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

[email protected]

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


• 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


• 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




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




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.

http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OThT6





http://www.opticsexpress.org/abstract.cfm?URI=oe-16-2-880














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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

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