## Comparison of the nonlinear transmission performance of quasi-Nyquist WDM and reduced guard interval OFDM |

Optics Express, Vol. 20, Issue 4, pp. 4198-4205 (2012)

http://dx.doi.org/10.1364/OE.20.004198

Acrobat PDF (881 KB)

### Abstract

The nonlinear transmission performance of quasi-Nyquist wavelength-division multiplexing (qN-WDM) and reduced guard interval orthogonal frequency-division multiplexing (RGI-OFDM) using polarization-division multiplexing quadrature phase-shift-keying (PDM-QPSK) and quadrature amplitude modulation (PDM-QAM-8 and PDM-QAM-16) with high information spectral densities have been compared for the first time, both by simulations and analytically. The results show that both systems are able to reach similar maximum transmission distances of approximately 6700km, 2600km and 1100km over standard single-mode fibre for the spectral efficiencies of 3.43 bits/s/Hz, 5.25 bits/s/Hz and 7 bits/s/Hz respectively.

© 2012 OSA

## 1. Introduction

1. E. Desurvire, “Capacity Demand and Technology Challenges for Lightwave Systems in the Next Two Decades,” J. Lightwave Technol. **24**, 4697–4710 (2006). [CrossRef]

2. R. Freund, M. Nölle, C. Schmidt-Langhorst, R. Ludwig, C. Schubert, G. Bosco, A. Carena, P. Poggiolini, L. Oxenløwe, M. Galili, H. C. H. Mulvad, M. Winter, D. Hillerkuss, R. Schmogrow, W. Freude, J. Leuthold, A. D. Ellis, F. C. G. Gunning, J. Zhao, P. Frascella, S. K. Ibrahim, and N. M. Suibhne, “Single-and multi-carrier techniques to build up Tb/s per channel transmission systems,” in Proc. ICTON, 2010, Paper Tu.D1.4.

3. 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**, 1129–1131 (2010). [CrossRef]

4. E. Torrengo, R. Cigliutti, G. Bosco, G. Gavioli, A. Alaimo, A. Carena, V. Curri, F. Forghieri, S. Piciaccia, M. Belmonte, A. Brinciotti, A. L. Porta, S. Abrate, and P. Poggiolini, “Transoceanic PM-QPSK Terabit superchannel transmission experiments at Baud-rate subcarrier spacing,” in Proc. ECOC, 2010, Paper We.7.C.2.

5. R. Cigliutti, E. Torrengo, G. Bosco, N. P. Caponio, A. Carena, V. Curri, P. Poggiolini, Y. Yamamoto, T. Sasaki, and F. Forghieri, “Transmission of 9x138 Gb/s Prefiltered PM-8QAM Signals Over 4000 km of Pure Silica-Core Fiber,” J. Lightwave Technol. **29**, 2310–2318 (2011). [CrossRef]

6. 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,” J. Lightwave Technol. **29**, 483–490 (2011). [CrossRef]

8. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature **411**, 1027–1030 (2001). [CrossRef] [PubMed]

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

3. 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**, 1129–1131 (2010). [CrossRef]

11. 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**, 742–744 (2011). [CrossRef]

12. W. Shieh and X. Chen, “Information Spectral Efficiency and Launch Power Density Limits Due to Fiber Nonlinearity for Coherent Optical OFDM Systems,” IEEE Photon. J. **3**, 158–173 (2011). [CrossRef]

## 2. Analytical Expressions

*I*

_{NL}, experimentally verified in [13], is given for N-WDM in [11

11. 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**, 742–744 (2011). [CrossRef]

*N*is the number of spans,

_{s}*γ*is the fiber non linear parameter,

*β*

_{2}is the group velocity dispersion parameter,

*L*

_{eff}is the nonlinear effective length,

*B*is the optical bandwidth, and

*I*

_{tx}is the optical signal power density. It is formally defined as

*I*

_{tx}=

*P*

_{tx}/Δ

*f*with

*P*

_{tx}being the optical power per channel and Δ

*f*the N-WDM channel spacing.

*et al*[12

12. W. Shieh and X. Chen, “Information Spectral Efficiency and Launch Power Density Limits Due to Fiber Nonlinearity for Coherent Optical OFDM Systems,” IEEE Photon. J. **3**, 158–173 (2011). [CrossRef]

*h*being the noise enhancement factor given as that describes the build-up of nonlinearities due to interference between them over several spans with

_{e}*α*being the fiber attenuation,

*ζ*representing the residual dispersion ratio after propagation and

*L*the length of the fibre span.

*I*

_{NL,2}a multi-span phase array effect is accounted for. This effect describes the build-up of nonlinearities due to interference between them over several spans. The second main difference addresses dispersion compensation. The expression for

*I*

_{NL,1}is only applicable to the case of systems with no in-line dispersion compensation whereas the Shieh approach can be used for an arbitrary in-line dispersion compensation ratio.

*I*

_{NL,i}of Eq. (1) or Eq. (2) can be expressed in a more concise form with the definition of nonlinear characteristic power density

*I*

_{o,i}as follows:

*N*achievable before the optical signal to noise ratio (OSNR) that corresponds to the target bit error rate BER is exceeded. The SNR of Eq. (10) is the symbol SNR evaluated at the target bit error rate (BER) for a particular modulation format and has to account for the implementation penalty of the transmitter and receiver.

_{s}## 3. Simulation setup

14. S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quant. **16**, 1164–1179 (2010). [CrossRef]

15. I. Fatadin, D. Ives, and S. J. Savory, “Laser Linewidth Tolerance for 16-QAM Coherent Optical Systems Using QPSK Partitioning,” IEEE Photon. Technol. Lett. **22**, 631–633 (2010). [CrossRef]

^{−3}.

## 4. Simulation results on maximum transmission reach for qN-WDM and RGI-OFDM

^{−3}evaluated for different channel launch powers, swept from −8dBm to 3dBm, in increments of 1dB. All the results obtained were plotted for the central channel. The back-to-back sensitivity for both systems using 9 channels was measured and is plotted in fig. (2). It can be seen from fig. (3) that the optimum launch power to achieve the maximum transmission distance was −2dBm for both systems and all modulation formats. As the minimum WDM channel spacing for error free transmission with the RGI-OFDM system was higher than that achievable with qN-WDM due to the inclusion of the cyclic prefix, to ensure a fair comparison we used the minimum RGI-OFDM channel spacing for both system simulations.

*h*in Eq. (2). which takes into account that the noise due to fibre nonlinearities is not independent of the nonlinearities in previous spans because the nonlinearities constructively build up while the signal is propagating over several spans. We can clearly see from both figs. (3) and (4) that the analytical expression for OFDM slightly underestimates the maximum transmission reach at a given spectral efficiency.

_{e}## 5. Conclusion

16. S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100GbE: QPSK versus OFDM,” Opt. Fiber Technol. **15**, 407–413 (2009). [CrossRef]

17. A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus Single-Carrier Transmission for 100 Gbps Optical Communication,” J. Lightwave Technol. **28**, 2537–2551 (2010). [CrossRef]

## References and links

1. | E. Desurvire, “Capacity Demand and Technology Challenges for Lightwave Systems in the Next Two Decades,” J. Lightwave Technol. |

2. | R. Freund, M. Nölle, C. Schmidt-Langhorst, R. Ludwig, C. Schubert, G. Bosco, A. Carena, P. Poggiolini, L. Oxenløwe, M. Galili, H. C. H. Mulvad, M. Winter, D. Hillerkuss, R. Schmogrow, W. Freude, J. Leuthold, A. D. Ellis, F. C. G. Gunning, J. Zhao, P. Frascella, S. K. Ibrahim, and N. M. Suibhne, “Single-and multi-carrier techniques to build up Tb/s per channel transmission systems,” in Proc. ICTON, 2010, Paper Tu.D1.4. |

3. | 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. |

4. | E. Torrengo, R. Cigliutti, G. Bosco, G. Gavioli, A. Alaimo, A. Carena, V. Curri, F. Forghieri, S. Piciaccia, M. Belmonte, A. Brinciotti, A. L. Porta, S. Abrate, and P. Poggiolini, “Transoceanic PM-QPSK Terabit superchannel transmission experiments at Baud-rate subcarrier spacing,” in Proc. ECOC, 2010, Paper We.7.C.2. |

5. | R. Cigliutti, E. Torrengo, G. Bosco, N. P. Caponio, A. Carena, V. Curri, P. Poggiolini, Y. Yamamoto, T. Sasaki, and F. Forghieri, “Transmission of 9x138 Gb/s Prefiltered PM-8QAM Signals Over 4000 km of Pure Silica-Core Fiber,” J. Lightwave Technol. |

6. | 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,” J. Lightwave Technol. |

7. | S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proc. ECOC, 2009, Supplement. |

8. | P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature |

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

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

11. | 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. |

12. | W. Shieh and X. Chen, “Information Spectral Efficiency and Launch Power Density Limits Due to Fiber Nonlinearity for Coherent Optical OFDM Systems,” IEEE Photon. J. |

13. | E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” in Proc. ECOC, 2011, Paper We.7.B.2. |

14. | S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quant. |

15. | I. Fatadin, D. Ives, and S. J. Savory, “Laser Linewidth Tolerance for 16-QAM Coherent Optical Systems Using QPSK Partitioning,” IEEE Photon. Technol. Lett. |

16. | S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100GbE: QPSK versus OFDM,” Opt. Fiber Technol. |

17. | A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus Single-Carrier Transmission for 100 Gbps Optical Communication,” J. Lightwave Technol. |

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 28, 2011

Revised Manuscript: January 12, 2012

Manuscript Accepted: January 30, 2012

Published: February 6, 2012

**Citation**

Sean Kilmurray, Tobias Fehenberger, Polina Bayvel, and Robert I. Killey, "Comparison of the nonlinear transmission performance of quasi-Nyquist WDM and reduced guard interval OFDM," Opt. Express **20**, 4198-4205 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4198

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### References

- E. Desurvire, “Capacity Demand and Technology Challenges for Lightwave Systems in the Next Two Decades,” J. Lightwave Technol.24, 4697–4710 (2006). [CrossRef]
- R. Freund, M. Nölle, C. Schmidt-Langhorst, R. Ludwig, C. Schubert, G. Bosco, A. Carena, P. Poggiolini, L. Oxenløwe, M. Galili, H. C. H. Mulvad, M. Winter, D. Hillerkuss, R. Schmogrow, W. Freude, J. Leuthold, A. D. Ellis, F. C. G. Gunning, J. Zhao, P. Frascella, S. K. Ibrahim, and N. M. Suibhne, “Single-and multi-carrier techniques to build up Tb/s per channel transmission systems,” in Proc. ICTON, 2010, Paper Tu.D1.4.
- 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, 1129–1131 (2010). [CrossRef]
- E. Torrengo, R. Cigliutti, G. Bosco, G. Gavioli, A. Alaimo, A. Carena, V. Curri, F. Forghieri, S. Piciaccia, M. Belmonte, A. Brinciotti, A. L. Porta, S. Abrate, and P. Poggiolini, “Transoceanic PM-QPSK Terabit superchannel transmission experiments at Baud-rate subcarrier spacing,” in Proc. ECOC, 2010, Paper We.7.C.2.
- R. Cigliutti, E. Torrengo, G. Bosco, N. P. Caponio, A. Carena, V. Curri, P. Poggiolini, Y. Yamamoto, T. Sasaki, and F. Forghieri, “Transmission of 9x138 Gb/s Prefiltered PM-8QAM Signals Over 4000 km of Pure Silica-Core Fiber,” J. Lightwave Technol.29, 2310–2318 (2011). [CrossRef]
- 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,” J. Lightwave Technol.29, 483–490 (2011). [CrossRef]
- S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proc. ECOC, 2009, Supplement.
- P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411, 1027–1030 (2001). [CrossRef] [PubMed]
- R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol.28, 662–701 (2010). [CrossRef]
- A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol.28, 423–433 (2010). [CrossRef]
- 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, 742–744 (2011). [CrossRef]
- W. Shieh and X. Chen, “Information Spectral Efficiency and Launch Power Density Limits Due to Fiber Nonlinearity for Coherent Optical OFDM Systems,” IEEE Photon. J.3, 158–173 (2011). [CrossRef]
- E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” in Proc. ECOC, 2011, Paper We.7.B.2.
- S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Sel. Top. Quant.16, 1164–1179 (2010). [CrossRef]
- I. Fatadin, D. Ives, and S. J. Savory, “Laser Linewidth Tolerance for 16-QAM Coherent Optical Systems Using QPSK Partitioning,” IEEE Photon. Technol. Lett.22, 631–633 (2010). [CrossRef]
- S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100GbE: QPSK versus OFDM,” Opt. Fiber Technol.15, 407–413 (2009). [CrossRef]
- A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus Single-Carrier Transmission for 100 Gbps Optical Communication,” J. Lightwave Technol.28, 2537–2551 (2010). [CrossRef]

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