## Optimizing the subcarrier granularity of coherent optical communications systems |

Optics Express, Vol. 19, Issue 9, pp. 8079-8084 (2011)

http://dx.doi.org/10.1364/OE.19.008079

Acrobat PDF (1099 KB)

### Abstract

In this paper, we use numerical simulations to show that the symbol rate has a significant effect on the nonlinearity-limited performance of coherent optical communication systems. We consider the case where orthogonal subcarriers are used to maximize the spectral efficiency. Symbol rates from 0.78125 Gbaud to 100 Gbaud and links of up to 3200 km, without inline dispersion compensation, were simulated. The results show that the optimal symbol rates for the 800-km link and 3200-km link were 6.25-Gbaud and 3.125-Gbaud respectively. The optimal baud rate decreases as the length of the link is increased. After 3200 km, the performance of the 100-Gbaud system was worst in the nonlinearity-limited regime producing a received *Q* 2.4-dB lower than the 3.125-Gband system. The variation in the nonlinearity-limited performance is explained by using Cross-Phase-Modulation (XPM) theory and by considering the RF spectra of the intensity fluctuations of the signal along the link. The findings of the paper suggest that the maximum capacity of nonlinear dispersive optical links can only be achieved by using multiple subcarriers carrying a few Gbaud each, and not by high symbol rate systems.

© 2011 OSA

## 1. Introduction

1. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” Lightwave Technology Journalism **29**, 483–490 (2011). [CrossRef]

2. 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]

3. R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. **101**(16), 163901 (2008). [CrossRef] [PubMed]

4. A. D. Ellis, Z. Jian, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. **28**(4), 423–433 (2010). [CrossRef]

5. F. Forghieri, “Granularity in WDM networks: the role of fiber nonlinearities,” IEEE Photon. Technol. Lett. **8**(10), 1400–1402 (1996). [CrossRef]

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

7. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. **42**(10), 587–589 (2006). [CrossRef]

1. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” Lightwave Technology Journalism **29**, 483–490 (2011). [CrossRef]

7. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. **42**(10), 587–589 (2006). [CrossRef]

8. A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. **27**(16), 3705–3713 (2009). [CrossRef]

9. A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. **17**(2), 504–506 (2005). [CrossRef]

10. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance Limits of Nyquist-WDM and CO-OFDM in High-Speed PM-QPSK Systems,” IEEE Photon. Technol. Lett. **22**(15), 1129–1131 (2010). [CrossRef]

11. B. Zhu, X. Liu, S. Chandrasekhar, D. W. Peckham, and R. Lingle, “Ultra-long-haul transmission of 1.2-Tb/s multicarrier no-guard-interval CO-OFDM superchannel using ultra-large-area fiber,” IEEE Photon. Technol. Lett. **22**(11), 826–828 (2010). [CrossRef]

12. T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. **14**(3), 249–260 (1996). [CrossRef]

## 2. Simulation setup

*sinc-like*in shape (near Nyquist pulse). Symbol rates from 0.78125-Gbaud to 100-Gbaud were simulated, where subcarrier spacing is equal to the symbol rate. An ideal optical multiplexer combined the orthogonally-spaced subcarriers to form a continuous 400-GHz wide optical super-channel carrying 800 Gb/s on a single polarization. Figure 1c shows the spectrum of the super-channel for a 50-Gbaud system. The ideal multiplexer and Nyquist filters prevented any linear crosstalk. This is similar to an ideal Nyquist WDM system [10

10. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance Limits of Nyquist-WDM and CO-OFDM in High-Speed PM-QPSK Systems,” IEEE Photon. Technol. Lett. **22**(15), 1129–1131 (2010). [CrossRef]

11. B. Zhu, X. Liu, S. Chandrasekhar, D. W. Peckham, and R. Lingle, “Ultra-long-haul transmission of 1.2-Tb/s multicarrier no-guard-interval CO-OFDM superchannel using ultra-large-area fiber,” IEEE Photon. Technol. Lett. **22**(11), 826–828 (2010). [CrossRef]

8. A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. **27**(16), 3705–3713 (2009). [CrossRef]

6. C. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, G.-D. Khoe, 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}, or 262144, symbols were simulated. This equates to 65536 symbols per subcarrier for the 100-Gbaud system and 512 symbols per subcarrier for the 0.78125-Gbaud system. The

*Q*was calculated from the spread in the received constellation assuming a Gaussian distribution in each Cartesian coordinate; the

*Q*values for subcarriers within the central 200 GHz were averaged.

## 3. Simulation results

*Q*against the launch power for 1600-km and 3200-km systems at four different symbol rates. At low powers, the systems are limited by amplified spontaneous emission (ASE). In this region, the

*Q*is almost identical for all systems. The 1.5625-Gbuad system was slightly poorer because of the long impulse response of the filters causing degradation on a large number of symbols. This effect was even greater for the 0.78125-Gbaud system, shown in Fig. 3 . At high powers, the systems are limited by fiber nonlinearity. The spread of the

*Q*is over 2 dB for launch powers of 2 dBm and above. This spread shows that the nonlinearity-limited performance is dependent on the symbol rate of the subcarriers.

*Q*against subcarrier carrier symbol rate after 800 km, 1600 km and 3200 km at a launch power of 2 dBm, which is in the nonlinearity-limited regime of Fig. 2. At 800 km, the optimal symbol rate is 6.25 Gbaud; at 1600 km, the optimal symbol rate reduces to between 3.125 and 6.25 Gbaud; at 3200 km, the optimal symbol rate is 3.125 Gbaud. These results show the optimal symbol rate decreases as the transmission distance is increased. These optimal symbol rates are consistent with an independent study conducted in [13

13. W. Shieh and T. Yan, “Ultrahigh-Speed Signal Transmission Over Nonlinear and Dispersive Fiber Optic Channel: The Multicarrier Advantage,” IEEE Photon. J. **2**(3), 276–283 (2010). [CrossRef]

*Q*across with symbol rate is significant for all transmission distances: choosing the correct baud rate will improve system performance.

## 4. Discussion

13. W. Shieh and T. Yan, “Ultrahigh-Speed Signal Transmission Over Nonlinear and Dispersive Fiber Optic Channel: The Multicarrier Advantage,” IEEE Photon. J. **2**(3), 276–283 (2010). [CrossRef]

12. T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. **14**(3), 249–260 (1996). [CrossRef]

*sinc-like*symbols, this theory applies to all coherent systems regardless of the pulse shape because the pulse spreading and distortion caused by CD dominates over the variations in pulse shape for different systems.

12. T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. **14**(3), 249–260 (1996). [CrossRef]

*α*is attenuation in Nepers/m,

*L*is the fiber’s length in m,

*D*is the CD constant in s/m

^{2}, Δ

*λ*is the wavelength separation between the ‘probe’ and ‘pump’ frequencies in m [12

**14**(3), 249–260 (1996). [CrossRef]

*ω*is the frequency of the intensity fluctuation in rad/s and

*N*is the number of spans in the link.

2. 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]

16. D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express **19**(4), 3449–3454 (2011). [CrossRef] [PubMed]

17. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. **26**(20), 3416–3425 (2008). [CrossRef]

## 5. Conclusion

3. R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. **101**(16), 163901 (2008). [CrossRef] [PubMed]

## Acknowledgements

## References and links

1. | X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” Lightwave Technology Journalism |

2. | 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 |

3. | R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. |

4. | A. D. Ellis, Z. Jian, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. |

5. | F. Forghieri, “Granularity in WDM networks: the role of fiber nonlinearities,” IEEE Photon. Technol. Lett. |

6. | C. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, G.-D. Khoe, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. |

7. | W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. |

8. | A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. |

9. | A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. |

10. | G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance Limits of Nyquist-WDM and CO-OFDM in High-Speed PM-QPSK Systems,” IEEE Photon. Technol. Lett. |

11. | B. Zhu, X. Liu, S. Chandrasekhar, D. W. Peckham, and R. Lingle, “Ultra-long-haul transmission of 1.2-Tb/s multicarrier no-guard-interval CO-OFDM superchannel using ultra-large-area fiber,” IEEE Photon. Technol. Lett. |

12. | T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. |

13. | W. Shieh and T. Yan, “Ultrahigh-Speed Signal Transmission Over Nonlinear and Dispersive Fiber Optic Channel: The Multicarrier Advantage,” IEEE Photon. J. |

14. | B. Goebel, S. Hellerbrand, and N. Hanik, “Link-aware precoding for nonlinear optical OFDM transmission,” in |

15. | L. B. Du and A. J. Lowery, “Improved nonlinearity precompensation for long-haul high-data-rate transmission using coherent optical OFDM,” Opt. Express |

16. | D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express |

17. | E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. |

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 8, 2011

Revised Manuscript: March 31, 2011

Manuscript Accepted: April 3, 2011

Published: April 12, 2011

**Citation**

Liang B. Du and Arthur J. Lowery, "Optimizing the subcarrier granularity of coherent optical communications systems," Opt. Express **19**, 8079-8084 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8079

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### References

- X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” Lightwave Technology Journalism 29, 483–490 (2011). [CrossRef]
- 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]
- R.-J. Essiambre, G. J. Foschini, G. Kramer, and P. J. Winzer, “Capacity limits of information transport in fiber-optic networks,” Phys. Rev. Lett. 101(16), 163901 (2008). [CrossRef] [PubMed]
- A. D. Ellis, Z. Jian, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. 28(4), 423–433 (2010). [CrossRef]
- F. Forghieri, “Granularity in WDM networks: the role of fiber nonlinearities,” IEEE Photon. Technol. Lett. 8(10), 1400–1402 (1996). [CrossRef]
- C. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, G.-D. Khoe, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008). [CrossRef]
- W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006). [CrossRef]
- A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. 27(16), 3705–3713 (2009). [CrossRef]
- A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005). [CrossRef]
- G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance Limits of Nyquist-WDM and CO-OFDM in High-Speed PM-QPSK Systems,” IEEE Photon. Technol. Lett. 22(15), 1129–1131 (2010). [CrossRef]
- B. Zhu, X. Liu, S. Chandrasekhar, D. W. Peckham, and R. Lingle, “Ultra-long-haul transmission of 1.2-Tb/s multicarrier no-guard-interval CO-OFDM superchannel using ultra-large-area fiber,” IEEE Photon. Technol. Lett. 22(11), 826–828 (2010). [CrossRef]
- T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators,” J. Lightwave Technol. 14(3), 249–260 (1996). [CrossRef]
- W. Shieh and T. Yan, “Ultrahigh-Speed Signal Transmission Over Nonlinear and Dispersive Fiber Optic Channel: The Multicarrier Advantage,” IEEE Photon. J. 2(3), 276–283 (2010). [CrossRef]
- B. Goebel, S. Hellerbrand, and N. Hanik, “Link-aware precoding for nonlinear optical OFDM transmission,” in Optical Fiber Communication Conference (OSA, 2010), OTuE4.
- L. B. Du and A. J. Lowery, “Improved nonlinearity precompensation for long-haul high-data-rate transmission using coherent optical OFDM,” Opt. Express 16(24), 19920–19925 (2008). [CrossRef] [PubMed]
- D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011). [CrossRef] [PubMed]
- E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

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