Information Theory and Digital Signal Processing in Optical …blog.catonic.us/kirby/2011 IEEE...

Peter J. WinzerBell Labs, Alcatel-Lucent, Holmdel, New Jersey, USA

Acknowledgment: G.J.Foschini, R.-J.Essiambre, G.Kramer, X.Liu, S.Chandrasekhar, R.Ryf,S.Randel, A.H.Gnauck, C.R.Doerr, R.W.Tkach, and A.R.Chraplyvy

IEEE CTW 2011, Barcelona, Spain

Information Theory and Digital Signal Processing in Optical

Communications

All Rights Reserved © Alcatel-Lucent 20112 | IEEE CTW, June 2011

Outline

• Network traffic growth and the role of optics

• High-speed interfaces and the scalability limits of WDM

• Shannon capacity limits for the nonlinear fiber channel

• Spatial multiplexing: Integration, crosstalk, and MIMO

1 Traffic scaling in data networksand the enabling role of optics


Network traffic is growing exponentially

Telepresence Panasonic’s LifeWall

Exponential network traffic growth is driven by high-bandwidth digital applicationsVideo-on-demand, telepresence, wireless backhaul, cloud computing & services

60% 10 log10(1.6) dB 2 dB


High-speed fiber optic networks

Line interface(e.g., 100 Gbit/s)

Router

Optical network

WDM: Wavelength-division multiplexing

Reconfigurable opticaladd/drop multiplexer

(ROADM)Client interface

(e.g., 4 x 25 Gbit/s)

WDM system(e.g., 80 x 100 Gbit/s)

2 High-speed interfaces: Finally using coherent detection ...


1986 1990 1994 1998 2002 2006

10

100

1

10

100Se

rial

Inte

rfac

e Ra

tes

and

WD

M C

apac

itie

s

Gb/

sTb

/s

2010 2014 20181

2022

High-speed optical interface research

Direct detection

Coherent detection

9.3 ps

• Recently demonstrated 448-Gb/s interfaces in research(224-Gb/s per polarization)


1986 1990 1994 1998 2002 2006

10

100

1

10

100Se

rial

Inte

rfac

e Ra

tes

and

WD

M C

apac

itie

s

Gb/

sTb

/s

2010 2014 20181

2022

High-speed optical interface product development

PDM-QPSKASIC: 70M+ gates

• Recently demonstrated 448-Gb/s interfaces in research(224-Gb/s per polarization)

• 112-Gbit/s interfaces commercially available since June 2010(56-Gb/s per polarization)

Direct detection

Coherent detection


Basic coherent optical receiver setup

Front-end optics Analog-to-digitalconversion

Back-end digital electronicsignal processing

High-speed sampling

Digitization

Ix + jQx

Iy + jQy

f

x pol.

y pol.


Higher interface rates via higher-order modulation

PDM 512-QAM3 GBaud (54 Gb/s)

[Okamoto et al., ECOC’10]


[Nakazawa et al., OFC’10]


[Gnauck et al., OFC’11]


[Winzer et al., ECOC’10]


[Zhou et al., OFC’11]

High D/A and A/D resolution High speed

•ENoB: Effective number of bits

[R.H. Walden, 1999 and 2008]














•f

Mod.Laser

Single-carrier transmitter

•f

Electrical spectrum

Optical spectrum

Optical OFDM transmitter

Mod.

Comb

•f•f

•f

•f

•f

Mod.

Mod.

Mod.

Laser •f+














60 GHz

448 Gb/s (10 subcarriers) 16-QAM5 bit/s/Hz

2000 km transm.[Liu et al., OFC’10]

65 GHz

606 Gb/s (10 subcarriers) 32-QAM7 bit/s/Hz

2000 km transm.[Liu et al., ECOC’10]

1.2 Tb/s (24 subcarriers) QPSK3 bit/s/Hz

7200 km transm.[Chandrasekhar et al., ECOC’09]

300 GHz


Fiber capacity increase through spectral efficiency

0.01

0.1

1

10

Spec

tral

eff

icie

ncy

[b/s

/Hz]

1990 1994 1998 2002 2006Year

2010

Laser & filter stability

x-pol

y-pol

x-pol

y-pol

Modulation

PDMDetection

Single polarizationPolarization interleavingPolarization multiplexing

•20 years ago: Device physics set engineeringlimits on spectral efficiency

•Today: Information theory sets fundamentallimits on spectral efficiencyFiber nonlinearity sets fundamental limits on per-fiber spectral efficiency

Tx Rx

~ 5 THz bandwidth ~ 100 km of fiber


1986 1990 1994 1998 2002 2006

10

100

1

10

100

Seri

al In

terf

ace

Rate

s an

d W

DM

Cap

acit

ies

Gb/

sTb

/s

2010 2014 20181

2022

Scaling WDM capacity through spectral efficiency

• ~10 Terabit/s WDM systems are now commercially available• ~100 Terabit/s WDM systems have been demonstrated in research• Growth of WDM system capacities has noticeably slowed down

[P.J.Winzer, IEEE Comm. Mag., June 2010]


Basic trade-off: Spectral efficiency versus sensitivity

Spectral efficiency comes at a fundamental cost:•Higher signal-to-noise ratio (SNR) requirements for higher-order modulationSpectral efficiency comes at a practical cost:•Implementation penalties are usually higher for higher constellations and symbol rates

• Must regain lost SNR through advanced FEC, optical nonlinearity compensation, lower-loss fibers, distributed Raman amplification, ... Optical line design remains critically important!

RxTx

RxTx RxTx RxTx

~ mW/(Gb/s)~ W/(Gb/s)

3 The role of fiber nonlinearity in optical communications


Optical fiber nonlinearities

• Core diameter ~8 µm• Cladding diameter ~125 µm• Light is kept within the core (total reflection)

Cladding (n1)

Core (n2 > n1)

Megawatt / cm2 optical intesities n2 = n2,0+n2,2 Popt + … Leads to nonlinear distortions over hundreds of kilometers


Physical phenomena at play

… Optical field propagating in the fiber’s transverse mode

(Nonlinear Schrödinger Equation)+ N

FiberNonlinearity

NoiseFilteringEffects

•Chromatic Dispersion•Optical Filtering (ROADMs)

•Spontaneous emission fromin-line optical amplifiers

ROADM … Reconfigurable optical add/drop multiplexer


Shannon limits in fiber-optic systems

Increasing the signal power (i.e. the SNR) creates signal distortions from fiber nonlinearity, eventually limiting system performance

SNR [dB]

Cap

acity

C [b

its/s

] Maximum capacity

Signal launch power [dBm]

Tx Rx

Distributed Noise

C = B log2 (1 + SNR)

Nonlinear distortions

Quantum mechanics dictates a lower bound on amplifier noiseR.-J. Essiambre et al., Phys. Rev. Lett. (2008) or J. Lightwave Technol. (2010)


Shannon limits in fiber-optic systems

Increasing the signal power (i.e. the SNR) creates signal distortions from fiber nonlinearity, eventually limiting system performance

SNR [dB]

Cap

acity

C [b

its/s

] Maximum capacity

Signal launch power [dBm]

Tx Rx

Distributed Noise

Numerical statistics

R.-J. Essiambre et al., Phys. Rev. Lett. (2008) or J. Lightwave Technol. (2010)

0 5 10 15 20 25 30 35 40SNR (dB)

Capa

city

per

uni

t ba

ndw

idth

(bit

s/s/

Hz)

0

1

2

3

4

5

6

8

71 ring2 rings4 rings8 rings

16 rings


0 5 10 15 20 25 30 35 40SNR (dB)

Capa

city

per

uni

t ba

ndw

idth

(bit

s/s/

Hz)

0

1

2

3

4

5

6

8

71 ring2 rings4 rings8 rings16 rings-0.2 -0.1 0 0.1 0.2

-0.2

-0.1

0

0.1

0.2

Imag

par

t of

fie

ld [

mW

1/2 ]

Real part of field [ mW1/2]

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1


Imag

par

t of

fie

ld [

mW

1/2 ]

-2 -1 0 1 2

-2

-1

0

1

2


Imag

par

t of

fie

ld [

mW

1/2 ]

Capacity limit estimates of the “fiber channel”

R.-J. Essiambre et al., Phys. Rev. Lett. (2008) or J. Lightwave Technol. (2010)

• Note: Capacity maximum occurs at fairly high SNRs


We are approaching the nonlinear Shannon limit

5

10

15

2100 1,000 10,000

Transmission distance [km]

Spec

tral

eff

icie

ncy

[b/s

/Hz]

~2x

[P. J. Winzer, Photon. Technol. Lett., 2011]

Current 100G products

Commercial WDM system, ca. 2015 - 2020

PolarizationFrequency

Time Quadrature

Current WDM products use all dimensions

Spacehttp://www.occfiber

.com/

but space

Physical dimensions

Linear Shannon at high SNR: 2SE x L = const.

4 Spatial multiplexing in optics: Integration, crosstalk, and MIMO


Spatial Multiplexing (or Space-Division Multiplexing, SDM)

TX RX

TX RX

TX RX

• Spatial multiplexing can scale fiber capacities by orders of magnitudeand can enable economic capacity scaling

• Integration is key to reduce cost (or energy) per bit compared to today’s systems

Integrated transponders, Integrated amplifiers, Multi-mode or Multi-core fiber

Schematic view


Integrated transponders for spatial multiplexing

4.0 mm

TE TM

MZI demux Grating coupler

Photodiode

Fiber

1234567

• Fully integrated receiver for 7-core fiber[C.R.Doerr et al., PTL 2011]


Spatial multiplexing in 7-core fiber: 112 Tb/s, 14 b/s/Hz, 77 km

•[B.Zhu et al., ECOC 2011 and OptEx, 2011]


How much crosstalk is tolerable ?

10 15 20 25 30 35 40 45

0

1

2

3

4

5

6

7

5

Crosstalk [dB]

OSN

R pe

nalt

y [d

B]

QPSK 16-QAM 64-QAM

[P.J. Winzer et al., ECOC 2011]


Spatial Multiplexing (or Space-Division Multiplexing, SDM)

TX RX

TX RX

TX RX

Integrated transponders, Integrated amplifiers, Multi-mode or Multi-core fiber

Schematic view

• If crosstalk between SDM paths (due to integration!) is unacceptably high: Need multiple-input multiple-output (MIMO) digital signal processing

• MIMO has been very successfully applied to scale capacity in wireless systems

• Spatial multiplexing can scale fiber capacities by orders of magnitudeand can enable economic capacity scaling

• Integration is key to reduce cost (or energy) per bit compared to today’s systems


MIMO channel

SDM and MIMO in fibers – Some differences to wireless MIMO

• Potential addressability of all propagation modes (complete set)

• High reliability requirements (99.999%), low outage probabilities (10-5)

• Distributed noise

• RX TX feedback almost always impossible

• Fiber nonlinearity (likely to set per-mode peak-power constraints)

• Nonlinear MIMO signal processing

MIM

OD

ecod

er

+

Channelmatrix H

MTN0

N0

+MR

MIM

OEn

code

r

M x M


Segment

MIM

OD

ecod

er

N1

n1H1

M

n2H2

+

nKHK

N2 NK

N1 N2 NK

MIM

OEn

code

r

M

+

+

+

+

+

Distributed noise loading

• In optics, noise loading is usually distributed over propagation(e.g., on a “per-span” or “per-segment” basis)

• Spatial noise correlation

• If segment matrices are unitary:[Winzer and Foschini, Optics Express, 2011]


Distributed noise loading for non-unitary segments

• Outage probabilities for M = 16 modes, K = 64 segments• Mode-dependent loss MDLi per segment

1

10-2

Out

age

prob

abilit

y

0.4 0.6 0.8 1

10-4

Capacity (C/M)

MDLi [dB] = 52

10.5

Noise loading at receiver


• Noise loading at receiver is worse than distributed noise loading• A per-segment MDL of 1 dB only reduces capacity by


Distributed noise loading for non-unitary segments

Even for K = 128 segments and 1-dB per segment MDL,MIMO capacity is only reduced by ~10%

•0.3

•0.4

•0.5

•0.6

•0.7

•0.8

•0.9

•1C

apac

ity a

t 10-

4ou

tage

(CP

/M

)ou

t

•0.1 •0.3 •0.5 •1 •3 •5•Mode-dependent loss per segment [dB]

K = 128

64

16

2

Noise loading at receiver


M = 16

[Winzer and Foschini, Optics Express, 2011]


First experimental results using 3 coupled spatial modes

SDM

MUX

3-mode fiber

• All guided modes are selectively launched and coherently detected(otherwise: System outage)

• Modes are strongly coupled during propagation in the fiber• Digital signal processing decouples received signals

Orthogonalmode

coupling

SDM

DEMUX

PD-CohRX0

Out1Out2Out3Out4Out5Out6

MIMO

DSP

Orthogonalmode

coupling

ModeMixing

PD-CohRX1

PD-CohRX2

n1n2n3n4n5n6

Ch1Ch2Ch3Ch4Ch5Ch6

PD: Polarization Diversity

LP01 X-pol LP11a X-pol LP11b X-pol

Inte

nsit

y

LP01 Y-pol LP11a Y-pol LP11b Y-pol

[R. Ryf et al., OFC 2011; S. Randel et al., Optics Express 2011]


Digital signal processing for 28-Gbaud 6 × 6 MIMO

• Network of 36 feed-forward equalizers (FFEs)

• ~100 taps per filter

TheoryGray: b2bColor: 33 km

[S. Randel et al., Optics Express 2011]


The first optical 6 x 6 coherent MIMO experiment


Summary

• Coherent detection with digital signal processing is now also key in optics• Blind and pilot based processing techniques• OFDM and single-carrier systems

• Spatial multiplexing will be needed to scale system capacity beyond WDM• Integrated optical amplifier technologies ?• Integrated transponder technologies ?• Multiple fiber strands or integrated fiber technologies ?

• If coupling between spatial multiplexing paths cannot be neglected• Need MIMO signal processing to undo crosstalk at receiver(but: MIMO ≠ MIMO !)

• This exciting new era in optical communications also opens up a rich fieldof new communication- and information-theoretic research problems!

• R.-J. Essiambre et al., “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28, 662 (2010).• P. J. Winzer, “Beyond 100G Ethernet,” IEEE Comm. Mag. 48, 26 (2010).• S. Randel et al., “6 x 56-Gb/s Mode-Division Multiplexed Transmission over 33-km Few-Mode Fiber Enabled

by 66 MIMO Equalization,” Optics Express (2011).• P. J. Winzer and G. J. Foschini, “MIMO Capacities and Outage Probabilities in Spatially Multiplexed Optical

Transport Systems,” Optics Express (2011).


www.alcatel-lucent.com


Part 1: Attenuation


This basic equation describes nonlinear propagation:

(Nonlinear Schroedinger Equation)

Attenuation

Change withdistance


Part 2: Dispersion



DispersionChange withdistance

Fourier transform:

Corresponds to

from previous page

“Allpass with quadratic phase”


Part 3: Kerr Nonlinearity



Change withdistance

KerrNonlinearity

Corresponds to

From previous page


Simulation steps

Step size ∆z∆z

0 2 3 4 5 6 7 81 Distance

Split-Step Fourier Transform Technique

• Consider short pieces of fiber (dispersion only, nonlinearity only)• Alternate between simple solution in t and f

Nonlinearity (but no dispersion)

Dispersion (but no nonlinearity)

Information Theory and Digital Signal Processing in Optical CommunicationsOutlineSlide Number 3Network traffic is growing exponentiallyHigh-speed fiber optic networksSlide Number 6High-speed optical interface researchHigh-speed optical interface product developmentBasic coherent optical receiver setupHigher interface rates via higher-order modulationHigher interface rates via higher-order modulationHigher interface rates via higher-order modulationFiber capacity increase through spectral efficiencyScaling WDM capacity through spectral efficiencyBasic trade-off: Spectral efficiency versus sensitivitySlide Number 16Optical fiber nonlinearitiesPhysical phenomena at playShannon limits in fiber-optic systemsShannon limits in fiber-optic systemsCapacity limit estimates of the “fiber channel”We are approaching the nonlinear Shannon limitSlide Number 23Spatial Multiplexing (or Space-Division Multiplexing, SDM)Integrated transponders for spatial multiplexingSpatial multiplexing in 7-core fiber: 112 Tb/s, 14 b/s/Hz, 77 kmHow much crosstalk is tolerable ?Spatial Multiplexing (or Space-Division Multiplexing, SDM)SDM and MIMO in fibers – Some differences to wireless MIMODistributed noise loadingDistributed noise loading for non-unitary segmentsDistributed noise loading for non-unitary segmentsFirst experimental results using 3 coupled spatial modesDigital signal processing for 28-Gbaud 6 × 6 MIMOThe first optical 6 x 6 coherent MIMO experimentSummarySlide Number 37Part 1: AttenuationPart 2: DispersionPart 3: Kerr NonlinearitySplit-Step Fourier Transform Technique

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