## Simple full-range carrier frequency offset estimation for high speed CO-OFDM |

Optics Express, Vol. 21, Issue 20, pp. 23896-23906 (2013)

http://dx.doi.org/10.1364/OE.21.023896

Acrobat PDF (1666 KB)

### Abstract

We propose a simple, full-range carrier frequency offset (CFO) algorithm for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. By applying the Chinese remainder theorem (CRT) to training symbol of single frequency, the proposed CFO algorithm has wide range with shorter training symbol. We numerically and experimentally demonstrate the performance of CRT-based algorithms in a 16-ary quadrature amplitude modulation (QAM) CO-OFDM system. The results show that the estimation range of the CRT-based algorithm is full-range corresponding to the sampling frequency. Also, the bit error ratio (BER) degradation of the proposed algorithm with one training symbol is negligible. These results indicate that the proposed algorithm can be used as a wide range CFO estimator with an increased data rate in high speed CO-OFDM systems.

© 2013 Optical Society of America

## 1. Introduction

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

3. T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. **45**(12), 1613–1621 (1997). [CrossRef]

10. M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J. **34**(3), 458–461 (2012). [CrossRef]

3. T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. **45**(12), 1613–1621 (1997). [CrossRef]

4. C. J. Youn, X. Liu, S. Chandrasekhar, Y.-H. Kwon, J.-H. Kim, J. S. Choe, D. J. Kim, K. S. Choi, and E. S. Nam, “Channel estimation and synchronization for polarization-division multiplexed CO-OFDM using subcarrier/polarization interleaved training symbols,” Opt. Express **19**(17), 16174–16181 (2011). [CrossRef] [PubMed]

3. T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. **45**(12), 1613–1621 (1997). [CrossRef]

6. S. Cao, S. Zhang, Y. Shaoliang, K. Changyuan, and P.-Y. Kam, “Full range pilot-assisted frequency offset estimation for OFDM systems,” in Proceedings of OFC’13, paper JW2A.53. [CrossRef]

7. X.-H. Fan, J. Yu, D. Qian, and G.-K. Chang, “A Fast and Efficient Frequency Offset Correction Technique for Coherent Optical Orthogonal Frequency Division Multiplexing,” J. Lightwave Technol. **29**(13), 1997–2004 (2011). [CrossRef]

8. X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express **20**(7), 7350–7361 (2012). [CrossRef] [PubMed]

9. H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. **24**(22), 2064–2066 (2012). [CrossRef]

## 2. Background of the Study

### 2.1 Background of CRT-based frequency offset estimation

*η(n)*, the sampled baseband signal

*r(n)*with carrier frequency offset (CFO)

*Δf*can be represented by:where

*s(n)*is the signal component and

*T*is the sampling period.

_{s}**45**(12), 1613–1621 (1997). [CrossRef]

*NT*) is estimated bywhere

_{s}*L*is the sample interval,

*N*is the size of the inverse fast Fourier transformation (IFFT), and

*P*is the correlate function.

_{L}*L*determines the accuracy and range of CFO estimation. The estimation range of the normalized CFO is [-

*N*/2

*L*,

*N*/2

*L*) and the variance of normalized CFO is described by Cramér-Rao bound (CRB) [3

**45**(12), 1613–1621 (1997). [CrossRef]

11. P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun. **42**(10), 2908–2914 (1994). [CrossRef]

*L*can be determined by the tradeoff between the estimation range and accuracy. As the sample interval increases, the accuracy of the estimation also increases, but the range of estimation decreases.

*L*,

_{1}*L*and

_{2}*L*[9

9. H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. **24**(22), 2064–2066 (2012). [CrossRef]

*LT*),

_{s}*L*and

_{1}*L*are coprime numbers, and

_{2}*L*is the product of

*L*and

_{1}*L*. Hence,

_{2}*L*has the highest accuracy among the three estimations.

*mod*represent the modular arithmetic. According to CRT, the integer obtained in Eq. (5) has a range of

*L*. The fractional part of CFO with high accuracy

*LT*) has the range of

_{s}*L*. Accordingly, the CRT-based CFO estimation has full-range and high accuracy.

### 2.2 Principle of single frequency CRT-based CFO estimation

*L*as shown in Fig. 1(a). The phase differences between subsymbols S

_{1}, S

_{2}, and training symbols T

_{1}are calculated for CFO estimation with the sample interval

*L*,

_{1}*L*, and

_{2}*L*, respectively.

*t(n)*is described as:where

*ϕ*is the phase difference between adjacent samples in the transmitted training symbol, and

_{s}*N*is the number of training symbol samples. Using Eq. (1) and Eq. (6), the received training symbol is described as:

_{TS}*L*can be obtained from any samples apart

_{1}*L*by subtracting the transmitted phase difference,

_{1}*ϕ*from the measured phase difference. As such, Eq. (4) can be described as:The rest of calculations are the same as in the previous CRT-based CFO algorithm.

_{s}·L_{1}*L*and

_{1}*L*, with condition

_{2}*L*·

_{1}*L*<

_{2}*N*. On the contrary, the product of co-prime set,

_{TS}*L*, should be the same as the training symbol size, 0.5

*N*, in the previous CRT-based estimation. Also, the previous training symbol structure consists of two training symbols and requires guard intervals between different subsymbols. Unlike the previous estimation, the proposed CFO estimation does not require a guard interval between the different sample intervals. Also, either one or two training symbols can be used for the proposed algorithm as shown in Fig. 1(b) and1(c).

_{TS}## 3. Simulation and experimental setup

### 3.1 Simulation and experiment

^{TM}. DSP structures of the transmitter and the receiver are shown in Fig. 2(a) and Fig. 2(b), respectively. At the transmitter, a 2

^{15}-1 pseudo random binary sequence (PRBS) was mapped to the OFDM subcarriers with 16-ary quadrature amplitude modulation (16 QAM). The mapped signal was transformed to the time domain using IFFT. After cyclic prefix insertion into the time domain signal, training symbols for CFO estimation, symbol synchronization, and channel estimation were attached at the beginning of each OFDM frame. To flatten unequal frequency response magnitude owing to the bandwidth of the channel, pre-emphasis was performed on the waveform. The coefficients for pre-emphasis were obtained from the estimated channel frequency response. Then the pre-equalized waveform was clipped [12

12. R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett. **23**(20), 1550–1552 (2011). [CrossRef]

13. L. Xiang, S. Chandrasekhar, Z. Benyuan, 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 ROADM,” J. Lightwave Technol. **29**(4), 483–490 (2011). [CrossRef]

14. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express **16**(26), 21944–21957 (2008). [CrossRef] [PubMed]

### 3.2 CFO monitoring

15. Z. Xian, Y. Xiaolong, L. Rui, and L. Keping, “Efficient Joint Carrier Frequency Offset and Phase Noise Compensation Scheme for High-Speed Coherent Optical OFDM Systems,” J. Lightwave Technol. **31**(11), 1755–1761 (2013). [CrossRef]

*f*was 2MHz. Assuming that the carrier frequency offset was static over one frame and laser linewidth was smaller than the frequency spacing, the monitoring accuracy was ±

_{spacing}*f*( ± 2 MHz). Also, the oscilloscope with the sampling rate of 40 GS/s gave the monitoring range of ± 20 GHz.

_{spacing}## 4. Results and discussion

*L*of 9,

_{1}*L*of 16, and

_{2}*L*of 144 were selected for CRT-based algorithms with two training symbols. Also,

*L*of 9,

_{1}*L*of 8, and

_{2}*L*of 72 were selected for the CRT-based algorithm with one training symbol. The phase difference φ

_{S}in Eq. (6) for the proposed training symbol was set to π/4. Since normalized CFO

*ε*has a different normalization factor for each algorithm, MSEE(

*ϕ*) is used instead of MSEE(

_{sample}*ε*), in which

*ϕ*is an estimated phase difference between adjacent samples.

_{sample}### 4.1 Simulation results

*D*was set to 2 ps/√km. The sampling rate of the simulation was set to 29 GHz to meet the transmission rate of 112 Gbps.

_{p}### 4.2 Experimental results in the absence of CFO

16. W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. **20**(8), 605–607 (2008). [CrossRef]

*L*samples, induced by the laser linewidth Δ√, can be described as [17]:Measured MSEE can be compared with the estimation error variance calculated from Eq. (9). For 100 kHz laser linewidth, MSEE due to phase noise of the system with

*L*of 144 and 72 were 4.36 × 10

^{−7}and 8.72 × 10

^{−7}, respectively. The experimental results indicated that laser phase noise could be more influential on CFO estimation than AWGN. Since estimation error variance is proportional to the laser linewidth, a CFO estimation algorithm considering phase noise may be required for higher linewidth, or higher accuracy.

^{−3}, which is an advanced 7% FEC threshold [13

13. L. Xiang, S. Chandrasekhar, Z. Benyuan, 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 ROADM,” J. Lightwave Technol. **29**(4), 483–490 (2011). [CrossRef]

### 4.3 Experimental CFO Estimation in the presence of CFO

8. X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express **20**(7), 7350–7361 (2012). [CrossRef] [PubMed]

*L*. However, the small increase of MSEE did not affect the BER as shown in Fig. 9.

18. C.-H. Yih, “BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels,” IEEE Commun. Lett. **11**(11), 842–844 (2007). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

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

2. | Optical Internetworking Forum, “Integrable Tunable Transmitter Assembly Multi Source Agreement,” OIF-ITTA-MSA-01.0, Nov. (2008). |

3. | T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. |

4. | C. J. Youn, X. Liu, S. Chandrasekhar, Y.-H. Kwon, J.-H. Kim, J. S. Choe, D. J. Kim, K. S. Choi, and E. S. Nam, “Channel estimation and synchronization for polarization-division multiplexed CO-OFDM using subcarrier/polarization interleaved training symbols,” Opt. Express |

5. | Z. Wang, Y. Qiao, and Y. Ji, “A Novel Joint Frequency Offset and Channel Estimation Method for CO-OFDM System,” Communications and Photonics Conference and Exhibition (ACP) 607–608 (2010). |

6. | S. Cao, S. Zhang, Y. Shaoliang, K. Changyuan, and P.-Y. Kam, “Full range pilot-assisted frequency offset estimation for OFDM systems,” in Proceedings of OFC’13, paper JW2A.53. [CrossRef] |

7. | X.-H. Fan, J. Yu, D. Qian, and G.-K. Chang, “A Fast and Efficient Frequency Offset Correction Technique for Coherent Optical Orthogonal Frequency Division Multiplexing,” J. Lightwave Technol. |

8. | X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express |

9. | H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. |

10. | M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J. |

11. | P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun. |

12. | R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett. |

13. | L. Xiang, S. Chandrasekhar, Z. Benyuan, 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 ROADM,” J. Lightwave Technol. |

14. | X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express |

15. | Z. Xian, Y. Xiaolong, L. Rui, and L. Keping, “Efficient Joint Carrier Frequency Offset and Phase Noise Compensation Scheme for High-Speed Coherent Optical OFDM Systems,” J. Lightwave Technol. |

16. | W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. |

17. | W. Shieh and I. Djordjevic, “Optical Communication Fundamentals,” in |

18. | C.-H. Yih, “BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels,” IEEE Commun. Lett. |

**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: July 24, 2013

Revised Manuscript: September 4, 2013

Manuscript Accepted: September 16, 2013

Published: September 30, 2013

**Citation**

Hae Young Rha, Chun Ju Youn, Eun Soo Nam, and Hae-Wook Choi, "Simple full-range carrier frequency offset estimation for high speed CO-OFDM," Opt. Express **21**, 23896-23906 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23896

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### References

- W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006). [CrossRef]
- Optical Internetworking Forum, “Integrable Tunable Transmitter Assembly Multi Source Agreement,” OIF-ITTA-MSA-01.0, Nov. (2008).
- T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997). [CrossRef]
- C. J. Youn, X. Liu, S. Chandrasekhar, Y.-H. Kwon, J.-H. Kim, J. S. Choe, D. J. Kim, K. S. Choi, and E. S. Nam, “Channel estimation and synchronization for polarization-division multiplexed CO-OFDM using subcarrier/polarization interleaved training symbols,” Opt. Express19(17), 16174–16181 (2011). [CrossRef] [PubMed]
- Z. Wang, Y. Qiao, and Y. Ji, “A Novel Joint Frequency Offset and Channel Estimation Method for CO-OFDM System,” Communications and Photonics Conference and Exhibition (ACP) 607–608 (2010).
- S. Cao, S. Zhang, Y. Shaoliang, K. Changyuan, and P.-Y. Kam, “Full range pilot-assisted frequency offset estimation for OFDM systems,” in Proceedings of OFC’13, paper JW2A.53. [CrossRef]
- X.-H. Fan, J. Yu, D. Qian, and G.-K. Chang, “A Fast and Efficient Frequency Offset Correction Technique for Coherent Optical Orthogonal Frequency Division Multiplexing,” J. Lightwave Technol.29(13), 1997–2004 (2011). [CrossRef]
- X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express20(7), 7350–7361 (2012). [CrossRef] [PubMed]
- H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.24(22), 2064–2066 (2012). [CrossRef]
- M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012). [CrossRef]
- P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994). [CrossRef]
- R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011). [CrossRef]
- L. Xiang, S. Chandrasekhar, Z. Benyuan, 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 ROADM,” J. Lightwave Technol.29(4), 483–490 (2011). [CrossRef]
- X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express16(26), 21944–21957 (2008). [CrossRef] [PubMed]
- Z. Xian, Y. Xiaolong, L. Rui, and L. Keping, “Efficient Joint Carrier Frequency Offset and Phase Noise Compensation Scheme for High-Speed Coherent Optical OFDM Systems,” J. Lightwave Technol.31(11), 1755–1761 (2013). [CrossRef]
- W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.20(8), 605–607 (2008). [CrossRef]
- W. Shieh and I. Djordjevic, “Optical Communication Fundamentals,” in OFDM for Optical Communications, 1-st ed. (Academic Press, 2009).
- C.-H. Yih, “BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels,” IEEE Commun. Lett.11(11), 842–844 (2007). [CrossRef]

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