## Digital coherent superposition of optical OFDM subcarrier pairs with Hermitian symmetry for phase noise mitigation |

Optics Express, Vol. 22, Issue 11, pp. 13454-13459 (2014)

http://dx.doi.org/10.1364/OE.22.013454

Acrobat PDF (1967 KB)

### Abstract

Digital coherent superposition (DCS) provides an approach to combat fiber nonlinearities by trading off the spectrum efficiency. In analogy, we extend the concept of DCS to the optical OFDM subcarrier pairs with Hermitian symmetry to combat the linear and nonlinear phase noise. At the transmitter, we simply use a real-valued OFDM signal to drive a Mach-Zehnder (MZ) intensity modulator biased at the null point and the so-generated OFDM signal is Hermitian in the frequency domain. At receiver, after the conventional OFDM signal processing, we conduct DCS of the optical OFDM subcarrier pairs, which requires only conjugation and summation. We show that the inter-carrier-interference (ICI) due to phase noise can be reduced because of the Hermitain symmetry. In a simulation, this method improves the tolerance to the laser phase noise. In a nonlinear WDM transmission experiment, this method also achieves better performance under the influence of cross phase modulation (XPM).

© 2014 Optical Society of America

## 1. Introduction

1. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. **43**(3), 183–185 (2007). [CrossRef]

5. S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. **52**(11), 1988–1996 (2004). [CrossRef]

6. X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. **26**(10), 1309–1316 (2008). [CrossRef]

7. J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. **47**(3), 365–369 (1999). [CrossRef]

8. X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, and D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express **20**(17), 19088–19095 (2012). [CrossRef] [PubMed]

*et al.*have proposed phase-conjugated twin waves on two polarization tributaries over a record distance in fiber [9

9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics **7**(7), 560–568 (2013). [CrossRef]

*et al.*has demonstrated a conjugated copy via four-wave mixing, which can cancel the phase noise after DCS [10

10. Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, and T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express **21**(4), 5099–5106 (2013). [CrossRef] [PubMed]

11. X. Yi, X. Chen, C. Li, M. Luo, Q. Yang, Z. Li, and K. Qiu, “Experimental demonstration of digital coherent superposition of optical OFDM subcarrier pairs for mitigation of linear and nonlinear phase noise,” in *Optical Fiber Commun. Conf**.* (2014), Tu3G.6. [CrossRef]

8. X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, and D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express **20**(17), 19088–19095 (2012). [CrossRef] [PubMed]

10. Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, and T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express **21**(4), 5099–5106 (2013). [CrossRef] [PubMed]

7. J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. **47**(3), 365–369 (1999). [CrossRef]

12. Y. Wu, J. Li, C. Zhao, Y. Zhao, F. Zhang, and Z. Chen, “Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation,” Chin. Opt. Lett. **8**, 634–638 (2010). [CrossRef]

12. Y. Wu, J. Li, C. Zhao, Y. Zhao, F. Zhang, and Z. Chen, “Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation,” Chin. Opt. Lett. **8**, 634–638 (2010). [CrossRef]

## 2. ICI reduction by DCS of OFDM subcarrier pairs with Hermitian symmetry

*X(k)*denote the transmitted data in subcarrier of an OFDM symbol. The low-pass equivalent output after IDFT with a length of

*N*can be expressed as

*s(m)*with polarity to the optical domain, we use an intensity MZ modulator biased at the null point [13

13. Y. Tang, W. Shieh, X. Yi, and R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. **19**(7), 483–485 (2007). [CrossRef]

1. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. **43**(3), 183–185 (2007). [CrossRef]

5. S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. **52**(11), 1988–1996 (2004). [CrossRef]

*I(0)*[14

14. X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. **19**(12), 919–921 (2007). [CrossRef]

15. T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. **43**(2/3/4), 191–193 (1995). [CrossRef]

*I*is the IDFT output of

_{DCS}(k)*A*. We obtain

## 3. Simulation of DCS-OFDM under the laser phase noise

1. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. **43**(3), 183–185 (2007). [CrossRef]

3. S. L. Jansen, I. Morita, C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. **26**(1), 6–15 (2008). [CrossRef]

^{−3}. DCS-OFDM in Case III has the smallest OSNR penalty of 0.5 dB at BER of 10

^{−3}, which means a better tolerance to the laser phase noise. With 1-MHz linewidth, from Case II to III, the OSNR is drastically reduced, much more than 3 dB, which follows the derivation in Section 2. The inset constellations in Fig. 1 also demonstrate this significant improvement, which results from the simple operation of Eq. (9).

## 4. Experiment of DCS-OFDM in a nonlinear WDM transmission

16. Q. Yang, Y. Tang, Y. Ma, and W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. **27**(3), 168–176 (2009). [CrossRef]

6. X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. **26**(10), 1309–1316 (2008). [CrossRef]

9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics **7**(7), 560–568 (2013). [CrossRef]

8. X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, and D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express **20**(17), 19088–19095 (2012). [CrossRef] [PubMed]

9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics **7**(7), 560–568 (2013). [CrossRef]

**7**(7), 560–568 (2013). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. |

2. | A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in |

3. | S. L. Jansen, I. Morita, C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. |

4. | D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in |

5. | S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. |

6. | X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. |

7. | J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. |

8. | X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, and D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express |

9. | X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics |

10. | Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, and T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express |

11. | X. Yi, X. Chen, C. Li, M. Luo, Q. Yang, Z. Li, and K. Qiu, “Experimental demonstration of digital coherent superposition of optical OFDM subcarrier pairs for mitigation of linear and nonlinear phase noise,” in |

12. | Y. Wu, J. Li, C. Zhao, Y. Zhao, F. Zhang, and Z. Chen, “Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation,” Chin. Opt. Lett. |

13. | Y. Tang, W. Shieh, X. Yi, and R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. |

14. | X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. |

15. | T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. |

16. | Q. Yang, Y. Tang, Y. Ma, and W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.4080) Fiber optics and optical communications : Modulation

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

**ToC Category:**

Optical Communications

**History**

Original Manuscript: April 16, 2014

Revised Manuscript: May 19, 2014

Manuscript Accepted: May 20, 2014

Published: May 27, 2014

**Citation**

Xingwen Yi, Xuemei Chen, Dinesh Sharma, Chao Li, Ming Luo, Qi Yang, Zhaohui Li, and Kun Qiu, "Digital coherent superposition of optical OFDM subcarrier pairs with Hermitian symmetry for phase noise mitigation," Opt. Express **22**, 13454-13459 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-13454

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### References

- W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007). [CrossRef]
- A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Commun. Conf., Anaheim, CA (2006), Paper PDP39. [CrossRef]
- S. L. Jansen, I. Morita, C. W. Schenk, N. Takeda, H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]
- D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Commun. Conf., USA (2011), paper PDPB5.
- S. Wu, Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004). [CrossRef]
- X. Yi, W. Shieh, Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]
- J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999). [CrossRef]
- X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express 20(17), 19088–19095 (2012). [CrossRef] [PubMed]
- X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]
- Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express 21(4), 5099–5106 (2013). [CrossRef] [PubMed]
- X. Yi, X. Chen, C. Li, M. Luo, Q. Yang, Z. Li, and K. Qiu, “Experimental demonstration of digital coherent superposition of optical OFDM subcarrier pairs for mitigation of linear and nonlinear phase noise,” in Optical Fiber Commun. Conf. (2014), Tu3G.6. [CrossRef]
- Y. Wu, J. Li, C. Zhao, Y. Zhao, F. Zhang, Z. Chen, “Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation,” Chin. Opt. Lett. 8, 634–638 (2010). [CrossRef]
- Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007). [CrossRef]
- X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007). [CrossRef]
- T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995). [CrossRef]
- Q. Yang, Y. Tang, Y. Ma, W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009). [CrossRef]

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