parametric-gain approach to the analysis of dpsk dispersion-managed systems

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



Milan

Parma

Rome

Xi’an, Oct. 23, 2006



Outline

Introduction

State of the Art: BER tools in DPSK transmission The PG Approach:

Key Assumptions Tools Results

Conclusions

Xi’an, Oct. 23, 2006



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.

Xi’an, Oct. 23, 2006



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.

Xi’an, Oct. 23, 2006



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

Xi’an, Oct. 23, 2006



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

Xi’an, Oct. 23, 2006



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

Xi’an, Oct. 23, 2006



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?

Xi’an, Oct. 23, 2006



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.

Xi’an, Oct. 23, 2006



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.

Xi’an, Oct. 23, 2006



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.

Xi’an, Oct. 23, 2006



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

Xi’an, Oct. 23, 2006



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

Xi’an, Oct. 23, 2006



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

Xi’an, Oct. 23, 2006



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.

parametric-gain approach to the analysis of dpsk dispersion-managed systems

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