Università di Parma
Parametric-Gain Approach to the Analysis
of DPSK Dispersion-Managed Systems
A. Bononi, P. Serena, A. Orlandini, and N. Rossi
Dipartimento di Ingegneria dell’Informazione, Università di Parma
Viale degli Usberti, 181A, 43100 Parma, Italy
e-mail: [email protected]
Xi’an, Oct. 23, 2006
A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 1/21
Università di Parma
Milan
Parma
Rome
Xi’an, Oct. 23, 2006
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Outline
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
Introduction
State of the Art: BER tools in DPSK transmission
 The PG Approach:
 Key Assumptions
 Tools
 Results
 Conclusions

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Introduction
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 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.
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State of the Art
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 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
Tx
SPM
only
Matched
filter
[2] K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879, Sept. 2003.
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State of the Art
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 Wang and Kahn [3] computed the exact BER for DPSK (but
provided no algorithm details) using Forestieri’s 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.
Tx
OBPF
LPF
no SPM
[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
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 Also our group [5] computed the BER for DPSK using
Forestieri’s 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
N
Tx
OBPF
LPF
[5] P. Serena et al., JLT, vol. 24, pp. 2026-2037, May 2006.
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DPSK DM System
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DPSK RX
N
in-line
Tx
OBPF
post
pre
D
A
LPF
Dispersion
Map
 KL method requires
Gaussian field statistics
at receiver (RX), after
optical filter
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Why Gaussian Field?
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 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
Im[E]
Im[E]
0412
D= 3
ps/nm/km
in-line
Re[E]
D
Re[E]
Din =0
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?
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 Even at zero
dispersion...PDF of ASE RX field AFTER OBPF Gaussianizes [6]
before OBPF
Iafter OBPF, Bo=10 GHz
Red: Monte Carlo (MC)
Blue: Multicanonical MC
(MMC)
OSNR=10.8 dB/0.1 nm, FNL=0.2p, ASE BW BM=80 GHz
[6] A. Orlandini et al., ECOC’06, Sept. 2006.
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Why Gaussian Field?
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Reason is that a white ASE over band BM remains white after SPM
h(t)
w(t)
SPM

n(t)
OBPF
n( t ) 
 w(  )h( t   )d

If optical filter bandwidth Bo << BM, n(t) is the sum of many
comparable-size independent samples
Central Limit
Theorem
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Gaussian whatever the
input noise distribution
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 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.
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Linear PG Model
Linearized NLSE
CW
Rx ASE is
Gaussian
CW
t
t
Small perturbation
[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
DM, finite N spans
[5] P. Serena et al., JLT, vol. 24, pp. 2026-2037, May 2006.
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DM, infinite spans
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Linear PG Model
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No pre-, post-comp.
Red : quadrature ASE
»
Blue: in-phase ASE
Parametric Gain =
Gain (dB) over white-ASE case
due to Parametric interaction
signal-ASE
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Limits of Linear PG Model
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linear PG model (dashed) versus Monte-Carlo BPM simulation (solid)
FNL= 0.55 p rad, D=8 ps/nm/km, Din=0
/0.1 nm
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/0.1 nm
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@ PG doubling
strengths for
10 Gb/s NRZ
end-line OSNR (dB/0.1nm)
1.4
21
F [rad/p]
NL
1.2
DM systems
with Din=0.
( N>>1 spans)
19
17
15
1
0.8
For fixed OSNR (e.g. 15dB)
in region well below red
PG-doubling curve:
 Linear PG model holds
 ASE ~ Gaussian
0.6
0.4
0.2
00
0.2
0.4
0.6
0.8
Map strength S 
(
DR2 )
1
[10] P.Serena et al., JLT, vol. 23, pp. 2352-2363, Aug. 2005.
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Our BER Algorithm
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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 Forestieri’s KL BER evaluation
algorithm, suitably adapted to DPSK.
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Results
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
Check with experimental results [H. Kim et al., PTL, Feb. ’03]
10 Gb/s single-channel system, 6100 km NZDSF
NRZ
RZ-33%
Theory
Exp.
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Results
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R=10 Gb/s single-channel, 20100 km, D=8 ps/nm/km, Din=0. OSNR=11 dB/0.1 nm, Bo=1.8R
Noiseless optimized Dpre, Dpost
NRZ-DPSK
1E-9
BER
1E-4
1E-2
NRZ-OOK
RZ-DPSK 50%
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Results
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10 Gb/s single-channel system, 20100 km, Din=0. Bo=1.8R . Noiseless optimized Dpre, Dpost.
DPSK-NRZ
DPSK-RZ (50%)
@ D=8 ps/nm/km
PG
no PG
ΦNL=0.5p
ΦNL=0.5p
ΦNL=0.3p
ΦNL=0.1p
Strength (  DR2)
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ΦNL=0.3p
Strength (  DR2)
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Conclusions
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 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.
More information on our work:
www.tlc.unipr.it
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