parametric-gain approach to the analysis of dpsk dispersion-managed systems
DESCRIPTION
Parametric-Gain Approach to the Analysis of DPSK Dispersion-Managed Systems. 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]. Milan. Parma. Rome. - PowerPoint PPT PresentationTRANSCRIPT
Xi’an, Oct. 23, 2006
Università di Parma
A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 1/21
Parametric-Gain Approach to the Analysisof 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
Università di Parma
A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 2/21
Milan
Parma
Rome
Xi’an, Oct. 23, 2006
Università di Parma
A. Bononi, China-Italy Workshop Photon. Commun. & Sens. 3/21
Outline
Introduction
State of the Art: BER tools in DPSK transmission The PG Approach:
Key Assumptions Tools Results
Conclusions
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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.
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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 MatchedfilterSPM
only
State of the Art
[2] K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879, Sept. 2003.
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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.
State of the Art
[3] J. Wang et al., JLT, vol. 22, pp. 362-371, Feb. 2004.[4] E. Forestieri, JLT, vol. 18, pp. 1493-1503, Nov. 2000.
Tx OBPF
no SPM
LPF
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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
The PG Approach
[5] P. Serena et al., JLT, vol. 24, pp. 2026-2037, May 2006.
Tx OBPF LPF
N
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DPSK DM System
Tx OBPF LPF
N
pre post
in-line
DPSK RX
AD
DispersionMap
KL method requires Gaussian field statistics at receiver (RX), after optical filter
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0
Single spanOSNR= 25 dB/0.1nmNL = 0.15 rad
2 341
Re[E]
Im[E]
Re[E]
Im[E]
D= ps/nm/km
…but with some dispersion, PDF contours become elliptical Gaussian PDF
D
Din =0
in-line
At zero dispersion, PDF of ASE RX field before OBPF is strongly non-Gaussian [2]
Why Gaussian Field?
[2] K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879, Sept. 2003.
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Even at zero dispersion...
OSNR=10.8 dB/0.1 nm, NL=0.2, ASE BW BM=80 GHz
Red: Monte Carlo (MC)
Blue: Multicanonical MC
(MMC)
before OBPF
Why Gaussian Field?
Iafter OBPF, Bo=10 GHz
[6] A. Orlandini et al., ECOC’06, Sept. 2006.
PDF of ASE RX field AFTER OBPF Gaussianizes [6]
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Reason is that a white ASE over band BM remains white after SPM
d)t(h)(w)t(nOBPFw(t) n(t)
h(t)
SPM
If optical filter bandwidth Bo << BM, n(t) is the sum of many comparable-size independent samples
Gaussian whatever the input noise distribution
Central Limit Theorem
Why Gaussian Field?
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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
L in ea rize d N L S E
C Wt
C Wt
Small perturbation
Rx ASE is Gaussian
DM, finite N spans
[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, infinite spans
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Red : quadrature ASE
Blue: in-phase ASE
»
No pre-, post-comp.
Linear PG Model
Parametric Gain =
Gain (dB) over white-ASE case
due to Parametric interaction
signal-ASE
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Limits of Linear PG Model
NL=0.55 radD=8 ps/nm/km, Din=0
linear PG model (dashed) versus Monte-Carlo BPM simulation (solid)
/0.1 nm /0.1 nm
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@ PG doublingstrengths for 10 Gb/s NRZ
For fixed OSNR (e.g. 15dB) in region well below red PG-doubling curve:
Linear PG model holds ASE ~ Gaussian
15 17
19
21
15
1
DM systemswith Din=0.
( N>>1 spans)
0 0.2 0.4 0.6 0.8Map strength S ( DR2 )
0
0.2
0.4
0.6
0.8
1
1.2
1.4
NL [r
ad/
]end-line OSNR (dB/0.1nm)
[10] P.Serena et al., JLT, vol. 23, pp. 2352-2363, Aug. 2005.
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Steps of our semi-analytical BER evaluation algorithm:
Our BER 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 NL) or estimated off-line from Monte-Carlo BPM simulations (large NL). Reference NL 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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Check with experimental results [H. Kim et al., PTL, Feb. ’03]
NRZ RZ-33%
Exp.Theory
10 Gb/s single-channel system, 6100 km NZDSF
Results
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RZ-DPSK 50%
NRZ-DPSK
NRZ-OOK
Results
R=10 Gb/s single-channel, 20100 km, D=8 ps/nm/km, Din=0. OSNR=11 dB/0.1 nm, Bo=1.8R
Noiseless optimized Dpre, Dpost
1E-9
1E-4
1E-2
BE
R
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Results
DPSK-NRZ DPSK-RZ (50%)
10 Gb/s single-channel system, 20100 km, Din=0. Bo=1.8R . Noiseless optimized Dpre, Dpost.
@ D=8 ps/nm/km
Strength ( DR2) Strength ( DR2)
PG
no PG
ΦNL=0.1
ΦNL=0.3
ΦNL=0.5
ΦNL=0.5
ΦNL=0.3
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More information on our work:
www.tlc.unipr.it
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.