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1
Parametric-Gain Approach to the Analysis of DPSK
Dispersion-Managed Systems

• Bononi, P. Serena, A. Orlandini, and N. Rossi
• Dipartimento di Ingegneria dellInformazione,
  Università di Parma
• Viale degli Usberti, 181A, 43100 Parma, Italy
• e-mail bononi_at_tlc.unipr.it

2
Milan
Parma
Rome
3
Outline

• Introduction
• State of the Art BER tools in DPSK transmission
• The PG Approach
• Key Assumptions
• Tools
• Results
• Conclusions

4
Introduction

• Amplified spontaneous emission (ASE) noise from
  optical amplifiers makes the propagating field
  intensity time-dependent even in
  constant-envelope modulation formats such as
  DPSK.
• Random intensity fluctuations, through
  self-phase modulation (SPM), cause nonlinear
  phase noise 1, which is the dominant impairment
  in single-channel DPSK.
• Most existing analytical models focus on the
  statistics of the nonlinear phase noise.

1 J. Gordon et al., Opt. Lett., vol. 15, pp.
1351-1353, Dec. 1990.
5
State of the Art

• K.-Po Ho 2 computed the probability density
  function (PDF) of nonlinear phase noise and
  derived a BER expression for DPSK systems with
  optical delay demodulation. Very elegant work,
  but
• model assumes zero chromatic dispersion (GVD)
• does not account for the impact of practical
  optical/electrical filters on both signal and ASE

2 K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879,
Sept. 2003.
6
State of the Art

• Wang and Kahn 3 computed the exact BER for
  DPSK (but provided no algorithm details) using
  Forestieris Karhunen-Loeve (KL) method 4 for
  quadratic receivers in Gaussian noise
• Model accounts for impact of practical
  optical/electrical filters on both signal and ASE
• ....but ignores nonlinearity it concentrates on
  GVD only.

3 J. Wang et al., JLT, vol. 22, pp. 362-371,
Feb. 2004. 4 E. Forestieri, JLT, vol. 18, pp.
1493-1503, Nov. 2000.
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The PG Approach

• Also our group 5 computed the BER for DPSK
  using Forestieris KL method. Our model
• besides accounting for impact of practical
  optical/electrical filters
• also accounts for the interplay of GVD and
  nonlinearity, including the signal-ASE nonlinear
  interaction using the tools developed in the
  study of parametric gain (PG)
• is tailored to dispersion-managed (DM) long-haul
  systems

5 P. Serena et al., JLT, vol. 24, pp.
2026-2037, May 2006.
8
DPSK DM System

• KL method requires Gaussian field statistics at
  receiver (RX), after optical filter

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Why Gaussian Field?

• At zero dispersion, PDF of ASE RX field before
  OBPF is strongly non-Gaussian 2

but with some dispersion, PDF contours become
elliptical ? Gaussian PDF
ImE
ImE
2
3
4
0
1

D
ReE
ReE
Single span OSNR 25 dB/0.1nm FNL 0.15p rad
2 K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879,
Sept. 2003.
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Why Gaussian Field?

• Even at zero dispersion...

PDF of ASE RX field AFTER OBPF Gaussianizes 6
before OBPF
Red Monte Carlo (MC) Blue Multicanonical MC
(MMC)

• OSNR10.8 dB/0.1 nm, FNL0.2p, ASE BW BM80 GHz

11
Why Gaussian Field?
Reason is that a white ASE over band BM remains
white after SPM
h(t)
w(t)
n(t)
OBPF
SPM
12

• Having shown the plausibility of the Gaussian
  assumption for the RX field, it is now enough to
  evaluate its power spectral density (PSD) to get
  all the needed information, to be passed to the
  KL BER routine.
• A linearization of the dispersion-managed
  nonlinear Schroedinger equation (DM-NLSE) around
  the signal provides the desired PSDs, according
  to the theory of parametric gain.

13
Linear PG Model
7 C. Lorattanasane et al., JQE, July 1997 8
A. Carena et al., PTL, Apr. 1997 9 M. Midrio
et al., JOSA B, Nov. 1998 5 P. Serena et al.,
JLT, vol. 24, pp. 2026-2037, May 2006.
DM, finite N spans
DM, infinite spans
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Linear PG Model
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Limits of Linear PG Model

• linear PG model (dashed) versus Monte-Carlo BPM
  simulation (solid)

FNL 0.55 p rad, D8 ps/nm/km, Din0
/0.1 nm
/0.1 nm
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_at_ PG doubling
strengths for 10 Gb/s NRZ
end-line OSNR (dB/0.1nm)
DM systems with Din0. ( Ngtgt1 spans)
1.4
21
1.2
19
17
1

p
15
15
0.8
rad/

• For fixed OSNR (e.g. 15dB) in region well below
  red PG-doubling curve
• Linear PG model holds
• ASE Gaussian

NL
F
0.6
0.4
0.2
0
1
0
0.2
0.4
0.6
0.8
Map strength S ( DR2 )

10 P.Serena et al., JLT, vol. 23, pp.
2352-2363, Aug. 2005.
17
Our BER Algorithm
Steps of our semi-analytical BER evaluation
algorithm

1. Rx DPSK signal obtained by noiseless BPM
   propagation (includes ISI from DM line)
2. ASE at RX assumed Gaussian. PSD obtained either
   from linear PG model (small FNL) or estimated
   off-line from Monte-Carlo BPM simulations (large
   FNL). Reference FNL for PSD computation suitably
   decreased from peak value to average value for
   increasing transmission fiber dispersion (map
   strength).
3. Data from steps 1, 2 passed to Forestieris KL
   BER evaluation algorithm, suitably adapted to
   DPSK.

18
Results

• Check with experimental results H. Kim et al.,
  PTL, Feb. 03

10 Gb/s single-channel system, 6?100 km NZDSF
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Results
R10 Gb/s single-channel, 20?100 km, D8
ps/nm/km, Din0. OSNR11 dB/0.1 nm, Bo1.8R
Noiseless optimized Dpre, Dpost
1E-9
BER
1E-4
1E-2
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Results
10 Gb/s single-channel system, 20?100 km, Din0.
Bo1.8R . Noiseless optimized Dpre, Dpost.
DPSK-NRZ
DPSK-RZ (50)
_at_ D8 ps/nm/km
PG
no PG
FNL0.5?
FNL0.5?
FNL0.3?
FNL0.1?
FNL0.3?

Strength ( DR2)

Strength ( DR2)
21
Conclusions

• Novel semi-analytical method for BER estimation
  in DPSK DM optical systems.
• The striking difference between OOK and DPSK is
  that in DPSK PG impairs the system at much lower
  nonlinear phases, when the linear PG model still
  holds. Hence for penalties up to 3 dB one can
  use the analytic ASE PSDs from the linear PG
  model instead of the time-consuming off-line MC
  PSD estimation.
• Hence our mehod provides a fast and effective
  tool in the optimization of maps for DPSK DM
  systems.