## Analysis of dispersion-enhanced phase noise in CO-OFDM systems with RF-pilot phase compensation |

Optics Express, Vol. 19, Issue 24, pp. 24030-24036 (2011)

http://dx.doi.org/10.1364/OE.19.024030

Acrobat PDF (982 KB)

### Abstract

We show that dispersion-enhanced phase noise (DEPN) induces performance degradations in both conventional CO-OFDM systems and reduced-guard-interval (RGI) CO-OFDM systems employing RF-pilot phase compensation. After analytically studying DEPN, we show that DEPN causes a 2 to 6 dB optical signal-to-noise ratio (OSNR) penalty at transmission distances of 3200 km and 1600 km for 28 and 56 Gbaud QPSK systems, respectively, using lasers with 2 MHz linewidths. At such distances, DEPN reduces the linewidth tolerance at 1 dB OSNR penalty to 250-500 kHz while in the back-to-back case the tolerance is 1-3 MHz for both systems. When fiber nonlinearity is included, we observe similar performance degradations.

© 2011 OSA

## 1. Introduction

1. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?[Invited],” J. Opt. Netw. **7**(3), 234–255 (2008). [CrossRef]

2. 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. 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**(17), 2537–2551 (2010). [CrossRef]

7. S. L. Jansen, I. Morita, T. 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]

7. S. L. Jansen, I. Morita, T. 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]

7. S. L. Jansen, I. Morita, T. 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]

10. Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express **19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

11. 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]

4. 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**(4), 483–490 (2011). [CrossRef]

4. 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**(4), 483–490 (2011). [CrossRef]

10. Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express **19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

^{−3}for both 28 and 56 Gbaud DP-QPSK systems in the back-to-back case, the OSNR penalty is increased by 2-6 dB after 3200 km and 1600 km transmission for the 28 and 56 Gbaud systems respectively. Moreover, at such transmission distances, the laser linewidth tolerance of the RF-pilot compensation scheme at 1 dB OSNR penalty is reduced from 1-3 MHz to 250-500 kHz for both systems because of DEPN. Finally, when nonlinearities are considered, similar performance degradations are observed. Here we find that DEPN induced penalties in conventional CO-OFDM systems cannot be easily mitigated whereas DEPN-induced penalties in RGI CO-OFDM systems can be mitigated using maximum-likelihood algorithms [10

10. Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express **19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

## 2. Analysis of dispersion-enhanced phase noise with RF-pilot phase compensation

*r*(

*t*) (RF-pilot tone is not included) can then be expressed similar to [10

**19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

*N*is the number of subcarriers,

_{c}*c*denotes the symbol transmitted on the

_{k}*k*th subcarrier, Δ

*f*is the subcarrier frequency spacing, and

*z*(

*t*) is the ASE noise.

*T*is the dispersion-induced walk-off between the

_{k}*k*th subcarrier and the RF-pilot tone which is calculated as in [10

**19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

*ϕ*(

_{t}*t*) and

*ϕ*(

_{r}*t*) denote the laser phase noise caused by the transmitter and receiver lasers, respectively. They are both modeled as Wiener processes with a variance of

*2πβt*and

*β*denotes the linewidth for each individual laser.

*ϕ*(t) is the phase of the filtered ASE noise, the power of which is determined by the pilot-to-signal ratio and the bandwidth of the filter used to extract the RF-pilot [7

_{n}**26**(1), 6–15 (2008). [CrossRef]

**19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

17. 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]

*Z*(k) is the DFT of

*ICI*(

*k*) is obtained by

*I*(

_{k}*p*) including

*I*(0) is given bywhere

_{k}*T*is the sample duration.

_{s}*I*(0) term in Eq. (4) on the subcarrier index

_{k}*k*, whereas ICI results from the

*ICI*(

*k*) term in Eq. (4) which arises from other subcarriers interfering with the

*k*th subcarrier [10

**19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

17. 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]

*ϕ*(

_{t}*n*) -

*ϕ*(

_{t}*n + D*)] term in Eq. (5), which represents the dispersion-induced difference between the transmit laser phase applied to the RF-pilot tone and that applied to the data subcarrier. Therefore, both RPS and ICI will be enhanced with the increase of the walk-off

_{k}*D*, which is proportional to the transmission distance

_{k}*L*and the baud rate.

**19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

^{2}), whereas for ICI it is defined as the amplitude noise normalized to the average power of the signal. First, in the back-to-back case, the noise variance is larger with shorter symbol duration (top left constellation for each figure). This has been explained in [9] by the larger spectral leakage into the RF-pilot for shorter symbol duration. Next, by comparing Fig. 2(a), 2(b) and 2(c), it is seen that as the number of subcarriers increases, the variance of RPS is reduced due to the enhanced correlation between the phases acquired by data subcarriers and the RF-pilot tone, which results from the longer time duration in which their samples overlap. In contrast to RPS, the variance of ICI increases for longer symbol durations because each symbol becomes more vulnerable to ICI for a given phase difference. These two key observations can be also verified by the top right constellations of each figure as the phase noise dominates for systems with 80 subcarriers, whereas amplitude noise dominates for systems with 1280 subcarriers.

## 3. Simulation results and discussions

### 3.1 Channel including only CD and ASE noise

*D*= 17 ps/(nm·km) and ASE noise. The linewidths of the transmit and receive lasers were both 2 MHz for all simulations, if not otherwise specified. For conventional CO-OFDM, the number of subcarriers was set to 1280 and 2560 for the 28 and 56 Gbaud systems respectively in order to make the cyclic prefix overhead identical at

*L*= 3200 km (28 Gbaud) and 1600 km (56 Gbaud). For RGI CO-OFDM systems, a frequency domain equalizer compensates CD prior to OFDM demodulation [4

4. 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**(4), 483–490 (2011). [CrossRef]

*L*for both conventional CO-OFDM and RGI CO-OFDM systems. In the back-to-back case, OSNR penalties for all systems are around 1 dB, which is consistent with previous works [7

**26**(1), 6–15 (2008). [CrossRef]

*L*≤ 2000 km, however at

*L*= 3200 km penalties increase to 3.3-5.5 dB depending on the number of subcarriers. When the baud rate is doubled to 56 Gbaud, the penalties reach 3.8-6.8 dB at

*L*= 1600 km, although they are still only 1 dB in the back-to-back case. Therefore, the impact of DEPN should be considered when designing long-haul transmission systems, especially for high baud rate systems.

*β*for various scenarios. For the back-to-back case, linewidth tolerances at 1 dB penalty are larger than 1 MHz for all systems. It should be pointed out that the performance for larger linewidths can be further improved if the spectral overhead and filter bandwidth are optimized as shown in [9]. After transmission over 3200 km for the 28 Gbaud systems and 1600 km for the 56 Gbaud systems, the linewidth tolerance is reduced to 250-500 kHz, which means ECLs might be required even with RF-pilot phase compensation.

### 3.2 Optical channel

*β*= 2 MHz without the grouped maximum-likelihood (GML) algorithm and

*β*= 0 MHz (without any phase compensation), we notice that OSNR penalties are larger than 4 dB and might reach 8 dB for RGI systems (

*N*= 80). The inherent penalty of the RF-pilot phase noise compensation is around 1 dB in the back-to-back case as previously observed from Fig. 3. Therefore, we claim that most of these large penalties arise from DEPN, which is seen to be also significant in a real optical transmission system when nonlinearities are included. The increased OSNR penalties compared to those in Fig. 3 can be explained by the raised noise floor due to the addition of nonlinear impairments. Next, since RPS is a continuous phase noise [10

_{c}**19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

**19**(5), 4472–4484 (2011). [CrossRef] [PubMed]

## 4. Conclusions

## References and links

1. | W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?[Invited],” J. Opt. Netw. |

2. | 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. |

3. | S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1000 km of SSMF,” J. Lightwave Technol. |

4. | 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. |

5. | X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4x 80-Gsamples/s ADCs,” in Proc. ECOC’10, Paper PD2.6 (2010). |

6. | A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus single-carrier transmission for 100 Gbps optical communication,” J. Lightwave Technol. |

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

8. | S. Randel, S. Adhikari, and S. L. Jansen, “Analysis of RF-pilot-based phase noise compensation for coherent optical OFDM systems,” IEEE Photon. Technol. Lett. |

9. | S. L. Jansen, A. Lobato, S. Adhikari, B. Inan, and D. van den Borne, “Optical OFDM for ultra-high capacity long-haul transmission applications,” in Proc. ONDM’11, pp. 1–4 (2011). |

10. | Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express |

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

12. | F. Buchali, R. Dischler, M. Mayrock, X. Xiao, and Y. Tang, “Improved frequency offset correction in coherent optical OFDM systems,” in Proc. ECOC’08, Paper Mo.4.D.4 (2008). |

13. | B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, “Pilot-tone-based nonlinearity compensation for optical OFDM systems,” in Proc. ECOC’10, Paper Tu.4.A.6 (2010). |

14. | A. Lobato, B. Inan, S. Adhikari, and S. L. Jansen, “On the efficiency of RF-Pilot-based nonlinearity compensation for CO-OFDM,” in Proc. OFC’11, Paper OThF2 (2011). |

15. | M. H. Morsy-Osman, L. R. Chen, and D. V. Plant, “Joint mitigation of laser phase noise and fiber nonlinearity using pilot-aided transmission for single-carrier systems,” in Proc. ECOC’11, Paper Tu.3.A.3 (2011). |

16. | Q. Zhuge and D. V. Plant, “Compensation for dispersion-enhanced phase noise in reduced-guard-interval CO-OFDM transmissions,” in Proc. SPPCom’11, Paper SPTuC4 (2011). |

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

**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: August 25, 2011

Revised Manuscript: October 21, 2011

Manuscript Accepted: October 24, 2011

Published: November 10, 2011

**Citation**

Qunbi Zhuge, Mohamed Morsy-Osman, and David V. Plant, "Analysis of dispersion-enhanced phase noise in CO-OFDM systems with RF-pilot phase compensation," Opt. Express **19**, 24030-24036 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24030

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### References

- W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?[Invited],” J. Opt. Netw.7(3), 234–255 (2008). [CrossRef]
- 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]
- S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1000 km of SSMF,” J. Lightwave Technol.27(3), 177–188 (2009). [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(4), 483–490 (2011). [CrossRef]
- X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4x 80-Gsamples/s ADCs,” in Proc. ECOC’10, Paper PD2.6 (2010).
- 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(17), 2537–2551 (2010). [CrossRef]
- S. L. Jansen, I. Morita, T. 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]
- S. Randel, S. Adhikari, and S. L. Jansen, “Analysis of RF-pilot-based phase noise compensation for coherent optical OFDM systems,” IEEE Photon. Technol. Lett.22(17), 1288–1290 (2010). [CrossRef]
- S. L. Jansen, A. Lobato, S. Adhikari, B. Inan, and D. van den Borne, “Optical OFDM for ultra-high capacity long-haul transmission applications,” in Proc. ONDM’11, pp. 1–4 (2011).
- Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express19(5), 4472–4484 (2011). [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]
- F. Buchali, R. Dischler, M. Mayrock, X. Xiao, and Y. Tang, “Improved frequency offset correction in coherent optical OFDM systems,” in Proc. ECOC’08, Paper Mo.4.D.4 (2008).
- B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, “Pilot-tone-based nonlinearity compensation for optical OFDM systems,” in Proc. ECOC’10, Paper Tu.4.A.6 (2010).
- A. Lobato, B. Inan, S. Adhikari, and S. L. Jansen, “On the efficiency of RF-Pilot-based nonlinearity compensation for CO-OFDM,” in Proc. OFC’11, Paper OThF2 (2011).
- M. H. Morsy-Osman, L. R. Chen, and D. V. Plant, “Joint mitigation of laser phase noise and fiber nonlinearity using pilot-aided transmission for single-carrier systems,” in Proc. ECOC’11, Paper Tu.3.A.3 (2011).
- Q. Zhuge and D. V. Plant, “Compensation for dispersion-enhanced phase noise in reduced-guard-interval CO-OFDM transmissions,” in Proc. SPPCom’11, Paper SPTuC4 (2011).
- 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]

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