Signal Processing Techniques for Coherent Fiber-Signal Processing Techniques for Coherent Fiber-Optic Communication Systems in Presence of Optic Communication Systems in Presence of

Kerr NonlinearityKerr Nonlinearity

Ph.D. Thesis Defense

Department of Electrical EngineeringStanford UniversityMarch 10, 2008

Alan Pak Tao Lau

22

OutlineOutline

Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory Kerr nonlinearity induced system impairmentsKerr nonlinearity induced system impairments

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN)Nonlinear Phase Noise (NLPN)

SummarySummary

33

Long-haul fiber-optic Long-haul fiber-optic communication systemscommunication systems

Terrestrial link (1500 ~ 3000 km)Submarine link (5000 ~ 10000 km)

44

Tech. Evolution: Optical amplifiers, Tech. Evolution: Optical amplifiers, Wavelength Division Multiplexing (WDM),Wavelength Division Multiplexing (WDM), Forward Error Correction (FEC)Forward Error Correction (FEC)

Long-haul fiber-optic Long-haul fiber-optic communication systemscommunication systems

TAT-8: 280 Mb/s, (1988)TAT-8: 280 Mb/s, (1988)

TAT-12/13: 5 Gb/s, (1996)TAT-12/13: 5 Gb/s, (1996)

TAT-14: 64 x 10 Gb/s, (2001)TAT-14: 64 x 10 Gb/s, (2001)

TPC5: 5Gb/s (1996)TPC5: 5Gb/s (1996)

Bit Rate: 2.5 Gb/s ->10 Gb/s -> 40 Gb/s -> 100 Gb/sBit Rate: 2.5 Gb/s ->10 Gb/s -> 40 Gb/s -> 100 Gb/s

Spectral Efficiency: 0.0005 b/s/Hz -> 0.2 b/s/Hz -> 0.8 b/s/Hz Spectral Efficiency: 0.0005 b/s/Hz -> 0.2 b/s/Hz -> 0.8 b/s/Hz

Next technological breakthrough: Electronic signal processing!Next technological breakthrough: Electronic signal processing!

55

Coherent detectionCoherent detection Traditionally in fiber-optics, information encoded in pulse energy – On-Traditionally in fiber-optics, information encoded in pulse energy – On-

Off Keying (OOK)Off Keying (OOK) Differentially coherent detection – information encoded in phase Differentially coherent detection – information encoded in phase

difference between neighboring symbols: DPSK, DQPSKdifference between neighboring symbols: DPSK, DQPSK Coherent detection – information encoded in both phase and Coherent detection – information encoded in both phase and

amplitude: QPSK, 16-QAM amplitude: QPSK, 16-QAM Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM

modulation format in future. modulation format in future.

tELOLO

tE )(Re tEi

tEtE LO2

1

tEtE LO2

1

3-dB coupler

BPSKMPSK/QAM

90°

LO tELO

tE

)(Re tEiI

)(Im tEiQ

D-MPSK

tE T

T

90°

)()(Re * TtEtE

)()(Im * TtEtE

Delay

Receiver

tEI

90°

MZ

MZ tEQ

Transmitter

Laser

tVI

tVQ

tE

MZ– Mach Zehnder Modulator

66

Digital Signal Processing Digital Signal Processing Currently available: 40 Gb/s FEC encoder/decoderCurrently available: 40 Gb/s FEC encoder/decoder 40 Gb/s clock/data recovery40 Gb/s clock/data recovery 10 Gb/s MLSD10 Gb/s MLSD Arbitrary signal generation/detection, arbitrary signal Arbitrary signal generation/detection, arbitrary signal

processing processing

Communication theory / signal processing Communication theory / signal processing techniques becomes practicallytechniques becomes practically relevant and important !!relevant and important !!

Information theory is also getting more attentionInformation theory is also getting more attention Fiber-optic channel is different from wireless / wireline Fiber-optic channel is different from wireless / wireline

communicationscommunications

77

Signal propagation in optical fibersSignal propagation in optical fibers

Erbium Doped Fiber Amplifiers (EDFA)Erbium Doped Fiber Amplifiers (EDFA)

)(

0

P

EH

BE

B

D

j

j

))((),(),(),,,( tzjx etzEyxFtzyx E

z1n

2n

EEjEt

Ej

z

E 22

22 ||

22

Nonlinear Schrödinger Equation (NLSE)Nonlinear Schrödinger Equation (NLSE)

Mode

Pulse envelope

Carrier frequency

(~193 THz or 1550 nm)

Japan USA

E

Dispersion Compensating Fibers (DCF)Dispersion Compensating Fibers (DCF)

amplifieramplifier amplifier

Attenuation

t

)0,(tE

t

),( ztE

Chromatic

Dispersion

SMFSMF SMFDCF DCFDCF

Kerr

nonlinearity

x

y

Kerr nonlinearity – not a LTI effectKerr nonlinearity – not a LTI effect Dominant transmission impairment in long-haul systems!Dominant transmission impairment in long-haul systems!

88

Kerr Nonlinearity in optical fibersKerr Nonlinearity in optical fibers

)( 3)3()1(0 EE P

effA

E

nnn

2

0

)3(

0

||

8

)Re(3

induced intensity dependent refractive index induced intensity dependent refractive index )3(

Electric Polarization of moleculesElectric Polarization of molecules

effAn0

)3(

8

)Re(32

(NLSE) ||22

22

22 EEjE

t

Ej

z

E

Kerr induced nonlinear phase shiftKerr induced nonlinear phase shift

Linear Regime

EI

EQ

E

Nonlinear Regime

EI

EQ

E2

ELeffNL

99

Impairments in long-haul systems Impairments in long-haul systems with coherent detectionwith coherent detection

Noise limits communication system performanceNoise limits communication system performance BPSK / QPSK / DQPSK – phase noiseBPSK / QPSK / DQPSK – phase noise

Laser phase noiseLaser phase noise Amplified Spontaneous Emission (ASE) noise from inline Amplified Spontaneous Emission (ASE) noise from inline

amplifiersamplifiers Receiver shot/thermal noiseReceiver shot/thermal noise Noise and inter-symbol interference (ISI) resulting from Kerr

nonlinearity and its interaction with amplifier noise and other propagation effects

Amplitude noise and phase noise are generally Amplitude noise and phase noise are generally differentdifferent

1010

OutlineOutline

Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems

Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory

Kerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM)

Nonlinear Phase Noise (NLPN)Nonlinear Phase Noise (NLPN)

SummarySummary

1111

OutlineOutline

Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems

Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory

Kerr nonlinearity induced phase noiseKerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM)

Nonlinear Phase Noise (NLPN)Nonlinear Phase Noise (NLPN)

SummarySummary

1212

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM)

Pulse trainsPulse trains , ),(),( k

kkk

k UxkTtzUxtzE

pml

pmlpml UUUxxxj,,

**

kkk uuU

pml

pmlpmlkkk uuuxxxju

t

uj

z

u

,,

**2

22

22

First-order perturbation theoryFirst-order perturbation theory

Linear solution to NLSE

IFWM: not FWM!IFWM: not FWM! pmlk )( pmlk

Nonlinear perturbation

Pulse shape

Phase modulated info

IFWM is ISI caused by interaction of dispersion and Kerr nonlinearityIFWM is ISI caused by interaction of dispersion and Kerr nonlinearity

Et

Ej

z

E

22 2

22

EEj 2|| (NLSE)(NLSE)

1313

IFWM - induced phase noiseIFWM - induced phase noise

IFWM-induced phase noise on time slot 0IFWM-induced phase noise on time slot 0

ml

mlmlml tCxxxxt,

2,*0

*0 ),,,(Im)(

Highly nonlinear ISIHighly nonlinear ISI Each term in summation is a triple product of info. symbolsEach term in summation is a triple product of info. symbols Triple product comes from future and past symbols combined in a strange way Triple product comes from future and past symbols combined in a strange way

Too complicated to be fully exploited (at present)Too complicated to be fully exploited (at present) Considered noise most of the timeConsidered noise most of the time

1414

ProbabilityProbability distribution ofdistribution of

Need to know the probability Need to know the probability distribution of to distribution of to analytically characterize analytically characterize system bit error ratio (BER)system bit error ratio (BER)

Empirical distribution of Empirical distribution of only. BER obtained by only. BER obtained by numerical methodsnumerical methods

Is it possible to at least Is it possible to at least approximate the probability approximate the probability distribution ? distribution ?

ml

mlmlml Cxxxx,

,*0

*0 Im

0

Ho, PTL vol. 17, no. 4, Apr. 2005, pp. 789-791)(

0p

0

1515

ml mlmlml Cxxxxt

, ,*0

*0 Im)( Insight: terms in are Insight: terms in are

pairwise independent. For example, pairwise independent. For example,

are independentare independent

31

21

xxz

xxy

i.i.d. iixm ,1,,1

zxxzyz ppp 21||

41

02

2

3

A consequence of modulo addition in phase ofA consequence of modulo addition in phase of Not jointly independent Not jointly independent

mx

ml

mlp,

, )()()(00

)(0pApproximate probability distributionApproximate probability distribution

Approximation:Approximation:

2,1*0

*3211,1

*0

*211 ImIm CxxxxCxxxx ,

1616

for QPSK/DQPSK systemsfor QPSK/DQPSK systems

QPSK DQPSK

DQPSK: Group terms from that are correlated with DQPSK: Group terms from that are correlated with each other each other

10 ,

)(0p

1717

Tail Probability of Tail Probability of

QPSK DQPSK

)(Q

)(0p

1818

areare correlatedcorrelated

Exploiting Correlation structure of Exploiting Correlation structure of

Wei and Liu, Optics Letters, Vol. 28, no. 23, pp. 2300-2302, 2003

k

10 ,

No analytical knowledge of correlation structure of IFWM-induced No analytical knowledge of correlation structure of IFWM-induced phase noisephase noise

1919

Correlation Correlation ][)( 0 kEkR

ccCCxxxxxxxxE

CCxxxxxxxxEkR

kqkpmlkkqpqpmlml

ml qpkqkpmlkkqpqpmlml

.][

][4

1)(

,*,

**0

**

, ,,,

***0

*

0]|||||||[| when 0][ 2222 EMbxE ba

m

kmkmm

kmmmkm CCCCkR ,,*

,, Re2

1Re

2

1)(

mkmkm

mkmmmkm

mkmkm

mkmmmkm

CCCC

CCCCkR

*,,,,

,,*

,,

Re2

1Re

2

1

Re2

1Re

2

1)(

MPSKMPSK

BPSKBPSK

2020

)(kR for 40 GSym/s QPSK systemsfor 40 GSym/s QPSK systems

L (km)L (km)

SMFSMF 8080 .25.25 1717 1.21.2

DCFDCF 1616 .6.6 -85-85 5.35.3

(dB/km) km)-(ps/nm2 km)(/W

0 )( pst5.2 5

Sampling points

SMF DCF

Pulse shape: 33% RZ Pulse shape: 33% RZ Gaussian Gaussian

2121

Exploiting Exploiting )(kR Optimal linear prediction of Optimal linear prediction of

11111 , xx

1i

ikikkk ax

,)3(

)2(

)1(

1

3

2

1

R

R

R

Ra

a

a

topelitz

1.8 dB improvement when dominates1.8 dB improvement when dominates 0.8-1.2 dB improvement in presence of amplifier noise0.8-1.2 dB improvement in presence of amplifier noise

k

)(),( jiRjiRtopelitz

k

2222

IFWM-induced phase noise and IFWM-induced phase noise and amplitude noiseamplitude noise

ml

mlmlml Cxxxx,

,*0

*0 Im

ml

mlmlml Cxxxxr,

,*0

*0 Re

MPSK0

BPSK2/}Im{][

2,

00mlCrE

Received amplitude uncorrelated with phase Received amplitude uncorrelated with phase noise for QPSK/DQPSK systemsnoise for QPSK/DQPSK systems

0

0r

A.P.T. Lau, S. Rabbani and J.M. Kahn, to appear in OSA/IEEE JLT

2323

OutlineOutline

Long-haul fiber-optic communication systemsLong-haul fiber-optic communication systems Coherent detection, DSP, communication theoryCoherent detection, DSP, communication theory Kerr nonlinearity induced phase noiseKerr nonlinearity induced phase noise

Intra-channel four-wave mixing (IFWM)Intra-channel four-wave mixing (IFWM)Nonlinear Phase Noise (NLPN)

SummarySummary

2424

Nonlinear phase noise (NLPN)Nonlinear phase noise (NLPN)

2effNL || nEL

Kerr nonlinearity induced nonlinear phase shift:Kerr nonlinearity induced nonlinear phase shift:

corrupted by Amplified Spontaneous Emission (ASE) noise from corrupted by Amplified Spontaneous Emission (ASE) noise from inline amplifiersinline amplifiersE

EI

EQ

Linear Regime

EI

EQ

Nonlinear Regime

EI

EQ

Linear Regime

En

Etot

Nonlinear Regime

EI

EQ

Etot

NL|Etot|2

),0(~ , 2InnE N

Nonlinear phase noise or Gordon-Mollenauer effectNonlinear phase noise or Gordon-Mollenauer effect

2525

Joint probability distribution (PDF) Joint probability distribution (PDF) of received amplitude and phaseof received amplitude and phase

,/Er

1

)(, )(

1)(),(

m

jmmRice

o

oserCerfrf

)2(1

)( 0)( 2

sr

Rice rIrerf s

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

,2/1

s

PLx

jmxsm sec )2/(tan jmxjmxsm

jmxm

sejmx tan sec

m

mm

s

r

m

mm s

rIe

s

rrC m

m 2

22

)(

Transmitted signal with power , phase Transmitted signal with power , phase s 0

2626

PDF and maximum likelihood (ML) decision PDF and maximum likelihood (ML) decision boundaries for 40G Sym/s QPSK Signalsboundaries for 40G Sym/s QPSK Signals

L=5000 km, P=-4 dBm, L=5000 km, P=-4 dBm, km,/1.2,0.25dB/km WdB 5.4nF

2727

Maximum Likelihood (ML) DetectionMaximum Likelihood (ML) Detection

To implement ML To implement ML detection, need to know detection, need to know the ML boundariesthe ML boundaries

Need to knowNeed to know With ,can either de-With ,can either de-

rotate the received phase rotate the received phase or use a lookup tableor use a lookup table

rc rc

4

rc

4

rc

rc

2828

With approximations With approximations ML decision boundaryML decision boundary rc

zezIzzzzzz zm 2/)( ,3/tan ,3/sin 33

it can be shown that it can be shown that )(arg)(arg 1 rCmrCm

0)()(argsin4

sin|)(| 11

rrCmm

rC cm

m

xx

xxx

rCrc

2cos2cosh

2sinh2sin

2

)(arg)(

1

2r

xx

xxxxxs2cos2cosh

2/sinh2/cos2/cosh2/sin

24

r )(xh

2/1

s

PLx

2929

Received phase rotation by Received phase rotation by

Before rotationBefore rotation After rotationAfter rotation

Straight line ML decision boundaries after rotationStraight line ML decision boundaries after rotation

rc

3030

Symbol Error Rate (SER) for MPSK SystemsSymbol Error Rate (SER) for MPSK Systems

)(4

)(;1,

2

2

)1()(2

)2(5.0)(

!

))(()(

21

2

11

1 0)2(5.01

xa

xm

kmF

mxa

kmx

k

xjgxse

M

MSER

m

m

m kkm

mm

mm

km

m

Numerical results Analytical

3131

SER for D-MPSK Systems SER for D-MPSK Systems

1

2 sinc 21

mm M

mD

NM

MSER

0

)( drrCD mm

3232

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 inter-symbol reduce inter-symbol interference compared interference compared to 2-PSK or 4-PSK.to 2-PSK or 4-PSK.

3333

16-QAM transmitter16-QAM transmitterLaser

3434

Maximum likelihood detection for 16-Maximum likelihood detection for 16-QAM systems in presence of NLPN QAM systems in presence of NLPN

No analytical formula for ML No analytical formula for ML decision boundaries for 16-decision boundaries for 16-QAM system as power of QAM system as power of signal points not constantsignal points not constant

Boundaries distorted from Boundaries distorted from straight linesstraight lines

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?

3535

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 probability distribution corresponding to each Modes of conditional probability distribution corresponding to each signal point do not form a square constellationsignal point do not form a square constellation

Pre-rotate phase by the negative of mean nonlinear phase shiftPre-rotate phase by the negative of mean nonlinear phase shift

3636

NLPN post-compensationNLPN post-compensation Rotate the received phase by proportional to received Rotate the received phase by proportional to received

intensity for phase noise variance minimizationintensity for phase 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

3737

Performance of phase rotation Performance of phase rotation methods in 16-QAM systemsmethods in 16-QAM systems

(No phase comp.)

3838

Signal Constellation Optimization in Signal Constellation Optimization in Presence of NLPN Presence of NLPN

QPSKQPSK 1-2-11-2-1

1-31-3 2-22-2A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, pp. 3008-3016, Oct 2007

3939

Orthogonal Frequency Division Orthogonal Frequency Division Multiplexing (OFDM)Multiplexing (OFDM)

Well-known in wireless/DSLWell-known in wireless/DSL Multiplexing of large number of low rate sub-carriersMultiplexing of large number of low rate sub-carriers FFT based processingFFT based processing

R

ofdmT2

…

OFDMOFDM

R

Single CarrierSingle Carrier

4040

OFDM in Fiber-OpticsOFDM in Fiber-OpticsWireless / DSLWireless / DSL Fiber-OpticsFiber-Optics

Spectrum Spectrum ConfinementConfinement

Much more confined Much more confined than SCthan SC

SameSame

Equalization Equalization

ComplexityComplexity

in OFDM vs. in OFDM vs. in SC in SC

SameSame

Channel Channel EqualizationEqualization

Bit loading to achieve Bit loading to achieve info. theoretic capacityinfo. theoretic capacity

Dispersion:Dispersion:

High signal High signal peakspeaks

Peak-to-Avg Power Peak-to-Avg Power Ratio (PAPR)Ratio (PAPR)

Fiber nonlinearity!Fiber nonlinearity!

SC – Single CarrierSC – Single Carrier

12/22 Lje

NN log 2N

4141

Nonlinearity induced impairments in Nonlinearity induced impairments in Optical OFDMOptical OFDM

Nonlinear perturbations Nonlinear perturbations originate from FWM originate from FWM products between sub-products between sub-carriers with perfect phase carriers with perfect phase matching matching

For a system with For a system with KK sub- sub-carriers, noise variance at carriers, noise variance at sub- sub-carrier carrier kk is given by is given by

A.P.T. Lau, D.J. Barros and J.M. Kahn, in preparation.

)322()5.32( 2222 kkKkKPL seffk 1,1,0 Kk

4242

Comparison of various phase Comparison of various phase noises in long-haul systemsnoises in long-haul systems

ASE induced ASE induced (Linear) (Linear) phase noisephase noise

IFWM-induced IFWM-induced phase noisephase noise

Nonlinear Nonlinear Phase NoisePhase Noise

Signal Signal PowerPower

Amplifier Amplifier noise powernoise power

System System LengthLength

RemarksRemarks Dominant in Dominant in terrestrial linksterrestrial links

Dominant in Dominant in Submarine linksSubmarine links

sP

12sP sP

2n 2

n~L 2L 3L

4343

SummarySummary Coherent detection and DSP technologies results in the Coherent detection and DSP technologies results in the

relevance and importance of communication theory in next-relevance and importance of communication theory in next-generation long-haul communication system design generation long-haul communication system design

Performance of long-haul systems limited by Kerr Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, nonlinearity induced system impairments such as IFWM, NLPNNLPN

System BER characterization in presence of IFWM, NLPNSystem BER characterization in presence of IFWM, NLPN Appropriate signal processing techniques and system Appropriate signal processing techniques and system

designs for performance improvementsdesigns for performance improvements Much more work remains to understand/improve long-haul Much more work remains to understand/improve long-haul

system performance!system performance!

4444

Thank you!Thank you!

4545

Design of inline amplifier gains and Design of inline amplifier gains and spacings to mitigate phase noisespacings to mitigate phase noise

Amplifier Amplifier Amplifier

Conventionally, amplifiers Conventionally, amplifiers uniformly spaced along the link uniformly spaced along the link and the their gain exactly and the their gain exactly compensates for the signal loss in compensates for the signal loss in the previous spanthe previous span

Better design of amplifier Better design of amplifier gains/spacings in the link to gains/spacings in the link to mitigate phase noise?mitigate phase noise?

4646

Design of inline amplifier gains and Design of inline amplifier gains and spacings to mitigate phase noisespacings to mitigate phase noise

Linear Phase NoiseLinear Phase Noise

)arg( 21L NnnnE

Amplifier Amplifier Amplifier

Nonlinear Phase NoiseNonlinear Phase Noise

21

221

21

effNL||

||||

NnnE

nnEnEL

)1()1(),,0(~ˆ22 ilα

ioptspiii ebGnhIn Ν

EI

EQ

En

L

4747

Variance of phase noiseVariance of phase noise

Linear phase noise variance – for high SNR,Linear phase noise variance – for high SNR,

i

j

lli

jjeEE1

ˆ22 ||||

22

22

22

1

2 ,||

1

||

1

||

1ii

TL EEE

Nonlinear phase noise varianceNonlinear phase noise variance

Signal after amplifier:Signal after amplifier:thi

],u[4 22 DTNL

,1

,||

||u ,

22

,

il

ie

N

iji

jjei

eL

E

EL

2, ,0

||

||

ijT

iji

jie

ij MMDij

ijE

EL

M

wherewhere

4848

Minimization of joint phase Minimization of joint phase noise variancenoise variance

When , the optimization problem can When , the optimization problem can be shown to be convex in .be shown to be convex in .

1, il Ge i

are uncorrelatedare uncorrelated Minimize the variance of total phase noiseMinimize the variance of total phase noise

LN

N

eGGG

Llll

NN

21

21

22 )()(min

andtosubjectNLL

NLL and

ii Gl log,

4949

Uniformly spaced amplifiers with per-Uniformly spaced amplifiers with per-span loss compensationspan loss compensation

22

222

2

22

||

)1(

)1(||3

)12)(1(2

)1(3

)1)(1(2)1(

)()(E

eNb

ebENNN

ebNNNN

eNN

N

L

N

L

N

L

N

L

NLL

Distributed amplification is not optimal ! Distributed amplification is not optimal ! (contrary to Yariv, (contrary to Yariv, Opt. Lett.,Opt. Lett., vol. 15, no. 19,1990 ) vol. 15, no. 19,1990 )

5050

Optimal amplifier spacing in presence of NLPNOptimal amplifier spacing in presence of NLPN

15.2)2()1(30 **2

**

YeYeN

YY

LDefine span length Y*=L/N*. As .02

N

A.P.T. Lau and J.M. Kahn, paper JWB23, OSA COTA, June 2006

Overall phase noise variance reduction by 40%.Overall phase noise variance reduction by 40%.

Optimal Optimal NN

5151

Amplifier gain optimization in Amplifier gain optimization in presence of NLPNpresence of NLPN

Reduction in variance: 23% (3000 km), 81% (10000 km)Reduction in variance: 23% (3000 km), 81% (10000 km)

Terrestrial link (3000 km)Terrestrial link (3000 km) Submarine link (10000 km)Submarine link (10000 km)

5252

Joint amplifier spacing and gain Joint amplifier spacing and gain optimization in presence of NLPNoptimization in presence of NLPN

Reduction of variance: 45% (3000 km), 83% (10000 km)Reduction of variance: 45% (3000 km), 83% (10000 km)

A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, Mar 2006, pp.1334-1341

Terrestrial link (3000 km)Terrestrial link (3000 km) Submarine link (10000 km)Submarine link (10000 km)

5353

Comparison of various phase Comparison of various phase noises in long-haul systemsnoises in long-haul systems

ASE induced ASE induced (Linear) (Linear) phase noisephase noise

IFWM-induced IFWM-induced phase noisephase noise

Nonlinear Nonlinear Phase NoisePhase Noise

Signal Signal PowerPower

Amplifier Amplifier noise powernoise power

System System LengthLength

RemarksRemarks Dominant in Dominant in terrestrial linksterrestrial links

Dominant in Dominant in Submarine linksSubmarine links

sP

12sP sP

2n 2

n~L 2L 3L

5454

SummarySummary Coherent detection and DSP technologies results in the Coherent detection and DSP technologies results in the

relevance and importance of communication theory in next-relevance and importance of communication theory in next-generation long-haul communication system design generation long-haul communication system design

Performance of long-haul systems limited by Kerr Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, nonlinearity induced system impairments such as IFWM, NLPNNLPN

System BER characterization in presence of IFWM, NLPNSystem BER characterization in presence of IFWM, NLPN Appropriate signal processing techniques and system Appropriate signal processing techniques and system

designs for performance improvementsdesigns for performance improvements Much more work remains to understand/improve long-haul Much more work remains to understand/improve long-haul

system performance!system performance!

5555

Research PapersResearch Papers A.P.T. Lau and J.M. Kahn, “Design of Inline Amplifiers Gain and Spacing to Minimize A.P.T. Lau and J.M. Kahn, “Design of Inline Amplifiers Gain and Spacing to Minimize

Phase Noise in Optical Transmission Systems,” Phase Noise in Optical Transmission Systems,” OSA/IEEE Journal of Lightwave OSA/IEEE Journal of Lightwave TechnologyTechnology, Mar 2006, pp.1334-1341., Mar 2006, pp.1334-1341.

A.P.T. Lau and J.M. Kahn, “Signal Design and Detection in Presence of Nonlinear A.P.T. Lau and J.M. Kahn, “Signal Design and Detection in Presence of Nonlinear Phase Noise,” Phase Noise,” OSA/IEEE Journal of Lightwave TechnologyOSA/IEEE Journal of Lightwave Technology, vol. 25, no. 10, pp. , vol. 25, no. 10, pp. 3008-3016, Oct. 2007.3008-3016, Oct. 2007.

A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the Statistics of Intra-channel Four-Wave A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the Statistics of Intra-channel Four-Wave Mixing in Phase-Modulated Optical Communication Systems,” to appear in Mixing in Phase-Modulated Optical Communication Systems,” to appear in OSA/IEEE OSA/IEEE Journal of Lightwave TechnologyJournal of Lightwave Technology..

E. Ip, A.P.T. Lau, D.J.F. Barros and J.M. Kahn E. Ip, A.P.T. Lau, D.J.F. Barros and J.M. Kahn (Invited)(Invited), “Coherent Detection in , “Coherent Detection in Optical Fiber Systems,” to appear in Optical Fiber Systems,” to appear in OSA Optics Express, 2008OSA Optics Express, 2008..

A.P.T. Lau and J.M. Kahn, “Non-Optimality of Distributed Amplification in Presence of A.P.T. Lau and J.M. Kahn, “Non-Optimality of Distributed Amplification in Presence of Nonlinear Phase Noise”, paper JWB23, Nonlinear Phase Noise”, paper JWB23, OSA Coherent Optical Technologies and OSA Coherent Optical Technologies and Applications (COTA)Applications (COTA), Whistler, BC, Canada, June 2006. , Whistler, BC, Canada, June 2006.

A.P.T. Lau and J.M. Kahn,"16-QAM Signal Design and Detection in Presence of A.P.T. Lau and J.M. Kahn,"16-QAM Signal Design and Detection in Presence of Nonlinear Phase Noise," Paper TuA4.4, 2007 Nonlinear Phase Noise," Paper TuA4.4, 2007 IEEE/LEOS Summer Topical MeetingsIEEE/LEOS Summer Topical Meetings, , Portland, OR, July 23-25, 2007.Portland, OR, July 23-25, 2007.

A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the statistics of Intra-channel Four-Wave A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the statistics of Intra-channel Four-Wave Mixing in phase modulated systems,” paper JThA52, Mixing in phase modulated systems,” paper JThA52, OFC/NFOEC, OFC/NFOEC, San Diego, CA, San Diego, CA, Feb. 24-28, 2008.Feb. 24-28, 2008.

5656

AcknowledgementsAcknowledgements

Prof. Joseph KahnProf. Joseph KahnProf. Shanhui FanProf. Shanhui FanProf. David MillerProf. David MillerProf. John GillProf. John Gill

Group members: Ezra, Rahul, Dany, Group members: Ezra, Rahul, Dany, Daniel, Mahdieh, Jeff, SahandDaniel, Mahdieh, Jeff, Sahand

5757

AcknowledgementsAcknowledgements Prof. Frank Kschischang, University of TorontoProf. Frank Kschischang, University of Toronto

5858

AcknowledgementsAcknowledgementsFinancial SupportFinancial Support National Science and National Science and

Engineering Research Council Engineering Research Council (NSERC) of Canada(NSERC) of Canada

Macau Special Administrative Macau Special Administrative Region Post-Graduate Region Post-Graduate Scholarship, Macau, ChinaScholarship, Macau, China

5959

Thank you!Thank you!

6060

How good is the variance measure?How good is the variance measure?

BER/Capacity optimized at close vicinity of N BER/Capacity optimized at close vicinity of N that minimize phase noise variancethat minimize phase noise variance

6161

Per-Span Loss Compensation (fixed Per-Span Loss Compensation (fixed NN))

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6262

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6464

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6565

Research OutlookResearch Outlook

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