Post on 07-Jan-2017
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Optimized 4 and 8 Dimensional Modulation Formats for Variable Capacity in Optical Networks
Michael Reimer, Shahab Oveis Gharan, Andrew D. Shiner and Maurice O’Sullivan
March 21, 2016
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Four available dimensions of the optical field: In-phase (I) and quadrature (Q) components of two polarizations.
2D symbols encoded on I and Q of each orthogonal polarization.Data on each polarization can be decoded independently of data on other polarization.
X-pol
Y-pol
Encoded symbol2D symbols encoding 1 bit
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4D symbols encoded across I and Q of two orthogonal polarizations.Examples: PS-QPSK, 32-SP-QAM, 128-SP-QAM, etc.
4D symbols encoding 2 bits
X-pol
Y-pol
Encoded symbol
E. Agrell, et al., J. Lightwave Technol. 27(22), 2009P. Poggiolini, Opt. Expr., 18(11), 2010M. Chagnon, et al., Opt. Expr., 21(25) 2013R. Rios-Muller, et al., Proc. ECOC, Th.2.D.2, 2013H. Sun, et al., Proc. ECOC, Th.2.D.3, 2013
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OSNR (dB)
BER
3% bit error rate
4D-8QAM PM-8QAM
0.48 dB
35 GBd signaling rate
Example: 4D encoding at 8QAM capacity Linear performance advantage can be realized through novel 4D encoding.
Control of optical power characteristics through constellation “power-balancing”.
Constant 4D symbol modulus for reduced inter-channel nonlinear interference.
Example: 4D-8QAM - 4D constant modulus encoding at PM-8QAM equivalent capacity.
0.48 dB OSNR improvement at 0.03 BER relative to PM-8QAM.
� + � = constant for all symbols
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X-pol
Y-pol
Encoded symbol8D symbols encoding 4 bits
8D symbols encoded across I and Q of two orthogonal polarizations of two time slots (or optical wavelengths, spatial modes, etc.)
D. Millar, et al., Opt. Expr., 22(7), 2014D. Millar, et al., Proc. OFC, M3A.4, 2014T. Eriksson, et al. Proc. ECOC, Th.2.D.4, 2013.A. D. Shiner, et al., Opt. Expr., 22(17), 2014
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Linear performance advantage can be realized through novel 8D constellation designs.
e.g. 0.62 dB OSNR improvement at 0.03 BER relative to PM-BPSK using 8D biorthogonal constellation.
OSNR (dB)B
ER
3% bit error rate
8D biorthogonal PM-BPSK
0.62 dB
35 GBd signaling rate
Example: 8D Biorthogonal
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Poincaré sphere
WDM spectrum
Reduced cross polarization modulation (XPolM)
8D polarization balanced channel
Linear performance advantage can be realized through novel 8D constellation designs.
e.g. 0.62 dB OSNR improvement at 0.03 BER relative to PM-BPSK using 8D biorthogonal constellation.
Control over the temporal characteristics of transmit symbols: “polarization-balancing”
A. D. Shiner, et al., Opt. Express, 22(17), 2014
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Linear performance advantage can be realized through novel 8D constellation designs.
e.g. 0.62 dB OSNR improvement at 0.03 BER relative to PM-BPSK using 8D biorthogonal constellation.
Control over the temporal characteristics of transmit symbols: “polarization-balancing”
Simplified hardware implementation.PM-BPSK spectral efficiency requires decoding of 16 symbols in 8D space.
Example: 8D-2QAM - 8D pol. balanced encoding at PM-BPSK equivalent capacity.
A. D. Shiner, et al., Opt. Express, 22(17), 2014Poincaré sphere
Reduced cross polarization modulation (XPolM)
8D polarization balanced channel
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3% pre-FEC (uncoded) bit error rate
BPSK
OSNR (dB)
8D QPSK 16QAM
BER
8QAM
35 GBd signaling rate
Track required OSNR (ROSNR) for an example 0.03 pre-FEC BER over range of capacity. ROSNR dependent on Euclidean and Hamming distance properties of the modulation.
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35 GBd signaling rate
0.03 pre-FEC (uncoded) BER
25% overhead
PM-32QAM10 bits/interval
PM-STARQAMPM-16QAM8 bits/interval
PM-8QAM6 bits/interval
PM-QPSK4 bits/interval
PM-BPSK2 bits/interval
Standard QAM
Shannon
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PM-32QAM10 bits/interval
PM-STARQAMPM-16QAM8 bits/interval
PM-8QAM6 bits/interval
Standard QAM
PM-32QAM
PM-16QAM PM-STARQAM
PM-8QAM
PM-QPSK PM-BPSK
Shannon
PM-BPSK2 bits/interval
PM-QPSK4 bits/interval
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4D Set partitioning
32-SP-QAM5 bits/interval
64-SP-QAM6 bits/interval
128-SP-QAM7 bits/interval
128-SP-QAM
64-SP-QAM
32-SP-QAM
R. Rios-Muller, et al., Proc. ECOC, Th.2.D.2, 2013H. Sun, et al., Proc. ECOC, Th.2.D.3, 2013
Shannon
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4D Constant modulus formats
PS-QPSK3 bits/interval
6Pol-QPSK~ 4.6 bits/interval
PM-8PSK6 bits/interval
8Pol-QPSK5 bits/interval
PM-8PSK
8Pol-QPSK
PS-QPSK
P. Poggiolini, Opt. Expr., 18(11), 2010M. Chagnon, et al., Opt. Expr., 21(25) 2013H. Bulow, Proc. OFC, OWG.2, 2009
6Pol-QPSK
K. Kojima, Proc. ECOC, P.3.25, 2015
Shannon
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Time Domain Hybrid QAM (TDHQ) Constellations of differing cardinality within a single TDHQ frame.
Shannon
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Time Domain Hybrid QAM (TDHQ)
Shannon
Constellations of differing cardinality within a single TDHQ frame.
Increased ROSNR apparent at � ≤ � ≤ � b/s/Hz.Q. Zhuge, Proc. OECC, 2015
M. Reimer, Proc. SPPCom, 2015
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Constellations of differing cardinality within a single TDHQ frame.
Increased ROSNR apparent at � ≤ � ≤ � b/s/Hz.
> 0.5 dB ROSNR improvement through 4D format optimization.
4D Numerical Optimization
Q. Zhuge, Proc. OECC, 2015
M. Reimer, Proc. SPPCom, 2015Shannon
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Region enlarged
0.54 dB
4D Numerical Optimization
PM-8QAM6 bits/interval
32-SP-QAM5 bits/interval
0.53 dB
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Region enlarged
4D-8QAM0.48 dB
4D-8QAM: 4-dimensional encoding of 64 symbols (6 bits).
Constant 4D symbol modulus.
PM-8QAM6 bits/interval
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8D polarization balanced formats
X-constellation / 8D Biorthogonal2 bits/interval
Establish performance bounds of 8D pol-balanced formats.
8D polarization balanced2 – 4 bits/interval
A. D. Shiner, et al., Opt. Express, 22(17), 2014
Shannon
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8D polarization balanced formats Establish performance bounds of 8D pol-balanced formats.
Cost of 8D pol-balancing:3 dB ROSNR per 1 b/s/Hz increase in capacity.
Linear performance advantage with 8D pol-balancing up to 2.4 b/s/Hz (PS-QPSK)
3 dB ROSNR per 1 b/s/Hz
Shannon
8D polarization balanced2 – 4 bits/interval
X-constellation / 8D Biorthogonal2 bits/interval
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Dis
pers
ion
(ps/
nm)
Distance (km)
Txpo
wer
spe
ctru
m (d
B)
Wavelength (nm)
�� �, 50 GHz WDM spacing
System margin: dBs of additional noise that can be tolerated before FEC limit. Difference between line-delivered OSNR and OSNR required for FEC limit (ROSNR).
Measured 2430 km reach with PM-8QAM.
PM-8QAM2430 km
System margin
Zero margin reach
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Single 4D-8QAM, PM-8QAM interferers
PM-8QAM2430 km
2600 km
7% increased reach (170 km) measured for 4D-8QAM in presence of PM-8QAM WDM nonlinear interference.
Dis
pers
ion
(ps/
nm)
Distance (km)
Txpo
wer
spe
ctru
m (d
B)
Wavelength (nm)
�� �, 50 GHz WDM spacing
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4D-8QAM 2950 km
PM-8QAM2430 km
2600 km
Significant reduction of inter-channel nonlinear interference due to constant 4D symbol modulus.
20% measured increase in reach (520 km) with 4D-8QAM.
Dis
pers
ion
(ps/
nm)
Distance (km)
Txpo
wer
spe
ctru
m (d
B)
Wavelength (nm)
�� �, 50 GHz WDM spacing
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Polarization and time-switched QPSK: 1 bit selects time slot, 1 bit selects polarization, 2 bit QPSK symbol
0.62 dB improvement in OSNR required for 0.03 BER relative to PM-BPSK.
8D symbols encoding 4 bits.2 of 16 possible symbols shown.
X-pol
Y-pol
Encoded symbol
Y-polarized time slot
X-polarized time slot
Zero amplitude
Zero amplitude
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Dis
pers
ion
(ps/
nm)
Distance (km)
� = ���� ��
�= ���� ��
Increased nonlinear interference due to amplitude variations of 8D Biorthogonal. Max reach < PM-BPSK despite 0.62 dB improvement in required OSNR (ROSNR).
Zero margin reach (km)
Pow
er (d
Bm
)
PM-BPSK nonlinear polarization sensitivity
Large effective area fiber (LEAF), � ≈ 70 ��90% inline optical dispersion compensation, 6.5 dB NF9 WDM channels, 38 GHz separation35 GBd signaling rate
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Poincaré sphere
Identify an 8D rotation that: Equalizes the symbol modulus between time slots. Achieves orthogonal polarization states between time slots (polarization balancing).
8D rotation preserves the linear performance advantage of 8D biorthogonal.
8D symbols encoding 4 bits.2 of 16 possible symbols shown.
X-pol
Y-pol
Encoded symbol
A. D. Shiner, et al., Opt. Expr., 22(17), 2014
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> 30% increase in reach (3600 km) relative to PM-BPSK achieved through polarization balancing.
> 40% reach increase (> 4000 km) relative to standard 8D Biorthogonal
Zero margin reach (km)
Pow
er (d
Bm
)
Dis
pers
ion
(ps/
nm)
Distance (km)
� = ���� ��
�= ���� ��
Large effective area fiber (LEAF), � ≈ 70 ��90% inline optical dispersion compensation, 6.5 dB NF9 WDM channels, 38 GHz separation35 GBd signaling rate
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��
Polarization state of interfering BPSK channels
Interfering WDM channels
Central “probe” wavelength
Best case polarization orientation
Worst case polarization orientation
�
�
Poincaré sphere
PM-BPSK performance varies with polarization state of interfering PM-BPSK WDM channels due to XPolM.
XPolM
XPolM
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< 0.05 dB margin difference with respect to WDM polarization state.
“Best case” pol. alignment
2D projection of X-const. symbols
“Worst case” pol. alignment
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8D-PB-QPSK: 8D polarization balanced format with QPSK projection (3 bits/interval). > 25% increase in reach (2200 km) relative to PS-QPSK.
Zero margin reach (km)
Pow
er (d
Bm
)
Dis
pers
ion
(ps/
nm)
Distance (km)
� = ���� ��
�= ���� ��
Large effective area fiber (LEAF), � ≈ 70 ��90% inline optical dispersion compensation, 6.5 dB NF9 WDM channels, 38 GHz separation35 GBd signaling rate
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Single 8D-2QAM, PM-BPSK interferers
Wavelength (nm)
Txpo
wer
spe
ctru
m (d
B)
Dis
pers
ion
(ps/
nm)
65 �, 50 GHz WDM spacing
� = ����.� ��
Distance (km)PM-BPSK
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1.2 dB measured increase in system margin with 8D polarization balancing.
Minimal temporal variation of BER observed with 8D-2QAM.
1.2 dB margin
8D-2QAM
PM-BPSK
� = ����.� ��Temporal variation of � (dB)
8D-2QAM
PM-BPSK
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�= ���� ��
� = ���� ��SSMF
Improvement due mainly to the increased Euclidean distance of the multidimensional encoding.~ 16% and 13% increased reach at 5 and 6 bits/interval, respectively, using optimized 4D.> 6% increased reach with 8D pol-balancing up to 3 bits/interval spectral efficiency.
Dis
pers
ion
(ps/
nm)
Distance (km)
Max
imum
reac
h (k
m)
2 Pol. Capacity (b/s/Hz)
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Dis
pers
ion
(ps/
nm)
�= ���� ��
� = ���� ��
Max
imum
reac
h (k
m)
LEAF, 90% CD comp
≥ 20% increased reach at 5 and 6 bits/interval using optimized 4D formats.
> 25% increased reach with 8D pol-balancing up to 3 bits/interval spectral efficiency.
Distance (km)
2 Pol. Capacity (b/s/Hz)
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Z. Tian, L. Berg, M. Hubbard and P. Mehta, Ciena Submarine Line System Development
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Linear advantage of X-const. provides 0.6 dB margin improvement relative to PM-BPSK, with optimum electronic dispersion pre-compensation.
Power (dBm)
Rel
ativ
e m
argi
n (d
B)
PM-BPSK, 50% electronic CD pre-comp
X-const.
PM-BPSK, no electronic CD pre-comp
BPSK no CD pre-comp
BPSK with CD pre-comp
4000 km standard single mode fiber (SSMF)Dispersion uncompensated9 WDM channels, 38 GHz separation35 GBd signaling rate
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Phase conjugate twin wave (PCTW) QPSK – unitary transformation of PM-BPSK, with optimum electronic CD pre-compensation and appropriate receiver DSP.
PCTW-QPSK performance equal to PM-BPSK with optimum CD pre-compensation.
Linear advantage of X-const. improves margin by 0.6 dB relative to PCTW-QPSK.
PCTW-QPSK, 4 dBm X-constellation, 4 dBm
X. Liu, et al., Nat. Photon., vol. 7, pp. 560-568 (2013)
PM-BPSK with optimum CD pre-comp
� = �� (� + �)
�
8D
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Symbol DOP 1.0
4000 km LEAF90% inline optical CD compensation-1 dBm power
A
B
A
B
X
Y
Effective symbol polarization
� × cross-polarized symbols
AB
B
A
�� × co-polarized symbolsX
Y
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Symbol DOP 0.75
Effective symbol polarization
AB
X
Y
� × cross-polarized symbols
AB
B
A
�� × co-polarized symbolsX
Y
4000 km LEAF90% inline optical CD compensation-1 dBm power
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Symbol DOP 0.5
Effective symbol polarization
X
Y
A B
� × cross-polarized symbols
AB
B
A
� × co-polarized symbolsX
Y
4000 km LEAF90% inline optical CD compensation-1 dBm power
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Symbol DOP 0.25
Effective symbol polarization
X
Y
AB
�� × cross-polarized symbols
AB
B
A
� × co-polarized symbolsX
Y
4000 km LEAF90% inline optical CD compensation-1 dBm power
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Symbol DOP 0
Effective symbol polarization
X
Y
A
B
�� × cross-polarized symbols
AB
B
A
� × co-polarized symbolsX
Y
4000 km LEAF90% inline optical CD compensation-1 dBm power
X-constellation
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Distance (km)
Dis
pers
ion
(ps/
nm)
�= ���� ��
� = ���� ��SSMF
~ 2 dB SNR variation across range of spectral efficiency. Nonlinear signal-to-noise ratio (SNR) ~ constant for all amplitude modulated formats. Moderate SNR improvement through 8D pol-balanced encoding.
2 Pol. Capacity (b/s/Hz)
Non
linea
r SN
R (d
B)
-1 dBm launch powerWith electronic CD pre-comp
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Dis
pers
ion
(ps/
nm)
Distance (km)
� = ���� ��
� = ���� ��
LEAF, 90% CD comp
-5 dBm launch powerWith electronic CD pre-comp
2 Pol. Capacity (b/s/Hz)
Non
linea
r SN
R (d
B)
Nonlinear signal-to-noise ratio (SNR) ~ constant for amplitude modulated formats.
≥ 4 dB nonlinear SNR improvement through 8D pol-balanced encoding.
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Dis
pers
ion
(ps/
nm)
Distance (km)
� = ���� ��
� = ���� ��
LEAF, 90% CD comp
-5 dBm launch powerWith electronic CD pre-comp
2 Pol. Capacity (b/s/Hz)
Non
linea
r SN
R (d
B)
Nonlinear signal-to-noise ratio (SNR) ~ constant for amplitude modulated formats.
≥ 4 dB nonlinear SNR improvement through 8D pol-balanced encoding.
4D power balancing (constant symbol modulus)
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Dis
pers
ion
(ps/
nm)
Distance (km)
� = ���� ��
� = ���� ��
LEAF, 90% CD comp
-5 dBm launch powerWith electronic CD pre-comp
2 Pol. Capacity (b/s/Hz)
Non
linea
r SN
R (d
B)
Nonlinear signal-to-noise ratio (SNR) ~ constant for amplitude modulated formats.
≥ 4 dB nonlinear SNR improvement through 8D pol-balanced encoding.
4D power balancing (constant symbol modulus)
8D polarization balancing