## Channel estimation and synchronization for polarization-division multiplexed CO-OFDM using subcarrier/polarization interleaved training symbols |

Optics Express, Vol. 19, Issue 17, pp. 16174-16181 (2011)

http://dx.doi.org/10.1364/OE.19.016174

Acrobat PDF (1711 KB)

### Abstract

We propose and demonstrate the use of subcarrier/polarization-interleaved training symbols for channel estimation and synchronization in polarization-division multiplexed (PDM) coherent optical orthogonal frequency-division multiplexed (CO-OFDM) transmission. The principle, the computational efficiency, and the frequency-offset tolerance of the proposed method are described. We show that the use of subcarrier/polarization interleaving doubles the tolerance to the frequency offset between the transmit laser and the receiver’s optical local oscillator as compared to conventional schemes. Using this method, we demonstrate 43-Gb/s PDM CO-OFDM transmission with 16-QAM subcarrier modulation over 5,200-km of ultra-large-area fiber.

© 2011 OSA

## 1. Introduction

1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express **16**(2), 841–859 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-841. [CrossRef] [PubMed]

2. 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]

5. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “Long-haul transmission of 16 x 52.5 Gbits/s polarization-divisionmultiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. **7**(2), 173–182 (2008). [CrossRef]

6. X. Liu and F. Buchali, “A Novel Channel Estimation Method for PDM-OFDM Enabling Improved Tolerance to WDM Nonlinearity,” in Proc. Optical Fiber Commun. Conf. (OFC) 2009, Paper OWW5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2009-OWW5.

6. X. Liu and F. Buchali, “A Novel Channel Estimation Method for PDM-OFDM Enabling Improved Tolerance to WDM Nonlinearity,” in Proc. Optical Fiber Commun. Conf. (OFC) 2009, Paper OWW5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2009-OWW5.

7. X. Liu, F. Buchali, and W. Robert, “Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. **27**(16), 3632–3640 (2009). [CrossRef]

## 2. Principle

_{1}, t

_{2}, and t

_{3}, for synchronization and channel estimation [8]:where subscript x and y denote the x and y polarization components of the signal to be transmitted, respectively, and

*E (O)*is a symmetric (anti-symmetric) symbol whose even (odd) subcarriers are modulated with known pseudo-random bit sequences (PRBS) while the odd (even) subcarriers are unfilled or have zero power. The amplitude of the filled subcarriers of

*E*and

*O*are scaled up by 2 in order for the average power of each SI-DP TS to be the same as that of the payload symbols.

6. X. Liu and F. Buchali, “A Novel Channel Estimation Method for PDM-OFDM Enabling Improved Tolerance to WDM Nonlinearity,” in Proc. Optical Fiber Commun. Conf. (OFC) 2009, Paper OWW5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2009-OWW5.

7. X. Liu, F. Buchali, and W. Robert, “Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. **27**(16), 3632–3640 (2009). [CrossRef]

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

*ε*) can be estimated by [3, 8]where

*f*and

_{offset}*r*(

*n*) and

*r**(

*n*) is the n-th received time sample and its complex conjugate, respectively. The phase difference between the received time samples

*π*. Note that the subcarrier spacing

_{s}/N, where R

_{s}is the sampling rate. Figure 1(b) shows the structure of the subcarrier allocation using the proposed SI-DP TSs in PDM CO-OFDM. The SI-DP TS based method can also provide the reduced WDM nonlinear effects since there is no difference between the average power of the TSs and that of the payload symbols. The first TS consists of identical

*E*symbols in both x- and y-polarization states. The first and second halves of the first TS

*E*are identical since only even subcarriers of the

*E*symbol are modulated [3]. Thus, the autocorrelation of the first TS with ½-symbol delay results in a maximum that can be used for frame synchronization. In addition, the phase difference between the received time samples

*N*/2 samples instead of

*N*samples in Eq. (2), and the normalized frequency offset can be estimated by

5. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “Long-haul transmission of 16 x 52.5 Gbits/s polarization-divisionmultiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. **7**(2), 173–182 (2008). [CrossRef]

^{nd}and 3

^{rd}SI-DP TSs are subcarrier/polarization interleaved symbols. This facilitates the decomposition of the 2×2 Jones matrix, [

*a(k) b(k)*;

*c(k) d(k)*] as follows.

*r*and

_{2}*r*are the received training symbols, x and y denotes the x- and y-polarizations defined at the receiver, and

_{3}*k*and

_{odd}*k*are respectively the indices for the modulated odd and even subcarriers in the two SI-DP TSs defined in Eq. (1). As can be seen in Eq. (4), each channel matrix coefficient for a given subcarrier is efficiently obtained through a single complex division. The previous channel estimation methods such as those reported in Refs. 5

_{even}5. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “Long-haul transmission of 16 x 52.5 Gbits/s polarization-divisionmultiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. **7**(2), 173–182 (2008). [CrossRef]

**7**(2), 173–182 (2008). [CrossRef]

## 3. Experimental Setup

^{15}-1 was mapped onto 72 subcarriers with 16-QAM modulation, together with 8 pilot subcarriers, one unfilled DC subcarrier, and 47 unfilled edge subcarriers. The time domain signal was generated through an inverse fast Fourier transform (IFFT) operation of size 128, and a small guard interval (GI) of length 4 was inserted, resulting in an OFDM symbol size of 132. Four training symbols, [E E O E] were inserted at the beginning of each OFDM frame. After a PDM emulator with one symbol delay between the two polarizations, three SI-DP TSs as described earlier were obtained for frame synchronization, frequency offset estimation, and channel estimation. Each OFDM frame consisted of the four TSs and 300 OFDM payload symbols, as shown in inset (b) of Fig. 2. The real and imaginary parts of the OFDM time waveform were amplified and used to drive an optical I/Q modulator whose sub-Mach-Zehnders were biased at the transmission null. An external-cavity laser (ECL) with 100-kHz linewidth was used as transmit laser at 1550 nm. The data rate and subcarrier spacing of the PDM CO-OFDM signal were 43 Gb/s (=10GS/s*8*72/132*300/304) and 78.1 MHz (=10 GHz/128), respectively. The optical bandwidth of the 43-Gb/s signal was only 6.3 GHz. The signal was launched into a recirculating loop [10]. It consisted of four Raman-amplified 100-km spans of ULAF. The fiber loss, dispersion, and effective area were 0.185 dB/km, 19.9 ps/nm/km, and 120 μm

^{2}, respectively. The loop contained a 50-GHz-grid wavelength-selective-switch (WSS) and an acousto-optic switch (SW) that shifted the optical signal frequency by 25 MHz every round trip, which allowed us to accurately assess the frequency-offset tolerance of the PDM CO-OFDM system. Another SW with a 25-MHz frequency shift was used before the signal entered the loop.

12. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s Reduced-Guard-Interval CO-OFDM Signal with a 60-GHz Optical Bandwidth over 2000 km of ULAF and Five 80-GHz-Grid ROADMs,” in Proc. Optical Fiber Commun. Conf. (OFC) 2010, post-deadline paper PDPC2. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2010-PDPC2

## 4. Experimental results

_{SC}), which is twice as large as that of the previous methods [5

**7**(2), 173–182 (2008). [CrossRef]

^{2}factor, derived from the measured BER, as a function of the signal launch power after 3200-km transmission. Without nonlinearity compensation (NLC), the optimum launch power and the Q

^{2}factor were around −9 dBm and ~8.5 dB, respectively. With the use of multi-step NLC [11–13

13. 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]

^{2}factor was increased by 1.6 dB to 10.1 dB. The multi-steps NLC was performed at the receiver and the number of steps used was the same as the number of the transmission spans. The inter-polarization cross phase modulation (XPM) was taken into consideration by using an inter-polarization XPM factor of 1 [13

13. 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]

^{2}factor as a function of the transmission distance when the signal launch power is fixed at −6 dBm. The Q

^{2}factor values shown in Fig. 5 were obtained by averaging over two polarization components of the signal, which performed very similarly. Without NLC, the BER of the 43-Gb/s PDM CO-OFDM signal after 2,400-km transmission is below 3.8x10

^{−3}, the threshold of enhanced hard-decision forward-error correction with 7% overhead [14]. With the use of multi-step NLC, the BER of the 43-Gb/s signal is below 3.8x10

^{−3}after 5,200-km transmission, more than doubling the transmission distance achieved without using NLC.

## 5. Conclusions

## Acknowledgments

## References and links

1. | W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express |

2. | 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. |

3. | T. M. Schmidl and D. C. Cox, “Robust Frequency and Timing Synchronization for OFDM,” IEEE Trans. Wirel. Comm. |

4. | X. Hu, Y. Huang, and Z. Hong, “Residual Synchronization Error Elimination in OFDM Baseband Receivers,” ETRI J. |

5. | S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “Long-haul transmission of 16 x 52.5 Gbits/s polarization-divisionmultiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. |

6. | X. Liu and F. Buchali, “A Novel Channel Estimation Method for PDM-OFDM Enabling Improved Tolerance to WDM Nonlinearity,” in Proc. Optical Fiber Commun. Conf. (OFC) 2009, Paper OWW5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2009-OWW5. |

7. | X. Liu, F. Buchali, and W. Robert, “Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. |

8. | C. J. Youn, X. Liu, S. Chandrasekhar, Y.-H. Kwon, J.-H. Kim, J.-S. Choe, K.-S. Choi, and E. S. Nam, “An Efficient and Frequency-Offset-Tolerant Channel Estimation and Synchronization Method for PDM CO-OFDM Transmission,” in Proc. European Conf. Optical Commun. 2010, Paper P4.06. |

9. | S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. |

10. | 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. European Conf. Optical Commun. 2009, post-deadline paper PD2.6. |

11. | D. S. Millar, S. Makovejs, V. Mikhailov, R. I. Killey, P. Bayvel, and S. J. Savory, “Experimental Comparison of Nonlinear Compensation in Long-Haul PDM-QPSK Transmission at 42.7 and 85.4 Gb/s,” in Proc. European Conf. Optical Commun. 2009, Paper 9.4.4. |

12. | X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s Reduced-Guard-Interval CO-OFDM Signal with a 60-GHz Optical Bandwidth over 2000 km of ULAF and Five 80-GHz-Grid ROADMs,” in Proc. Optical Fiber Commun. Conf. (OFC) 2010, post-deadline paper PDPC2. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2010-PDPC2 |

13. | 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. |

14. | ITU-T Recommendation G.975.1, 2004, Appendix I.9. |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: May 25, 2011

Revised Manuscript: July 17, 2011

Manuscript Accepted: July 21, 2011

Published: August 9, 2011

**Citation**

Chun Ju Youn, Xiang Liu, S. Chandrasekhar, Yong-Hwan Kwon, Jong-Hoi Kim, Joong-Seon Choe, Duk-Jun Kim, Kwang-Seong Choi, and Eun Soo Nam, "Channel estimation and synchronization for polarization-division multiplexed CO-OFDM using subcarrier/polarization interleaved training symbols," Opt. Express **19**, 16174-16181 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-16174

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### References

- W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-841 . [CrossRef] [PubMed]
- 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]
- T. M. Schmidl and D. C. Cox, “Robust Frequency and Timing Synchronization for OFDM,” IEEE Trans. Wirel. Comm. 45(12), 1613–1621 (1997).
- X. Hu, Y. Huang, and Z. Hong, “Residual Synchronization Error Elimination in OFDM Baseband Receivers,” ETRI J. 29(5), 596–606 (2007). [CrossRef]
- S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “Long-haul transmission of 16 x 52.5 Gbits/s polarization-divisionmultiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. 7(2), 173–182 (2008). [CrossRef]
- X. Liu and F. Buchali, “A Novel Channel Estimation Method for PDM-OFDM Enabling Improved Tolerance to WDM Nonlinearity,” in Proc. Optical Fiber Commun. Conf. (OFC) 2009, Paper OWW5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2009-OWW5 .
- X. Liu, F. Buchali, and W. Robert, “Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009). [CrossRef]
- C. J. Youn, X. Liu, S. Chandrasekhar, Y.-H. Kwon, J.-H. Kim, J.-S. Choe, K.-S. Choi, and E. S. Nam, “An Efficient and Frequency-Offset-Tolerant Channel Estimation and Synchronization Method for PDM CO-OFDM Transmission,” in Proc. European Conf. Optical Commun. 2010, Paper P4.06.
- S. L. Jansen, I. Morita, T. 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]
- 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. European Conf. Optical Commun. 2009, post-deadline paper PD2.6.
- D. S. Millar, S. Makovejs, V. Mikhailov, R. I. Killey, P. Bayvel, and S. J. Savory, “Experimental Comparison of Nonlinear Compensation in Long-Haul PDM-QPSK Transmission at 42.7 and 85.4 Gb/s,” in Proc. European Conf. Optical Commun. 2009, Paper 9.4.4.
- X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s Reduced-Guard-Interval CO-OFDM Signal with a 60-GHz Optical Bandwidth over 2000 km of ULAF and Five 80-GHz-Grid ROADMs,” in Proc. Optical Fiber Commun. Conf. (OFC) 2010, post-deadline paper PDPC2. http://www.opticsinfobase.org/abstract.cfm?URI=NFOEC-2010-PDPC2
- 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]
- ITU-T Recommendation G.975.1, 2004, Appendix I.9.

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