrat 155 Mb/s; photodiod fficincy 0.6 and cntral wavlngth 1550 nm. In Fig.8 and Fig.9, a diffrnt wight valus hav bn chosn to obsrv th incras of th wight on th prformanc. It is shown that, th prformanc of th systm improvs whn th wight incrass which incrass th SNR. In Fig 8, th paramtr takn: w=4, w obsrv th numbr of usrs supportd by ZVCC ar quit much du to non-ovrlapping compar with MDW and larg compard with Hadamard, whil in Fig.9 th wight takn is W=6. It is clar that, th ffct of MAI and PIIN is rducd whn th wight incrass rgardlss for th numbr of usrs. Bit rror rat (BER) MDW (W=4) Hadamard ZVCC (W=4) Numbr of simultanous usrs Fig.8. BER vrsus th numbr of simultanous usrs

7 6 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.8 No.3, March 008 Bit rror rat (BER) (w=4) MDW (w=6) Hadamard ZVCC (w=6) Numbr of Simultanous Usrs Fig.8. BER vrsus th numbr of simultanous usrs (w=6) 8. CONLUSTION In this work, construction mthods for nw cod familis with zro cross corrlation for SAC-OCDMA systm, ZVCC has bn proposd. Th proprtis and thortical dvlopmnt of nw family hav bn provd. Nw dsign for transmittr sid and rcivr sid using dirct filtrs to rcovry and rproduc th original data namly dirct rcovry schm (DRS) has bn xamind. Th nw transmittr has bn analyzd using ZVCC taking into considration th ffct of noiss such as thrmal nois and shot nois. Th study showd that, compard with a formr cod such as Hadamard and MDW bttr prformanc du to limination of th ffct of phas induc intnsity nois. Morovr, th way of constructing ZVCC is vry flxibly in choosing th numbr of usrs and th wight. It has shown that, a lot of possibilitis for cod gnration can b obtaind and no diffrnc btwn thm in trms of systm prformanc. provisioning, IEEE Ntwork, vol. 14, no. 6, pp. 4 46, Nov [5] S.A.Aljunid,,M.Ismail, A.R.Ramli, Borhanuddin M Ali, and Mohamad Khazani Abdullah, A NwFamily of Optical Cod Squncs for Spctral-Amplitud-Coding Optical CDMA Systms IEEE Photonics Tchnology Lttrs, Vol. 16, No. 10, Octobr 004 [6] Syd Alw Aljunid, Zuraidah Zan, Siti Barirah Ahmad Anas and Mohd. Khazani Abdullah "A Nw Cod for Optical Cod Division Multipl Accss Systms," Malaysian Journal of Computr Scinc, Vol. 17 No., Dcmbr 004, pp [7] Ivan B. Djordjvic and Ban Vasic, Combinatorial Constructions of Optical Orthogonal Cods for OCDMA Systms. IEEE Communications Lttrs, Vol. 8, No. 6, Jun 004. [8] M. Kavhrad, and D. Zaccarh, "Optical Cod-Division- Multiplxd Systms Basd on Spctral Encoding of Noncohrnt Sourcs," Journal oflightwav Tchnology, Vol. 13, No. 3, March 1995 [9] Syd Alw Aljunid, Zuraidah Zan, Siti Barirah Ahmad Anas and Mohd. Khazani Abdullah "A Nw Cod for Optical Cod Division Multipl Accss Systms," Malaysian Journal of Computr Scinc, Vol. 17 No., Dcmbr 004, pp [10] Zou Wi, H. Ghafouri-Shiraz, "Cods for Spctral-Amplitud- Coding Optical CDMA Systms," Journal of Lightwav Tchnology, Vol. 50, August 00, pp [11] S. Anuar, S.A. Aljunid, A.Mohammd, E.I.Babkir and N.M.Saad, Dvlopmnt of Zro Cross-Corrlation cod for Spctral-Amplitud Coding Optical cod Division Multipl Accss (OCDMA. Hassan Yousif Ahmd rcivd th B.Eng. in Computr Enginring (Ntwork) and M.Sc in Computr Sinc and Information from Gzira Univrsity, Sudan in 00 and 007 rspctivly. His rsarch intrsts ar on Computr Ntwork, wirlss communications ntworks, optical communications, and h is currntly working toward Ph.D dgr in optical communications, working at Univrsity Tcknolgi PETRONAS dpartmnt of Elctrical and Elctronic, Malaysia I. REFERENCES [1] J. A. Salhi, Cod division multipl accss tchniqus in optical fibr ntwork Par I: Fundamntal principls, IEEE Trans. Commun., vol.37, pp , [] J. A. Salhi and C. A. Bracktt, Cod division multipl accss tchniqus in optical fibr ntwork Part II: Systm prformanc analysis, IEEE Trans. Commun., vol. 37, pp , [3] P. R. Prucnal, M. A. Santoro, and T. R. Fan, Sprad-spctrum fibr-optic local ara ntwork using optical procssing, J. Lightwav Tchnol., vol. LT-4, pp , May [4] A. Stok and E. H. Sargnt, Lighting th local ntwork: Optical cod division multipl accss and quality of srvic