Performance Limiaions of an Opical Heerodyne CPFSK Transmission Sysem Affeced by Polarizaion Mode Dispersion in a Single Mode Fiber M. S. Islam, Member, IEEE, and S. P. Majumder, Member, IEEE Absrac--A heoreical analysis is developed o evaluae he bi error rae (BER performance degradaion of an opical heerodyne CPFSK sysem caused by signal phase disorion due o polarizaion mode dispersion (PMD in a single mode fiber. The average BER performance resuls are evaluaed a a bi rae of Gb/s considering Maxwellian disribuion for he differenial group delay (DGD. The resuls show ha he performance of opical heerodyne CPFSK direc deecion sysem suffers power penaly of.75 db,.95 db, 4. db and 9.5 db corresponding o mean DGD of ps, 3 ps, 4 ps and 6 ps respecively a a BER of -9 operaing a Gb/s. Furhermore, a increased values of he mean DGD here occur BER floors above -9, which can no be lowered by furher increasing he signal power. I is noiced ha BER floors occur a abou x -8, -5 and.5x -4 corresponding o mean DGD of 6 ps, 7 ps and 8 ps respecively a Gb/s and modulaion index of.5. The effec of PMD is found o be more derimenal a higher modulaion index. Index Terms-- Polarizaion mode dispersion, Differenial group delay, Bi error rae, Maxwellian disribuion, Heerodyne deecion. O I. INTRODUCTION PTICAL coninuous-phase FSK (CPFSK wih low modulaion index ( h is an aracive modulaion scheme for fuure muli-channel opical sysem. However, a high bi rae operaion of such sysems in convenional single mode fiber, he major limiaion is he group velociy dispersion (GVD, unless a dispersion compensaion scheme is used []. ]. Furher, a single mode fiber is acually a wo-mode fiber because i can suppor wo orhogonally polarized eigenmodes. Due o imperfecions in he fiber manufacure and deploymen, he propagaion M. S. Islam is wih he Insiue of Informaion and Communicaion Technology (IICT of Bangladesh Universiy of Engineering and Technology (BUET, Dhaka-, Bangladesh (Phone: 88--966-565-8 (PABX Ex. 755, Fax: 88--86-36, E-mail: mdsaifulislam@iic.bue.ac.bd S. P. Majumder is wih he Elecrical and Elecronic Engineering Deparmen of Bangladesh Universiy of Engineering and Technology (BUET, Dhaka-, Bangladesh (Phone: 88--966-565-8 (PABX Ex. 7, 78, Fax: 88--86-36, E-mail: spmajumder@eee.bue.ac.bd -444-37-7/6/$. 6 IEEE consans of he wo eigenmodes are in general differen and mode coupling occurs as ligh propagaes hrough a fiber. The differen propagaion speeds resul in PMD and maximum dispersion happens when wo modes are equally excied. Consequenly, an inciden linearly polarized wave may be subjeced o random phase flucuaion which causes specral broadening of he ransmied signal ha leads o bi paern corrupion and higher bandwidh requiremen, and evenually conribues o BER deerioraion, performance variaion or sysem fading even a moderae bi raes []-[9]. PMD consiues one of he main limiing facors for reliable opical fiber sysem ransmission performance a bi rae Gb/s or higher. The effec of PMD has been he subjec of considerable research ineress during he pas few years and he developed ideas are briefly described in a series of publicaions [3]-[9]. The simulaion resuls on he effecs of PMD on an amplified IM-DD sysem is repored in ref. [3] as a funcion of he DGD. The effec of PMD on he condiional bi error rae performance of heerodyne FSK sysem is presened [6]. Recenly, he performance of opical DPSK sysem wih direc deecion receiver is repored in presence of PMD [8], [9]. In his paper, we provide an analyical approach o evaluae he BER performance limiaions of an opical heerodyne CPFSK wih delay-demodulaion sysem impaired by PMD. The mehod is based on he linear approximaion of he oupu phase of a linearly filered angle-modulaed signal such as he CPFSK signal. The probabiliy densiy funcion (pdf of he random phase flucuaion due o PMD and group velociy dispersion (GVD a he oupu of he receiver is deermined analyically. Based on he pdf of he random phase flucuaion, a condiional BER expression is derived. The emporal behaviors of he fiber PMD are of saisical in naure due o randomness of he birefringence variaions along he fiber srucure. Therefore o assess accuraely he opical ransmission impairmen due o PMD, we deermine he average BER and power penaly for differen mean values of DGD, considering Maxwellian probabiliy densiy funcion for he DGD, a he receiver oupu in he presence of receiver noise. The bi error rae performance and power penaly suffered by he sysem due o PMD a a BER of -9 are evaluaed a a bi rae of Gb/s.
Inpu signal Opical Coupler Balanced Opical Fron- end V ( IF Filer Low Pass Filer Decision Circui Oupu LO AFC Fig.. Block diagram of a heerodyne CPFSK delay demodulaion receiver II. RECEIVER MODEL The block diagram of a CPFSK delay demodulaion receiver is shown in Fig.. The received opical signal is combined wih he opical signal oupu from he local oscillaor and he wo signals are deeced by phoo-deecor. The oupu of he phoodeecor which is an inermediae frequency (IF signal is amplified by he receiver preamplifier and hen filered by a gaussian filer wih cener frequency se o he IF. The bandwidh of he IF is kep wice he bi rae for opimum demodulaion. The oupu of he filer is hen demodulaed using a delay line discriminaor. The oupu of he discriminaor is hen filered by a low-pass filer and fed o a sampler followed by a comparaor. The hreshold volage of he comparaor is se o zero value. If he oupu volage is greaer han zero han a binary is deeced, oherwise a binary is deeced. III. THEORITICAL ANALYSIS The complex elecric field a he oupu of he coninuous phase FSK (CPFSK ransmier and inpu o he fiber is represened as: E = P exp[ jπ f + jφ ( ][ ( ( T c s e E( = PT exp[ jπ fc + jφs( ][ c. e] ( where, f c is he carrier frequency, P T is he ransmied opical power and he CPFSK modulaing phase φ s ( is given by φ ( = π I ( d + φ ( and I ( = a p( kt s n k k = wih a k = ± is he kh bi of random NRZ bi paern, f, he peak frequency deviaion, p (, he elemenary pulse shape of duraion T seconds and φ n (, he phase noise of he ransmiing laser. Here, c, c represen uni vecors and e, e represen he wo principal saes of polarizaion (PSPs respecively. The elecric field oupu of he fiber is hen given by E = P exp[ jπ f + jφ ( ][ c. e ] h ( (3 E ( T c s ( T c s = P exp[ jπ f + jφ ( ][ c. e ] h ( (4 where denoes convoluion, h ( and h ( are he inverse Fourier ransform of he low pass equivalen ransfer funcion of a non-dispersion shifed lossless fiber H ( f and H ( f respecively, which include he effec of PMD and group velociy dispersion and are given by, H( f = α exp[ jπf ( jγ ( πft ] (5 H ( f = α exp[ jπf ( jγ ( πft ] (6 where α is he PMD power spliing raio, represens he DGD beween he wo PSPs and γ is chromaic dispersion index. Here, we assume ha here is a negligible amoun of polarizaion dependen loss. Now, assuming linear phase approximaion, he oupu elecric fields for wo polarizaion saes can be given as, E = P exp[ jπ f + jφ ( ][ (7 E ( s c e ( s c e ( = π a k Re[ p( kt h ( ] d ( = π f a k Re[ p ( kt h ( ] d where, = P exp[ jπ f + jφ ( ][ (8 φ (8a φ (8b The signal a he oupu of he IF filer is given by, i ( = Rd Ps PLo {exp[ jπf IF + jφ ( ] + exp[ jπf + jφ ( ]} + i ( IF where i n ( represens he oal noise curren consising of sho noise and receiver hermal noise, R d is he responsiviy of he phoodeecor, P s is he oupu power a he fiber end, P Lo is he local oscillaor power, f IF is he IF frequency. The phases φ ( and φ ( are given by ( k φ ( = π f a k g ( kt d g( Re[ p( h ( hif ( g( Re[ p( h ( hif ( n (9 φ = π a g ( kt d ( ( where, = ] (a = ] (b where h IF ( is he impulse response of he IF filer. The IF signal curren is hen given by, i = R P P cosφ ( cos[π f + φ ( ] i ( ( ( d s Lo IF + n
φ + φ φ where, φ φ ( = and φ ( = The oupu of he IF filer can be expressed as, v = R P P a( cos[π f + φ ( ] n( (3 ( d s Lo IF + where, a( = cosφ (, which is he ampliude flucuaions due o PMD and GVD, n ( is he receiver sho noise wih variance σ n = e ( Ps + PLo BIF, B IF being he IF filer bandwidh. Following he delay demodulaion (delay ime and low pass filering (wide enough o pass he signal undisored, he low pass filer (LPF oupu is given by, v ou ( = A( cos[ φ (, ] (4 where A ( = R d P s P Lo cosφ ( ; A( is he ampliude and he differenial oupu phase of v ou ( of he LPF can be expressed as, φ, = πf + φ (, θ (, ( IF + n φ (, = π a g ( kt d+ ak g ( kt d (5 which can be rewrien as, φ (, = π q( + π a k q( kt (6a where, k = φ(, + ξ (6b q( = g ( d and g ( = [ g( + g( ] In delay demodulaion receiver he daa decisions are based on he polariy of v ou (. Assuming a mark is ransmied (say a = and under ideal CPFSK demodulaion condiion, π π π f IF = (n + ; n is an ineger and π = for NRZ daa. Now, applying he above condiions, he phase of v ou ( a he sampling insan can be wrien as, π π π π φ(, = π fif + + q( + q( kt θn(, + (7 Noe ha he firs wo erms in (7 provide he expeced phase change during he demodulaion inerval corresponding o he ideal siuaion, he nex hree erms, in fac, represen he undesired conribuion o he phase due o PMD and GVD and he las erm, θn (, represens he phase disorion due o receiver noise. Denoing he phase disorion of he signal only due o PMD and GVD as π π π η = + q( + akq( kt = α (, + ξ (8 where, α (, is he mean oupu phase error and ξ is random oupu phase flucuaion due o ISI for random bi paern caused by PMD and GVD. V We define he IF SNR as ρ =. For a given IF SNR, σ n he condiional bi error probabiliy, P ( e ξ condiioned on a given value of ξ and differenial group delay, can be obained following Ref. []. The probabiliy densiy funcion (pdf of ξ, P ξ (ξ can be obained by invering he characerisic funcion of ξ. The characerisic funcion of random oupu phase, ξ can be expressed as, i ( jξ Fξ ( jξ = cos[ ξ qi ( ] = M i (9 (i! i= i= Where q i ( = q ( it, M i are he even order momens of he characerisic funcion of random oupu phase ξ. Momens M i can be evaluaed by using he following recursive relaions, M r = Yr ( N ( Where Y r C j r r r ( i C jy j ( i j= r j i = q ( is he binominal coefficien and N is he acual number of erms The pdf of he random oupu phase, ξ can be wrien as, Pξ ( ξ = F [ Fξ ( jξ ] ( So for a given value of insananeous differenial group delay (DGD, he condiional BER can be expressed as, So for a given value of differenial group delay (DGD, he condiional BER can be expressed as, BER ( = P ( e ξ P ξ ( ξ d ξ (3 where P ξ (ξ is he pdf of ξ which can be evaluaed following Ref.[].The above inegraion can be carried ou by Gaussquadraure rule. PMD is a sochasic process. The random configuraion of birefringence, which causes PMD, depends on he sress induced by spooling, cabling, emperaure changes and any oher environmenal facor ha may cause he core of he fiber o deviae from being perfecly cylindrical. The saisical properies of PMD have been experimenally and heoreically sudied and found ha he evoluion of DGD a paricular frequency over ime yields a Maxwellian probabiliy densiy funcion given by, ( 3 exp 4, > = 3 (4 P π π where is he quadraic mean of insananeous DGD,. Thus, he average error probabiliy can be evaluaed as, BER = BER ( P ( d ( (5
IV. RESULTS AND DISCUSSION Following he analyical approach oulined above, we evaluaed he bi error rae performance resul of an opical heerodyne CPFSK ransmission sysem wih delay demodulaion for several values mean DGD a a bi rae of Gb/s. The plos of average BER versus received power, Ps are shown in Fig. and Fig.3. a modulaion index of.5 and. respecively a a bi are Gb/s for differen values of mean DGD. The resuls show ha he BER performance is more affeced a higher values of mean DGD and a higher modulaion index Fig.. Plos of average BER versus received power, Ps for heerodyne CPFSK receiver impaired by PMD a modulaion index.5 The penaly due o PMD suffered by he heerodyne CPFSK sysem a BER -9 is ploed in Fig.4 as a funcion of DGD normalized by bi duraion. I is observed from Fig. ha he penaly a BER = -9 is increasing wih increasing values of he mean DGD. From Fig., he amoun of penaly is found o be approximaely.75 db,. db, 3.5 db and 5.7 db corresponding o mean DGD of ps, 3 ps, 4 ps and 5 ps respecively. Furher increase of DGD leads o a BER floor above -9 which can no be lowered by furher increasing he signal power. Fig. 4. PMD-induced power penaly as a funcion of DGD/bi duraion A. (( < > / T for NRZ- and RZ-OOK, NRZ-DPSK and heerodyne B. NRZ-CPFSK sysem. I is noiced ha BER floors occur a abou x -8, -5 and.5x -4 corresponding o mean DGD of 6 ps, 7 ps and 8 ps respecively a Gb/s and modulaion index of.5. The amoun of penaly is approximaely 6.8 db when mean DGD is 4 ps a modulaion index. The plos of penaly due o oher modulaion schemes as repored in [7] are also shown in Fig. 4 for comparison. I is furher noiced ha penaly suffered by heerodyne deecion CPFSK wih modulaion index.5 is higher han ha of NRZ-OOK sysem. Bu a higher modulaion index, penaly suffered by heerodyne CPFSK is also higher han ha of OOK and DPSK sysem. V. CONCLUSION An analyical approach is presened o evaluae he impac of polarizaion mode dispersion on he BER performance of heerodyne CPFSK sysem. The resuls show ha he penaly due o PMD suffered by he heerodyne CPFSK sysem is significan a higher modulaion index and higher values of he differenial group delay beween he wo eigenmodes. VI. REFERENCES Fig. 3. Plos of average BER versus received power,ps for heerodyne CPFSK impaired by PMD a modulaion index. [] A. F. Elrefaie and R. E. Wagner, Chromaic dispersion limiaions for FSK and DPSK sysems wih direc deecion receivers, IEEE Phoon. Technol. Le., Vo. 3, no., pp. 7-73 99. [] C. D. Poole, R.W. Tkach, A.R. Chraplyvy and D.A. Fishman, Fading in lighwave sysem due o polarizaion mode dispersion, IEEE phoon. Technol. Le.,, Vol..3, no., pp. 68-7, 99. [3] C. D. Angelis, A. Galarossa, C. Campanile and F. Maera, Performance evaluaion of ASK and DPSK opical coheren sysems affeced by chromaic dispersion and polarizaion mode dispersion, Journal of opical communicaions, Vol.6, no.5, pp.73-78, 995. [4] C. De Angelis, A. Galarossa, G. Gianello, F. Maera and M. Schiano, Time evoluion of polarizaion mode dispersion in long erresrial links, IEEE J. Lighw. Technol, Vol., no.5, pp.55-555, 995. [5] F. Bruyere, Impac of firs and second order PMD in opical digial ransmission sysems, Opical Fiber Technology, Vol., no., pp. 69-8, 996.
[6] S. P. Majumder, M. Z. Yusoff, A. F. Muhammad and H.T. Chuah, Effec of polarizaion mode dispersion on opical heerodyne CPFSK sysem, Conference proceedings, Telecommunicaion global conference, GLOBECOM, vol., pp.33-36,. [7] Jin Wang, Joseph M. Kahn, Impac of chromaic and polarizaion mode dispersion on DPSK sysem using inerferomeric demodulaion and direc deecion, J. Lighw. Technol., Vol., no., pp.36-37, 4. [8] Chongjin Xie, Moller, L, Sysem penalies induced by second-order polarizaion mode dispersion, 3 s European conference on opical communicaion, 5, ECOC, vol. 3, pp.345-346, 5. [9] H. Yoon, N.Y. Kim, N. Park, Sudy on he PMD Impairmen of Opical Mulilevel DPSK Sysems and is Miigaion Mehods, IEEE Phoon. Technol. Le. Vol. 7, no., pp.577-579, 5. [] S. P. Majumder, R. Gangopadhaya, E. Foresieri and G. Prai, Sensiiviy penaly for AMI coded CPFSK in heerodyne delay demodulaion receiver, IEEE Phoon. Technol. Le, Vol. 7, no., pp.7-9, 995. M. S. Islam received he B. Sc. degree in Elecrical and Elecronic Engineering from he Bangladesh Universiy of Engineering and Technology (BUET, Bangladesh in 989 and M. Sc. in Compuer Science and Engineering from Shanghai Universiy, China, in 997. He is currenly pursuing he Ph. D. degree in he Deparmen of Elecrical and Elecronic Engineering a BUET, Bangladesh. His main research ineres is he performance evaluaion research ineres is he performance evaluaion of long-haul fiber-opic communicaion sysem. S. P. Majumder received he B.S. and M.S. degrees in Elecrical and Elecronic Engineering from Bangladesh Universiy of Engineering and Technology (BUET, Dhaka, Bangladesh, in 98 and 984 respecively. He did Ph.D. degree in Elecrical Engineering from he Indian Insiue of Technology (IIT, Kharagpur, India, in 993. Presenly, he is a Professor and Head of Elecrical and Elecronic Engineering Deparmen a BUET. His research ineress include opical communicaion sysems, signal processing, saellie communicaion and digial sysems.