## On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems |

Optics Express, Vol. 20, Issue 26, pp. B204-B216 (2012)

http://dx.doi.org/10.1364/OE.20.00B204

Acrobat PDF (2946 KB)

### Abstract

We show that the accumulation rate of nonlinearity in highly-dispersive long-haul coherent links can also be measured from the nonlinear threshold decrease rate, and provide simulations of such rates for both single- and cross-channel effects. We then show how the estimated rate can be used for the overall system design.

© 2012 OSA

## 1. Introduction

*P̂*

_{1}versus distance (i.e., versus spans

*N*) at a fixed symbol rate

*R*= 28 Gbaud and Δ

*f*=50 GHz (

*η*= 0.56) for a homogeneous WDM PDM-QPSK system over a

*N*x50 km SMF DU link, and we compare it to the one obtained with standard in-line dispersion management (DM). We use the nonlinear effects separation procedure [10] to estimate the slope at which the NLT due to individual self-and cross-nonlinear effects decreases at increasing

*N*in both DU and DM systems. Section 4 finally provides a comprehensive view of the system implications of the 1dB NLT

*P̂*

_{1}and of the slope parameter

*ε*.

## 2. Simulated DU and DM systems

*f*=50 GHz. All channels were modulated with 2

^{10}and 2

^{14}independent random symbols in the DM and DU cases, respectively. Each channel was filtered by a supergaussian filter of order 2 with bandwidth 0.9

*R*. The state of polarization (SOP) of each carrier was randomized on the Poincaré sphere. The transmission line consisted of

*N*spans of 50km of SMF (

*D*=17 ps/nm/km,

*α*=0.2 dB/km,

*γ*=1.3 W

^{−1}km

^{−1}). Propagation used the vector split-step Fourier method (SSFM) with zero polarization mode dispersion and Manakov nonlinear step [10]. In the DM case, an inline residual dispersion per span (RDPS) of 30 ps/nm and a straight-line rule precompensa-tion [16, 17

17. A. Bononi, P. Serena, and A. Orlandini, “A unified design framework for single-channel dispersion-managed terrestrial systems,” J. Lightwave Technol. **26**(22), 3617–3631 (2008). [CrossRef]

*P̂*

_{1}versus distance when nonlinearities (NL) are selectively activated [10]. The NLT

*P̂*

_{1}is obtained from a series of BER Monte Carlo estimations (averaged over input polarization states) at increasing amplifiers noise figure until the target

*BER*

_{0}is obtained, as detailed in [18

18. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. **16**(2), 73–85 (2010). [CrossRef]

18. A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. **16**(2), 73–85 (2010). [CrossRef]

19. M. Winter, C.-A. Bunge, D. Setti, and K. Petermann, “A statistical treatment of cross-polarization modulation in DWDM systems,” J. Lightwave Technol. **27**(17), 3739–3751 (2009). [CrossRef]

19. M. Winter, C.-A. Bunge, D. Setti, and K. Petermann, “A statistical treatment of cross-polarization modulation in DWDM systems,” J. Lightwave Technol. **27**(17), 3739–3751 (2009). [CrossRef]

20.. “Optilux Toolbox,” [Online]. Available http://www.optilux.sourceforge.net

## 3. Results

**DU system.**Figure 2(a) shows the corresponding NLT

*P̂*

_{1}versus distance, with span number

*N*ranging from 5 to 320. We first remark that at all distances single-channel effects (SPM) dominate at this

*η*= 0.56 bandwidth fill-factor [12]. The effect of the comparable-size cross-nonlinearities XPM and XPolM on the overall NLT (WDM) is felt only at distances below 2000 km. The reason is that single-channel nonlinearity accumulates at a faster rate than cross-channel nonlinearity so that at longer distances it becomes largely dominant. Equation (18) predicts on this log-log plot a NLT decrease with a slope −(1 +

*ε*)/2 dB/dB. From Fig. 2 (a) on the narrow-range up to 2000 km (40 spans) by least mean-square fitting data with straight lines we find

*ε*≅ 0.32,

_{SPM}*ε*≅ 0.22,

_{XPM}*ε*≅ −0.08 and

_{XPolM}*ε*≅ 0.16, while fitting on the wide-range (up to 320 spans) we measure

_{WDM}*ε*≅ 0.28,

_{SPM}*ε*≅ 0.08,

_{XPM}*ε*≅ −0.08 and

_{XPolM}*ε*≅ 0.22. We first note that the wide-range

_{WDM}*ε*value is consistent with measurements in [11] at similar

_{WDM}*η*, while the narrow-range

*ε*is in agreement with [13]. However, the most novel piece of information we learn from Fig. 2 is that the smaller slope of cross-nonlinearity observed in [13] is indeed an average of the XPolM and scalar XPM slopes, where scalar XPM seems to accumulate at a slightly faster rate. However, in DU links the rate difference is small. The negative measured

_{SPM}*ε*is ascribed to an insufficient pattern length, as discussed below.

_{XPolM}**DM system.**It is instructive to also take a look at the NLT curves when the DU link is changed into a legacy DM link. Figure 2(b) shows both the unrealistic case of noise loading (solid lines) and the realistic case of ASE distributed at each amplifier, where nonlinear signal-ASE interactions are fully accounted for (dashed lines). We remark that pre-compensation is here

*changed at each value of N*according to (3), hence the measured NLTs do not truly portray the noise accumulation with

*N*in the

*same*line. Figure 2(b) confirms that [12]:

- scalar XPM plays a minor role in the PDM-QPSK constant intensity format, and is quite sensitive to signal-noise interactions, here manifested as nonlinear phase noise (NLPN);
- single channel (SPM) effects also play a minor role up to about 4000 km, and in that range are also quite sensitive to NLPN;
- the dominant nonlinearity is XPolM up to about 4000 km, but eventually SPM effects become dominant as they accumulate at a faster rate. XPolM is not impacted by signal-ASE interactions.

*ε*≅ 1, but such a slope decreases at larger distances, since the RDPS starts contributing enough cumulated dispersion to make the DM system look more similar to a DU system. Within the first ∼2000 km we also measure (with NLPN)

_{SPM}*ε*≅ 0.73 and

_{XPM}*ε*≅ 0.66. The fact that XPolM is less “resonant” than scalar XPM is seen in the lowering of the local XPolM slope after 2000 km. The intuitive reason of XPolM’s smaller slope is easily understood in a truly resonant DM map (i.e., with RDPS=0). In such a case the walkoff completely realigns the interfering pattern intensities, hence scalar XPM is identical at each span, i.e., it is truly resonant. Instead, the rotations induced by XPolM never bring back the final SOP to the same starting SOP at each span, hence XPolM is never truly resonant.

_{WDM}## 4. System implications of slope parameter and NLT

*Q*-factor [5

5. E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express **19**(13), 12781–12788 (2011). [CrossRef] [PubMed]

*S*

*, versus power*

^{dB}*P*

*and number of spans*

^{dB}*N*

*(for any variable*

^{dB}*x*, we will denote

*x*

*= 10Log(*

^{dB}*x*)). It is the objective of this section to summarize the analytical properties of such a surface and explain how the exponent

*ε*and the

*P̂*

_{1}vs.

*N*curves fit into such a global view. Section 4.1 describes the properties of the “vertical cuts”

*S*vs.

*P*at a fixed distance

*N*, known as the “bell curves”. Section 4.2 describes the properties of the “horizontal cuts”

*P*vs.

*N*at a desired level

*S*

_{0}, tackling the issue of maximum transmission distance. Note that according to the models in [6

6. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of non-Linear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol. **30**(10), 1524–1539 (2012). [CrossRef]

7. A. Bononi, P. Serena, N. Rossi, E. Grellier, and F. Vacondio, “Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing,” Opt. Express **20**(7), 7777–7791 (2012). [CrossRef] [PubMed]

*a*depends on the modulation format only through its symbol rate. Hence, by varying

_{NL}*S*

_{0}, one finds the performance of any zero-mean format at a given symbol rate.

### 4.1. Vertical cuts: the bell curves

*S*versus

*P*at a fixed distance

*N*. More information can be found in [3,5

5. E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express **19**(13), 12781–12788 (2011). [CrossRef] [PubMed]

*P*for fixed values of ASE power

*N*and nonlinearity

_{A}*a*where the two asymptotes are indicated by dashed lines. Equation (1) can be rearranged as where

_{NL}*SP*is the sensitivity penalty in linear units, and in dB it is the distance of the SNR curve from the linear asymptote

*S*, as seen in Fig. 5.

_{L}#### 4.1.1. Unconstrained nonlinear threshold

*P*that maximizes the bell curve. By setting

_{NLT}*NA*= 2(

*a*

_{NL}*P*

^{3}), i.e., at the optimal power ASE noise is twice the nonlinear noise, and the SP is

5. E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express **19**(13), 12781–12788 (2011). [CrossRef] [PubMed]

*P*. The corresponding maximum SNR is:

_{B}*P*we reach a penalty of

_{y}*y*. The answer is found by imposing

^{dB}*SP*= 10

^{ydB/10}and rearranging Eq. (4):

*P*=

_{y}*P*· [2(10

_{NLT}^{ydB/10}− 1)]

^{1/3}. For instance,

#### 4.1.2. Constrained NLT

*S*

_{0}, it was shown in ([7

7. A. Bononi, P. Serena, N. Rossi, E. Grellier, and F. Vacondio, “Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing,” Opt. Express **20**(7), 7777–7791 (2012). [CrossRef] [PubMed]

*S*

_{0}when ASE power is

*constrained NLT*at

*S*

_{0}. When

*N*<

_{A}*N̂*, the SNR

_{A}*S*exceeds

*S*

_{0}over the whole range

*P*<

_{m}*P*<

*P*, where

_{M}*N*>

_{A}*N̂*, the target

_{A}*S*

_{0}is unachievable. The penalty corresponding to the extremes

*P*,

_{m}*P*is found as

_{M}*S*

_{0}

*N*is the required minimal power to achieve

_{A}*S*

_{0}in the linear regime. Figure 3(b) in [7

7. A. Bononi, P. Serena, N. Rossi, E. Grellier, and F. Vacondio, “Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing,” Opt. Express **20**(7), 7777–7791 (2012). [CrossRef] [PubMed]

*SP*versus power. When

_{m,M}*P*≡

_{m}*P*we know the SP with respect to

_{M}*S*

_{0}is 1.76 dB. For any other SP value

*y*, it is also interesting to find the power

^{dB}*P̂*(i.e., either

_{y}*P*when

_{m}*y*< 1.76, or

^{dB}*P*when

_{M}*y*> 1.76.) achieving

^{dB}*SP*=

*y*. We call

^{dB}*P̂*the

_{y}*constrained NLT*at

*y*of penalty. Defining we already showed in [7

^{dB}**20**(7), 7777–7791 (2012). [CrossRef] [PubMed]

*c*(1) = 1.27, hence the constrained 1dB NLT

*P̂*

_{1}is 1.04 dB below

*P̂*(while we have seen that the unconstrained

_{NLT}*P*

_{1}is 0.95 dB below the unconstrained

*P*).

_{NLT}*c*(

*y*) curve can be obtained as follows. Let

^{dB}*SP*= 10

^{ydB/10}and

*x*=

*N*/

_{A}*N̂*∈ [0, 1], and look for the solution of the nonlinear equation

_{A}*y*≤ 1.76, and of

^{dB}*y*> 1.76. Once

^{dB}*x*is found, calculate

*c*(

*y*

^{dB}^{)}= 3/(2

*x*· 10

^{ydB/10}). The result is plotted in Fig. 6. In blue we show the dB value of the curve

*c*(

*y*), which is zero at

^{dB}*y*= 1.76, while in green we show the curve

^{dB}*x*(

*y*).

^{dB}### 4.2. Horizontal cuts

*N*=

_{A}*β*

*N*, where

*β*=

*hνFGB*depends on photon energy

_{RX}*hν*at signal frequency

*ν*, amplifiers noise figure

*F*, gain

*G*, and two-sided receiver noise bandwidth

*B*. We now assume for

_{RX}*a*a simplified distance scaling law as in Eq. (2) and want to check the impact of the exponent factor

_{NL}*ε*.

*S*(

*N,P*) at levels

*S*

_{0}spaced by 1 dB. In the figure we assumed

*ε*= 0.22. The analytical shape of each contour is obtained from which yields the explicit contour equation

*P*versus

*N*. The two solutions of the cubic Eq. (10) are the powers

*P*(top branch up to the red circle) and

_{M}*P*(bottom branch) whose analytical expression is given in Eq. (8). Each contour level has two asymptotes, obtained by suppressing either ASE or NLI in Eq. (10):

_{m}#### 4.2.1. Unconstrained NLT

*N*

_{0},

*P*

_{0}) at each

*S*

_{0}level, marked with red circles in Fig. 7. Information on how (

*N*

_{0},

*P*

_{0}) change with

*S*

_{0}is useful to understand the effect of the modulation format: at a given symbol rate, in general different formats will require different SNR

*S*

_{0}to reach a desired target Q-factor

*Q*

_{0}or BER value

*BER*

_{0}. It is thus important to understand by how much maximum distance and optimal power change as the modulation format is changed. The points (

*N*

_{0},

*P*

_{0}) are such that

*P*≡

_{m}*P*, i.e., they correspond to a distance

_{M}*N*

_{0}where power

*P*

_{0}coincides with

*P̂*, the constrained NLT at

_{NLT}*S*

_{0}. Therefore each red circle corresponds to the top of the “vertical cut” at

*N*

_{0}. In other words, the magenta-line is the “crest” of the

*S*surface, or equivalently the locus of the

*unconstrained NLT P*as

_{NLT}*N*varies. As such, given

*N*

_{0}, we have from Eq. (5), Eq. (6):

*S*versus

^{dB}*N*

_{0}is a straight line with slope

*k*times the NLI power at coordinate

*N*satisfies which proves that the whole

_{k}*S*surface sketched in Fig. 4 is composed of parallel straight-lines.

^{dB}#### 4.2.2. Constrained NLT

*P̂*versus

_{NLT}*N*is a straight line parallel to

*P*but lowered by

_{H}*c*(

*y*) is shown in Fig. 6. A similar scaling law was already reported in [23] for DU systems with

^{dB}*ε*= 0. Hence for instance

*P̂*

_{1}is a straight line parallel to

*P̂*but lowered by ∼ 1.04 dB as reported in blue solid line in Fig. 8. The parameters

_{NLT}*NLT*

_{1}and

*ε*used in the figure were obtained by straight-line fitting the simulated

*P̂*

_{1}vs.

*N*“WDM” curve in Fig. 2(a).

*N*was measured in ([26], Fig. 1) to be ∼0.31 dB/dB for a 50 GHz spaced 28 Gbaud PDM-QPSK system over an

*N*x100 km DU SMF link, consistently with the experimentally estimated value

*ε*∼ 0.37 [8

8. F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express **20**(2), 1022–1032 (2012). [CrossRef] [PubMed]

*P*

_{0},

*N*

_{0}) as the

*β*factor (i.e., amplifiers noise figure for instance) is varied. This was already proven in [5

**19**(13), 12781–12788 (2011). [CrossRef] [PubMed]

*P̂*

_{1}is obtained in simulations by varying the received ASE until 1 dB of penalty is measured. Similarly, the locus of maximum distance points (

*P*

_{0},

*N*

_{0}) as the

*α*factor is varied with

_{NL}*β*held constant is a straight line parallel to the linear asymptote and 1.76 dB above it, since from Eq. (14) we have

27. V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 100 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. **22**(19), 1446–1448 (2010). [CrossRef]

*N*

_{0}is obtained from the two relations in Eq. (14) as and its associated “optimal” power as

*N*

_{0}by 2.76/(1 +

*ε*/3) dB and the true

*P*

_{0}by (3 − 1.76

*ε*)/(3 +

*ε*) dB, as seen in Fig. 8.

**i) Sensitivity**. By differentiating Eq. (20), Eq. (21) we immediately get

*S*

_{0}(e.g. modulation format or coding),

*β*(e.g. amplifiers noise figure) and

*α*(e.g. fiber parameters such as nonlinearity and dispersion). Such changes need not be small, since the surface is made of straight lines. For instance, from the top left relation we see that if a more powerful code lowers the SNR

_{NL}*S*

_{0}by 1dB (without appreciably increasing the symbol rate), maximum distance is extended by

*ε*= 0. The top right relation tells us that

*P*

_{0}is very weakly dependent on SNR

*S*

_{0}, hence on modulation format. We can also use the middle relations Eq. (22) to conclude that in Fig. 8 when

*β*is doubled (+3dB), the optimal power

*P*

_{0}is increased by

*N*

_{0}is decreased by

*α*brings about a modest decrease by less than 1/3 dB in both

_{NL}*N*

_{0}[28

28. P. Poggiolini, “The GN model of non-Linear propagation in uncompensated coherent optical systems,” J. Light-wave Technol. (2012), Early Access. [CrossRef]

*P*

_{0}. It is the same decrease for both

*N*

_{0}and

*P*

_{0}, since the optimal (

*N*

_{0},

*P*

_{0}) in this case slides along a 1 dB/dB straight line parallel to the lower asymptote, as we already remarked.

*P*(

_{H}*N*)/

*P*(

_{L}*N*), corresponding to the vertical dB spread of the contour at

*S*

_{0}between the asymptotes at

*N*. Similarly, Eq. (20) tells us that maximum reach

*N*

_{0}at

*S*

_{0}only depends on the power budget

*S*

_{0}at

*N*= 1 span from 1.76 dB above the lower linear asymptote

*P*(1) =

_{L}*LT*

_{1}up to the magenta dash-dotted line

*P̂*(1) =

_{NLT}*NLT*

_{1}. Also, by using the second form of Eq. (20) and Eq. (19) one can estimate the extra distance ratio

*N*

_{0}/

*N*from the

*measured*value of the constrained NLT

*P̂*(

_{NLT}*N*) at

*S*

_{0}at given distance

*N*as which only depends on the local power budget

*BER*

_{0}(hence at possibly different

*S*

_{0,}

*,*

_{A}*S*

_{0,}

*) one can estimate by how much the best format extends the maximum reach from: where*

_{B}*BER*

_{0}) of the two formats in the linear regime. Clearly, a format A that has

*x*dB larger NLT than B, but also

*x*dB worse sensitivity than B, achieves the same maximum distance.

## 5. Conclusions

*ε*can also be measured through the nonlinear threshold decrease rate with distance, and we have provided the accumulation rates of the individual self- and cross-channel nonlinear effects, thus corroborating and complementing recent simulation and lab results [8

8. F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express **20**(2), 1022–1032 (2012). [CrossRef] [PubMed]

*ε*(when all nonlinear effects are taken into account) as well as the 1dB nonlinear threshold can be used to predict the ultimate transmission performance.

## Acknowledgments

## References and links

1. | M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. S. Pak, R. Noe, I. Shpantzer, and V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express |

2. | X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express |

3. | G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in |

4. | P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. |

5. | E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express |

6. | A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of non-Linear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol. |

7. | A. Bononi, P. Serena, N. Rossi, E. Grellier, and F. Vacondio, “Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing,” Opt. Express |

8. | F. Vacondio, O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J.-C. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems,” Opt. Express |

9. | A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in |

10. | A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlinearity in long-haul PDM-QPSK coherent transmissions?,” in |

11. | O. V. Sinkin, J.-X. Cai, D. G. Foursa, H. Zhang, A. N. Pilipetskii, G. Mohs, and Neal S. Bergano, “Scaling of nonlinear impairments in dispersion-uncompensated long-Haul transmission,” in |

12. | A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in |

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14. | A. Bononi, N. Rossi, and P. Serena, “Nonlinear threshold decrease with distance in 112 Gb/s PDM-QPSK coherent systems,” in |

15. | J. C. Antona and S. Bigo, “Physical design and performance estimation of heterogeneous optical transmission systems,” C. R. Physique |

16. | Y. Frignac, J.-C. Antona, and S. Bigo, “Enhanced analytical engineering rule for fast optimization of dispersion map in 40 Gbit/s-based transmission systems,” in |

17. | A. Bononi, P. Serena, and A. Orlandini, “A unified design framework for single-channel dispersion-managed terrestrial systems,” J. Lightwave Technol. |

18. | A. Bononi, P. Serena, and N. Rossi, “Nonlinear signal-noise interactions in dispersion-managed links with various modulation formats,” Opt. Fiber Technol. |

19. | M. Winter, C.-A. Bunge, D. Setti, and K. Petermann, “A statistical treatment of cross-polarization modulation in DWDM systems,” J. Lightwave Technol. |

20.. | “Optilux Toolbox,” [Online]. Available http://www.optilux.sourceforge.net |

21. | J.-C. Antona, E. Grellier, A. Bononi, S. Petitreaud, and S. Bigo, “Revisiting binary sequence length requirements for the accurate emulation of highly dispersive transmission systems,” in |

22. | E. Grellier, J.-C. Antona, A. Bononi, and S. Bigo, “Revisiting binary sequence length requirements to accurately emulate optical transmission systems in highly dispersive regime,” SPIE |

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24. | V. A. J. M. Sleiffer, M. S. Alfiad, D. van den Borne, S. L. Jansen, M. Kuschnerov, S. Adhikari, and H. De Waardt, “A comparison of 43-Gb/s POLMUX-RZ-DPSK and POLMUX-RZ-DQPSK modulation for long-haul transmission systems,” in |

25. | M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80×100-Gbit/s transmission over 9,000km using erbium-doped fibre repeaters only,” in |

26. | E. Grellier, J.-C. Antona, and S. Bigo, “Revisiting the evaluation of non-linear propagation impairments in highly dispersive systems,” in |

27. | V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance evaluation of long-haul 100 Gb/s PM-QPSK transmission over different fiber types,” IEEE Photon. Technol. Lett. |

28. | P. Poggiolini, “The GN model of non-Linear propagation in uncompensated coherent optical systems,” J. Light-wave Technol. (2012), Early Access. [CrossRef] |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

**ToC Category:**

Transmission Systems and Network Elements

**History**

Original Manuscript: September 26, 2012

Revised Manuscript: November 6, 2012

Manuscript Accepted: November 6, 2012

Published: November 29, 2012

**Virtual Issues**

European Conference on Optical Communication 2012 (2012) *Optics Express*

**Citation**

A. Bononi, N. Rossi, and P. Serena, "On the nonlinear threshold versus distance in long-haul highly-dispersive coherent systems," Opt. Express **20**, B204-B216 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-26-B204

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### References

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