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Optik 123 (2012) 1520– 1524

Contents lists available at SciVerse ScienceDirect

Optik

j o ur nal homepage: www.elsev ier .de / i j leo

mpact of PMD induced penalties on 40 Gb/s duobinary optical communicationystem for fixed and variable scattering section dispersion

arjit Singh, Anu Sheetal ∗

epartment of Electronics Technology, Guru Nanak Dev University, Regional Campus, Gurdaspur, Punjab, India

r t i c l e i n f o

rticle history:eceived 21 March 2011

a b s t r a c t

In this paper, we evaluate the performance of 40 Gb/s duobianry optical transmitter for different scat-tering section dispersion and polarization-mode dispersion coefficient of single mode fiber. We observe

ccepted 16 August 2011

eywords:olarization mode dispersion (PMD)

that the variable scattering section dispersion considerably improves the performance of duobinary opti-cal system as compared to fixed scattering section dispersion where the Q value fluctuates over widefrequency range. Also, duobinary system observes pulse delay of 7 ps for the fixed scattering section dis-persion while there is no delay in the received output signal if variable scattering section dispersion isconsidered.

ifferential group delay (DGD)cattering section dispersion

. Introduction

Polarization mode dispersion (PMD), in high data rate systems>40 Gb/s), can significantly diminish the data-carrying capacity of

telecommunications links [1,2]. PMD originates from optical bire-ringence and is a stochastic phenomenon in transmission fibershat varies randomly with environmental changes including tem-erature and stress, making it a difficult problem to manage. Ideally,he core of an optical fiber is perfectly circular and therefore hashe same index of refraction for two polarization states. However,

echanical and thermal stresses introduced during manufacturingesult in asymmetries in the fiber core geometry causing birefrin-ence. Birefringence creates differing optical axes (slow and fastxes) thus causing one polarization mode to travel faster than thether, resulting in a difference of the propagation time called theifferential group delay (DGD).

A major challenge in the design of the optical transmission sys-em is to minimize the channel outages due to the PMD effector which a meaningful specification for PMD tolerance should beiven. Nelson et al. [3] evaluated the PMD tolerance of 40 Gb/sRZ polarizing multiplexing (PM) system in the presence of therst-order PMD using the Maxwellian distribution and the resultshowed that the PM increased the PMD sensitivity five timesue to coherent crosstalk. The maximum cable induced DGD, forER ≈ 10−9 was proposed to be 5.0 ps with the maximum PMD

oefficient of 0.10 ps/

√km to support 40 Gb/s RZ transmission over

00 km [4]. Another proposal for 40 Gb/s RZ applications with aaximum link DGD of 11.5 ps with 33% duty cycle, acclaimed that

∗ Corresponding author.E-mail address: nripanu@yahoo.co.in (A. Sheetal).

030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2011.09.020

© 2011 Elsevier GmbH. All rights reserved.

this DGD value would induce a 1 dB penalty and a total allowedpath penalty of 3 dB (including PMD effects) [5]. Recently, Lima et al.and Shtaif [6,7] developed importance sampling (IS), multicanon-ical Monte Carlo and Brownian-bridge methods and applied themto investigate the PMD-induced penalties as they can effectivelygenerate the exact DGD distribution.

Liu et al. [8] reported that the PMD-induced system penaltydepends on many factors, such as modulation format and receivercharacteristics. They discussed on-off keying (OOK), differentialphase-shift keying (DPSK) and differential quadrature phase-shiftkeying (DQPSK) modulation formats using the Importance Sam-pling method. As alternative to these formats, duobinary (DB)modulation format can also be used to compensate the PMD effects.DB format is mainly attractive to increase dispersion toleranceand improve spectral efficiency of WDM systems at 40 Gb/s. Asin this format, the pulse-to-pulse interaction at 40 Gb/s can bereduced by alternating the optical phase of adjacent bits, whichsuppresses all discrete frequency tones that appear in the conven-tional RZ signal spectrum. DB format also offers the least timingjitter and amplitude distortion. Also, this format can operate ataverage channel powers higher than the conventional RZ format[9,19]. So, here in this paper, the investigations have been carriedto reduce PMD-induced penalties in a 40 Gb/s duobinary opticaltransmission system using different scattering section dispersionand PMD coefficient for the wide wavelength range. We mea-sure the system penalty in terms of Q factor, timing jitter and eyediagrams.

Here, Section 2, the theory of pulse broadening and PMD induced

penalties has been discussed. Section 3, explains the simulationmodel and its parameters. In Section 4, comparison of results hasbeen reported for fixed and variable scattering section dispersionand finally in Section 5, conclusions have been drawn.

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H. Singh, A. Sheetal / O

. Theory

Polarization mode dispersion occurs when different planes ofight inside a fiber travel at slightly different speeds, making it dif-cult to transmit data reliably at high speed. To analyze the PMDenalties, here we have considered a model using concatenationf many birefringence sections which yields a distribution for dif-erential group delay close to Maxwellian function [10,11].In theptical communication system, mathematically, the propagationf a pulse in linear birefringent fiber, in the absence of loss, withn arbitrary polarization with respect to the principal polariza-ion axes is described by the following nonlinear Schrödinger (NLS)quation [12](

∂u

∂�+ ı

∂u

∂�

)+ D2

∂2u

∂�2− iD3

∂3u

∂�3+ N1

(|u|2 + 2

3|v|2

)u = 0 (1)

(∂v∂�

+ ı∂v∂�

)+ D2

∂2v∂�2

− iD3∂3v∂�3

+ N1

(|v|2 + 2

3|u|2

)v = 0 (2)

here ı = (ˇ1x − ˇ1y) T0/(2|ˇ2|), and ˇ1x − ˇ1y is the differentialroup delay or the normalized group velocity mismatch betweenhe two polarization components.

= Z

LD,

D is dispersion length and is equal to T20 /|ˇ2|.

� = (t − ¯̌ 1z)/T0 is the normalized time, where

¯ 1 = 12

(ˇ1 + ˇ2)

ˇ1 is the group delay and ˇ2 is second order dispersion (GVDarameter).The electric filed envelopes are normalized accordingo (u, v) =

√�LD(ExEy).

N describes the order of pulse and is given as

2 = LD

LNL= �P0T2

0

|ˇ2|here LNL = �P0, LNL is the nonlinear length and � is the nonlinear

oefficient.It is a well-known fact that the broadening of a “veryhort” (Dirac-shaped) pulse is mainly caused by PMD. Let us con-ider the time-dependent intensity at position z along a fiber withigh polarization mode coupling, when a short (with respect to theolarization mode delay) pulse is launched. The expression for theMS width of the pulse is given by [13–16]

��)2 = �2h2

2

(2Z

h− 1 + exp

(−2z

h

))(3)

here

� =

√∫t2I(t, z)dt∫I(t, z)dt

−(∫

tI(t, z)dt∫I(t, z)dt

)2

Fig. 1. Simulatiottp://www.atis.org/tg2k/ analog signal.html.

23 (2012) 1520– 1524 1521

h is the mean coupling length and � is one half of the difference ofthe group delays per unit length between the fast and slow axes ofthe fiber.

Within the limit z»h (high polarization mode coupling) I(t, z) isclose to Gaussian, �� is the full width and Eq. (3) becomes

(��)2 = �2hz (4)

The PMD coefficient parameter in the optical fiber isDPMD = 2�

√h.In this simulation model the “coarse-step method”

has been used to evaluate the PMD effects in the “Stochastic” modewith fixed and variable scattering section dispersion of the fiber.The lengths of the sections are random numbers with a Gaussiandistribution. As the fiber is represented by a concatenation of fibersection with variable length, the average distribution (L′

scatt) is thefunction of scattering section length (Lscatt). The average value offiber length at which the polarization state of the signal is ran-domized by applying the scattering matrix and scattering sectiondispersion (�scatt) is given by [17,18]

f (L′scatt) = 1√

2��scatt

e

−(L′scatt

−Lscatt )2

2�2scatt (5)

For faithful transmission, the dispersion should be less than 20% ofthe average value.

The birefringence of each section is given by with DGD [17]

d

dω(�ˇ) = DPMD√

L′scatt

(6)

where DPMD is the PMD coefficient. The principal axes of the truncksare randomly oriented with respect to each other.

3. Simulation model and parameters

The optical communication system model considered for sim-ulation is shown in Fig. 1. Here, a 40 Gb/s duobinary transmitteris used. The duobinary transmitter is generated by first creatingan NRZ doubinary signal using a duobinary precoder, NRZ gen-erator and a duobinary pulse generator. The generator drives thefirst MZM, and then cascades this modulator with a second mod-ulator that is driven by a sinusoidal electrical signal with thefrequency of 40 GHz, phase = −90◦. The duobinary precoder usedhere is composed of an exclusive-or gate with a delayed feedbackpath. DRZ formats are very attractive, because their optical modu-lation bandwidth can be compressed to the data bit rate B, that is,the half-bandwidth of the NRZ format 2B [19].

In this model various simulation parameters consid-

ered are: bit rate = 40 Gb/s, sample rate = 64 × 1010, sequencelength = 64 bits, samples/bit = 16, number of samples = 1024, fre-quency = 193–195 THz, power = 0 dBm, linewidth = 10 MHz andextinction ratio = 20 dB.

n model.

1522 H. Singh, A. Sheetal / Optik 123 (2012) 1520– 1524

Fig. 2. (a) Comparison of input and output optical signals using fixed scatter-i

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4

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Fig. 3. (a) Q-factor as function of carrier frequency using fixed scattering sectiondispersion at �scatt = 0 m after 200 km fiber and DPMD = 0.5 ps/

√km. (b) Q-factor

as function of carrier frequency using variable scattering section dispersion at�scatt = 2000 m after 200 km fiber and DPMD = 0.5 ps/

√km.

ng section dispersion at �scatt = 0 m after 200 km fiber and DPMD = 0.5 ps/ km. (b)omparison of input and output optical signals using variable scattering sectionispersion at �scatt = 2000 m after 200 km fiber and DPMD = 0.5 ps/

√km.

The duobinary transmitter section is followed by a standardingle mode fiber (SSMF) having length = 200 km, attenua-ion = 0.2 dB/km, dispersion = 16.76 ps/nm/km, differential groupelay = 0.2 ps/km, PMD coefficient = 0.5 ps/

√km, mean scattering

ection length = 10,000 m and variable scattering section disper-ion = 2000 m.The output of the fiber is fed to receiver consistingf PIN photo diode, low pass Bessel filter followed by 3R generatornd BER analyzer. The responsitivity of PIN photo diode = 1 A/W,ark current = 10 nA, center frequency = 193.1 THz and sampleate = 3.2 × 1012. This detected signal is then passed to the low passessel filter with a cut of frequency = 0.75 * bit rate and order ofhe filter = 4. It is then fed to 3R generator to regenerate an electri-al signal for BER analysis. BER analyzer derives different metricsrom the eye diagram, such as Q factor, eye opening, eye closure,xtinction ratio, eye height, and jitter. It also plots BER patterns andstimate system penalties and margins.

To ensure the statistical independence of the collected datahile working with the scattering section length of the fiber, the

pectral interval covered by the simulation has been kept smallerhan the spectral period of the DGD.

. Results and discussion

To assess the performance of duobinary optical communicationystem for different PMD models we compare the impact of PMDsing fixed and variable scattering section dispersion. We exam-

ne the PMD-induced penalties for the system described in Section

Fig. 4. (a) Q-factor as function of frequency (for 193–195 THz) using fixed scatteringsection dispersion at �scatt = 0 m after 200 km fiber and DPMD = 0.5 ps/

√km. (b) Q-

factor as function of frequency (for 193–195 THz) using variable scattering sectiondispersion at �scatt = 2000 m after 200 km fiber and DPMD = 0.5 ps/

√km.

H. Singh, A. Sheetal / Optik 123 (2012) 1520– 1524 1523

Fig. 5. (a) Q-factor as function of PMD coefficient (DPMD = 0.1–1.0 ps/√

km)using fixed scattering section dispersion at �scatt = 0 m after 200 km fiber andDGD = 0.2 ps/km. (b) Q-factor as function of PMD coefficient (DPMD = 0.1–1.0 ps/

√km)

uD

2tPd�f

srfittedts

q�Mflpbgbt

Fig. 6. (a) Eye diagram, using fixed scattering section dispersion at �scatt = 0 m after200 km fiber, DPMD = 0.5 and DGD = 0.2 ps/km, showing the presence of timing jit-

The comparison of various system penalties for fixed and

sing variable scattering section dispersion at �scatt = 2000 m after 200 km fiber andGD = 0.2 ps/km.

.The statistical specifications of PMD on optical fiber cable are usedo investigate the implications of scattering section dispersion andMD coefficient on the system performance. Here, two models ofuobinary system using scattering section dispersion �scatt = 0 andscatt = 2000 m have been considered where PMD coefficient varies

rom 0.1 to 1 ps/√

km.Fig. 2(a) and (b) illustrates the effect of fixed and variable

cattering section dispersion, i.e. �scatt = 0 m and �scatt = 2000 m,espectively, for the same PMD coefficient DPMD = 0.5 ps/

√km and

ber length = 200 km as described by Eq. (5). It is seen from Fig. 2(a)hat the signal received after the fiber is delayed by 7 ps than theransmitted signal if fixed scattering section dispersion is consid-red. While for variable scattering section dispersion there is noelay between input and output optical signal. It is worth men-ioning here that even a very small delay of 0.01 ps/km can causeevere deterioration in the system performance [10].

Fig. 3(a) and (b) shows the variation of Q factor over the fre-uency range of 193–195 THz. It can be seen that for �scatt = 0 andscatt = 2000 m, the Q-factor is not a periodic function of frequency.oreover, in case of fixed scattering section dispersion, the Q-factor

uctuates more rapidly than for the variable scattering section dis-ersion. These fluctuations are due to the fact that the period foroth the cases is observed as the inverse DGD induced by a sin-

le scattering section. Also, for �scatt = 0, the maximum Q factor iselow the desired 11.8 dB at a number of frequency points withinhe frequency range. Whereas for �scatt = 2000 m, the maximum Q

ter with marked region at 193.1 THz frequency. (b) Eye diagram, using variablescattering section dispersion at �scatt = 2000 m after 200 km fiber, DPMD = 0.5 andDGD = 0.2 ps/km, with no timing jitterat 193.1 THz frequency.

factor is below 11.8 dB only near 194.3 THz. The results reportedare consistent with the result presented in Ref. [2].

Fig. 4(a) and (b) shows the 3D view of the dependence of Q factorfrom 193 to 195 THz. Fig. 4(a) clearly indicates that for �scatt = 0,the fluctuations are quite high within 193–195 THz. Whereas for�scatt = 2000 m, almost constant Q value has been observed for thesame operating frequency range.

Fig. 5(a) and (b) shows the variation of Q factor by varyingthe PMD coefficient from 0.1 to 1.0 ps/

√km for the fixed and

variable scattering section dispersion, respectively. It is clearlyvisible in Fig. 5(a) that for �scatt = 0 m, maximum Q value fluctu-ates between 6 and 16 dB within 0.1–0.6 ps/

√km beyond which

the value decreases drastically. Whereas Fig. 5(b) shows that for�scatt = 2000 m, the Q value is almost stable at almost 16 dB anddeteriorates only after 0.9 ps/

√km after which a sharp decline in

the Q-factor is observed.Fig. 6(a) and (b) shows the eye diagram at 193.1 THz

using �scatt = 0 m and �scatt = 2000 m after 200 km fiber andDGD = 0.2 ps/km. The better performance is due to the fact that thefixed scattering section dispersion is affected more by the timingjitter as can be clearly visualized in Fig. 6(a). The value of timingjitter for �scatt = 0 m is approximately 2.42E−17 at the user definedinstant and for variable scattering section dispersion there is notiming jitter over a one bit period. This further validates our results.

variable scattering section dispersion after 200 km fiber andDPMD = 0.5 ps/

√km has been reported in Table 1. It is obvious from

the table that maximum eye opening for fixed scattering section

1524 H. Singh, A. Sheetal / Optik 123 (2012) 1520– 1524

Table 1Comparison of various system penalties for fixed and variable scattering section dispersion at �scatt = 0 m and �scatt = 2000 m after 200 km fiber and DPMD = 0.5 ps/

√km.

Frequency (THz) Max. eye opening Q factor from min BER (dB) RMS timing jitter

�scatt = 0 m �scatt = 2000 m �scatt = 0 m �scatt = 2000 m �scatt = 0 m �scatt = 2000 m

193 0.944214 0.949274 17.9257 19.7137 1.62E−17 0193.2 0.847096 0.936916 6.54005 15.8519 0.057282 0193.4 0.862385 0.947861 7.26667 19.1796 0.05 2.42E−17193.6 0.920386 0.896331 12.5606 17.4613 0.066815 0193.8 0.893375 0.932966 9.3787 14.9179 0.01265 0194 0.902177 0.916023 10.2226 11.908 0.035935 8.08E−18194.2 0.915113 0.924625 11.7804 15.70205 0.08119 0194.4 0.66265 0.93524 2.96428 15.4416 0.142278 2.42E−17

5.06458.74064.8224

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194.6 0.782547 0.929098

194.8 0.885592 0.903383

195 0.932535 0.941715 1

s quite less than that of the variable scattering section and alsohe value of eye opening for �scatt = 0 m within frequency range94.4–194.6 THz is less than the desired 0.8 value. Further, the

factor is less than 11.8 dB at number of frequency points forscatt = 0 m, while the value reduces below it only at 194.8 THz forscatt = 2000 m. Similarly, almost negligible timing jitter is observed

or �scatt = 2000 m against the noticeable value for �scatt = 0 m, as canlso be seen in Fig. 6(a). The timing jitter value is quite large after94.8 THz.

. Conclusion

The investigation of PMD-induced penalties for 40 Gb/s duo-ianry optical transmission link, has been carried out we obtainedhe results for different values of the PMD coefficients for frequencyange from 193 to 195 THz. We concluded that PMD-induced penal-ies degrade system performance. A delay of 7 ps over 200 km fibers observed in the received signal if fixed scattering section disper-ion is considered. While for variable scattering section dispersionhis delay is compensated. Also, the Q value fluctuates more rapidlyor fixed scattering section as the period is observed as the inverseGD induced by a single scattering section between 6 and 16 dBithin 0.1–0.6 ps/

√km and quite above the desired limits up to

or 0.9 ps/√

km for fixed and variable scattering section dispersion,espectively. Further, it is concluded that the fixed scattering sec-ion dispersion is affected more by the timing jitter (2.42E−17 athe user defined instant) as compared to variable scattering sectionispersion. So we infer from the discussion of the results that theerformance of optical system with duobianry transmitter usingariable scattering section dispersion is always better than the fixedcattering section dispersion.

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[

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17.1571 0.027063 0.065611

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