Calculation of error probability in WDM RZ systems in the presence of bitpatterndependent nonlinear

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Calculation of error probability in WDM RZ
systems in the presence of bit-pattern-dependent
nonlinear impairments and of noise
Oleg V. Sinkin
Department of Computer Science and Electrical
Engineering University of Maryland Baltimore
County
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My collaborators
University of Maryland Baltimore
County Vladimir S. Grigoryan Ronald
Holzlöhner Brian Marks Curtis R.
Menyuk John Zweck University of Colorado Mark
Ablowitz Cory Ahrens Andrew Docherty
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Calculation of BER in simulations
NL-limited
Linear impairments
BER
Input power
Problem Nonlinear penalty is a statistical effect
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Nonlinear interchannel bit-pattern dependency
Simulation results with the same bit pattern in
the center channel but different bit patterns in
the other channels
pattern 1 pattern 2 pattern 3
??50 GHz L5000 km
Nonlinear penalty is bit-pattern dependent
E
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How to model the pattern dependence

• NLS with PRBS in each channel (single
  realization)
• Common and simplest approach
• Accuracy not guaranteed
• NLS Monte-Carlo simulations
• Accurate Q
• Accurate BER with biased simulations
• Time-consuming
• Reduced deterministic methods
• Physical understanding
• System-specific

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Previous work NRZ
XPM-induced penalty Small signal analysis
Cartaxo Hui

• Additive perturbation
• Distortion for given waveforms
• White noise assumption for Q
• Neglects signal dispersion

Ciaramella

• Multiplicative perturbation
• Distortion for given waveforms
• Includes signal dispersion

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Previous work RZ
Shapiro

• Unbiased Monte-Carlo
• Q calculations
• Different pattern lengths

• Collision-induced timing jitter
• Soliton or quasilinear systems
• Jitter calculation

Jenkins Ablowitz Grigoryan
Xu

• Time shifts in soliton collisions
• Worst pattern calculation

BER has not been accurately calculated
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Nonlinear penalty Probabilistic model

• Sample space
• Set of all bit realizations in all WDM channels
• Random variable of interest
• Received current in the target channel

GOAL Compute the pdf of the current and BER

• Biased Monte Carlo simulations
• Reduced deterministic method

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Model of transmission system

• Propagation distance 5000 km
• D /D fibers (OFS Fitel)
• Channel bit rate 10 Gb/s
• 9 WDM channels, ?? 50 GHz
• 32 bits/channel

ltDgt-0.5 ps/nm-km
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Motivation

• Observation

XPM-induced timing jitter dominates in RZ systems

• Monte Carlo Simulations

Noise-free eye
E
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Time shift calculations
Goal time shift of the target pulse

• Assumptions
• Time shifts are additive
• Collisions are elastic

Grigoryan and Richter, J. Lightwave Technol.
No.8, 2000 Ahrens et al.,Optics Lett., No.1, 2006
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Time shift calculations
Collision-induced frequency and time shifts
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Calculations of time shift PDF
Assumptions
Uncorrelated data and
(in principle, we can use any PDF of )
Time shift Linear combination of independent
random variables
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Calculations of the PDF
Characteristic function
Time shift PDF
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Distribution of the time shift
Characteristic function Gaussian IS Monte Carlo
PDF
105 Importance-sampled Monte Carlo simulations
Time shift (ps)
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Distribution of received current of marks
Nonlinearity only, no noise
PDF
105 Importance-sampled Monte Carlo simulations
0 0.2 0.4 0.6 0.8 1.0
Relative current of marks (a.u.)
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BER in presence of noise and nonlinearity

• Compute and convolve with time
  shift PDF

BER5.81012 BER3.31015
PDF
0 0.2 0.4 0.6 0.8 1.0
Relative current of marks (a.u.)
Forestieri, J. Lightwave Technol. No.11, 2000
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Multi-pulse interactions (unpublished)
Random sequences in the target channel
IS Monte Carlo Nonlinearity only, no noise
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Multi-pulse interactions Results
Nonlinearity only, no noise
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How good is the Gaussian approximation?
PDF
Time shift (ps)
Characteristic function Gaussian IS Monte Carlo
Gaussian approximation works well for BER and Q
but the exact PDF calculation can be important
and should be used
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Summary

• Accurately characterized data-dependent penalties
  induced by inter-channel XPM using
• Deterministic method
• Statistical method (biased Monte Carlo)
• Deterministically calculated BER in presence of
  nonlinearity and ASE noise

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References
1. A. Cartaxo, J. Lightwave Technol. 17, 178-190
(1999). 2. R. Hui, K. R. Demarest, and C. T.
Allen, J. Lightwave Technol. 17, 1018-1026
(1999). 3. H. J. Thiele, R. I. Killey, and P.
Bayvel, Electron. Lett. 35, 408-409 (1999). 4. E.
G. Shapiro, M. P. Fedoruk, and S. K. Turitsyn,
Electron. Lett. 37, 1179-1181 (2001). 5. Z. Jiang
and F. Chongcheng, J. Lightwave Technol. 21,
953-960 (2003). 6. H. Sugahara, H. Kato, T.
Inoue, A. Maruta, and Y. Kodama, J. Lightwave
Technol. 17, 1547-1559 (1999). 7. V. S. Grigoryan
and A. Richter, J. Lightwave Technol. 18,
1148-1154 (2000). 8. E. A. Golovchenko, A. N.
Pilipetskii, N. S. Bergano, C. R. Davidson, F. I.
Khatri, R. M. Kimball, and V. J. Mazurczyk in J.
Sel. Topics Quantum Electronics. 6, 337-347. 9.
O. V. Sinkin, V. S. Grigoryan, R. Holzlohner, A.
Kalra, J. Zweck, and C. R. Menyuk, in Optical
Fiber Communication Conference Vol. 95 of OSA
Optics and Photonics Trends Series (Optical
Society of America, 2004), Paper TuN4. 10. O. V.
Sinkin, V. S. Grigoryan, J. Zweck, C. R. Menyuk,
A. Docherty, and M. Ablowitz, Opt. Lett. 30,
2056-2058 (2005). 11. E. Forestieri, J. Lightwave
Technol. 18, 1493-1503 (2000). 12. C. Ahrens, M.
J. Ablowitz, A. Docherty, O. V. Sinkin, J. Zweck,
V. S. Grigoryan, and C. R. Menyuk, Opt. Lett. 31,
5-7 (2006).
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Extras Deterministic approach

• Idea
• Compute PDF of the time shift
• Convert time shift to received current

received current i(t)
?T
shifted pulse
I(?T)i(t ?T)
I(?T)
t
E
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Monte Carlo simulations
Rx current histogram
Nonlinear transmission
Random input
b
01110...101
10101...011
Center channel fixed
00..01000
11100...010
0111...100
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Monte Carlo simulations
Rx current histogram
Nonlinear transmission
Random input
b
01110...101
10101...011
11100...010
0111...100
00..01000
Center channel fixed
Standard Monte Carlo
Tails of the histogram are undersampled
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Multicanonical Monte Carlo method
Rx current histogram
Nonlinear transmission
Random input
H
All histogram bins have a sizable hit count
Berg and Neuhaus, Phys. Rev. Lett., No.1, 1992