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1636IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 15, NO. 11, NOVEMBER 2003

Numerical Simulation of the SPM Penalty in a

10-Gb/s RZ-DPSK System

Xing Wei, Xiang Liu, and Chris Xu

Abstract—The impact of self-phase modulation-induced non-

linear phase noise in a 10-Gb/s return-to-zero differential phase-

shift keying system is studied by numerical simulation. We show

that the simple differential phase

approximation for the phase noise provides a relatively good esti-

mate of the nonlinear penalty.

method based on the Gaussian

Index Terms—Bit-error rate (BER), differential phase-shift

keying (DPSK), optical communication, self-phase modulation

(SPM).

I. INTRODUCTION

T

much attention for high-speed long-haul and ultralong-haul

optical transmission. Experiments have been carried out at

40-Gb/s [1], [2] and 10-Gb/s [3]–[6] bit rates. Numerical

simulations have also been reported [7]–[10]. One limiting

factor in long-haul and ultralong-haul DPSK systems is the

Gordon–Mollenauer nonlinear phase noise (or phase jitter)

which arises from the interaction between amplified sponta-

neous emission (ASE) noise and self-phase modulation (SPM)

[11], [12]. This effect has been studied experimentally [5],

[6]. In numerical simulations, however, a simple and reliable

method to assess the phase-noise penalty in DPSK systems

remains an unsolved issue. In this letter, we study the SPM

penalty in a single-channel 10-Gb/s RZ-DPSK system by nu-

merical simulation. Furthermore, we propose a simple method

for bit-error-rate (BER) estimation, which takes into account

the effect of phase noise.

HE

(RZ-DPSK) modulation format has recently attracted

return-to-zerodifferentialphase-shift keying

II. SIMULATION DETAILS

The RZ-DPSK system used for the simulation is illustrated

in Fig. 1. The transmitter consists of a continuous-wave laser,

a 33% duty cycle optical pulse generator, a 10-Gb/s input

pseudorandom bit sequence (PRBS) of length

ential encoder, and a Mach–Zehnder modulator to modulate

the phases of the optical pulses. Predispersion compensation

of

100 ps nm is used before transmission. The RZ-DPSK

signal is then transmitted over an optical link made of 40 fiber

spans separated by erbium-doped fiber amplifiers (EDFAs) and

, a differ-

Manuscript received March 10, 2003; revised June 18, 2003.

X. Wei is with Bell Laboratories, Lucent Technologies, Murray Hill, NJ

07974 USA (e-mail: xingwei@lucent.com).

X. Liu is with Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733

USA.

C. Xu is with the Applied and Engineering Physics Department, Cornell Uni-

versity, Ithaca, NY 14853 USA.

Digital Object Identifier 10.1109/LPT.2003.818664

dispersion compensating fibers (DCFs). Each span consists

of an EDFA to boost the optical power to the desired launch

power, 100 km of nonzero dispersion-shifted fiber (NZDSF)

with a dispersion of 4 ps/nm km, a DCF to compensate 95%

of the dispersion of the NZDSF (20-ps/nm residual dispersion

per span), and a second EDFA before the DCF to partially

compensate for the span loss. The last DCF has an additional

dispersion of

350 ps nm to bring the total residual dispersion

of the link to 350 ps/nm. The loss of the NZDSF is 0.23 dB/km,

and the nonlinear coefficient is 1.6 rad/W km. For simplicity,

the fiber birefringence and the nonlinearity of the DCF are

neglected since they would not change our general conclusion

in a significant way. On the receiver side, the signal is filtered

by a Gaussian optical bandpass filter (BPF) with a 3-dB

bandwidth of 15 GHz to remove the ASE noise power outside

the signal bandwidth. The filtered optical signal is detected by

a delay interferometer and a balanced receiver. All the receiver

filtering is performed in the optical domain and no electrical

filter is used. All components in the transmitter and the receiver

are assumed to be ideal.

When the ASE is included in the simulations, we use a noise

figure (NF) of 7 dB for the EDFAs. We note that the NF of

state-of-the-art EDFAs can be less than 5 dB. We intentionally

use a larger NF because this allows for direct counting of the

errors in the simulation (for BER higher than

sumptions on the noise probability density function (pdf) at the

receiver. Depending on the BER level, it is sometimes neces-

sarytorepeatthesimulationforhundredsoftimeswithdifferent

ASE noise to achieve sufficient accuracy for one BER value. It

is alsocrucial that theASE is loaded alongthetransmission link

rather than only at the receiver. It is known that the noise distri-

bution at the receiver can be distorted due to nonlinear interac-

tion between the signal and noise, and this may have a more no-

ticeable effect in DPSK systems than in ON–OFF keying (OOK)

systems because of the Gordon–Mollenauer phase-noise effect

[5].

) without as-

III. RESULTS AND DISCUSSION

Fig. 2 shows the BER as a function of the launch power. The

solid square symbols are obtained from direct error counting in

thesimulation, and theopen symbols are obtained from two dif-

ferent models that will be explained later. The directly counted

BER results in Fig. 2 show that the optimum launch power of

this RZ-DPSK system is around

power, the system performance degrades due to fiber nonlin-

earity. Note that if the transmission system were linear, a 6-dB

increase in power (from

7 to

from

to below

3 dBm. With higher launch

1 dBm) would bring the BER

. The fact that the BER with

1041-1135/03$17.00 © 2003 IEEE

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WEI et al.: NUMERICAL SIMULATION OF THE SPM PENALTY IN A 10-Gb/s RZ-DPSK SYSTEM1637

Fig. 1.Schematic diagram of the RZ-DPSK transmission system.

Fig. 2.

(b) estimation using the conventional ? factor method, and (c) estimation

using the differential phase ? method.

BER obtained from different methods: (a) direct error counting,

1-dBm launch power is on the order of

nonlinear penalty is very large at this power level. Since the

pulse overlap is not significant in this system, the dominating

source of nonlinear penalty is SPM.

Based on a simplifiedmodel, [11] predicted that theoptimum

power in a DPSK system corresponds to a total SPM phase

shift of

1 radian. This can now be verified directly with our

simulation. The loss of the fiber 0.23 dB/km corresponds to

an effective nonlinear length of approximately 19 km in each

span. With the optimum launch power

the average SPM phase shift at the end of the transmission is

rad W kmkm

SPM phase shift at the center of a pulse should be somewhat

larger. This agrees quite well with the prediction of [11].

Although the direct error counting is proven effective to esti-

mate the SPM penalty, it is rather time-consuming and still not

practical for a BER on the order of

tive methods which can provide a quick estimate of the system

performance under different conditions will be useful. In sim-

ulations of OOK systems, it is a common practice to exclude

ASE and evaluate the eye-closure penalty as an indication of

nonlinear effects. We shall now show that this approach may

lead to erroneous result for DPSK systems. We have simulated

the balanced electrical eye diagrams (Fig. 3) at different launch

powers with the ASE noise excluded. With

power, no eye-closure degradation is observed. From these eye

diagrams, it appears that SPM may actually help “open up” the

eye by counteracting the effect of the residual chromatic disper-

sion, which is known as the “soliton” effect. Here, the eye-clo-

sure methodhas completelyfailed topredicttheSPM penaltyin

this RZ-DPSK system. A simple explanation for this is that the

Gordon–Mollenauer phase noise arises from the interaction be-

tween the ASE noise and SPM, and therefore, it does not show

up in a simulation without ASE.

shows that the

3 dBm or 0.5 mW,

mWrad, and the

. Therefore, alterna-

1-dBm launch

Fig. 3.

?7 dBm (left), ?4 dBm (middle), and ?1 dBm (right). The vertical scale is

normalized with the launch power.

Eye diagrams from the balanced receiver with launch powers of

One may also consider to plot these eye diagrams with the

ASE noise included (not shown) and estimate the BER from the

“

factor” through

BER

(1)

It is known that this

estimate of the BER in OOK system simulations although the

noisedistributionafterthesquare-lawdetectionisnotGaussian.

We find, however, this method has also failed to predict the

SPM penalty, as shown by the open triangles in Fig. 2. This

method underestimates the system performance in the linear

regime and overestimates the performance in the highly non-

linear regime. No significant nonlinear penalty is observed even

with the highest launch power

dicts the result from direct error counting. This large discrep-

ancy is due to the fundamentally non-Gaussian nature of the

pdf of the receiver output signal. Therefore, the conventional

factor method should also be avoided in numerical simulations

of RZ-DPSK systems.

We find, however, that a slightly modified model can be used

to estimate the SPM penalty in such an RZ-DPSK system. We

still use the

factor concept but it is now definedfor theoptical

phase of the received signal. Fig. 4 shows a “differential phase”

eye diagram of the received RZ-DPSK signal after the 15-GHz

optical BPF. The “differential phase” is the phase difference be-

tween two sampling points separated by one bit period mapped

to the range of

to. In Fig. 4, the center of the bit

slot is located at 50 ps (or 150 ps) and the divergence of the dif-

ferential phase at 100 ps is due to the fact that the intensity of

the light signal is nearly zero. We then assume a Gaussian dis-

tribution for the noise at the center of each bit slot and define a

differential phase

as

factor method usually gives a fairly good

1 dBm, which strongly contra-

(2)

where

differential phase on the 0 and

andrepresent the standard deviations of the

rails, respectively.

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1638IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 15, NO. 11, NOVEMBER 2003

Fig. 4.Differential phase eye diagram with a launch power of ?3 dBm.

The open circles in Fig. 2 are obtained from the expression

BER

(3)

which can be derived from the Gaussian approximation for the

differential phase noise. We find that (3) qualitatively repro-

duces the result obtained from the direct error counting method,

and in particular, (3) predicts the optimum launch power quite

accurately.Thereisarelativelysmallyetnoticeablediscrepancy

between the BER values obtained from the direct error counting

and the differential phase

methods. This is understandable

because the pdf of the differential phase noise in the received

signal is not exactly Gaussian.

IV. CONCLUSION

We have shown that the Gordon–Mollenauer nonlinear phase

noise must be taken into account in numerical simulations of

RZ-DPSK systems in which such phase noise is the dominating

source of nonlinear penalty. A simplified model based on the

differential phase

appears to provide a relatively good esti-

mate of such nonlinear penalty. Compared with the direct error

counting method, the differential phase

the computation time tremendously.

method can reduce

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