## Study of EEPN mitigation using modified RF pilot and Viterbi-Viterbi based phase noise compensation |

Optics Express, Vol. 21, Issue 10, pp. 12351-12362 (2013)

http://dx.doi.org/10.1364/OE.21.012351

Acrobat PDF (1909 KB)

### Abstract

We propose – as a modification of the optical (RF) pilot scheme - a balanced phase modulation between two polarizations of the optical signal in order to generate correlated equalization enhanced phase noise (EEPN) contributions in the two polarizations. The method is applicable for *n-*level PSK system. The EEPN can be compensated, the carrier phase extracted and the *n*PSK signal regenerated by complex conjugation and multiplication in the receiver. The method is tested by system simulations in a single channel QPSK system at 56 Gb/s system rate. It is found that the conjugation and multiplication scheme in the Rx can mitigate the EEPN to within ½ orders of magnitude. Results are compared to using the Viterbi-Viterbi algorithm to mitigate the EEPN. The latter method improves the sensitivity more than two orders of magnitude. Important novel insight into the statistical properties of EEPN is identified and discussed in the paper.

© 2013 OSA

## 1. Introduction

1. P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. **21**(12), 1862–1879 (1985). [CrossRef]

7. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express **16**(2), 804–817 (2008). [CrossRef] [PubMed]

4. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. **16**(2), 674–676 (2004). [CrossRef]

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express **18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

5. A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s Receiver with digital equaliser using maximum likelihood sequence estimation,” in *Proceeding of IEEE European Conference on Optical Communication* (Stockholm, Sweden, 2004), paper Th4.1.5.

7. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express **16**(2), 804–817 (2008). [CrossRef] [PubMed]

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express **18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express **18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express **16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

21. S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in *Proceeding of IEEE European Conference on Optical Communication* (Torino, Italy, 2010), paper Mo.1.C.2. [CrossRef]

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express **16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express **16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express **18**(16), 17239–17251 (2010). [CrossRef] [PubMed]

14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express **18**(16), 17239–17251 (2010). [CrossRef] [PubMed]

14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express **18**(16), 17239–17251 (2010). [CrossRef] [PubMed]

15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express **20**(24), 26568–26582 (2012). [CrossRef] [PubMed]

15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express **20**(24), 26568–26582 (2012). [CrossRef] [PubMed]

**16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

**16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express **19**(8), 7756–7768 (2011). [CrossRef] [PubMed]

23. G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express **19**(15), 14487–14494 (2011). [CrossRef] [PubMed]

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express **19**(8), 7756–7768 (2011). [CrossRef] [PubMed]

23. G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express **19**(15), 14487–14494 (2011). [CrossRef] [PubMed]

23. G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express **19**(15), 14487–14494 (2011). [CrossRef] [PubMed]

## 2. Theory

### 2.1 Principle and structure for Rx using optical (RF) pilot tone or distributed phase modulation in combination with CD equalization

*n*PSK signal and the other polarization for the optical (RF) pilot tone the conjugation and multiplication in the Rx will cancel the intrinsic phase noise from the Tx and LO lasers and recover the carrier phase.

**18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

26. M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), paper 8.3.6. [CrossRef]

27. M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express **16**(14), 10611–10616 (2008). [CrossRef] [PubMed]

*n*PSK modulation in two polarizations - considered in this paper.

*n*-level PSK modulation is considered, i.e.

*A*is the modulated (real-valued) amplitude,

*m(t)*represents the phase modulation. The optical (RF) pilot tone is a CW optical signal from the same optical signal source as the modulated signal (i.e. it has the same phase noise but possibly a different carrier phase

*B*is an arbitrary constant amplitude. The conjugated signal operation that eliminates the intrinsic laser phase noise is given (within the arbitrary amplitude constant,

*B*) as:where ‘*’ denotes complex conjugation. In Eq. (3)

### 2.2 Phase noise analysis

**16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

*λ*is the central wavelength of the transmitted optical carrier wave,

*c*is the light speed in vacuum,

*D*is the chromatic dispersion coefficient of the transmission fiber,

*L*is the transmission fiber length,

*Δf*is the 3-dB linewidth of the LO laser,

_{LO}*Δf*is the 3 dB linewidth associated with EEPN and

_{EE}*T*is the symbol period of the transmission system. The effective phase noise variance specified in Eq. (5) has 2/3 contribution from the phase noise of EEPN and 1/3 from the amplitude noise [13

_{s}**16**(20), 15718–15727 (2008). [CrossRef] [PubMed]

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express **19**(8), 7756–7768 (2011). [CrossRef] [PubMed]

*Δf*is the 3-dB transmitter laser linewidth,

_{Tx}*Δf*is the 3-dB local oscillator laser linewidth and

_{LO}**19**(8), 7756–7768 (2011). [CrossRef] [PubMed]

29. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express **17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

*n*PSK Rx) [22

**19**(8), 7756–7768 (2011). [CrossRef] [PubMed]

30. G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett. **46**(10), 698–700 (2010). [CrossRef]

*n-*level PSK systems which effectively utilize two polarizations to transmit the capacity of a normal one polarization system. The same total capacity can be implemented by using both polarizations for transmission with a capacity per polarization which is halved. Then the symbol time

*T*is doubled and Eq. (5)–Eq. (7) show that the

_{s}*BER*floor position is moved down. If the floor position system with high single channel capacity is

*BER*then the floor for the system with low capacity is in the order of

_{HC}*BER*. Thus the dual polarization system can very much eliminate the EEPN influence. For dual polarization operation the carrier phase extraction cannot be done using the optical (RF) pilot scheme as used in this paper, a single tap NLMS filter or the Viterbi-Viterbi algorithm has to be applied [31

_{LC}≈(BER_{HC})^{2}31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. **293**, 54–60 (2013). [CrossRef]

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. **293**, 54–60 (2013). [CrossRef]

## 3. Simulation method, results and discussion

### 3.1 Use of distributed QPSK modulation

*D = 16*ps/nm/km and zero dispersion slope. The transmission distance

*L*is 2000 km. We consider an intrinsic intermediate frequency 3 dB linewidth of

*Δf*MHz. This gives an effective linewidth of

_{LO}= Δf_{Tx}= 5*Δf*MHz (see Eq. (6)). We utilize the software tool from VPI [25] for the system simulations, and we evaluate the Bit-Error-Rate versus optical signal-to-noise ratio (OSNR). In the Rx we apply optical (RF) pilot tone principle (see section 2.1) for carrier phase extraction.

_{EE}= 206^{−4}– see dashed blue line. When the cases of α = 0.6/0.5 are considered, part of the EEPN is cancelled resulting in a BER-floor of 1.7·10

^{−4}in the best case (α = 0.5).

_{Eff}

^{2}= (1-ρ)

^{2}σ

_{EEPN}

^{2}- where σ

_{Eff}

^{2}corresponds to the BER-floor position – Eq. (7). In our case we find ρ = 0.0807 where a value of 1 corresponds to full correlation i.e. complete EEPN mitigation.

### 3.2 Using the Viterbi-Viterbi algorithm

29. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express **17**(3), 1435–1441 (2009). [CrossRef] [PubMed]

*n-*level PSK systems with

*n*> 4.

15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express **20**(24), 26568–26582 (2012). [CrossRef] [PubMed]

### 3.3 Comparison of shared modulation and Viterbi-Viterbi EEPN mitigation techniques for practical systems

**18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

*N*in the Viterbi-Viterbi algorithm. This is required when dealing with EEPN dominated noise (in the order of

_{VV}*N*35 in our case). This may especially be a problem when transmitting real time services that do not allow buffering in the receiver or services requiring low latency. Also the Viterbi-Viterbi method (as implemented as in [31

_{vv}≈31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. **293**, 54–60 (2013). [CrossRef]

*n*-level PSK modulation but not for classical

*n-*level QAM modulation (with non-circular constellations) where the single tap NLMS carrier phase extraction or the classical (unmodulated) optical (RF) pilot tone implementation works well.

*n-*level PSK modulated systems. It does not allow dual polarization operation. It gives less improvement of the EEPN sensitivity – about ½ order of magnitude for BER-floor position. However, it is computational effective and suited for real time system operation with low latency.

## 4. Conclusions

**293**, 54–60 (2013). [CrossRef]

*n-*level PSK systems which effectively utilize two polarizations to transmit the capacity of a normal one polarization system. The same total capacity can be implemented by using both polarizations for transmission with a capacity per polarization which is halved. Then the symbol time

*T*is doubled and Eq. (5)–Eq. (7) shows that the

_{s}*BER*floor position is moved down. If the floor position system with high single channel capacity is

*BER*then the floor for the system with low capacity is about BER

_{HC}_{LC}

*≈*(BER

_{HC})

^{2}. Thus the dual polarization system design can significantly eliminate the EEPN influence and the influence is mitigated further using the Viterbi-Viterbi algorithm. For dual polarization operation the carrier phase extraction cannot be done using the optical (RF) pilot scheme as used in this paper, a single tap NLMS filter or the Viterbi-Viterbi algorithm has to be applied. It is to be noted that the BER-floor approximation in Eq. (7) (without using the Viterbi-Viterbi algorithm) becomes poor (too optimistic by one order of magnitude or more) for dual polarization QPSK systems when the EEPN is significant and the carrier phase is estimated using the single tap NLMS filter or using the Viterbi-Viterbi algorithm (see e.g [31

**293**, 54–60 (2013). [CrossRef]

*n-*level PSK systems - to

*n-*level QAM systems. For practical coherent

*n*-level QAM systems, the use of optical (RF) pilot tone phase noise compensation using distributed modulation does not seem to be feasible. Nor does the Viterbi-Viterbi algorithm (in its current implementation [31

**293**, 54–60 (2013). [CrossRef]

33. G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol. **29**(18), 2790–2800 (2011). [CrossRef]

**18**(15), 16243–16257 (2010). [CrossRef] [PubMed]

33. G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol. **29**(18), 2790–2800 (2011). [CrossRef]

## Acknowledgment

## References and links

1. | P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. |

2. | G. P. Agrawal, |

3. | J. G. Proakis, |

4. | M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. |

5. | A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s Receiver with digital equaliser using maximum likelihood sequence estimation,” in |

6. | S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express |

7. | S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express |

8. | S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in |

9. | K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “Coherent optical transmission with frequency-domain equalization,” in |

10. | M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in |

11. | R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in |

12. | T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express |

13. | W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express |

14. | A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express |

15. | R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express |

16. | A. P. T. Lau, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission with coherent detection,” in |

17. | K. P. Ho, A. P. T. Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Opt. Lett. |

18. | C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in |

19. | C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express |

20. | I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express |

21. | S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in |

22. | T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express |

23. | G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express |

24. | G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun. |

25. | |

26. | M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), paper 8.3.6. [CrossRef] |

27. | M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express |

28. | S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSFM enabled by RF-pilot tone for phase noise compensation”, in |

29. | Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express |

30. | G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett. |

31. | T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. |

32. | A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory |

33. | G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol. |

**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: February 27, 2013

Revised Manuscript: April 5, 2013

Manuscript Accepted: May 8, 2013

Published: May 13, 2013

**Citation**

Gunnar Jacobsen, Tianhua Xu, Sergei Popov, and Sergey Sergeyev, "Study of EEPN mitigation using modified RF pilot and Viterbi-Viterbi based phase noise compensation," Opt. Express **21**, 12351-12362 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12351

Sort: Year | Journal | Reset

### References

- P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron.21(12), 1862–1879 (1985). [CrossRef]
- G. P. Agrawal, Fiber-optic communication systems 3rd Edition (John Wiley & Sons, Inc., 2002), Chap. 2.
- J. G. Proakis, Digital Communications 5th Edition (McGraw-Hill Companies, Inc., 2008), Chap. 10.
- M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004). [CrossRef]
- A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s Receiver with digital equaliser using maximum likelihood sequence estimation,” in Proceeding of IEEE European Conference on Optical Communication (Stockholm, Sweden, 2004), paper Th4.1.5.
- S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007). [CrossRef] [PubMed]
- S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008). [CrossRef] [PubMed]
- S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper Mo.3.D.1.
- K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “Coherent optical transmission with frequency-domain equalization,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper We.2.E.3.
- M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT1. [CrossRef]
- R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT3. [CrossRef]
- T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express18(15), 16243–16257 (2010). [CrossRef] [PubMed]
- W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16(20), 15718–15727 (2008). [CrossRef] [PubMed]
- A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express18(16), 17239–17251 (2010). [CrossRef] [PubMed]
- R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express20(24), 26568–26582 (2012). [CrossRef] [PubMed]
- A. P. T. Lau, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission with coherent detection,” in Proceedings of OptoElectronics and Communications Conference (Hong Kong, 2009), paper FQ3.
- K. P. Ho, A. P. T. Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Opt. Lett.36(4), 585–587 (2011). [CrossRef] [PubMed]
- C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT4. [CrossRef]
- C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17(6), 4815–4823 (2009). [CrossRef] [PubMed]
- I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express18(15), 16273–16278 (2010). [CrossRef] [PubMed]
- S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proceeding of IEEE European Conference on Optical Communication (Torino, Italy, 2010), paper Mo.1.C.2. [CrossRef]
- T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express19(8), 7756–7768 (2011). [CrossRef] [PubMed]
- G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express19(15), 14487–14494 (2011). [CrossRef] [PubMed]
- G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun.32, 257–261 (2012).
- www.vpiphotonics.com
- M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), . [CrossRef]
- M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express16(14), 10611–10616 (2008). [CrossRef] [PubMed]
- S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSFM enabled by RF-pilot tone for phase noise compensation”, in Proceeding of Conference on Optical Fiber Communications, (Anaheim, California, 2007), paper PDP 15.
- Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express17(3), 1435–1441 (2009). [CrossRef] [PubMed]
- G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett.46(10), 698–700 (2010). [CrossRef]
- T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun.293, 54–60 (2013). [CrossRef]
- A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983). [CrossRef]
- G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol.29(18), 2790–2800 (2011). [CrossRef]

## 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.