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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4174–4182
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Intra-channel nonlinearity compensation for PM-16QAM traffic co-propagating with 28Gbaud m-ary QAM neighbours

Danish Rafique, Stylianos Sygletos, and Andrew D. Ellis  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4174-4182 (2013)
http://dx.doi.org/10.1364/OE.21.004174


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Abstract

We quantify the benefits of intra-channel nonlinear compensation in meshed optical networks, in view of network configuration, fibre design aspect, and dispersion management. We report that for a WDM optical transport network employing flexible 28Gbaud PM-mQAM transponders with no in-line dispersion compensation, intra-channel nonlinear compensation, for PM-16QAM through traffic, offers significant improvements of up to 4dB in nonlinear tolerance (Q-factor) irrespective of the co-propagating modulation format, and that this benefit is further enhanced (1.5dB) by increasing local link dispersion. For dispersion managed links, we further report that advantages of intra-channel nonlinear compensation increase with in-line dispersion compensation ratio, with 1.5dB improvements after 95% in-line dispersion compensation, compared to uncompensated transmission.

© 2013 OSA

1. Introduction

In particular, electronic signal processing employing linear and nonlinear compensation using digital back-propagation (DBP) has been proposed [6

6. 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 16(2), 880–888 (2008). [CrossRef] [PubMed]

,7

7. D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011). [CrossRef] [PubMed]

]. Typically, wide bandwidth DBP (inter-channel nonlinear compensation) is considered to be impractical, partly due to high computational load and partly due to limited access to all wavelength division multiplexed (WDM) channels [7

7. D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011). [CrossRef] [PubMed]

]. Single-channel DBP (SC-DBP, intra-channel nonlinear compensation) has been shown to only enable modest improvements between ~1-2dB, compared to linear compensation only [7

7. D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011). [CrossRef] [PubMed]

9

9. X. Zhou, E. F. Mateo, and G. Li, “Fiber Nonlinearity Management-from Carrier Perspective,” Optical Fiber Communication Conference, OFC ’11, NThB4 (2011).

]. However, this has only been verified for systems employing homogenous network traffic, where all the channels carry same power [8

8. S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of Interchannel Nonlinearities on a Split-Step Intrachannel Nonlinear Equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010). [CrossRef]

]. As the network upgrades are carried out, it is likely that channels employing different multi-level formats will become operational, and the network traffic will become inhomogeneous [10

10. A. Nag, M. Tornatore, and B. Mukherjee, “Optical Network Design With Mixed Line Rates and Multiple Modulation Formats,” J. Lightwave Technol. 28(4), 466–475 (2010). [CrossRef]

12

12. D. Rafique and A. D. Ellis, “Nonlinear Penalties in Dynamic Optical Networks Employing Autonomous Transponders,” IEEE Photon. Technol. Lett. 23(17), 1213–1215 (2011). [CrossRef]

]. The impact of network planning strategies and cross-channel interaction involving on-off keyed neighbours has been quantified in [13

13. T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport Over Deployed Optical Networks,” Optical Fiber Communication Conference, OFC’08, NTuB3, (2008).

15

15. C. Fürst, J. Elbers, H. Wernz, H. Griesser, S. Herbst, M. Camera, F. Cavaliere, A. Ehrhardt, D. Breuer, D. Fritzsche, S. Vorbeck, M. Schneiders, W. Weiershausen, R. Leppla, J. Wendler, M. Schroedel, T. Wuth, C. Fludger, T. Duthel, B. Milivojevic, and C. Schulien, “Analysis of Crosstalk in Mixed 43 Gb/s RZ-DQPSK and 10.7 Gb/s DWDM Systems at 50 GHz Channel Spacing,” Optical Fiber Communication Conference, OFC’07, OThS2 (2007).

], confirming the value of channel power allocation schemes in upgrading current networks [12

12. D. Rafique and A. D. Ellis, “Nonlinear Penalties in Dynamic Optical Networks Employing Autonomous Transponders,” IEEE Photon. Technol. Lett. 23(17), 1213–1215 (2011). [CrossRef]

,13

13. T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport Over Deployed Optical Networks,” Optical Fiber Communication Conference, OFC’08, NTuB3, (2008).

].

It has been suggested that for green field deployments, DSP based impairment compensation would enable reductions in operational cost through the suppression of dual-stage amplifiers (only one amplifier would suffice) and dispersion compensation modules. However, as networks evolve it is inevitable that high-speed channels will also traverse through the existing dispersion-managed infrastructure. A vital aspect, from system design viewpoint, is then to determine the benefits available with DSP in already existing maps, and if dispersion management has any role to play in future network deployments.

2. Transmission model

Figure 1
Fig. 1 Simulation setup for 28Gbaud PM-mQAM. PRBS: Pseudo random bit sequence, IQ: In-phase/Quadrature, DCF: dispersion compensating fibre, LO: local oscillator, PBC/S: polarisation beam combiner/splitter, ADC: analogue-to-digital converter, FIR: finite impulse response
illustrates the simulation setup. The transmission system comprised fifteen WDM channels employing 28Gbaud polarisation multiplexed quadrature amplitude modulation (PM-mQAM), m = 4, 16, 64, spaced at 50GHz. The central channel was always 28Gbaud PM-16QAM (at 1550nm), and the neighbours were selected to be PM-mQAM channels. For all the carriers both the polarisation states were independently modulated using de-correlated 215 and 216 pseudo-random bit sequences (PRBS), for x- and y- polarisation states, respectively. The optical transmitters consisted of continuous wave lasers (5kHz line-width) followed by two nested Mach-Zehnder Modulator structures for x- and y polarisation states, and the two polarization states were combined using an ideal polarization beam combiner. The simulation conditions ensured 16 samples per symbol, and 213 symbols per polarization per channel.

3. Results and discussions

3.1 Impact of network configurations

In this section, we explore various network configurations, and report the benefits of intra-channel nonlinear compensation in such scenarios. Typical results of our simulations are shown in Fig. 2(a)
Fig. 2 (a) Q2 of central PM-16QAM channel vs. launch power of PM-16QAM channel after 3,200km. Circles, Squares, Stars: PM-4QAM/PM-16QAM/PM-64QAM neighbours at 0dBm, Diamonds: PM-4QAM neighbours at 4dBm, Lines: curve fits PM-16QAM neighbours with launch power optimized with test-channel. Solid symbols and solid line: SC-DBP, Open symbols and dashed line: LC, (b) Q2 with LC/SC-DBP, for various cases in (a).
as a function of signal launch power (PL) for the central PM-16QAM channel, after 3,200km transmission. Specifically, we show four heterogeneous transmission scenarios: Circles, Squares and Stars, PM-4QAM/PM-16QAM/PM-64QAM neighbours respectively with 0dBm launch power for interfering channels, Diamonds, PM-4QAM neighbours with 4dBm launch power, and a fully homogenous scenario with all PM-16-QAM channels. Note that channel power allocation in a meshed network is an important system design choice [13

13. T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport Over Deployed Optical Networks,” Optical Fiber Communication Conference, OFC’08, NTuB3, (2008).

], and in this work, the launch power of all the PM-mQAM neighbours was fixed at the near-optimal power of 0dBm for heterogeneous transmission, as shown in [12

12. D. Rafique and A. D. Ellis, “Nonlinear Penalties in Dynamic Optical Networks Employing Autonomous Transponders,” IEEE Photon. Technol. Lett. 23(17), 1213–1215 (2011). [CrossRef]

] (unless specified otherwise).

3.2 Impact of fibre design parameter

Having established the available benefits from SC-DBP in a flexible network, in this section, we explore the impact of fibre dispersion when higher power high bit-rate signals (PM-16QAM at its optimal launch power) co-propagate with lower power neighbours (PM-4QAM channels at 0dBm).

In this regime of high dispersion even greater benefits are enabled by SC-DBP, as shown in Fig. 3(a). This can be attributed to the compensation of the increased intra-channel nonlinear effects at high local dispersion by the SC-DBP, allowing greater inter-channel benefit from reduced phase-matching. In particular, with a local dispersion of ± 80ps/nm/km, Q-factor may be improved by 3.5dB, compared to that of standard single-mode fibre (17ps/nm/km), hinting that commercially available negative dispersion fibres (with slightly higher loss than 0.2dB/km) may be deployed with a net performance benefit, e.g. IDF-45E [21

21. K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” OFC 3(5), 292–339 (2006).

]. Figure 3(b) shows the direct benefit of enabling SC-DBP, with up to 5.5dB improvements in Q-factor over the LC performance at ± 80ps/nm/km of local dispersion. Note that the performance improvements are largely consistent with analytical predictions of [1

1. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010). [CrossRef]

], except in the very-low dispersion regime (inter-channel parametric process dominate due to extreme phase-matching) where the approach of [20

20. J. Tang, “The multispan effects of Kerr nonlinearity and amplifier noises on Shannon channel capacity of a dispersion-free nonlinear optical fiber,” J. Lightwave Technol. 19(8), 1110–1115 (2001). [CrossRef]

] should be adopted to predict the performance. One may argue that a high dispersion coefficient may result in increased complexity of SC-DBP. However, recently proposed correlated [22

22. D. Rafique, M. Mussolin, M. Forzati, J. Mårtensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express 19(10), 9453–9460 (2011). [CrossRef] [PubMed]

, 23

23. L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation Efficient Nonlinear Equalizer Based on Correlated Digital Backpropagation,” Optical Fiber Communication Conference, OFC ‘11, OWW3 (2011).

] and folded [24

24. L. Zhu and G. Li, “Nonlinearity compensation using dispersion-folded digital backward propagation,” Opt. Express 20(13), 14362–14370 (2012). [CrossRef] [PubMed]

] DBP may be effectively employed to take dispersion into account. Also, pre-dispersed spectral inversion has been demonstrated which may offset any complexity associated with receiver electronics [25

25. D. Rafique and A. D. Ellis, “Various Nonlinearity Mitigation Techniques Employing Optical and Electronic Approaches,” IEEE Photon. Technol. Lett. 23(23), 1838–1840 (2011). [CrossRef]

].

3.3 Impact of dispersion management

4. Conclusions

Acknowledgments

This work was supported by Science Foundation Ireland under Grant numbers 06/IN/I969 and 08/CE/11523. We would like to thank N.J. Doran for useful discussions.

References and links

1.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010). [CrossRef]

2.

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally Efficient Long-Haul Optical Networking Using 112-Gb/s Polarization-Multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010). [CrossRef]

3.

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett. 31(23), 2027–2029 (1995). [CrossRef]

4.

C. Fürst, C. Scheerer, and G. Mohs, J. -. Elbers, and C. Glingener, “Influence of the dispersion map on limitations due to cross-phase modulation in WDM multispan transmission systems,” Optical Fiber Communication Conference, OFC ’01, MF4 (2001).

5.

A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Optical vs. Electronic Chromatic Dispersion Compensation in WDM Coherent PM-QPSK Systems at 111 Gbit/s,” Optical Fiber Communication Conference, OFC ’08, JThA57 (2008).

6.

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 16(2), 880–888 (2008). [CrossRef] [PubMed]

7.

D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011). [CrossRef] [PubMed]

8.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of Interchannel Nonlinearities on a Split-Step Intrachannel Nonlinear Equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010). [CrossRef]

9.

X. Zhou, E. F. Mateo, and G. Li, “Fiber Nonlinearity Management-from Carrier Perspective,” Optical Fiber Communication Conference, OFC ’11, NThB4 (2011).

10.

A. Nag, M. Tornatore, and B. Mukherjee, “Optical Network Design With Mixed Line Rates and Multiple Modulation Formats,” J. Lightwave Technol. 28(4), 466–475 (2010). [CrossRef]

11.

C. Meusburger, D. A. Schupke, and A. Lord, “Optimizing the Migration of Channels with Higher Bitrates,” J. Lightwave Technol. 28(4), 608–615 (2010). [CrossRef]

12.

D. Rafique and A. D. Ellis, “Nonlinear Penalties in Dynamic Optical Networks Employing Autonomous Transponders,” IEEE Photon. Technol. Lett. 23(17), 1213–1215 (2011). [CrossRef]

13.

T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport Over Deployed Optical Networks,” Optical Fiber Communication Conference, OFC’08, NTuB3, (2008).

14.

D.v.d Borne, C.R.S. Fludger, T. Duthel, T. Wuth, E.D. Schmidt, C. Schulien, E. Gottwald,G.D. Khoe, and H. de Waardt, “Carrier phase estimation for coherent equalization of 43-Gb/s POLMUX-NRZDQPSK transmission with 10.7-Gb/s NRZ neughbours,” ECOC'07, 7.2.3 (2007).

15.

C. Fürst, J. Elbers, H. Wernz, H. Griesser, S. Herbst, M. Camera, F. Cavaliere, A. Ehrhardt, D. Breuer, D. Fritzsche, S. Vorbeck, M. Schneiders, W. Weiershausen, R. Leppla, J. Wendler, M. Schroedel, T. Wuth, C. Fludger, T. Duthel, B. Milivojevic, and C. Schulien, “Analysis of Crosstalk in Mixed 43 Gb/s RZ-DQPSK and 10.7 Gb/s DWDM Systems at 50 GHz Channel Spacing,” Optical Fiber Communication Conference, OFC’07, OThS2 (2007).

16.

R.-J. Essiambre, G. Raybon, and B. Mikkelsen, Optical Fiber Telecommunications IV (Academic, 2002), chap.6.

17.

C. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent Equalization and POLMUX-RZ-DQPSK for Robust 100-GE Transmission,” J. Lightwave Technol. 26(1), 64–72 (2008). [CrossRef]

18.

D. Rafique and A. D. Ellis, “Nonlinear penalties in long-haul optical networks employing dynamic transponders,” Opt. Express 19(10), 9044–9049 (2011). [CrossRef] [PubMed]

19.

D. Rafique and A. D. Ellis, “Nonlinear and ROADM induced penalties in 28 Gbaud dynamic optical mesh networks employing electronic signal processing,” Opt. Express 19(18), 16739–16748 (2011). [CrossRef] [PubMed]

20.

J. Tang, “The multispan effects of Kerr nonlinearity and amplifier noises on Shannon channel capacity of a dispersion-free nonlinear optical fiber,” J. Lightwave Technol. 19(8), 1110–1115 (2001). [CrossRef]

21.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” OFC 3(5), 292–339 (2006).

22.

D. Rafique, M. Mussolin, M. Forzati, J. Mårtensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express 19(10), 9453–9460 (2011). [CrossRef] [PubMed]

23.

L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation Efficient Nonlinear Equalizer Based on Correlated Digital Backpropagation,” Optical Fiber Communication Conference, OFC ‘11, OWW3 (2011).

24.

L. Zhu and G. Li, “Nonlinearity compensation using dispersion-folded digital backward propagation,” Opt. Express 20(13), 14362–14370 (2012). [CrossRef] [PubMed]

25.

D. Rafique and A. D. Ellis, “Various Nonlinearity Mitigation Techniques Employing Optical and Electronic Approaches,” IEEE Photon. Technol. Lett. 23(23), 1838–1840 (2011). [CrossRef]

26.

T. Tanimura, S. Oda, T. Hoshida, L. Li, Z. Tao, and J. C. Rasmussen, “Experimental Characterization of Nonlinearity Mitigation by Digital Back Propagation and Nonlinear Polarization Crosstalk Canceller under High PMD condition,” Optical Fiber Communication Conference, OFC’11, JWA020 (2011).

27.

L. B. Du and A. J. Lowery, “Experimental Demonstration of XPM Compensation for CO-OFDM Systems with Periodic Dispersion Maps,” Optical Fiber Communication Conference, OFC’11, OWW2 (2011).

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.4254) Fiber optics and optical communications : Networks, combinatorial network design

ToC Category:
Transmission Systems and Network Elements

History
Original Manuscript: September 4, 2012
Revised Manuscript: October 30, 2012
Manuscript Accepted: October 30, 2012
Published: February 11, 2013

Citation
Danish Rafique, Stylianos Sygletos, and Andrew D. Ellis, "Intra-channel nonlinearity compensation for PM-16QAM traffic co-propagating with 28Gbaud m-ary QAM neighbours," Opt. Express 21, 4174-4182 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4174


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References

  1. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol.28(4), 423–433 (2010). [CrossRef]
  2. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally Efficient Long-Haul Optical Networking Using 112-Gb/s Polarization-Multiplexed 16-QAM,” J. Lightwave Technol.28(4), 547–556 (2010). [CrossRef]
  3. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba, “Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,” Electron. Lett.31(23), 2027–2029 (1995). [CrossRef]
  4. C. Fürst, C. Scheerer, and G. Mohs, J. -. Elbers, and C. Glingener, “Influence of the dispersion map on limitations due to cross-phase modulation in WDM multispan transmission systems,” Optical Fiber Communication Conference, OFC ’01, MF4 (2001).
  5. A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Optical vs. Electronic Chromatic Dispersion Compensation in WDM Coherent PM-QPSK Systems at 111 Gbit/s,” Optical Fiber Communication Conference, OFC ’08, JThA57 (2008).
  6. 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. Express16(2), 880–888 (2008). [CrossRef] [PubMed]
  7. D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express19(6), 5219–5224 (2011). [CrossRef] [PubMed]
  8. S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of Interchannel Nonlinearities on a Split-Step Intrachannel Nonlinear Equalizer,” IEEE Photon. Technol. Lett.22(10), 673–675 (2010). [CrossRef]
  9. X. Zhou, E. F. Mateo, and G. Li, “Fiber Nonlinearity Management-from Carrier Perspective,” Optical Fiber Communication Conference, OFC ’11, NThB4 (2011).
  10. A. Nag, M. Tornatore, and B. Mukherjee, “Optical Network Design With Mixed Line Rates and Multiple Modulation Formats,” J. Lightwave Technol.28(4), 466–475 (2010). [CrossRef]
  11. C. Meusburger, D. A. Schupke, and A. Lord, “Optimizing the Migration of Channels with Higher Bitrates,” J. Lightwave Technol.28(4), 608–615 (2010). [CrossRef]
  12. D. Rafique and A. D. Ellis, “Nonlinear Penalties in Dynamic Optical Networks Employing Autonomous Transponders,” IEEE Photon. Technol. Lett.23(17), 1213–1215 (2011). [CrossRef]
  13. T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport Over Deployed Optical Networks,” Optical Fiber Communication Conference, OFC’08, NTuB3, (2008).
  14. D.v.d Borne, C.R.S. Fludger, T. Duthel, T. Wuth, E.D. Schmidt, C. Schulien, E. Gottwald,G.D. Khoe, and H. de Waardt, “Carrier phase estimation for coherent equalization of 43-Gb/s POLMUX-NRZDQPSK transmission with 10.7-Gb/s NRZ neughbours,” ECOC'07, 7.2.3 (2007).
  15. C. Fürst, J. Elbers, H. Wernz, H. Griesser, S. Herbst, M. Camera, F. Cavaliere, A. Ehrhardt, D. Breuer, D. Fritzsche, S. Vorbeck, M. Schneiders, W. Weiershausen, R. Leppla, J. Wendler, M. Schroedel, T. Wuth, C. Fludger, T. Duthel, B. Milivojevic, and C. Schulien, “Analysis of Crosstalk in Mixed 43 Gb/s RZ-DQPSK and 10.7 Gb/s DWDM Systems at 50 GHz Channel Spacing,” Optical Fiber Communication Conference, OFC’07, OThS2 (2007).
  16. R.-J. Essiambre, G. Raybon, and B. Mikkelsen, Optical Fiber Telecommunications IV (Academic, 2002), chap.6.
  17. C. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent Equalization and POLMUX-RZ-DQPSK for Robust 100-GE Transmission,” J. Lightwave Technol.26(1), 64–72 (2008). [CrossRef]
  18. D. Rafique and A. D. Ellis, “Nonlinear penalties in long-haul optical networks employing dynamic transponders,” Opt. Express19(10), 9044–9049 (2011). [CrossRef] [PubMed]
  19. D. Rafique and A. D. Ellis, “Nonlinear and ROADM induced penalties in 28 Gbaud dynamic optical mesh networks employing electronic signal processing,” Opt. Express19(18), 16739–16748 (2011). [CrossRef] [PubMed]
  20. J. Tang, “The multispan effects of Kerr nonlinearity and amplifier noises on Shannon channel capacity of a dispersion-free nonlinear optical fiber,” J. Lightwave Technol.19(8), 1110–1115 (2001). [CrossRef]
  21. K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” OFC3(5), 292–339 (2006).
  22. D. Rafique, M. Mussolin, M. Forzati, J. Mårtensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express19(10), 9453–9460 (2011). [CrossRef] [PubMed]
  23. L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation Efficient Nonlinear Equalizer Based on Correlated Digital Backpropagation,” Optical Fiber Communication Conference, OFC ‘11, OWW3 (2011).
  24. L. Zhu and G. Li, “Nonlinearity compensation using dispersion-folded digital backward propagation,” Opt. Express20(13), 14362–14370 (2012). [CrossRef] [PubMed]
  25. D. Rafique and A. D. Ellis, “Various Nonlinearity Mitigation Techniques Employing Optical and Electronic Approaches,” IEEE Photon. Technol. Lett.23(23), 1838–1840 (2011). [CrossRef]
  26. T. Tanimura, S. Oda, T. Hoshida, L. Li, Z. Tao, and J. C. Rasmussen, “Experimental Characterization of Nonlinearity Mitigation by Digital Back Propagation and Nonlinear Polarization Crosstalk Canceller under High PMD condition,” Optical Fiber Communication Conference, OFC’11, JWA020 (2011).
  27. L. B. Du and A. J. Lowery, “Experimental Demonstration of XPM Compensation for CO-OFDM Systems with Periodic Dispersion Maps,” Optical Fiber Communication Conference, OFC’11, OWW2 (2011).

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