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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 10 — May. 9, 2011
  • pp: 9044–9049

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Nonlinear penalties in long-haul optical networks employing dynamic transponders

Danish Rafique and Andrew D. Ellis  »View Author Affiliations


Optics Express, Vol. 19, Issue 10, pp. 9044-9049 (2011)
http://dx.doi.org/10.1364/OE.19.009044


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Abstract

We report for the first time, the impact of cross phase modulation in WDM optical transport networks employing dynamic 28 Gbaud PM-mQAM transponders (m = 4, 16, 64, 256). We demonstrate that if the order of QAM is adjusted to maximize the capacity of a given route, there may be a significant degradation in the transmission performance of existing traffic for a given dynamic network architecture. We further report that such degradations are correlated to the accumulated peak-to-average power ratio of the added traffic along a given path, and that managing this ratio through pre-distortion reduces the impact of adjusting the constellation size of neighboring channels.

© 2011 OSA

1. Introduction

The communication traffic volume handled by trunk optical transport networks has been increasing year by year [1

R. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010). [CrossRef]

]. The resultant change in traffic patterns not only requires a quantitative increase in total traffic volume, but also requires an increase in the speed of individual clients. This is particularly true for shorter links across the network, where the improved optical signal to noise ratio (OSNR) would allow the use of a higher capacity. One of the options to improve resource utilization in a static network is the deployment of spectrally efficient higher-order modulation formats enabled by digital coherent detection [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

D. Rafique, J. Zhao, and A. D. Ellis, “Performance improvement by fibre nonlinearity compensation in 112 Gb/s PM M-ary QAM,” Optical Fiber Communication Conference, OFC ’11 (accepted for publication).

]. However, as attested by the rapid growth in reported constellation size [4

S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDMQAM16 transmission at 112 Gbit/s over 2400 km,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OMJ6.

–6

S. Okamoto, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “256 QAM (64 Gbit/s) Coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OThD5.

], the optical hardware for a wide variety of coherently detected modulation formats is identical. This has led to the suggestion that a common transponder may be deployed and the format adjusted on a link by link basis to either maximize the link capacity given the achieved OSNR, or if lower, match the required client interface rate [7

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]

]. Such dynamic, potentially self adjusting, networks may be desirable to enable graceful capacity growth, ready resource allocation and transponder cost reductions. However many additional trade-offs and challenges associated with such networks are presented to system designers and network planners. One such challenge is associated with the nonlinear transmission impairments which strongly link the achievable channel reach for a given modulation format and symbol-rate [7

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]

,8

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]

]. Compensation of many of the linear and nonlinear fibre impairments can be achieved by employing electronic signal processing using digital back-propagation (DBP) [9

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]

–11

D. Rafique, J. Zhao, and A. D. Ellis, “Impact of dispersion map management on the performance of back-propagation for nonlinear WDM transmissions,” OptoElectronics and Communications Conference, OECC ’10 (2010), paper 9B2–4.

]. Although the future potential of nonlinear impairment compensation using DBP in a dynamic optical network is unclear due to its significant computational burden and limited access to the full dense wave-division multiplexing band, simplification of nonlinear DBP algorithm using single-channel processing at the receiver has already commenced [12

S. Oda, T. Tanimura, T. Hoshida, C. Ohshima, H. Nakashima, Z. Tao, and J. C. Rasmussen, “112 Gb/s DP-QPSK transmission using a novel nonlinear compensator in digital coherent receiver,” Optical Fiber Communication Conference’09 (2009), paper OThR6.

,13

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010). [CrossRef] [PubMed]

]

In such a dynamic network, there is a large range of options to provide the desired flexibility including symbol rate [14

T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport over deployed optical networks,” Optical Fiber Communication Conference, OFC 2008 (2008), paper NTuB3.

], sub-carrier multiplexing [15

W. Wei, Z. Lei, and Q. Dayou, “Wavelength-based sub-carrier multiplexing and grooming for optical networks bandwidth virtualization,” Optical Fiber Communication Conference, OFC ’08 (2008), paper PDP35.

], network configuration [16

R. Peter, and C. Brandon, “Evolution to colorless and directionless ROADM architectures,” Optical Fiber Communication Conference, OFC ’08 (2008), paper NWE2.

] and signal constellation [3

D. Rafique, J. Zhao, and A. D. Ellis, “Performance improvement by fibre nonlinearity compensation in 112 Gb/s PM M-ary QAM,” Optical Fiber Communication Conference, OFC ’11 (accepted for publication).

]. In this paper we focus on the signal constellation and report the impact of periodic addition of PM-mQAM (m = 4, 16, 64, 256) transmission schemes on existing PM-4QAM traffic in a 28 Gbaud WDM optical network with a maximum transparent optical path of 9,600 km. We demonstrate that the periodic addition of traffic at reconfigurable optical add-drop multiplexer (ROADM) sites degrades through traffic, and that this degradation increases with the constellation size of the added traffic. In particular, we demonstrate that undistorted PM-mQAM signals have the greatest impact on the through traffic, with the degradation strongly correlated to the total peak-to-average power ratio (PAPR) of the added traffic. Using this observation, we propose the use of linear pre-distorting of the added channels to reduce the impact of the cross-channel impairments.

2. Transmission model

Figure 1 illustrates the simulation setup. The optical link comprised nine WDM channels, employing 28 Gbaud PM-mQAM (m = 4, 16, 64, 256). The central channel was always 112 Gb/s PM-4QAM, and the immediate neighbours (left and right) were periodically selected to be PM-mQAM channels. All the transmitters were operated at a constant baud-rate of 28Gbaud with a channel spacing of 50 GHz. For all the carriers, both the polarization states were modulated independently using de-correlated 215 and 216 pseudo-random bit sequences (PRBS) with different random number seeds, for x- and y-polarization states, respectively. Each PRBS was de-multiplexed separately into two multi-level output symbol streams which were used to modulate an in-phase and a quadrature phase carrier. The optical transmitters consisted of a continuous wave laser source, the central transmitter was operated at 1550 nm, followed by two nested Mach-Zehnder Modulator structures for x- and y-polarization states, and the two polarization states were combined using an ideal polarization beam combiner. The simulation conditions ensured 16 samples per symbol with 213 total simulated symbols per polarization, corresponding to a total 32,768, 65,536, 98,304, and 131072 bits for PM-mQAM (m = 4, 16, 64, 256 respectively). All the channels had the same average power level and were combined using a multiplexer with a 30 GHz 3 rd order Gaussian pass band. For simplicity we neglected polarization mode dispersion and laser line-width in this paper (for the worst-case scenario employing 256QAM, 80 kHz linewidth can be tolerated [17

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]

]).

Fig. 1 Simulation setup for 28 Gbaud PM-mQAM transmission. M: Number of spans between ROADM nodes.

The signal was propagated over standard single mode fibre (SSMF) transmission link with 80 km spans, no inline dispersion compensation and single-stage erbium doped fibre amplifiers (EDFAs). The fibre had attenuation of 0.2 dB/km, dispersion of 20 ps/nm/km, and a nonlinearity coefficient (γ) of 1.5/W/km. Each amplifier stage was modelled with a 4.5 dB noise figure and the total amplification gain was set to be equal to the total loss in each span. Note that the total optical path was fixed to be 9,600 km and after every M spans, a ROADM stage was employed and the channels to the left and right of the central channel were dropped and new channels were added. The dropped channels were coherently detected after first ROADM and the central channel after the last ROADM link.

At the coherent receiver the signals were pre-amplified (constant power of 0 dBm), filtered with a 50 GHz 3rd order Gaussian de-multiplexing filter, coherently-detected using four balanced detectors to give the baseband electrical signal and sampled at 2 samples/symbol. Transmission impairments were digitally compensated in two scenarios. Firstly by using electronic dispersion compensation (EDC) alone (the back-propagation section in Fig. 1 was by-passed), employing finite impulse response (FIR) filters (T/2-spaced taps) adapted using a least mean square algorithm. In the second case, electronic compensation was applied via single-channel DBP (SC-DBP), which was numerically implemented by up-sampling the received signal to 16 samples/symbol and reconstructing the optical field from the in-phase and quadrature samples, followed by split-step Fourier method based solution of nonlinear Schrödinger equation. The upper bound on the step-size was set to be 1 km and the step length was chosen adaptively during the integration along the fibre based on the condition that in each step the nonlinear effects must change the phase of the optical field by no more than 0.05 degrees. Polarization de-multiplexing and residual dispersion compensation was then performed using FIR filters. Finally, the symbol decisions were made, and the performance assessed by direct error counting (converted into an effective Q-factor (Qeff)). All the numerical simulations were carried out using VPItransmissionMaker® v8.5, and the digital signal processing was performed in MATLAB® v7.10.

3. Results and discussions

The maximum performance of the central PM-4QAM channel after the maximum optical path (9,600 km) occurred for a launch power of −1 dBm. The launch power of all the added channels was also fixed at −1 dBm, such that all channels had equal launch powers. Figure 2 illustrates the performance of the central test channel (1550 nm) after the last node (solid), along with the performance of two co-propagating channels (1550 ± 0.4 nm) employing various modulation formats after the first ROADM node (half-solid), at a fixed total transmission distance of 9,600 km for a number of ROADM spacing’s, using both SC-DBP (Fig. 2a) and EDC (Fig. 2b). It can be seen that SC-DBP offers a Qeff improvement of ~1.5 dB compared to EDC based system. This performance improvement is strongly constrained by inter-channel nonlinearities, such that intra channel effects are not dominant.. Moreover, the figure shows that as the number of ROADM nodes are increased, or distance between ROADMs decreases, the performance of higher-order neighboring channels improves significantly due to the improved OSNR. However, even when the add drop traffic is PM-4QAM, the performance of the through channel degrades as the number of ROADM nodes is increased, despite the reduction in peak-to-average power ratio (PAPR). The PAPR evolutions for the various formats are shown in Fig. 3 . The asymptotic values are reached after approximately 30 km, and reach a slightly higher value for m ≥ 16. Significantly, the PAPR is reduced at the ROADM site, particularly so for PM-4QAM. Figure 3 implies that harmful increases in the instantaneous amplitude of the interfering channels are not the cause of the penalty experienced by the through channel; we can therefore only conclude that this results from interplay between channel walk off and nonlinear effects. Given that walk-off is known to induce short and medium range correlation in crosstalk between subsequent bits [18

Y. Weizhen, T. Zhenning, L. Lei, T. Hoshida, and J. C. Rasmussen, “A simplified model for XPM in coherent PSK systems,” OptoElectronics and Communications Conference, OECC ’10 (2010) paper 9B2–2.

], effectively low pass filtering the crosstalk [19

L. E. Nelson, A. H. Gnauck, R. I. Jopson, and A. R. Chraplyvy, “Cross-phase modulation resonances in wavelength-division-multiplexed lightwave transmission,” European Conference on Optical Communication, ECOC 1998 (1998), pp. 309–310.

]. We thus believe that the most likely cause of the penalty experienced by the through channel is the randomization of the crosstalk by the periodic replacement of the interfering data pattern, and that this effect dominates over the slight reduction in PAPR observed.

Fig. 2 Qeff as a function of number of ROADMs (and distance between ROADM nodes) for 28 Gbaud PM-mQAM showing performance of central PM-4QAM (solid), and neighbouring PM-mQAM (open). a) with single-channel DBP, b) with EDC. Square: 4QAM, circle: 16QAM, up triangle: 64QAM, star: 256QAM. Up arrows indicate that no errors were detected, implying that the Qeff was likely to be above 13 dB.
Fig. 3 Variation in PAPR, for 4QAM (black), 16QAM (red), 64QAM (green) and 256QAM (blue) for a loss-less linear fibre with 20 ps/nm/km dispersion.

It can also be seen from Fig. 2 that added channels with higher-order formats induce greater degradation of the through channel. In particular if there are 30 ROADM sites (320 km ROADM spacing) allocated to transmit PM-64QAM according to an OSNR analysis taking into account the inevitable 2.5 dB required OSNR penalty [3

D. Rafique, J. Zhao, and A. D. Ellis, “Performance improvement by fibre nonlinearity compensation in 112 Gb/s PM M-ary QAM,” Optical Fiber Communication Conference, OFC ’11 (accepted for publication).

], whilst this traffic operates with significant margin, the through traffic falls below the FEC threshold (BER of 3.8x10−3). This increased penalty is due to the increased nonlinear degradation encountered in the first span after the ROADM node, where higher order formats induce greater XPM than PM-4QAM by virtue of their increased PAPR.

This is further confirmed in Fig. 4 which plots the Qeff of PM-4QAM after last node, for both EDC and SC-DBP, in terms of a figure of merit (FOM) related to the increased amplitude modulation experienced by the test channel in the spans immediately following the ROADM node, defined as,
FO M PM−mQAM(m)=(ROAD MN)× [ I max(m)/ I all(m)¯]
(1)
where m represents the modulation order, ROADMN represents number of add-drop nodes, Imax and Iall are the maximum and total intensity of the given modulation format. A strong correlation between the penalty and change in PAPR is observed. For instance, for a high number of ROADMs the system would be mostly influenced by relatively un-dispersed signals and the difference between peak-to-average fluctuations for multi-order QAM varies significantly. This leads to higher-order modulation formats impinging worse cross-channel effects on existing traffic for shorter routes.

Fig. 4 Qeff of the PM-4QAM through channel for 28 Gbaud PM-mQAM add/drop traffic after 9,600 km as a function of a figure of merit (FOM) defined in the text for various add drop configurations. Solid: with single-channel DBP, open: with EDC.

Having observed that the nonlinear penalty is determined by the reduction in the correlation of nonlinear phase shift between bits arising from changing bit patterns, and to changes in PAPR arising from undistorted signals, it is possible to design a mitigation strategy to minimize these penalties. Figure 5 illustrates, for both EDC and SC-DBP systems, that if the co-propagating higher-order QAM channels are linearly pre-distorted, the performance of the PM-4QAM through traffic can be improved. The figure shows that when positive pre-distortion is applied, such that the neighboring channel constellation is never, along its entire inter node transmission length, restored to a well-formed shape, the impact of cross-channel impairments on existing traffic is reduced significantly.

Fig. 5 Qeff of the PM-4QAM through channel with 30 ROADM sites, when the neighbouring PM-64QAM channel is linearly pre-distorted (dispersion only). Solid: with single-channel DBP, open: with EDC.

On the other hand, when negative pre-distortion (dispersion pre-compensation) of less than the node-length (distance per node) is employed, the central test channel is initially degraded further. This behavior can be attributed to the increased impact of the PAPR of the undispersed constellation which is restored in the middle of the link. However, if negative pre-distortion of more than the node-length is employed, the penalty is reduced due to lower PAPR induced XPM, and the performance saturates for higher values of pre-distortion, similar to the case of positive pre-distortion. This behavior is consistent with the postulate that ROADM nodes destroy the inter bit XPM correlation typically encountered in a point to point link [18

Y. Weizhen, T. Zhenning, L. Lei, T. Hoshida, and J. C. Rasmussen, “A simplified model for XPM in coherent PSK systems,” OptoElectronics and Communications Conference, OECC ’10 (2010) paper 9B2–2.

] which enables a degree of compensation of WDM crosstalk, and that this effect is increased if there is a significant difference in the PAPR of the signal. Note that the performance is never restored to the point to point, homogenous PM-4QAM system owing to a combination of slightly increased PAPR for the higher order formats, and the reduction in data correlation associated with the data exchange at the ROADM sites.

4. Conclusions

We have reported that cross-channel nonlinear impairments strongly constrain the transmission performance of a 28 Gbaud PM-4QAM through channel in the presence of heterogeneous PM-mQAM neighbors (m = 4, 16, 64, 256) for a WDM dynamic optical network. It has been shown that increasing the network capacity by introducing higher-order formats incur a significant penalty on the existing traffic due to strong XPM effects. Such penalties are shown to be correlated to the total variation in peak-to-average power ratio of the higher-order channel along the path of the through channel and it has been demonstrated that such effects can be reduced given higher-order channels are linearly pre-distorted.

Acknowledgments

This work is supported by Science Foundation Ireland under Grant numbers 06/IN/I969 and 08/CE/11523.

References and links

1.

R. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (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.

D. Rafique, J. Zhao, and A. D. Ellis, “Performance improvement by fibre nonlinearity compensation in 112 Gb/s PM M-ary QAM,” Optical Fiber Communication Conference, OFC ’11 (accepted for publication).

4.

S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDMQAM16 transmission at 112 Gbit/s over 2400 km,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OMJ6.

5.

J. Yu, X. Zhou, Y.-K. Huang, S. Gupta, M.-F. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ 64QAM optical signal generation and transmission on a 12.5GHz WDM grid,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OThM1.

6.

S. Okamoto, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “256 QAM (64 Gbit/s) Coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OThD5.

7.

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]

8.

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]

9.

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]

10.

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]

11.

D. Rafique, J. Zhao, and A. D. Ellis, “Impact of dispersion map management on the performance of back-propagation for nonlinear WDM transmissions,” OptoElectronics and Communications Conference, OECC ’10 (2010), paper 9B2–4.

12.

S. Oda, T. Tanimura, T. Hoshida, C. Ohshima, H. Nakashima, Z. Tao, and J. C. Rasmussen, “112 Gb/s DP-QPSK transmission using a novel nonlinear compensator in digital coherent receiver,” Optical Fiber Communication Conference’09 (2009), paper OThR6.

13.

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010). [CrossRef] [PubMed]

14.

T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport over deployed optical networks,” Optical Fiber Communication Conference, OFC 2008 (2008), paper NTuB3.

15.

W. Wei, Z. Lei, and Q. Dayou, “Wavelength-based sub-carrier multiplexing and grooming for optical networks bandwidth virtualization,” Optical Fiber Communication Conference, OFC ’08 (2008), paper PDP35.

16.

R. Peter, and C. Brandon, “Evolution to colorless and directionless ROADM architectures,” Optical Fiber Communication Conference, OFC ’08 (2008), paper NWE2.

17.

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]

18.

Y. Weizhen, T. Zhenning, L. Lei, T. Hoshida, and J. C. Rasmussen, “A simplified model for XPM in coherent PSK systems,” OptoElectronics and Communications Conference, OECC ’10 (2010) paper 9B2–2.

19.

L. E. Nelson, A. H. Gnauck, R. I. Jopson, and A. R. Chraplyvy, “Cross-phase modulation resonances in wavelength-division-multiplexed lightwave transmission,” European Conference on Optical Communication, ECOC 1998 (1998), pp. 309–310.

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
(060.4256) Fiber optics and optical communications : Networks, network optimization

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 7, 2011
Manuscript Accepted: February 22, 2011
Published: April 25, 2011

Citation
Danish Rafique and Andrew D. Ellis, "Nonlinear penalties in long-haul optical networks employing dynamic transponders," Opt. Express 19, 9044-9049 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9044


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References

  1. R. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (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. D. Rafique, J. Zhao, and A. D. Ellis, “Performance improvement by fibre nonlinearity compensation in 112 Gb/s PM M-ary QAM,” Optical Fiber Communication Conference, OFC ’11 (accepted for publication).
  4. S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDMQAM16 transmission at 112 Gbit/s over 2400 km,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OMJ6.
  5. J. Yu, X. Zhou, Y.-K. Huang, S. Gupta, M.-F. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ 64QAM optical signal generation and transmission on a 12.5GHz WDM grid,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OThM1.
  6. S. Okamoto, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “256 QAM (64 Gbit/s) Coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” Optical Fiber Communication Conference, OFC ’10 (2010), paper OThD5.
  7. 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]
  8. 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]
  9. E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]
  10. 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]
  11. D. Rafique, J. Zhao, and A. D. Ellis, “Impact of dispersion map management on the performance of back-propagation for nonlinear WDM transmissions,” OptoElectronics and Communications Conference, OECC ’10 (2010), paper 9B2–4.
  12. S. Oda, T. Tanimura, T. Hoshida, C. Ohshima, H. Nakashima, Z. Tao, and J. C. Rasmussen, “112 Gb/s DP-QPSK transmission using a novel nonlinear compensator in digital coherent receiver,” Optical Fiber Communication Conference’09 (2009), paper OThR6.
  13. L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010). [CrossRef] [PubMed]
  14. T. Wuth, M. W. Chbat, and V. F. Kamalov, “Multi-rate (100G/40G/10G) Transport over deployed optical networks,” Optical Fiber Communication Conference, OFC 2008 (2008), paper NTuB3.
  15. W. Wei, Z. Lei, and Q. Dayou, “Wavelength-based sub-carrier multiplexing and grooming for optical networks bandwidth virtualization,” Optical Fiber Communication Conference, OFC ’08 (2008), paper PDP35.
  16. R. Peter, and C. Brandon, “Evolution to colorless and directionless ROADM architectures,” Optical Fiber Communication Conference, OFC ’08 (2008), paper NWE2.
  17. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]
  18. Y. Weizhen, T. Zhenning, L. Lei, T. Hoshida, and J. C. Rasmussen, “A simplified model for XPM in coherent PSK systems,” OptoElectronics and Communications Conference, OECC ’10 (2010) paper 9B2–2.
  19. L. E. Nelson, A. H. Gnauck, R. I. Jopson, and A. R. Chraplyvy, “Cross-phase modulation resonances in wavelength-division-multiplexed lightwave transmission,” European Conference on Optical Communication, ECOC 1998 (1998), pp. 309–310.

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