Download + N - 2011 IEEE CTW

Information Theory and Digital
Signal Processing in Optical
Communications
Peter J. Winzer
Bell 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
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
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1
Traffic scaling in data networks
and the enabling role of optics
Network traffic is growing exponentially
Telepresence
Panasonic’s LifeWall
60%  10 log10(1.6) dB  2 dB
Exponential network traffic growth is driven by high-bandwidth digital applications
Video-on-demand, telepresence, wireless backhaul, cloud computing & services
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High-speed fiber optic networks
Client interface
(e.g., 4 x 25 Gbit/s)
Router
Reconfigurable optical
add/drop multiplexer
(ROADM)
Line interface
(e.g., 100 Gbit/s)
Optical network
WDM system
(e.g., 80 x 100 Gbit/s)
WDM: Wavelength-division multiplexing
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2
High-speed interfaces: Finally
using coherent detection ...
Tb/s
100
10
Coherent detection
1
Direct detection
100
Gb/s
Serial Interface Rates and WDM Capacities
High-speed optical interface research
9.3 ps
10
1
1986
1990
1994
1998
2002
2006 2010
2014
2018
• Recently demonstrated 448-Gb/s interfaces in research
(224-Gb/s per polarization)
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2022
Tb/s
100
10
Coherent detection
1
Direct detection
100
Gb/s
Serial Interface Rates and WDM Capacities
High-speed optical interface product development
10
1
1986
1990
1994
1998
2002
2006 2010
2014
2018
2022
• 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)
8 | IEEE CTW, June 2011
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PDM-QPSK
ASIC: 70M+ gates
Basic coherent optical receiver setup
High-speed sampling
x pol.
Digitization
f
y pol.
Ix + jQx
Iy + jQy
Front-end optics
9 | IEEE CTW, June 2011
Analog-to-digital
conversion
Back-end digital electronic
signal processing
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Higher interface rates via higher-order modulation
PDM 512-QAM
3 GBaud (54 Gb/s)
PDM 256-QAM
4 GBaud (64 Gb/s)
[Okamoto et al., ECOC’10] [Nakazawa et al., OFC’10]
PDM 32-QAM
9 GBaud (90 Gb/s)
[Zhou et al., OFC’11]
PDM 64-QAM
PDM 16-QAM
21 GBaud (256 Gb/s) 56 GBaud (448 Gb/s)
[Gnauck et al., OFC’11]
High D/A and A/D resolution
[Winzer et al., ECOC’10]
High speed
[R.H. Walden, 1999 and 2008]
•ENoB: Effective number of bits
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Higher interface rates via higher-order modulation
PDM 512-QAM
3 GBaud (54 Gb/s)
PDM 256-QAM
4 GBaud (64 Gb/s)
[Okamoto et al., ECOC’10] [Nakazawa et al., OFC’10]
PDM 32-QAM
9 GBaud (90 Gb/s)
[Zhou et al., OFC’11]
PDM 64-QAM
PDM 16-QAM
21 GBaud (256 Gb/s) 56 GBaud (448 Gb/s)
[Gnauck et al., OFC’11]
High D/A and A/D resolution
[Winzer et al., ECOC’10]
High speed
Electrical spectrum
Mod.
Optical spectrum
•f
Laser
•f
Mod.
•f
Laser
Comb
Single-carrier transmitter
Mod.
Mod.
•f +
•f
Mod.
Optical OFDM transmitter
11 | IEEE CTW, June 2011
•f
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•f
•f
Higher interface rates via higher-order modulation
PDM 512-QAM
3 GBaud (54 Gb/s)
PDM 256-QAM
4 GBaud (64 Gb/s)
[Okamoto et al., ECOC’10] [Nakazawa et al., OFC’10]
PDM 32-QAM
9 GBaud (90 Gb/s)
[Zhou et al., OFC’11]
PDM 64-QAM
PDM 16-QAM
21 GBaud (256 Gb/s) 56 GBaud (448 Gb/s)
[Gnauck et al., OFC’11]
High D/A and A/D resolution
[Winzer et al., ECOC’10]
High speed
65 GHz
300 GHz
60 GHz
448 Gb/s (10 subcarriers) 16-QAM
5 bit/s/Hz
2000 km transm.
[Liu et al., OFC’10]
12 | IEEE CTW, June 2011
606 Gb/s (10 subcarriers) 32-QAM
7 bit/s/Hz
2000 km transm.
[Liu et al., ECOC’10]
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1.2 Tb/s (24 subcarriers) QPSK
3 bit/s/Hz
7200 km transm.
[Chandrasekhar et al., ECOC’09]
Spectral efficiency [b/s/Hz]
Fiber capacity increase through spectral efficiency
10
•20 years ago: Device physics set engineering
limits on spectral efficiency
1
0.1
0.01
1990
Single polarization
Polarization interleaving
Polarization multiplexing
1994
1998
Year
2002
•Today: Information theory sets fundamental
limits on spectral efficiency
Fiber nonlinearity sets fundamental
limits on per-fiber spectral efficiency
2006 2010
x-pol x-pol
~ 5 THz bandwidth ~ 100 km of fiber
y-pol y-pol
Tx
Laser & filter stability
Modulation
Detection
PDM
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Rx
Tb/s
100
10
1
100
Gb/s
Serial Interface Rates and WDM Capacities
Scaling WDM capacity through spectral efficiency
10
1
1986
[P.J.Winzer, IEEE Comm. Mag., June 2010]
1990
1994
1998
2002
2006 2010
2014
2018
2022
• ~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
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Basic trade-off: Spectral efficiency versus sensitivity
~ W/(Gb/s)
~ mW/(Gb/s)
RxTx
RxTx
RxTx
RxTx
Spectral efficiency comes at a fundamental cost:
•Higher signal-to-noise ratio (SNR) requirements for higher-order modulation
Spectral 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!
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The role of fiber nonlinearity
in optical communications
Optical fiber nonlinearities
Cladding (n1)
Core (n2 > n1)
• Core diameter ~8 µm
• Cladding diameter ~125 µm
• Light is kept within the core (total reflection)
 Megawatt / cm2 optical intesities  n2 = n2,0+n2,2 Popt + …
 Leads to nonlinear distortions over hundreds of kilometers
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Physical phenomena at play
… Optical field propagating in the fiber’s transverse mode
+N
(Nonlinear Schrödinger Equation)
Fiber
Nonlinearity
Filtering
Effects
Noise
• Chromatic Dispersion
• Optical Filtering (ROADMs)
• Spontaneous emission from
in-line optical amplifiers
ROADM … Reconfigurable optical add/drop multiplexer
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Shannon limits in fiber-optic systems
Increasing the signal power (i.e. the SNR) creates signal distortions from fiber
nonlinearity, eventually limiting system performance
Capacity C [bits/s]
Maximum
capacity
C = B log2 (1 + SNR)
SNR [dB]
Signal launch power [dBm]
Distributed Noise
Tx
Rx
Nonlinear distortions
Quantum mechanics dictates a lower bound on amplifier noise
R.-J. Essiambre et al., Phys. Rev. Lett. (2008) or J. Lightwave Technol. (2010)
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Shannon limits in fiber-optic systems
Capacity C [bits/s]
Maximum
capacity
SNR [dB]
Signal launch power [dBm]
Capacity per unit bandwidth
(bits/s/Hz)
Increasing the signal power (i.e. the SNR) creates signal distortions from fiber
nonlinearity, eventually limiting system performance
8
1 ring
2 rings
4 rings
8 rings
16 rings
7
6
5
4
3
2
1
0
0
5
10
Distributed Noise
Tx
20
25
30
35
SNR (dB)
Rx
Numerical statistics
R.-J. Essiambre et al., Phys. Rev. Lett. (2008) or J. Lightwave Technol. (2010)
20 | IEEE CTW, June 2011
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40
Imag part of field [ mW1/2]
0.2
0.1
8
1 ring
2 rings
4 rings
8 rings
16 rings
0
-0.2
-0.2
-0.1
0
0.1
0.2
1/2
Real part of field [ mW
]
7
6
0.5
0
-0.5
-1
-1
-0.5
0
0.5
1
1/2
Real part of field [ mW
]
5
4
3
2
2
1
0
-1
-2
-2
-1
0
1
2
1/2
Real part of field [ mW
1
0
0
5
10
15
20
25
30
SNR (dB)
• Note: Capacity maximum occurs at fairly high SNRs
R.-J. Essiambre et al., Phys. Rev. Lett. (2008) or J. Lightwave Technol. (2010)
21 | IEEE CTW, June 2011
1
Imag part of field [ mW1/2]
-0.1
Capacity per unit bandwidth
(bits/s/Hz)
Imag part of field [ mW1/2]
Capacity limit estimates of the “fiber channel”
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35
40
]
15
Commercial WDM system, ca. 2015 - 2020
~2x
Spectral efficiency [b/s/Hz]
We are approaching the nonlinear Shannon limit
10
Linear Shannon at high SNR: 2SE x L = const.
5
[P. J. Winzer, Photon. Technol. Lett., 2011]
2
100
1,000
10,000
Transmission distance [km]
Current 100G products
Polarization
Space
http://www.occfiber
.com/
Frequency
Physical dimensions
Time
Quadrature
Current WDM products use all dimensions but space
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4
Spatial multiplexing in optics:
Integration, crosstalk, and MIMO
Spatial Multiplexing (or Space-Division Multiplexing, SDM)
• Spatial multiplexing can scale fiber capacities by orders of magnitude
and can enable economic capacity scaling
• Integration is key to reduce cost (or energy) per bit compared to today’s systems
Schematic view
TX
RX
TX
RX
TX
RX
Integrated transponders, Integrated amplifiers, Multi-mode or Multi-core fiber
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Integrated transponders for spatial multiplexing
• Fully integrated receiver for 7-core fiber
[C.R.Doerr et al., PTL 2011]
1
2
3
4
5
6
7
TE
TM
Fiber
MZI demux
Photodiode
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Grating coupler
4.0 mm
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Spatial multiplexing in 7-core fiber: 112 Tb/s, 14 b/s/Hz, 77 km
•[B.Zhu et al., ECOC 2011 and OptEx, 2011]
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How much crosstalk is tolerable ?
OSNR penalty [dB]
7
6 QPSK
16-QAM 64-QAM
5
4
3
2
1
0
5
10
15
20
25
30
35
40
45
Crosstalk [dB]
[P.J. Winzer et al., ECOC 2011]
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Spatial Multiplexing (or Space-Division Multiplexing, SDM)
• Spatial multiplexing can scale fiber capacities by orders of magnitude
and can enable economic capacity scaling
• Integration is key to reduce cost (or energy) per bit compared to today’s systems
• 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
Schematic view
TX
RX
TX
RX
TX
RX
Integrated transponders, Integrated amplifiers, Multi-mode or Multi-core fiber
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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
+
N0
MxM
Channel
matrix H
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MIMO
Decoder
MR
+
MIMO
Encoder
MT
MIMO channel N
0
Distributed noise loading
• In optics, noise loading is usually distributed over propagation
(e.g., on a “per-span” or “per-segment” basis)
Segment
N1
N2
NK
M
+
H1
n1
+
H2
n2
+
HK
nK
+
+
+
N1
N2
NK
MIMO
Decoder
MIMO
Encoder
M
• Spatial noise correlation
• If segment matrices are unitary:
[Winzer and Foschini, Optics Express, 2011]
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Distributed noise loading for non-unitary segments
• Outage probabilities for M = 16 modes, K = 64 segments
• Mode-dependent loss MDLi per segment
1
Noise loading at receiver
Outage probability
Distributed noise loading
10-2
MDLi [dB] = 5
2
1
0.5
10-4
0.4
0.6
0.8
Capacity (C/M)
• Noise loading at receiver is worse than distributed noise loading
• A per-segment MDL of 1 dB only reduces capacity by <5%
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1
Capacity at 10-4 outage (CPout /M)
Distributed noise loading for non-unitary segments
•1
•0.9
M = 16
2
16
•0.8
•0.7
Noise loading at receiver
•0.6
Distributed noise loading
64
•0.5
K = 128
•0.4
•0.3
•0.1
•0.3
•0.5
•1
•3
•Mode-dependent loss per segment [dB]
 Even for K = 128 segments and 1-dB per segment MDL,
MIMO capacity is only reduced by ~10%
•5
[Winzer and Foschini, Optics Express, 2011]
32 | IEEE CTW, June 2011
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First experimental results using 3 coupled spatial modes
Ch1
Ch2
Ch3
Ch4
Ch5
Ch6
SDM
MUX
Orthogonal
mode
coupling
LP01 Y-pol
SDM
Mode
Mixing
DEMUX
Orthogonal
mode
coupling
LP11a X-pol
LP11a Y-pol
PD-Coh n1
RX0
n2
PD-Coh n3 MIMO
n4 DSP
RX1
PD-Coh n5
n6
RX2
Out1
Out2
Out3
Out4
Out5
Out6
PD: Polarization Diversity
LP11b X-pol LP11b Y-pol
Intensity
LP01 X-pol
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
[R. Ryf et al., OFC 2011; S. Randel et al., Optics Express 2011]
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Digital signal processing for 28-Gbaud 6 × 6 MIMO
• Network of 36 feed-forward
equalizers (FFEs)
• ~100 taps per filter
Theory
Gray: b2b
Color: 33 km
[S. Randel et al., Optics Express 2011]
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The first optical 6 x 6 coherent MIMO experiment
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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 field
of 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).
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Part 1: Attenuation
… Optical field propagating in the fiber’s transverse mode
This basic equation describes nonlinear propagation:
(Nonlinear Schroedinger Equation)
Change with
distance
Attenuation
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Part 2: Dispersion
… Optical field propagating in the fiber’s transverse mode
This basic equation describes nonlinear propagation:
Change with
distance
Dispersion
Fourier transform:

Corresponds to
from previous page
“Allpass with quadratic phase”
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Part 3: Kerr Nonlinearity
… Optical field propagating in the fiber’s transverse mode
This basic equation describes nonlinear propagation:
Change with
distance
Kerr
Nonlinearity
Corresponds to
From previous page

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Split-Step Fourier Transform Technique
• Consider short pieces of fiber (dispersion only, nonlinearity only)
• Alternate between simple solution in t and f
Simulation steps
0
1
2
3
4
5
6
7
8
∆z
Step size ∆z
Dispersion (but no nonlinearity)
Nonlinearity (but no dispersion)
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Distance