16 QAM Signal Design and Detection16 QAM Signal Design and Detectionin Presence of Nonlinear Phase Noisein Presence of Nonlinear Phase Noise

Department of Electrical Engineering

Stanford UniversityJuly 24, 2007

Alan Pak Tao Lau Joseph. M. Kahn

OutlineOutline

Nonlinear phase noise (Gordon-Mollenauer Nonlinear phase noise (Gordon-Mollenauer effect) in coherent communication systemseffect) in coherent communication systems

High-spectral-efficiency modulation formatsHigh-spectral-efficiency modulation formats Phase rotation techniques for 16-QAM systems Phase rotation techniques for 16-QAM systems

in presence of nonlinear phase noisein presence of nonlinear phase noise ConclusionsConclusions

Nonlinear phase noise (NLPN)Nonlinear phase noise (NLPN) Kerr nonlinearity: intensity-dependent refractive indexKerr nonlinearity: intensity-dependent refractive index

2eff

2eff

eff

02NL |||| ELEL

A

kn

Self-phase modulation-induced nonlinear phase shift:Self-phase modulation-induced nonlinear phase shift:

Nonlinear phase noise when corrupted by ASE noise from inline Nonlinear phase noise when corrupted by ASE noise from inline amplifiers: Gordon-Mollenauer effectamplifiers: Gordon-Mollenauer effect

2|| E

EI

EQ

Linear Regime

EI

EQ

Nonlinear Regime

16-QAM modulation formats16-QAM modulation formats

High spectral efficiency. High spectral efficiency. Together with coding, Together with coding, approach information-approach information-theoretic limits.theoretic limits.

For a given bit rate, For a given bit rate, reduce intersymbol reduce intersymbol interference compared interference compared to 2-PSK or 4-PSK.to 2-PSK or 4-PSK.

16-QAM transmitter16-QAM transmitter

Joint PDF of received amplitude and phaseJoint PDF of received amplitude and phase

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r

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K.P. Ho “K.P. Ho “Phase-Modulated Optical Communication SystemsPhase-Modulated Optical Communication Systems,” ,” Springer 2005Springer 2005

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PLx

jmxsm sec

)2/(tan jmxjmxsm

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sejmx tan sec

Assuming distributed amplification, neglecting dispersion:Assuming distributed amplification, neglecting dispersion:

Received PDF ML decision boundariesReceived PDF ML decision boundariesfor 16-QAM signals for 16-QAM signals

PDF Decision Boundaries

dBm 13avgP dBm 7avgP

km/1.2,0.25dB/km W,41.1 ,GSym/s 7.42 ,km 3000 spnRL

Maximum-likelihood (ML) detectionMaximum-likelihood (ML) detectionin 16-QAM systems in 16-QAM systems

No analytical formula for ML decision No analytical formula for ML decision boundaries for 16-QAM system boundaries for 16-QAM system

2-dimensional look-up table obtained 2-dimensional look-up table obtained by numerical methods, but still by numerical methods, but still complicated to implementcomplicated to implement

Approximate boundaries with straight Approximate boundaries with straight lineslines

Can we design/process the signals at the transmitter Can we design/process the signals at the transmitter and/or receiver such that ML detection can be better and/or receiver such that ML detection can be better approximated by straight lines?approximated by straight lines?

16-QAM signal phase pre-compensation16-QAM signal phase pre-compensation

With phase pre- comp.With phase pre- comp.Without phase pre-comp.Without phase pre-comp.

Pavg= -2.5 dBm

inNL LP

Modes of conditional pdfs corresponding to each signal pointModes of conditional pdfs corresponding to each signal pointdo not form a square constellation.do not form a square constellation.

Pre-rotate phase by negative of mean nonlinear phase shift:Pre-rotate phase by negative of mean nonlinear phase shift:

NLPN post-compensationNLPN post-compensation Phase rotation proportional to received intensity for Phase rotation proportional to received intensity for

phase noise variance minimizationphase noise variance minimization

2/recLP

With phase pre- comp. onlyWith phase pre- comp. only Phase pre- comp. with NLPN Phase pre- comp. with NLPN post-comp.post-comp.

Ho and Kahn, JLT vol.22 no. 3, Mar. 2004 Ly-Gagnon and Kikuchi, Paper 14C3-3, OECC 2004

Performance of phase rotation Performance of phase rotation methodsmethods

(No phase comp.)

ConclusionsConclusions

Thank you!Thank you!

Effects of nonlinear phase shift and nonlinear phase noise in Effects of nonlinear phase shift and nonlinear phase noise in 16-QAM systems with coherent detection16-QAM systems with coherent detection

Straight-line decision boundaries to approximate ML detectionStraight-line decision boundaries to approximate ML detection

Phase pre-compensation at the transmitterPhase pre-compensation at the transmitter

Nonlinear phase poise (NLPN) post-compensation at receiverNonlinear phase poise (NLPN) post-compensation at receiver

SER performance can outperform ML detection!SER performance can outperform ML detection!