Partially Polarized Noise in

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Partially Polarized Noise in Optical Fiber
Communications Systems Curtis R.
Menyuk Department of Computer Science and
Electrical Engineering University of Maryland
Baltimore County
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Based on the Ph.D. dissertations of Yu Sun
(Optium Corporation) and Ivan Lima (U. North
Dakota - Fargo) With important input from G. M.
Carter, A. O. Lima, D. Wang, L. Yan, J.
Zweck And special thanks to P. Runge, F.
Kerfoot (ATT-Bell Labs Tyco) D. Chernin, A.
Mondelli (SAIC)
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Introduction

• Work presented is based on two observations
• In academic work TRANSMISSION
  receivertransmission effects get most of the
  attention
• In the real world transmission
  RECEIVERaccurately modeling the receiver is more
  important

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Introduction

• Work presented is based on two observations
• Full time-domain modeling of polarization effects
  is
• too slow
• many WDM channels must be kept to take into
  account amplifier effects
• many realizations must be run to take into
  account statistical effects
• often not necessary
• polarization effects are independent of
  nonlinearity and dispersion

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Introduction

• We introduce a reduced Stokes parameter
  modelwith the following features
• Four Stokes parameters are kept for signal and
  noise for every WDM channel
• nonlinearity and dispersion in transmission is
  neglected
• the noise Stokes parameters are random variables
  (means)
• the AWGN assumption is used for the optical
  power distribution

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Introduction

• We introduce a reduced Stokes parameter
  modelwith the following features
• The receiver is modeled accurately
• The pulse shape prior to the receiver is needed
• nonlinearity and dispersion are taken into
  account here
• Excellent agreement between theory and experiment
  is obtained!

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Polarization effects
Polarization effects
T1
G1
EDFA
G2
T2
T1
Input pulse
T2
Output pulse
Polarization dependent loss (PDL)
Polarization dependent gain (PDG)
Polarization mode dispersion (PMD)
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Polarization representation
Stokes Parameters
Degree of polarization
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Receiver structure

• This model is appropriate for digital systems
  with optical noise loading !

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System performance measures

• Often cited, BUT in many cases is really BER

How are they related?
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Receiver performance measures

• Receiver Sensitivity

• The minimum average signal
• power to achieve a BER 10 ?9

How is it related to other performance measures?
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Receiver modeling
Marcuse / Humblet-Azizoglu Model

• Flat-top optical bandpass filter
• Integrate-and-dump receiver
• Additive Gaussian white optical noise input

Probability distributions for the spaces and the
marks
These distributions are special cases of
chi-square distributions!
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Receiver Modeling

• ESNR electrical
  signal-to-noise ratio IS signal

B optical bandwidth T bit period
BOSA Bandwidth of optical spectrum analyzer
Then ESNR ? OSNR (BOSA/B), which relates
OSNR to Q

• Optimal current threshold and minimum BER cannot
  be analytically determined

BUT
A Gaussian approximation is often used
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Gaussian approximation
10 0
The Gaussian approximation yields poor results
for the threshold Good results for the
sensitivity
spaces
marks
BUT
Chi-square distributions
probability density
Maxwellian distributions
Two errors fortuitously cancel!
10-12
1
0
Voltage (a.u.)

• The results are independent of pulse shape and
  uniquely relate

OSNR Q BER
This is no longer true with realistic filters and
partial polarization

• This model extends easily to finite extinction
  ratios (with BOSA B)

,
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Accurate formula for the Q-factor
signal normalized Stokes vector,
signal normalized Stokes vector
The parameters ? and ? depend on the format and
the receiver
Noise co-polarized with signal
Unpolarized noise
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Accurate formula for the Q-factor
There is a large advantage to maximizing this
number! Hence, most of the advantage of RZ in
undersea systems
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Back-to-back experimental setup
10 Gb/s RZ 215 1 PRBS
Transmitter
BERT
Receiver
Attenuator
OSA
PC
Polarization Analyzer
Polarizer
ASE source 1
ASE source 2
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Variation of the Q-factor
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SNR 10.9 dB
measured DOPn 0.95
measured DOPn 0.5
Q
theoretical DOPn 0.95
theoretical DOPn 0.5
5
-1
1
Q varies with the angle between SOPs of signal
and noise There is less variation in Q for
smaller DOPn
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Distribution of the Q-factor
For fixed SNR and DOPn
Qmin Stokes vectors of signal and noise are
parallel Qmax Stokes vectors of signal and
noise are antiparallel
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Distribution of the Q-factor
0.4
DOPn 0.5 SNR 10.9 dB
pdf
0
10
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Q
The sharp cut-offs are at Qmax and Qmin
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Recirculating loop setup
SMF
S
D
DSF
Input scrambler
Polarization controller
IS
Loop-synchronous scrambler
LSS
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Degree of polarization evolution
measured DOP, PDL 0.22 dB
simulated DOP, PDL 0.2 dB
These curves are for the best performance
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Q factor distribution at 5,000 km
experimental result
simulated loop result
simulated straight line
Q
The loop experiment can overestimate the
performance of a line system.
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Q-factor distribution at 10,000 km
scrambled
2.5
with input scrambler
PDL 0.2 dB/round trip
no input scrambler
pdf
simulation
0
3
10
Q
With loop scrambling, the Q distribution
resembles that of a straight line
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Q-factor distribution at 10,000 km
PDL 0.6 dB/round trip
scrambled
1
with input scrambler
Simulation using a receiver that takes into
account the partially polarized noise
no input scrambler
pdf
0
1
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Q
The Q-factor distribution is asymmetric when
large PDL polarizes the noise
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Q-factor distribution at 10,000 km
PDL 0.6 dB/round trip
scrambled
1
with input scrambler
Simulation using a receiver that takes into
account the partially polarized noise
no input scrambler
pdf
Simulation assuming unpolarized noise at the
receiver
0
1
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Q
The Q-factor distribution is asymmetric when
large PDL polarizes the noise
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Conclusion

• Receiver model MUST account for partially
  polarized noise
• The noise polarization can be found accurately
  using a reduced Stokes parameter model
• The relation of OSNR ? Q ? BER is no longer unique

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Stokes Model
Jones representation of a WDM system with n
channels
Stokes parameters
where T is large.
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Stokes Model
PMD evolution in fibers Coarse step method

• Divide fiber segment into sections of length ? (
  50)
• Section is large compared to the
  correlation length
• Calculate in each section

wavelength dependent rotation
random rotation between steps
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Stokes Model
PMD evolution in fibers Coarse step method
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Stokes Model
Except one operates on the Jones vectors
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Stokes Model
The effect of PDL element
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Stokes Model
The EDFA module

• The effect of PDG

where

• ASE noise addition

• Gain saturation keep the output power constant

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Derivation of Receiver Model
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Derivation of Receiver Model
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Derivation of Receiver Model
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Derivation of Receiver Model
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Derivation of Receiver Model
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Derivation of Receiver Model