## Estimation and compensation of sample frequency offset in coherent optical OFDM systems |

Optics Express, Vol. 19, Issue 14, pp. 13503-13508 (2011)

http://dx.doi.org/10.1364/OE.19.013503

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### Abstract

Coherent optical OFDM systems employ DAC at the transmitters and ADC at the receivers. The sample frequencies of DAC and ADC in such systems need to be synchronized, especially in the context of high-speed transmissions. This paper presents a channel model including the effect of the sample frequency offset, which adds an additional phase shift proportional to the subcarrier index. The sample frequency offset monitoring and the compensation method are discussed and verified in experiment. It is expected that the synchronization can be achieved by feeding the monitoring result back to the receiver oscillator.

© 2011 OSA

## 1. Introduction

1. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. **42**(10), 587–589 (2006). [CrossRef]

2. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. **43**(3), 183–184 (2007). [CrossRef]

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 4x80-Gsamples/s ADCs,” in *36th European Conference and Exhibition on**Optical Communication (ECOC), 2010* (2010), pp. 1–3.

2. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. **43**(3), 183–184 (2007). [CrossRef]

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 4x80-Gsamples/s ADCs,” in *36th European Conference and Exhibition on**Optical Communication (ECOC), 2010* (2010), pp. 1–3.

8. R. Dischler, A. Klekamp, F. Buchali, W. Idler, E. Lach, A. Schippel, M. Schneiders, S. Vorbeck, and R.-P. Braun, "Transmission of 3x253-Gb/s OFDM-superchannels over 764km field deployed single mode fibers," in *National Fiber Optic Engineers Conference*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPD2.

3. 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]

9. R. P. Giddings and J. M. Tang, "World-first experimental demonstration of synchronous clock recovery in an 11.25Gb/s real-time end-to-end optical OFDM system using directly modulated DFBs," in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMS4.

10. R. P. Giddings and J. M. Tang, “Experimental demonstration and optimisation of a synchronous clock recovery technique for real-time end-to-end optical OFDM transmission at 11.25Gb/s over 25km SSMF,” Opt. Express **19**(3), 2831–2845 (2011). [CrossRef] [PubMed]

## 2. Channel model in the presence of sample frequency offset

11. 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]

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

*N*OFDM symbols in time and

_{f}*N*subcarriers in frequency. The indices of OFDM symbol and subcarrier are

_{SC}*i*and

*k*, respectively.

*k*takes values from [–

*N*/2 + 1

_{SC}*N*/2]. The preamble is added at the beginning to facilitate frame synchronization, DFT window synchronization, and channel estimation.

_{SC}*ϕ*which is proportional to the subcarrier index

*k*,

*f*and

_{s}*i*. This is because we assume that the DFT window synchronization is performed on a per OFDM block basis. The beginning OFDM symbol has good DFT window synchronization, so the SFO-caused phase shift is very small. However, the phase shift is accumulated and is more significant for the rear OFDM symbols within one OFDM block. In the worst case, the information on one OFDM symbol with a large OFDM symbol index cannot be sampled correctly and may be totally lost [6].

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

*k*th subcarrier,

*i*th OFDM symbol, and

*i*;(ii) the channel response and the SFO are semi-static, i.e., almost no change for tens of OFDM symbols. Then, with these assumptions, we can estimate the SFO as

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

*k*in Eq. (5) takes values from a set of pilot subcarriers, typically including eight ones.

## 3. Experimental setup

11. 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]

13. W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express **15**(16), 9936–9947 (2007). [CrossRef] [PubMed]

^{15}-1 PRBS into corresponding 36 subcarriers with 16-QAM encoding within multiple OFDM symbols, which are subsequently converted into the time domain using IDFT, and inserted with cyclic prefix (CP). The number of OFDM symbols in one OFDM block is 50. The length of IDFT is 128 and the CP is 1/17 of one OFDM symbol. Note that our choice of 36 subcarriers is to accommodate our heterodyne detection receiver with a relatively small bandwidth. Eight pilot-subcarriers are added for the SFO and laser phase noise estimation and therefore, the SFO compensation does not require additional pilot subcarriers. The waveform is loaded into an Arbitrary Waveform Generator (AWG) as DAC with a sample frequency of 10 Gs/s. The AWG outputs the complex-valued waveform using two ports. A dual MZM modulator configured as an IQ modulator up-converts the RF OFDM signal to the optical domain. The so-generated OFDM waveform carries 10.6-Gb/s data.

2. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. **43**(3), 183–184 (2007). [CrossRef]

11. 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]

13. W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express **15**(16), 9936–9947 (2007). [CrossRef] [PubMed]

## 4. Experimental results and discussions

**26**(10), 1309–1316 (2008). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. |

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

3. | 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. |

4. | Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission with orthogonal-band multiplexing and subwavelength bandwidth access,” 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 4x80-Gsamples/s ADCs,” in |

6. | M. Sliskovic, “Sampling frequency offset estimation and correction in OFDM systems,” in |

7. | M. Sliskovic, “Carrier and sampling frequency offset estimation and correction in multicarrier systems,” in |

8. | R. Dischler, A. Klekamp, F. Buchali, W. Idler, E. Lach, A. Schippel, M. Schneiders, S. Vorbeck, and R.-P. Braun, "Transmission of 3x253-Gb/s OFDM-superchannels over 764km field deployed single mode fibers," in |

9. | R. P. Giddings and J. M. Tang, "World-first experimental demonstration of synchronous clock recovery in an 11.25Gb/s real-time end-to-end optical OFDM system using directly modulated DFBs," in |

10. | R. P. Giddings and J. M. Tang, “Experimental demonstration and optimisation of a synchronous clock recovery technique for real-time end-to-end optical OFDM transmission at 11.25Gb/s over 25km SSMF,” Opt. Express |

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

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

13. | W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express |

**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: April 21, 2011

Revised Manuscript: May 19, 2011

Manuscript Accepted: May 22, 2011

Published: June 28, 2011

**Citation**

Xingwen Yi and Kun Qiu, "Estimation and compensation of sample frequency offset in coherent optical OFDM systems," Opt. Express **19**, 13503-13508 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13503

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### References

- W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006). [CrossRef]
- W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000km SSMF fibre,” Electron. Lett. 43(3), 183–184 (2007). [CrossRef]
- 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]
- Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission with orthogonal-band multiplexing and subwavelength bandwidth access,” J. Lightwave Technol. 28(4), 308–315 (2010). [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 4x80-Gsamples/s ADCs,” in 36th European Conference and Exhibition onOptical Communication (ECOC), 2010 (2010), pp. 1–3.
- M. Sliskovic, “Sampling frequency offset estimation and correction in OFDM systems,” in The 8th IEEE International Conference on Electronics, Circuits and Systems, 2001 (ICECS 2001) (IEEE, 2001), Vol 1, pp. 437–440.
- M. Sliskovic, “Carrier and sampling frequency offset estimation and correction in multicarrier systems,” in IEEE Global Telecommunications Conference, 2001. GLOBECOM '01 (IEEE, 2001), Vol. 1, pp. 285–289.
- R. Dischler, A. Klekamp, F. Buchali, W. Idler, E. Lach, A. Schippel, M. Schneiders, S. Vorbeck, and R.-P. Braun, "Transmission of 3x253-Gb/s OFDM-superchannels over 764km field deployed single mode fibers," in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPD2.
- R. P. Giddings and J. M. Tang, "World-first experimental demonstration of synchronous clock recovery in an 11.25Gb/s real-time end-to-end optical OFDM system using directly modulated DFBs," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMS4.
- R. P. Giddings and J. M. Tang, “Experimental demonstration and optimisation of a synchronous clock recovery technique for real-time end-to-end optical OFDM transmission at 11.25Gb/s over 25km SSMF,” Opt. Express 19(3), 2831–2845 (2011). [CrossRef] [PubMed]
- 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]
- X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007). [CrossRef]
- W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express 15(16), 9936–9947 (2007). [CrossRef] [PubMed]

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