Impact of Polarization Mode Dispersion on CPFSK Transmission Systems Using MZI Based Direct Detection Receiver

Transcription

1 Impa of Polarzaon Mode Dsperson on CPFSK ransmsson Sysems Usng MZI Based Dre Deeon Reever M. S. Islam, Member, I, and S. P. Majumder, Member, I Absra An analyal approah s presened o deermne he mpa of sgnal phase dsoron due o polarzaon mode dsperson (PMD) n a sngle mode fber (SMF) on he b error rae (BR) performane of an opal onnuous phase FSK (CPFSK) ransmsson sysem wh MZI based dre deeon reever. he probably densy funon (pdf) of he random phase fluuaon due o PMD and group veloy dsperson (GVD) a he oupu of he reever s deermned analyally. Based on he pdf of he random phase fluuaon he BR performane resuls are evaluaed a a b rae of 0 Gb/s fber wh dsperson o-effen D = 5 ps/m-nm for dfferen values of he mean dfferenal group delay (DGD). he ompued resuls show ha he dre deeon CPFSK sysem suffers a sgnfan amoun of power penaly due he effe of PMD a a b rae of 0 Gb/s. A a modulaon ndex of 0.5, he penaly a a BR of 0-9 s found o be 0.5 db,.0 db,.0 db and 3.50 db when he mean dfferenal group delay (DGD) s 0 ps, 30 ps, 40 ps and 50 ps respevely a modulaon ndex of 0.5 for a fber lengh of 00 m. A modulaon ndex of.0, he penaly s approxmaely 4.0 db for a mean DGD of 40 ps. he penaly s more sgnfan a hgher modulaon ndex and b rae. Index erms- B-error rae, polarzaon mode dsperson, probably densy funon, dfferenal group delay. o I. INRODUCION PICAL onnuous-phase FSK (CPFSK) s an arave modulaon forma as allows generaon of ompa spera ha allows for reever envelop deeon by properly seleng he modulaon ndex []. However, he effe of PMD onsues one of he man lmng faors for relable opal fber sysem performane a ggabs ransmsson raes. As he wo polarzaon felds move a dfferen group M. S. Islam s wh he Insue of Informaon and Communaon ehnology (IIC) of Bangladesh Unversy of ngneerng and ehnology (BU), Dhaa-000, Bangladesh (Phone: (PABX); fax: , e-mal: mdsafulslam@.bue.a.bd). S. P. Majumder s wh he leral and leron ngneerng Deparmen of Bangladesh Unversy of ngneerng and ehnology (BU), Dhaa-000, Bangladesh (Phone: (PABX); e-mal: spmajumder@eee.bue.a.bd) /06/$ I veloes wh a dfferenal group delay (DGD), here s a fluuaon n sgnal phase beween he wo prnpal saes of polarzaon whh auses a random phase fluuaon of he sgnal self resulng n speral broadenng of he ransmed sgnal ha leads o b paern orrupon and hgher bandwdh requremen, and evenually onrbues o BR deeroraon, performane varaon or sysem fadng even a moderae b rae []-[5]. he effe of PMD has been he subje of onsderable researh neress durng he pas few years and he developed deas are brefly desrbed n a seres of publaon [6]-[]. he effe for PMD on he error probably s heoreally assessed a a b rae of.5 Gb/s for an IM-DD sysem and he BR n a IM/DD has been shown o srongly depend on he sae of polarzaon and DGD [6]. Some sudes reaed PMD as deermns erm n numeral soluon or are based on smple analyal approah of deermnng he ondonal b error probably [7]. he smulaon resuls on he effes of PMD on an amplfed IM-DD sysem s repored n Ref. [8] as a funon of he DGD. he effe of PMD on he b error rae performane of heerodyne FSK sysem s also repored [3]. Reenly, he performane of opal DPSK sysem wh dre deeon reever s repored n presene of PMD [4]. Several aemps have been repored o ompensae he effe of PMD n eleron as well as n opal doman [5]-[7]. Alhough here are many approahes repored o mnmze he effe of PMD, here s no analyal developmen o evaluae he mpa of PMD on he BR performane of an opal ransmsson sysem. In hs paper, we provde an analyal approah o evaluae he BR performane lmaons of an opal dre deeon CPFSK sysem mpared by PMD. he mehod s based on he lnear approxmaon of he oupu phase of a lnearly flered angle-modulaed sgnal suh as he CPFSK sgnal. he expresson for he overall degradaon n sgnal phase s derved followng an analyal approah by usng an equvalen ransfer funon of a sngle fber whh nludes he effes of PMD n presene of group veloy dsperson (GVD). he ondonal BR s hen deermned usng he pdf s of he random phase fluuaon due o PMD and GVD a he reever oupu n he presene of reever nose for

2 dfferen values of mean DGD. Power penaly suffered by he sysem due o PMD s evaluaed a a b rae of 0 Gb/s. II. SYSM MODL he blo dagram of an opal CPFSK ransmsson sysem wh dre deeon model s shown n Fg.. Fg. shows he low pass equvalen CPFSK sysem model onsderng PMD and hroma dsperson. he sgnal omponens n he wo oupu PSPs propagae ndependenly hrough he enre sysem from he modulaor o he balaned reever. In he ransmer, non-reurn o zero (NRZ) daa a 0 Gb/s s used o drely modulae a laser o generae he CPFSK sgnal ha s ransmed hrough a sngle mode fber. A he reevng end, MZI based dre deeon reever dees he reeved opal sgnal. he felds orrespondng o he wo PSPs are separaely deeed and he resulng phoourrens are summed. We deompose he enre sysem no a par of subsysems, eah orrespondng o one PSP. We sum he oupus of he wo subsysems o oban sampled deson varables m = m + m. he oupu phoourren s flered by a low pass fler and fed o a sampler followed by a omparaor. he hreshold volage of he omparaor s se o zero value. If he oupu volage s greaer han zero a bnary s deeed, oherwse a bnary 0 s deeed. ransmer Fber Reever Inpu sgnal Drver ru MZI Σ LPF Sampler Comp araor Oupu Fg.. Blo dagram of an opal CPFSK ransmsson sysem wh MZI based dre deeon reever Daa n H pmd (f) H (f) H d (f) Σ I (f). II (f). Σ m () MZI and PD par m () Σ m () LPF Sampler Comp araor Oupu I (f). H pmd (f) H d (f) II (f). Σ H (f) MZI and PD par Fber (SMF) MZI and PD (reever seon) Fg.. Low pass equvalen dre deeon CPFSK sysem model onsderng PMD and hroma dsperson

3 III. HORICAL ANALYSIS he omplex eler feld a he oupu of he CPFSK ransmer and npu o he fber s represened as: = P exp[ { ( )}][. ] j f + φ s e () = P exp[ j{ f + φs }][ ] () where f s he arrer frequeny, P s he ransmed opal power and he CPFSK modulang phase φ s () s gven by φ s = f a p( ) d n = + φ (3) where a s he random NRZ b, f s he pea frequeny devaon, p () s he elemenary pulse shape and φ n ( ) s he phase nose of he ransmng laser. Here, represen un veors and e, e represen he wo prnpal saes of polarzaon respevely. he eler feld a he oupu of he fber s hen gven by: 0 = P exp[ j{ f + φ s( )}][ ] (4) 0 = P exp[ j{ f + φ s( )}][ ] (5) where h ( ) and h are he nverse Fourer ransform of he fber ransfer funon H ( f ) and H ( f ) respevely whh nlude he effe of polarzaon mode dsperson and group veloy dsperson (GVD) and denoes onvoluon. he low pass equvalen expresson for H ( f ) and H ( f ) are gven by [4], H ( ) exp[ ( ) ( ) f = α j f jγ f ] (6) H ( ) exp[ ( ) ( ) f = α j f jγ f ] (7) where τ represens he dfferenal group delay (DGD) beween he wo prnpal saes of polarzaon (PSP), α s he PMD power-splng raon and γ s he hroma dsperson ndex. Here we assume ha here s neglgble polarzaon-dependen loss and we use he prnpal saes model o haraerze frs-order PMD. Assumng lnear phase approxmaon he oupu eler felds for he wo polarzaon saes an be wren as 0 = P s exp[ j{ f + φ s + θ n }][ ] (8) 0 = P s exp[{ j f + φ s + θ n }][ ] (9) where, φ s = Re[ φs ] = f a p d Re[ ( ) ( )] (0) φ s = Re[ φs ] = f a p d Re[ ( ) ( )] () In he FSK dre deeon reever wh Mah-Zehnder nerferomeer (MZI), he MZI a as an opal dsrmnaor and dfferenally dee he mar and spae of he reeved FSK sgnal, whh are hen drely fed o a par of phoo-deeors. he ransmanes of he wo branhes of he MZI are I (f) and II (f), and τ s he me delay beween he wo branhes. For a mar ransmsson, he urren a he oupu of he phoo-deeors an be expressed as: m P s os[f τ + φ s τ) + θ n τ)][ ] () m P s os[f τ + φ s τ) + θ n τ)][ ] (3) where φ s (, τ ) = φ s ( ) φ s ( τ ) (4) = f a g ( ) d φ s (, τ ) = φ s = f τ ( ) φ s τ a g ( τ ) ( ) d (5) For a mar ransmsson and deal CPFSK demodulaon ondon (assumng NRZ daa), we have f τ = (n + ), where n s an neger; and f τ =. hus, he urrens a he oupu of phoodeeor an be expressed as, m P s os[ f τ + + q + a q ( ) )][ ] 0 + θ n τ (6) m P s os[ f τ + + q + a ) (, )][ q ( + θn τ 0 ] (7) where, q = g d τ τ (7a) g( ) = Re[ p( ) LP ] (7b) and q = g ) d τ τ (7) g = Re[ p( ) h LP ] (7d) where h () represens he mpulse response of he LP eleral low pass fler, whh s assumed o be ffh-order Bessel funon ype. he ransfer funon of he low pass fler s gven by, 945 H LP ( f ) = (8) jf + 5F 05jF 40F + 945jF + 945

4 where F =.43 f / Be and B e s he 3-dB uoff frequeny. he oupu phase dsoron due o PMD and GVD s gven by, φ (, τ, ) = + q + a q ( ) 0 = ϕ s (, τ ) + ξ τ ) (9) φ τ. ) = + q + a q ( ) 0 = ϕ s τ ) + ξ τ ) (0) where ϕ s τ ) and ϕ s τ ) are mean oupu phase error; ξ (, τ ) and ξ (, τ ) are he random oupu phase fluuaon due o ISI b paern aused by PMD and GVD. he oal sgnal urren a he oupu of LPF orrespondng o a mar s gven by, m = R d P s x + R d P s x () where, x ( ) and x ( ) desrbe he phase nose ndued by he nerferomeer nensy due o random phase fluuaon and an be expressed as, x = os[ ϕ ] () x = os[ ϕ ] (3) where ϕ ( ) = φ (, τ, ) + ϕ n ( ) (3a) ϕ ( ) = φ (, τ, ) + ϕ n ( ) (3b) he low-pass fler oupu for mar ransmsson, a a samplng me s, m P s [os( δϕ ) os( ϕ)] + n( ) (4) φ,, ) where δϕ = (, τ, ) φ ( τ (4a) φ,, ) and (, τ, ) + φ ( τ ϕ = (4b) If we onsder he mean phase dsoron only hen he ondonal b error rae an be expressed as, P( e δϕ, ϕ) Q = erf (5) R d P s [os( δϕ ) os( ϕ) ] where, Q = (6) σ m he onrbuon of he erm (random phase fluuaon) ξ(, τ ) of (9) and ξ τ ) of (0) an be evaluaed by fndng he probably densy funon (pdf). Assumng { a } are ndependen and denally dsrbued (IID) random varables, he haraers funon of ξand ξ s gven by, ( j ( j q ) ) os[ )] M ( ξ Φ φ ξ = ξ = (7) = = ( )! j ( j ( q ) ) ξ Φ φ ξ = os[ ξ ( )] = M ()! (8) = = where, q = q ( ), q = q ( ), M and M are he even order momens of he haraers funon of random varableξ and ξ respevely. By usng he above wo equaons he pdf P δϕ (δϕ) of δϕ and he pdf P ϕ ( ϕ) of ϕ an be evaluaed followng Ref. [3]. For a gven value of mean dfferenal group delay (DGD) < >, he ondonal BR an be expressed as: BR ( < > ) = P( e δϕ, ϕ ) Pδϕ ( δϕ ) (9) P ϕ ( ϕ ) d ( δϕ ) d ( ϕ ) he average error probably an be evaluaed as BR = BR( < > ) P ( ) ( ) τ d τ (30) where, P ( τ ) s he pdf of τ whh has Maxwellan dsrbuon wh τ m as quadra mean of τ [8]. IV. RSULS AND DISCUSSION Followng he analyal approah, he b error rae performane resuls for dre deeon CPFSK reever wh pos deeon low pass fler are evaluaed a a b rae of 0 Gb/s wh several values of mean DGD and fber lenghs. Fg. 3. Condonal BR versus reeved power, Ps for dre deeon CPFSK sysem mpared by PMD (modulaon ndex, h=0.50)

5 he plos of ondonal BR versus reeved opal power Ps are shown n Fg. 3 for mean DGD of 0 ps, 0 ps, 30 ps, 40 ps, 50ps and 60 ps wh fber lengh of 00 m and modulaon ndex of 0.50 and plos for modulaon ndex.0 are shown n Fg.4. he resuls show ha he BR s hghly degraded when he mean DGD s hgher for a gven fber lengh and he sysem suffers a sgnfan amoun power penaly a BR = 0-9 whh s found o nrease wh nreasng value of he mean DGD. he amoun of power penaly s found o be approxmaely 0.50 db,.0 db,.0 db and 3.50 db for mean DGD of 0 ps, 30 ps, 40 ps and 50 ps respevely when he modulaon ndex s I s furher observed ha he penaly s muh hgher a hgher modulaon ndex suh as h= ompared o h=0.50.e., he penaly s approxmaely 4.0 db when mean DGD s 40 ps and h=.0. I s furher noed ha penaly suffered by dre deeon CPFSK s lower han ha of NRZ-OOK sysem. Bu a hgher modulaon ndex penaly suffered by CPFSK wh 0.50 s hgher han ha of OOK and DPSK sysem. For example, he penaly s.35 db and.40 db orrespondng o DGD/b duraon rao ( τ ) are 0.0 and 0.30 respevely for dre deeon CPFSK sysem a modulaon ndex.0. he orrespondng penaly values are 0.50 db,.35 db and 0.30 db, 0.80 db for NRZ-OOK and NRZ-DPSK respevely. V. CONCLUSION Fg. 4. Condonal BR versus reeved power, Ps for dre deeon CPFSK sysem mpared by PMD (modulaon ndex, h=.0) he penaly due o PMD suffered by he dre deeon CPFSK sysem wh pos deeon low pass fler a BR 0-9 s ploed n Fg. 5 as a funon of DGD normalzed by b rae. he plos of penaly due o oher modulaon sheme as repored n [4] are also shown for omparson. Fg. 5. PMD-ndued power penaly as a funon of DGD/ b duraon rao ( < > / ) for NRZ- and RZ-OOK, NRZ-DPSK and NRZ-CPFSK sysem. An analyal approah s presened o evaluae he mpa of PMD on he b error rae performane of dre deeon CPFSK sysem. he resuls show ha he penaly due o PMD suffered by he CPFSK sysem s sgnfan a hgher modulaon ndex and hgher value of he DGD beween wo-polarzaon modes. A dre-deeon CPFSK sysem wh modulaon ndex of 0.50 suffers almos same amoun of power penaly as dre deeon NRZ-OOK sysem VI. RFRNCS [] K. Iwasha and. Masumoo, Modulaon and deeon haraerss of opal onnuous-phase FSK ransmsson sysem, Journal of Lghwave ehnology, vol. L-5, Aprl 987, pp [] N. S. Bergano, C. D. Poole, and R.. Wagner, Invesgaon of polarzaon dsperson n long lenghs of sngle-mode fber usng mullongudnal mode lasers, Journal of Lghwave ehnology, vol. L-5, pp. 68-6, Nov [3] R.. Wagner and A.F. lrefae, Polarzaon dsperson lmaons n lghwave sysems, eh. Dg. Opal Fber Communaon Conferene OFC 88, p37, New Orleans, LA, 988. [4] A. F. lrefae and R.. Wagner, Chroma dsperson lmaons for FSK and DPSK sysems wh dre deeon reevers, I Phoons ehnology Leers, vol. 8, no., January 99. [5] C. D. Poole, R.W. ah, A.R. Chraplyvy and D.A. Fshman, Fadng n lghwave sysem due o polarzaon mode dsperson, I phoon. eh. Le., vol.3, pp , 99. [6]. Iannone, F. Maera, A. Galarossa, G. Ganello and M. Shano, ffe of polarzaon dsperson on he performane of IM-DD ommunaon sysem, I phoons eh. Le., vol. 5, no. 0, O. 993, pp [7] F. Bruyere and O. Audoun, Assessmen of sysem penales n a 5 Gb/s opally amplfed ransoean ln, I Phoons eh. Le., vol. 6, no. 3, Marh 994, pp [8] C. D. Angels, A. Galarossa, C. Campanle and F. Maera, Performane evaluaon of ASK and DPSK opal oheren sysems affeed by hroma dsperson and polarzaon mode dsperson, Journal of opal ommunaons, vol.6, no. 5, 995, pp [9] H. Bulow, Operaon of dgal opal ransmsson sysem wh mnmal degradaon due o polarzaon mode dsperson. lerons Leers, vol. 3, no.3, pp. 4-5, 995. [0] B.W. Ha, Polarzaon mode dsperson n a sngle mode fber, Journal of Lghwave ehnology, vol. 4, no. 0, pp. 0-08, 996

6 [] F. Bruyere, Impa of frs and seond order PMD n opal dgal ransmsson sysems, Opal Fber ehnology, vol., no. 3, pp , July 996. [] M. Karlsson, Polarzaon mode dsperson-ndued pulse broadenng n opal fbers, Ops Leers, vol. 3, no. 9, pp , May 998. [3] S. P. Majumder, M. Z. Yusoff, A. F. Muhammad and H.. Chuah, ffe of polarzaon mode dsperson on opal heerodyne CPFSK sysem, Conferene proeedngs, eleommunaon global onferene 000, GLOBCOM 00, vol., pp , 000. [4] Jn Wang, Joseph M. Kahn, Impa of hroma and polarzaon mode dsperson on DPSK sysem usng nerferomer demodulaon and dre deeon, Journal of Lghwave ehnology, vol., no., pp , February 004. [5] Buhal, H. Bülow, Adapve PMD Compensaon by leral and Opal ehnques, Journal of Lghwave ehnology, vol., no. 4, pp. 6-6, 004 [6] C. Anonell, A. Meozz, Pulse broadenng due o polarzaon mode dsperson wh frs-order ompensaon, Ops Leers, vol. 30. no. 3, pp , 005. [7] H. Yoon, N.Y. Km, N. Par, Sudy on he PMD Imparmen of Opal Mullevel DPSK Sysems and s Mgaon Mehods I Phoon. eh. Le., Vol. 7, no., pp , 005 M. S. Islam reeved he B. S. degree n leral and leron ngneerng from he Bangladesh Unversy of ngneerng and ehnology (BU), Bangladesh n 989 and M. S. n Compuer Sene and ngneerng from Shangha Unversy, Chna, n 997. He s urrenly pursung he Ph. D. degree n he Deparmen of leral and leron ngneerng a BU, Bangladesh. Hs man researh neres s he performane evaluaon of long-haul fber-op ommunaon sysem. S. P. Majumder reeved he B.S. and M.S. degrees n leral and leron ngneerng from Bangladesh Unversy of ngneerng and ehnology (BU), Dhaa, Bangladesh, n 98 and 984 respevely. He dd Ph.D. degree n leral ngneerng from he Indan Insue of ehnology (II), Kharagpur, Inda, n 993. Presenly, he s a Professor and Head of leral and leron ngneerng Deparmen a BU. Hs researh neress nlude opal ommunaon sysems, sgnal proessng, saelle ommunaon and dgal sysems.