Digital Back-Propagation for the Improvement of Link Design fileLNT Digital Back-Propagation for the...
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Digital Back-Propagation for the Improvement of Link Design
Roi Rath, Jochen Leibrich, Werner Rosenkranz
Christian-Albrechts-Universität zu Kiel
Workshop on Optical Communication Systems
October 2nd, 2012
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Contents
1. Motivation
2. Simulation Setup
3. Simulation Results
4. Conclusions and Outlook
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Motivation
Towards the minimization of implementation efforts and costs:
SMF 1G
Span 1 Span 2
T km
DCF 2G
Tx L km
Span 3
Rx
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Motivation
Towards the minimization of implementation efforts and costs:
• Step 1: Elimination of in-line dispersion compensators
– Means: Electrical Linear Equalization (LE)
SMF 1G
Span 1 Span 2
T km
Tx L km
Span 3
LE
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Motivation
Towards the minimization of implementation efforts and costs:
• Step 1: Elimination of in-line dispersion compensators
– Means: Electrical Linear Equalization (LE)
• Step 2: Reducing the number of EDFAs per link
– Maintaining link’s length Extension of span length Higher launch power
– High launch power Fiber Nonlinearities
• Solution: Electrical Nonlinear Equalization (NLE)
SMF NG
Span 1
T km
Tx
Span 2
L+L/2 km L+L/2 km
NLE
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Simulations Setup
Balanced Homodyne Receiver
EVM eval.
Pulse
Carver IQ-
MZM
Mapping & Shaping
PRMS Wave
Gen.
m spans
e B
s o s s f R R RZ-50 16-QAM
I Q EDFA
I
Q
e B
ADC
ADC
DSP Unit
LE
DBP j
Rs=26.75 Gbaud
RZ50-16QAM
Single-carrier
m spans of L km
Total length: 1000 km
No DCF
EDFA noise figure = 5 dB
nonlinear phase noise
Ros: 2, 3, 4
samples per
symbol
SSMF/
NZDSF
5th order
Butterworth filter
Be optimized
Symmetric SSFM
Step Size 10 km
m spans
EDFA
SSMF/
NZDSF
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Link Compositions
m spans
EDFA
SSMF/
NZDSF
Fiber α
(dB/km)
D
(ps/nm/km)
γ
(1/W/km)
SSMF 0.2 17 1.46
NZDSF 0.2 4 1.46
max. span
length
(km)
link composition for
1000 km total link
length
number of
EDFAs
50 20×50km 20
60 16×60km + 1×40km 17
80 12×80km + 1×40km 13
90 11×90km + 1×10km 12
100 10×100km 10
120 8×120km + 1×40km 9
150 6×150km + 1×100km 7
160 6×160km + 1×40km 7
180 5×180km + 1×100km 6
200 5×200km 5
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50 100 150 200 0
5
10
15
20
25
30
Span Length [km]
EV
M R
MS
@ O
pti
mal
Lau
nch
Po
wer
[%
]
LE
ABP
Simulation Results I
• Mapping of minimal EVM values for different span lengths: SSMF, linear
equalization vs. DBP, 32 samples per symbol, DBP’s step size << 10 km
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 0
5
10
15
20
25
30
Launch-Power [dBm]
EV
M R
MS
[%
]
L=50km
L=100km
L=150km
FEC Limit FEC Limit
DBP
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50 100 150 200 0
5
10
15
20
25
30
Span Length [km]
EV
M R
MS
@ O
pti
mal
Lau
nch
Po
wer
[%
]
LE
ABP
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 0
5
10
15
20
25
30
Launch-Power [dBm]
EV
M R
MS
[%
]
L=50km
L=100km
L=150km
Simulation Results I
• Mapping of minimal EVM values for different span lengths: SSMF, linear
equalization vs. DBP, 32 samples per symbol, DBP’s step size << 10 km
FEC Limit
Linear Equalization
FEC Limit
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50 100 150 200 0
5
10
15
20
25
30
Span Length [km]
EV
M R
MS
@ O
pti
mal
Lau
nch
Po
wer
[%
]
LE
ABP
Simulation Results I
• Mapping of minimal EVM values for different span lengths: SSMF, linear
equalization vs. DBP, 32 samples per symbol, DBP’s step size << 10 km
FEC Limit
• Trade-off: span length and
system performance
• Max. span length LE: 138 km
• Max. span length DBP: 183 km
• Achievable span length
extension : 45 km
45 km
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Simulation Results II – SSMF Link
• Minimal EVM values vs. span length: comparing different (and more realistic)
ADC sampling rates for SSMF and NZDSF Links, DBP's step size = 10 km
50 60 80 90 100 120 150 160 180 200 0
5
10
15
20
25
30
Span Length [km]
EV
M R
MS @
Op
tim
al L
aun
ch P
ow
er [
%]
LE(R o s
=2)
LE(R o s
=4)
DBP(R o s
=4)
DBP(R o s
=3)
DBP(R o s
=2)
-0.1 0 0.1
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Real Axis
Imag
. A
xis
Signal Constellation for Pin
= 8 dBm
FEC Limit
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Simulation Results II – NZDSF Link
• Minimal EVM values vs. span length: comparing different (and more realistic)
ADC sampling rates for SSMF and NZDSF Links, DBP's step size = 10 km
50 60 80 90 100 120 150 160 180 200 0
5
10
15
20
25
30
Span Length [km]
EV
M R
MS @
Op
tim
al L
aun
ch P
ow
er [
%]
LE(R o s
=2)
LE(R o s
=4)
DBP(R o s
=4)
DBP(R o s
=3)
DBP(R o s
=2)
FEC Limit
-0.1 0 0.1
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Real Axis
Imag
. A
xis
Signal Constellation for Pin
= 8 dBm
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Simulation Results II – Analysis
• Maximal span length (km) for the FEC limit, corresponding number of EDFAs
per link and the number of EDFAs omitted when using DBP instead of LE
• Number of EDFAs per link: reduction by up to 50% and at least 30%, when
comparing DBP with a linear equalizer
SSMF NZDSF
LE DBP LE DBP
Ros Lmax
(km) NEDFAs
Lmax
(km) NEDFAs
EDFAs
Omitted
Lmax
(km) NEDFAs
Lmax
(km) NEDFAs
EDFAs
Omitted
2 82 13 140 8 5 (38%) 61 17 124 9 8 (47%)
3 111 10 165 7 3 (30%) 98 11 158 7 4 (36%)
4 111 10 165 7 3 (30%) 99 11 162 7 4 (36%)
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Conclusions and Outlook
• Conclusions:
– Reduction of the number of EDFAs per link degrades the system’s
performance
– DBP allows to increase the system’s span length beyond the limits of linear
equalization and thereby to further reduce the number of EDFAs per link
– The amount of EDFAs was reduced by up to 50% and at least 30%, depending
on the type of fiber and the sampling rate of the receiver ADC, when DBP was
used instead of a linear equalizer
– Maximal span length (1000 km total link length) cannot exceed 183 km
• Outlook
– BER measurements for more accurate results
– Optimization of the launch power for the best cost-effective scenario
(Amplifiers with lower output power are cheaper)
– EDFA reduction potential for simplified DBP versions / low-complexity
nonlinear compensation methods
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References
1. I. Dedic, “56 Gs/s ADC: Enabling 100GBE,” in Optical Fiber Communication Conference. Optical Society of
America, 2010, p. OThT6. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OThT6
2. E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J.
Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, oct. 2008.
3. A. J. Lowery, “Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM,” Opt.
Express, vol. 15, no. 20, pp. 12965–12970, 2007.
4. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. Academic Press, January 2001.
5. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM
transmission impairments using coherent detection and digital signal processing,” Opt. Express, vol. 16, no. 2, pp.
880–888, 2008. [Online]. Available: http://www.opticsexpress.org/abstract.cfm?URI=oe-16-2-880
6. J. Leibrich, “Modeling and simulation of limiting impairments on the next generation’s transparent optical WDM
transmission systems with advanced modulation formats,” Ph.D. dissertation, Chair of Communications,
University of Kiel, 2007.
7. Q. Zhang and M. Hayee, “An SSF scheme to achieve comparable global simulation accuracy in WDM systems,"
IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 1869–1871, sep. 2005.
8. P. J. Winzer, M. Pfennigbauer, M. M. Strasser, and W. R. Leeb, “Optimum filter bandwidths for optically
preamplified NRZ receivers,” J. Lightw. Technol., vol. 19, no. 9, p. 1263, Sep 2001. [Online]. Available:
http://jlt.osa.org/abstract.cfm?URI=jlt-19-9-1263
9. B. Spinnler and C. Xie, “Performance assessment of DQPSK using pseudo-random quaternary sequences,” Optical
Communication (ECOC), 2007 33rd European Conference and Exhibition of, 16-20 Sep. 2007 pp.1–2.
10. R. A. Shafik, M. S. Rahman, and A. H. M. R. Islam, “On the extended relationships among EVM, BER and SNR as
performance metrics,” in Proc. ICECE’06, Bangladesh, Dec. 2006, pp. 408–411.
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Appendix - Digital Back-Propagation (DBP) I
• Theoretical background
– A DCF = negative dispersion only
– Needed – a fiber with negative dispersion, nonlinear coefficient and
attenuation
– A physical solution (fiber/material with the negative parameters) does not exist!
– Solution – a digital model!
( ) ( )e tE t E t
2 3, , ,
( )tE t( )rE t
2 3, , ,
ISMF SMF
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Appendix - Digital Back-Propagation (DBP) II
• DBP for a single fiber:
– Solving numerically the inverse NLSE using the split-step Fourier method
(SSFM)
– Realization with the asymmetric SSFM:
2 3
2 3
1 1exp exp
2 2 6z j z
F F -1
2( , )exp opt A zj z t
1LS 1NLS
First Step
2LS 2NLS
Second Step
Linear transfer function Nonlinear phase rotation
(0, )rS k
Digitized received
signal
NLS NNLS
nth Step
( , )rS L k
Equalized signal
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Appendix - Digital Back-Propagation (DBP) III
• Implementation of a transmission link:
DBP 0 ( )P l
lL0
lL0
DBP
Linear
equalization Residual Dispersion
Dis
pers
ion
[ps
/nm
]
DCF SMF ( )tE t ( )rE t
M spans
G
2, 3,, , ,s s s s 2, 3,, , ,d d d d
G
( )rS k ( )eS k
2, 3,, , ,d d d d 2, 3,, , ,s s s s
M spans
ND steps NS steps
IDCF 1
G
ISMF 1
G