## Semi-empirical system scaling rules for DWDM system design |

Optics Express, Vol. 20, Issue 3, pp. 2992-3004 (2012)

http://dx.doi.org/10.1364/OE.20.002992

Acrobat PDF (1852 KB)

### Abstract

Recently, several theoretical papers have derived relationships for fiber-optic transmission system performance in terms of associated physical layer parameters. At the same time, a large number of detailed experiments have been and continue being performed that demonstrate increasing capacities and unregenerated reach. We use this wealth of experimental data to validate the aforementioned relationships, and to propose a set of simple scaling rules for performance. We find that, despite substantial differences in experimental configurations, overall performance in terms of spectral efficiency and unregenerated reach is well explained by scaling rules. These scaling rules will be useful to carriers seeking to understand what they should expect to see in terms of network performance using deployed or easily accessible technology, which may be radically different from hero experiment results. These rules will also be useful to design engineers seeking cost effective tradeoffs to achieving higher performance using realistic upgrade strategies, and what might be encountered as a fundamental limit.

© 2012 OSA

## 1. Introduction

1. R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. **28**(4), 662–701 (2010). [CrossRef]

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

4. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett. **22**(6), 371–373 (2010). [CrossRef]

5. M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett. **22**(15), 1150–1152 (2010). [CrossRef]

6. 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]

7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express **18**(18), 19039–19054 (2010). [CrossRef] [PubMed]

7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express **18**(18), 19039–19054 (2010). [CrossRef] [PubMed]

*A*(dB), span length

_{s}*L*(km), number of spans

_{s}*N*, type of amplification (i.e. EDFA, hybrid EDFA Ramam, Raman only), and amplifier noise figure

_{s}*N*(dB). The following fiber characteristics also enter into analysis: attenuation

_{f}*α*(dB/km), non-linearity coefficient

*γ*(1/(W·km)), effective area of the optical mode

*A*(μm

_{eff}^{2}), and chromatic dispersion

*D*(ps/(nm·km)).

### 1.1 Impact of the number of channels on unregenerated reach

### 1.2 A nominal network for normalization

- • C-band EDFA only span amplification, with a Noise Figure of 5 dB
- • Span lengths of 80 km, with a loss per span of 20 dB to account for margin and aging
- • Fiber is standard single mode fiber (SSMF),
*γ*= 1.31 1/(W·km),*A*= 86 μm_{eff}^{2},*D*= 16.7 ps/(nm·km),*α*= 0.22 dB/km - • No inline optical dispersion compensation
- • FEC with a net effective coding gain (NECG) of 9.6 dB at 10
^{−15}BER, allowing us to operate at a pre-corrected bit error rate of 4.3 10^{−3}, or a Q^{2}of 8.4 dBQ. - • A receiver operating at a back-to-back OSNR of 3 dB from ideal performance for PDM- QPSK, 5 dB from ideal for PDM-16QAM, and PDM-64QAM

## 2. Simple scaling rules

10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. **23**(11), 742–744 (2011). [CrossRef]

*P*is the per channel power into a fiber span,

_{ch}*P*is the amplified spontaneous emission (ASE) noise power, and

_{ASE}*P*is noise power due to nonlinear effects. Assuming that we measure powers in both optical polarizations, that ASE accumulates linearly, and that all fiber spans are generally identical (as is the case for most lab experiments), we write Eq. (2),where

_{NL}*N*is the number of spans,

_{s}*A*is the span loss,

_{s}*N*is the optical noise figure of the span amplifier,

_{f}*h*is Planck’s constant,

*f*is the channel optical frequency, and

*B*is the equivalent channel bandwidth over which noise is measured (all in linear units). We now consider

_{n}*P*, nonlinear noise power, and make use of the analysis in [7

_{NL}7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express **18**(18), 19039–19054 (2010). [CrossRef] [PubMed]

10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. **23**(11), 742–744 (2011). [CrossRef]

*f*is equal to the channel symbol rate. However, we are interested in a different aspect: the impact of channel spacing while keeping the symbol rate constant, which is more aligned with published experimental results. While most papers have considered ITU-based 50 GHz spacing of channels, several have pursued improved spectral efficiency through tighter channel spacing. Channel spacing can be reduced to the symbol rate without deleterious linear crosstalk effects, using either Nyquist WDM or OFDM type signal filtering. This moves overall system performance closer to the Shannon limit boundary, and should not be confused with moving along the Shannon boundary via increased constellation density.

*D*·Δ

*f*) [12

12. Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple Fiber Model for Determination of XPM Effects,” J. Lightwave Technol. **29**(7), 974–986 (2011). [CrossRef]

*SE*) is inversely proportional to the channel spacing, Δ

*f*. Du, et al [13

13. L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of coherent optical communications systems,” Opt. Express **19**(9), 8079–8084 (2011). [CrossRef] [PubMed]

*L*~1/α, is the effective length of the fiber.

_{eff}14. V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance Evaluation of Long-Haul 111Gb/s PM-QPSK Transmission Over Different Fiber Types,” IEEE Photon. Technol. Lett. **22**(19), 1446–1448 (2010). [CrossRef]

*D*. Using Eq. (3), we express the nonlinear noise power in Eq. (1) aswhere

*κ*is a nonlinear noise power proportionality constant, which depends only on modulation format.

_{NL}*P*’s dependence on baud rate is implicit in channel noise bandwidth,

_{NL}*B*. Substituting Eq. (2) and Eq. (4) into Eq. (1), one obtains for the SNR:

_{n}*P*and

_{ASE}*P*). The optimal launch power density is then [8]:

_{NL}*B2B*) and the nominal transceiver’s penalty relative to ideal performance (

_{E}*B2B*).

_{N}*SNR*and

_{E}*SNR*, incorporating the adjustment factors defined above. We further note that

_{N}*κ*is assumed to be dependent on modulation format only, with other system factors being explicitly accounted for. Evaluating the difference in the number of spans between a nominal and experimental configuration, and casting the quantities into dB units, we obtain a single scaling rule with terms accounting for differences in BER, back-to-back transceiver performance, span loss, noise figure, dispersion, nonlinear coefficient, effective length, and spectral efficiency.

_{NL}*D*can be seen in evidence in the results of [7

**18**(18), 19039–19054 (2010). [CrossRef] [PubMed]

10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. **23**(11), 742–744 (2011). [CrossRef]

14. V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance Evaluation of Long-Haul 111Gb/s PM-QPSK Transmission Over Different Fiber Types,” IEEE Photon. Technol. Lett. **22**(19), 1446–1448 (2010). [CrossRef]

15. A. Carena, V. Curri, P. Poggiolini, G. Bosco, and F. Forghieri, “Maximum Reach Versus Transmission Capacity for Terabit Superchannels Based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM,” IEEE Photon. Technol. Lett. **22**(11), 829–831 (2010). [CrossRef]

*f*to improve spectral efficiency, and a reduction in span count,

*N*(i.e. a 3 dB spectral efficiency improvement only results in a 1 dB reduction in reach). Span count reduction may be even smaller in practice due to single-channel SPM effect contributions.

_{s}## 3. Example of normalization based on the described scaling rule

*α*= 0.161 dB/km,

*D*= 20.5 ps/nm·km,

*A*= 112 μm

_{eff}^{2}), and no optical dispersion compensation. First, we verify that the experiment itself follows the expected trends. Equation (5) shows that increasing system reach, while keeping overall system configuration the same, should produce a corresponding 1:1 linear decrease in SNR. This is clearly observed in Fig. 4 of [3] over the experimental range of 7200km to 10200km, confirming the basic validity of assumptions for this experiment.

*N*= 144, gives a normalized reach of 31 spans. The same paper reported additional system measurements at 180 spans, and 204 spans. All three configurations normalize to the same number of spans, i.e. 31. This conforms to the general result that for a given modulation format and spectral efficiency, all experiments will normalize to the same nominal span count, because the limiting factor is nonlinear noise power, which is determined by spectral efficiency, as opposed to bit or symbol rate [15

_{s,E}15. A. Carena, V. Curri, P. Poggiolini, G. Bosco, and F. Forghieri, “Maximum Reach Versus Transmission Capacity for Terabit Superchannels Based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM,” IEEE Photon. Technol. Lett. **22**(11), 829–831 (2010). [CrossRef]

*why not*(i.e. there’s a factor, unaccounted for, that might offer novel insight).

## 4. Results and discussion of additional normalizations

- • Self-consistency of reported OSNR with launch power and optical amplifier chain characteristics
- • Measured back-back characteristics within expected range from ideal
- • Optimum nonlinear-limited Q deviation from a pure linear limit by ~1.76 dB [17]
17. E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express

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

4. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett. **22**(6), 371–373 (2010). [CrossRef]

18. J. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s Capacity Transmission Over 6,860 km,” in *National Fiber Optic Engineers Conference*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB4.

21. G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72x100Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPB6.

5. M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett. **22**(15), 1150–1152 (2010). [CrossRef]

6. 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]

22. C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express **19**(14), 12879–12884 (2011). [CrossRef] [PubMed]

27. J. Yu and X. Zhou, “16 x 107-Gb/s 12.5-GHz-Spaced PDM-36QAM Transmission Over 400 km of Standard Single-Mode Fiber,” IEEE Photon. Technol. Lett. **22**(17), 1312–1314 (2010). [CrossRef]

28. A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizuguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM Transmission over 160 km Using Linewidth-Tolerant Pilotless Digital Coherent Detection,” in *Proceedings ECOC 2010*, Torino, Italy, 2010, Paper pd2_4.

*except the spectral efficiency (SE) term*. Also shown in Fig. 2 are lines representing span count corresponding to ideal transceiver performance for each basic approach considered (QPSK, 16QAM, 64QAM). Each line shows how we would expect the span count to vary with spectral efficiency, within that approach. They were obtained by normalizing the results of simulations [10

**23**(11), 742–744 (2011). [CrossRef]

30. 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]

*N*≅ 19 dB or 80 spans at an

_{s}*SE*~3.7 b/s/Hz (corresponding to the Nyquist limit for a 50 GHz channel). We then use the

*SE*term in Eq. (8) to compute the span count seen at the spectral efficiency at 50% of the Nyquist limit, essentially half filling that channel (90 spans, at 2.0 b/s/Hz). A trend line is drawn between those two points. The ideal span count values for 16QAM and 64QAM are computed in a similar fashion, resulting in a trend line for 16QAM drawn between 18 spans at 3b/s/Hz and 14 spans at 7.4b/s/Hz. A trend line for 64QAM is drawn between 5 spans at 4b/s/Hz and 3 spans at 11.1 b/s/Hz.

### 4.1 Clusters having a common modulation format, and common SE

*SE*has reach values that range from 28 spans to 35 spans. That difference represents −0.9 dB variation from the low to high span values. We assign these discrepancies to both experimental errors and data extraction inaccuracy and identify the range of 28-35 spans with a single cluster. The cluster within the PDM-16QAM data sharing a common modulation format and same

*SE*all cluster to four spans, with no variation.

### 4.2 Data sharing a common modulation format, but having a different SE

*SE*of 4.2. There are two results using that same modulation format with different

*SE*. They occur at 3 spans with 6.2 b/s/Hz [25] and 4 spans with 6.4 b/s/Hz [26]. Using Eq. (8), the difference in

*SE*of 4.2 and 6.2 should imply a −0.6 dB difference in spans, implying the reach at an

*SE*of 6.2-6.4 should be between 3 and 4 spans, which is in agreement with our normalization.

28. A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizuguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM Transmission over 160 km Using Linewidth-Tolerant Pilotless Digital Coherent Detection,” in *Proceedings ECOC 2010*, Torino, Italy, 2010, Paper pd2_4.

*SE*of 9 and 8. Using Eq. (8) the difference between the two results based on

*SE*alone results in a scaling difference of −0.5 dB. This is below the accuracy of our approximate technique, and the two results are indistinguishable.

### 4.3 Broad relationships across the data

*SE*, modulation format, and performance.

*SE*, we see consistent clustering with no significant or unexplainable variation. Data sharing a common modulation format but differing

*SE*, conform to the predictions of our

*SE*scaling rule within the expected accuracy of our normalization process. The overall position of the clusters themselves is consistent with theory with respect to modulation format performance and our

*SE*scaling rule.

### 4.4 Possible sources of inaccuracy

*α*,

*γ*,

*D*, channel spacing, transmission rate, number of channels, and channel frequencies, along with any other known deviations from ideal performance. The developed scaling rules do not explicitly take into account BER flooring effects, and all experiments considered were well above possible BER floor for the relevant modulation format.

## 5. What are the limits to performance?

*SE*is small enough to avoid inter-channel linear interference, i.e. channel spacing is larger than baud rate, assuming Nyquist-type filtering.

**is net effective coding gain of the applied FEC code, Δ**

*NECG***(dB) is transponder deviation from ideal QAM performance at relevant BER, and**

*B2B***(dB) is the allocation for field deployed margin (i.e. transponder aging, thermal effects, control loop errors, optical transients, etc…)**

*M*### 5.1 Impact of forward error correction overhead

31. J.-X. Cai, M. Nissov, A. N. Pilipetskii, A. J. Lucero, C. R. Davidson, D. Foursa, H. Kidorf, M. A. Mills, R. Menges, P. C. Corbett, D. Sutton, and N. S. Bergano, “2.4 Tb/s (120 x 20 Gb/s) Transmission over Transoceanic Distance using Optimum FEC Overhead and 48% Spectral Efficiency,” in *Optical Fiber Communication Conference*, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper PD20.

32. A. Agata, K. Tanaka, and N. Edagawa, “Study on the Optimum Reed-Solomon-Based FEC Codes for 40-Gb/s-Based Ultralong-Distance WDM transmission,” J. Lightwave Technol. **20**(12), 2189–2195 (2002). [CrossRef]

23. A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Packham, “10 x 224-Gb/s WDM Transmission of 28-Gbaud PDM 16-QAM on a 50-GHz Grid over 1,200 km of Fiber,” in *National Fiber Optic Engineers Conference*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB8.

**of 9.6 dB, utilizing ~7% overhead. As noted above, FEC codes providing a greater**

*NECG***, using soft decision logic and higher overheads have been studied. Consider, for example, a soft-decision FEC requiring 15% overhead providing a**

*NECG***of 11 dB [35]. This would provide a 1.4 dB improvement in reach, at a spectral efficiency penalty of ~7%, translating into an overall reach increase of ~38% (QPSK: 31 spans to 43 spans; 16QAM: 4 spans to 5 spans; 64QAM: no extension). However, if we are after the best possible spectral efficiency at a given optical reach, or use higher level modulation formats, a different conclusion may occur.**

*NECG*### 5.2 Use of high power Raman span amplification

36. J. Bromage, “Raman Amplification for Fiber Communications Systems,” J. Lightwave Technol. **22**(1), 79–93 (2004). [CrossRef]

*P*and

_{ASE}*P*. This is confirmed by our normalization results.

_{NL}### 5.3 Impact of modulation format optimization

37. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical Links?” Opt. Express **17**(13), 10814–10819 (2009). [CrossRef] [PubMed]

40. E. Torrengo, S. Makovejs, D. Millar, I. Fatadin, R. Killey, S. Savory, and P. Bayvel, “Influence of Pulse Shape in 112-Gb/s WDM PDM-QPSK Transmission,” IEEE Photon. Technol. Lett. **22**(23), 1714–1716 (2010). [CrossRef]

42. B. Châtelain, C. Laperle, K. Roberts, X. Xu, M. Chagnon, A. Borowiec, F. Gagnon, J. Cartedge, and D. V. Plant, “Optimized Pulse Shaping for Intra-channel Nonlinearities Mitigation in a 10 Gbaud Dual-Polarization 16-QAM System,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO5.

## 6. Conclusions

**, and taking a considered look at possible tradeoffs between tighter channel spacing and reach. Also on the topic of FEC, we discussed tradeoffs between overhead and**

*NECG**SE*, and determined an optimum overhead to

*SE*tradeoff at about 15%.

## Acknowledgments

## References and links

1. | R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. |

2. | A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. |

3. | M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in |

4. | G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett. |

5. | M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett. |

6. | 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. |

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

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

9. | C. Xia and D. van den Borne, “Impact of the Channel Count on the Nonlinear Tolerance in Coherently-detected POLMUX-QPSK modulation,” in |

10. | P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. |

11. | A. Bononi, N. Rossi, and P. Serena, “Transmission Limitations due to Fiber Nonlinearity,” in |

12. | Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple Fiber Model for Determination of XPM Effects,” J. Lightwave Technol. |

13. | L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of coherent optical communications systems,” Opt. Express |

14. | V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance Evaluation of Long-Haul 111Gb/s PM-QPSK Transmission Over Different Fiber Types,” IEEE Photon. Technol. Lett. |

15. | A. Carena, V. Curri, P. Poggiolini, G. Bosco, and F. Forghieri, “Maximum Reach Versus Transmission Capacity for Terabit Superchannels Based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM,” IEEE Photon. Technol. Lett. |

16. | C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Fibre Nonlinearities in WDM-Systems with Reduced Channel-Spacing and Symbol-Rate,” in |

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

18. | J. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s Capacity Transmission Over 6,860 km,” in |

19. | J. Yu, X. Zhou, D. Qian, M. Huang, P. N. Ji, and G. Zhang, “20x112Gbit/s, 50GHz spaced, PolMux-RZ-QPSK straight-line transmission over 1540km of SSMF employing digital coherent detection and pure EDFA amplification,” in |

20. | J. Downie, J. E. Hurley, J. Cartledge, S. R. Bickham, and S. Mishra, “Transmission of 112 Gb/s PM-QPSK Signals over 7200 km of Optical Fiber with Very Large Effective Area and Ultra-Low Loss in 100 km Spans with EDFAs Only,” in |

21. | G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72x100Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in |

22. | C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express |

23. | A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Packham, “10 x 224-Gb/s WDM Transmission of 28-Gbaud PDM 16-QAM on a 50-GHz Grid over 1,200 km of Fiber,” in |

24. | M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “Transmission of 11 x 224-Gb/s POLMUX-RZ-16QAM over 1500 km of LongLine and pure-silica SMF,” in |

25. | S. Yamanaka, T. Kobayashi, A. Sano, H. Masuda, E. Yoshida, Y. Miyamoto, T. Nakagawa, M. Nagatani, and H. Noaka, “11 x 171 Gb/s PDM 16-QAM Transmission over 1440 km with a Spectral Effiency of 6.4 b/s/Hz using High-Speed DAC,” in |

26. | A. Gnauck and P. J. Winzer, “Ultra-High-Spectral-Efficiency Transmission,” in |

27. | J. Yu and X. Zhou, “16 x 107-Gb/s 12.5-GHz-Spaced PDM-36QAM Transmission Over 400 km of Standard Single-Mode Fiber,” IEEE Photon. Technol. Lett. |

28. | A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizuguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM Transmission over 160 km Using Linewidth-Tolerant Pilotless Digital Coherent Detection,” in |

29. | J. Yu, X. Zhou, Y. Huang, S. Gupta, M. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ-64QAM optical signal generation and transmission on a 12.5GHz WDM Grid,” in |

30. | 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 |

31. | J.-X. Cai, M. Nissov, A. N. Pilipetskii, A. J. Lucero, C. R. Davidson, D. Foursa, H. Kidorf, M. A. Mills, R. Menges, P. C. Corbett, D. Sutton, and N. S. Bergano, “2.4 Tb/s (120 x 20 Gb/s) Transmission over Transoceanic Distance using Optimum FEC Overhead and 48% Spectral Efficiency,” in |

32. | A. Agata, K. Tanaka, and N. Edagawa, “Study on the Optimum Reed-Solomon-Based FEC Codes for 40-Gb/s-Based Ultralong-Distance WDM transmission,” J. Lightwave Technol. |

33. | M. O’Sullivan, “Expanding network application with coherent detection,” in |

34. | S. R. Desbruslais and S. J. Savory, “Relationship Between Electrical Bandwidth and FEC Overhead in a 100 GbE Digital Coherent Receiver,” in |

35. | S. Dave, L. Esker, F. Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision Forward Error Correction in a 40-nm ASIC for 100-Gbps OTN Applications,” in |

36. | J. Bromage, “Raman Amplification for Fiber Communications Systems,” J. Lightwave Technol. |

37. | M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical Links?” Opt. Express |

38. | H. Bülow and E. S. Masalkina, “Coded Modulation in Optical Communications,” in |

39. | L. Beygi, E. Agrell, and M. Karlsson, “Optimization of 16-point Ring Constellations in the Presence of Nonlinear Phase Noise,” in |

40. | E. Torrengo, S. Makovejs, D. Millar, I. Fatadin, R. Killey, S. Savory, and P. Bayvel, “Influence of Pulse Shape in 112-Gb/s WDM PDM-QPSK Transmission,” IEEE Photon. Technol. Lett. |

41. | I. Lyubomirsky, A. Nilsson, M. Mitchell, and D. Welch, “Signal Chirp Design for Supression of Nonlinear Polarization Scattering in DP-QPSK Transmission,” in |

42. | B. Châtelain, C. Laperle, K. Roberts, X. Xu, M. Chagnon, A. Borowiec, F. Gagnon, J. Cartedge, and D. V. Plant, “Optimized Pulse Shaping for Intra-channel Nonlinearities Mitigation in a 10 Gbaud Dual-Polarization 16-QAM System,” in |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: November 2, 2011

Revised Manuscript: January 16, 2012

Manuscript Accepted: January 17, 2012

Published: January 25, 2012

**Citation**

Brian DeMuth, Michael Y. Frankel, and Vladimir Pelekhaty, "Semi-empirical system scaling rules for DWDM system design," Opt. Express **20**, 2992-3004 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2992

Sort: Year | Journal | Reset

### References

- R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol.28(4), 662–701 (2010). [CrossRef]
- A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol.28(4), 423–433 (2010). [CrossRef]
- M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.7.C.3.
- G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett.22(6), 371–373 (2010). [CrossRef]
- M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett.22(15), 1150–1152 (2010). [CrossRef]
- 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]
- X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express18(18), 19039–19054 (2010). [CrossRef] [PubMed]
- G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO7.
- C. Xia and D. van den Borne, “Impact of the Channel Count on the Nonlinear Tolerance in Coherently-detected POLMUX-QPSK modulation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO1.
- P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett.23(11), 742–744 (2011). [CrossRef]
- A. Bononi, N. Rossi, and P. Serena, “Transmission Limitations due to Fiber Nonlinearity,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO7.
- Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple Fiber Model for Determination of XPM Effects,” J. Lightwave Technol.29(7), 974–986 (2011). [CrossRef]
- L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of coherent optical communications systems,” Opt. Express19(9), 8079–8084 (2011). [CrossRef] [PubMed]
- V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance Evaluation of Long-Haul 111Gb/s PM-QPSK Transmission Over Different Fiber Types,” IEEE Photon. Technol. Lett.22(19), 1446–1448 (2010). [CrossRef]
- A. Carena, V. Curri, P. Poggiolini, G. Bosco, and F. Forghieri, “Maximum Reach Versus Transmission Capacity for Terabit Superchannels Based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM,” IEEE Photon. Technol. Lett.22(11), 829–831 (2010). [CrossRef]
- C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Fibre Nonlinearities in WDM-Systems with Reduced Channel-Spacing and Symbol-Rate,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper P4.20.
- E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express19(13), 12781–12788 (2011). [CrossRef] [PubMed]
- J. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s Capacity Transmission Over 6,860 km,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB4.
- J. Yu, X. Zhou, D. Qian, M. Huang, P. N. Ji, and G. Zhang, “20x112Gbit/s, 50GHz spaced, PolMux-RZ-QPSK straight-line transmission over 1540km of SSMF employing digital coherent detection and pure EDFA amplification,” in Proceedings ECOC 2008, Brussels, Belgium, 2008, Paper Th.2.A.2.
- J. Downie, J. E. Hurley, J. Cartledge, S. R. Bickham, and S. Mishra, “Transmission of 112 Gb/s PM-QPSK Signals over 7200 km of Optical Fiber with Very Large Effective Area and Ultra-Low Loss in 100 km Spans with EDFAs Only,” in Optical Fiber Communications Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMI6.
- G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72x100Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPB6.
- C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express19(14), 12879–12884 (2011). [CrossRef] [PubMed]
- A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Packham, “10 x 224-Gb/s WDM Transmission of 28-Gbaud PDM 16-QAM on a 50-GHz Grid over 1,200 km of Fiber,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB8.
- M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “Transmission of 11 x 224-Gb/s POLMUX-RZ-16QAM over 1500 km of LongLine and pure-silica SMF,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.8.C.2.
- S. Yamanaka, T. Kobayashi, A. Sano, H. Masuda, E. Yoshida, Y. Miyamoto, T. Nakagawa, M. Nagatani, and H. Noaka, “11 x 171 Gb/s PDM 16-QAM Transmission over 1440 km with a Spectral Effiency of 6.4 b/s/Hz using High-Speed DAC,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.8.C.1.
- A. Gnauck and P. J. Winzer, “Ultra-High-Spectral-Efficiency Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWE4.
- J. Yu and X. Zhou, “16 x 107-Gb/s 12.5-GHz-Spaced PDM-36QAM Transmission Over 400 km of Standard Single-Mode Fiber,” IEEE Photon. Technol. Lett.22(17), 1312–1314 (2010). [CrossRef]
- A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizuguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM Transmission over 160 km Using Linewidth-Tolerant Pilotless Digital Coherent Detection,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper pd2_4.
- J. Yu, X. Zhou, Y. Huang, S. Gupta, M. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ-64QAM optical signal generation and transmission on a 12.5GHz WDM Grid,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OThM1.
- 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]
- J.-X. Cai, M. Nissov, A. N. Pilipetskii, A. J. Lucero, C. R. Davidson, D. Foursa, H. Kidorf, M. A. Mills, R. Menges, P. C. Corbett, D. Sutton, and N. S. Bergano, “2.4 Tb/s (120 x 20 Gb/s) Transmission over Transoceanic Distance using Optimum FEC Overhead and 48% Spectral Efficiency,” in Optical Fiber Communication Conference, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper PD20.
- A. Agata, K. Tanaka, and N. Edagawa, “Study on the Optimum Reed-Solomon-Based FEC Codes for 40-Gb/s-Based Ultralong-Distance WDM transmission,” J. Lightwave Technol.20(12), 2189–2195 (2002). [CrossRef]
- M. O’Sullivan, “Expanding network application with coherent detection,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper NWC3.
- S. R. Desbruslais and S. J. Savory, “Relationship Between Electrical Bandwidth and FEC Overhead in a 100 GbE Digital Coherent Receiver,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper P3.19.
- S. Dave, L. Esker, F. Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision Forward Error Correction in a 40-nm ASIC for 100-Gbps OTN Applications,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JWA014.
- J. Bromage, “Raman Amplification for Fiber Communications Systems,” J. Lightwave Technol.22(1), 79–93 (2004). [CrossRef]
- M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical Links?” Opt. Express17(13), 10814–10819 (2009). [CrossRef] [PubMed]
- H. Bülow and E. S. Masalkina, “Coded Modulation in Optical Communications,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America,2011), paper OThO1.
- L. Beygi, E. Agrell, and M. Karlsson, “Optimization of 16-point Ring Constellations in the Presence of Nonlinear Phase Noise,” in Optical Fiber communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO4.
- E. Torrengo, S. Makovejs, D. Millar, I. Fatadin, R. Killey, S. Savory, and P. Bayvel, “Influence of Pulse Shape in 112-Gb/s WDM PDM-QPSK Transmission,” IEEE Photon. Technol. Lett.22(23), 1714–1716 (2010). [CrossRef]
- I. Lyubomirsky, A. Nilsson, M. Mitchell, and D. Welch, “Signal Chirp Design for Supression of Nonlinear Polarization Scattering in DP-QPSK Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThF3.
- B. Châtelain, C. Laperle, K. Roberts, X. Xu, M. Chagnon, A. Borowiec, F. Gagnon, J. Cartedge, and D. V. Plant, “Optimized Pulse Shaping for Intra-channel Nonlinearities Mitigation in a 10 Gbaud Dual-Polarization 16-QAM System,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO5.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.