Post on 27-Jan-2021
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
All Rights Reserved © Alcatel-Lucent 20114 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 20115 | IEEE CTW, June 2011
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 ...
All Rights Reserved © Alcatel-Lucent 20117 | IEEE CTW, June 2011
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)
All Rights Reserved © Alcatel-Lucent 20118 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 20119 | IEEE CTW, June 2011
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.
All Rights Reserved © Alcatel-Lucent 201110 | IEEE CTW, June 2011
Higher interface rates via higher-order modulation
PDM 512-QAM3 GBaud (54 Gb/s)
[Okamoto et al., ECOC’10]
PDM 256-QAM4 GBaud (64 Gb/s)
[Nakazawa et al., OFC’10]
PDM 64-QAM21 GBaud (256 Gb/s)
[Gnauck et al., OFC’11]
PDM 16-QAM56 GBaud (448 Gb/s)
[Winzer et al., ECOC’10]
PDM 32-QAM9 GBaud (90 Gb/s)
[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]
All Rights Reserved © Alcatel-Lucent 201111 | IEEE CTW, June 2011
Higher interface rates via higher-order modulation
PDM 512-QAM3 GBaud (54 Gb/s)
[Okamoto et al., ECOC’10]
PDM 256-QAM4 GBaud (64 Gb/s)
[Nakazawa et al., OFC’10]
PDM 64-QAM21 GBaud (256 Gb/s)
[Gnauck et al., OFC’11]
PDM 16-QAM56 GBaud (448 Gb/s)
[Winzer et al., ECOC’10]
PDM 32-QAM9 GBaud (90 Gb/s)
[Zhou et al., OFC’11]
High D/A and A/D resolution High speed
•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+
All Rights Reserved © Alcatel-Lucent 201112 | IEEE CTW, June 2011
Higher interface rates via higher-order modulation
PDM 512-QAM3 GBaud (54 Gb/s)
[Okamoto et al., ECOC’10]
PDM 256-QAM4 GBaud (64 Gb/s)
[Nakazawa et al., OFC’10]
PDM 64-QAM21 GBaud (256 Gb/s)
[Gnauck et al., OFC’11]
PDM 16-QAM56 GBaud (448 Gb/s)
[Winzer et al., ECOC’10]
PDM 32-QAM9 GBaud (90 Gb/s)
[Zhou et al., OFC’11]
High D/A and A/D resolution High speed
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
All Rights Reserved © Alcatel-Lucent 201113 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201114 | IEEE CTW, June 2011
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]
All Rights Reserved © Alcatel-Lucent 201115 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201117 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201118 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201119 | IEEE CTW, June 2011
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)
All Rights Reserved © Alcatel-Lucent 201120 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201121 | IEEE CTW, June 2011
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
Real part of field [ mW1/2]
Imag
par
t of
fie
ld [
mW
1/2 ]
-2 -1 0 1 2
-2
-1
0
1
2
Real part of field [ mW1/2]
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
All Rights Reserved © Alcatel-Lucent 201122 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201124 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201125 | IEEE CTW, June 2011
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]
All Rights Reserved © Alcatel-Lucent 201126 | IEEE CTW, June 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]
All Rights Reserved © Alcatel-Lucent 201127 | IEEE CTW, June 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]
All Rights Reserved © Alcatel-Lucent 201128 | IEEE CTW, June 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
All Rights Reserved © Alcatel-Lucent 201129 | IEEE CTW, June 2011
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
All Rights Reserved © Alcatel-Lucent 201130 | IEEE CTW, June 2011
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]
All Rights Reserved © Alcatel-Lucent 201131 | IEEE CTW, June 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
Distributed noise loading
• Noise loading at receiver is worse than distributed noise loading• A per-segment MDL of 1 dB only reduces capacity by
All Rights Reserved © Alcatel-Lucent 201132 | IEEE CTW, June 2011
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
Distributed noise loading
M = 16
[Winzer and Foschini, Optics Express, 2011]
All Rights Reserved © Alcatel-Lucent 201133 | IEEE CTW, June 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]
All Rights Reserved © Alcatel-Lucent 201134 | IEEE CTW, June 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]
All Rights Reserved © Alcatel-Lucent 201135 | IEEE CTW, June 2011
The first optical 6 x 6 coherent MIMO experiment
All Rights Reserved © Alcatel-Lucent 201136 | IEEE CTW, June 2011
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).
All Rights Reserved © Alcatel-Lucent 201137 | IEEE CTW, June 2011
www.alcatel-lucent.com
All Rights Reserved © Alcatel-Lucent 201138 | IEEE CTW, June 2011
Part 1: Attenuation
… Optical field propagating in the fiber’s transverse mode
This basic equation describes nonlinear propagation:
(Nonlinear Schroedinger Equation)
Attenuation
Change withdistance
All Rights Reserved © Alcatel-Lucent 201139 | IEEE CTW, June 2011
Part 2: Dispersion
… Optical field propagating in the fiber’s transverse mode
This basic equation describes nonlinear propagation:
DispersionChange withdistance
Fourier transform:
Corresponds to
from previous page
“Allpass with quadratic phase”
All Rights Reserved © Alcatel-Lucent 201140 | IEEE CTW, June 2011
Part 3: Kerr Nonlinearity
… Optical field propagating in the fiber’s transverse mode
This basic equation describes nonlinear propagation:
Change withdistance
KerrNonlinearity
Corresponds to
From previous page
All Rights Reserved © Alcatel-Lucent 201141 | IEEE CTW, June 2011
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