## Simple and efficient frequency offset tracking and carrier phase recovery algorithms in single carrier transmission systems |

Optics Express, Vol. 21, Issue 7, pp. 8157-8165 (2013)

http://dx.doi.org/10.1364/OE.21.008157

Acrobat PDF (4561 KB)

### Abstract

In this paper, we propose a low-complexity and efficient carrier recovery algorithm for single carrier transmission systems that is capable of tracking frequency offset (FO) variations. Working as a FO tracking estimator, the algorithm demonstrates good accuracy in simulation and a FO drift of up to 200 MHz/μs can be compensated with minimal degradation in a QPSK system. In 112 Gb/s dual polarization (DP) QPSK experiments, the algorithm recovers a data sequence having >80 MHz of FO drift within 250 μs, providing better performance than a one-time estimator. In a regime that utilizes parallel processing of the data, we further demonstrate FO tracking and carrier phase recovery (CPR) using only one of the streams in a parallelized configuration, and we apply the carrier information to recover neighbouring streams directly. Consequently, the complexity of both the FO tracking and the CPR is further reduced.

© 2013 OSA

## 1. Introduction

## 2. Principle

6. X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett. **24**(1), 82–84 (2012). [CrossRef]

*R*/2,

_{s}*R*/2], where

_{s}*R*is the symbol rate. This wide estimation range is essential especially when a large global FO exists between the transmit laser and the LO.

_{s}*L*determining the tracking time resolution. Before the (

*n*+ 1)

^{th}block is processed for CPR, it is pre-compensated using the estimated FO of the

*n*

^{th}block that is denoted as

*f*. Then the FO increment, ∆

_{o,n}*f*is estimated for the current block, and is added to

_{o,n}*f*to get the FO estimation

_{o,n}*f*

_{o,n+}_{1}, as shown in Fig. 1 and Eq. (1)where

*C*is the pre-determined weighting coefficient of the estimated FO increment. The theoretical value of

*C*is 1. In both simulation and experiments, the value of

*C*can be optimized within 1~2 depending on the expected frequency drift rate, and larger

*C*values usually give better performance when FO drifts fast. Next the updated FO estimation

*f*

_{o,n+}_{1}is used for pre-compensating the next block, and the operations above are repeated. This process gives a good approximation if we choose the block length properly such that the FO drift inside a block is sufficiently small (e.g. several MHz).

*R*/2,

_{s}*R*/2] without ambiguity and the FO drift rate is tolerable to the tracking algorithm, our estimator can keep tracking the FO change and a large FO can be estimated even when it exceeds the limitation of [−

_{s}*R*/2,

_{s}*R*/2]. This benefit is crucial when we use a low-cost laser source with large end-of-life frequency inaccuracy.

_{s}12. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. **27**(8), 989–999 (2009). [CrossRef]

13. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. **27**(7), 901–914 (2009). [CrossRef]

12. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. **27**(8), 989–999 (2009). [CrossRef]

*P*, then for a certain stream, one symbol is extracted every

*P*symbols from the original sequence, as shown in Fig. 2 [14

14. Q. Zhuge, M. Morsy-Osman, X. Xu, M. E. Mousa-Pasandi, M. Chagnon, Z. A. El-Sahn, and D. V. Plant, “Pilot-aided carrier phase recovery for M-QAM using superscalar parallelization based PLL,” Opt. Express **20**(17), 19599–19609 (2012). [CrossRef] [PubMed]

*P*times in each de-multiplexed stream. In other words, the equivalent FO of each stream is

*P*times larger than the original serial sequence.

14. Q. Zhuge, M. Morsy-Osman, X. Xu, M. E. Mousa-Pasandi, M. Chagnon, Z. A. El-Sahn, and D. V. Plant, “Pilot-aided carrier phase recovery for M-QAM using superscalar parallelization based PLL,” Opt. Express **20**(17), 19599–19609 (2012). [CrossRef] [PubMed]

*φ*is estimated based on the previous symbols. This estimated phase error is used to de-rotate the phase of the current symbol

_{k}*r*. Next the symbol is decided, conjugated and multiplied by itself to get the complex error

_{k}*e*. Considering the majority of the FO is pre-compensated based on our algorithm, the phase of

_{k}*e*is small in most cases, so this phase can be approximated by simply extracting the imaginary part of

_{k}*e*as shown in Fig. 4. Then this phase difference is multiplied by a weighting parameter

_{k}*G*and added to the previous phase offset to provide the new estimated phase error. Using this DPLL in one parallel stream, the carrier phase error of each symbol can be obtained. By copying this carrier information directly as shown in Fig. 3, the phase compensation can be easily performed in the neighbouring streams. Therefore, the DPLL can be removed in those streams, and the overall complexity for CPR is reduced. However, the reduced tolerance to the laser phase noise and residual FO is the trade-off of the proposed parallel processing scheme.

## 3. Setup, results and discussions

### 3.1 Simulation evaluation

^{6}symbols is generated and contaminated by the laser phase noise and AWGN. The laser phase noise was modeled as a Wiener process, which results from a total system linewidth of 200 kHz, corresponding to the ~100 kHz linewidths of the ECLs at both the transmitter and the LO, and the optical signal-to-noise ratio (OSNR) is 13.5 dB. Then we set an FO manually and impose the FO-induced phase shift to the symbols. The back-to-back scenario is considered without transmission impairments and other effects. 10

^{4}symbols are allocated to the training sequence, which is used to estimate the initial FO. The phase of the following data symbols are recovered through the DPLL. Differential coding/decoding is employed to avoid the cycle slip.

^{4}symbols. From the simulation result, we can see the variation of the FO is successfully tracked by the proposed algorithm with estimation errors smaller than 1 MHz. This deviation is small enough to be tolerated by CPR algorithms [1

1. L. Li, Z. Tao, S. Oda, T. Hoshida, and J. C. Rasmussen, “Wide-range, accurate and simple digital frequency offset compensator for optical coherent receivers,” in Proc. OFC’08, Paper OWT4. [CrossRef]

*C*value for each case. The FEC limit refers to a BER of 3.8 × 10

^{−3}. From the figure, we can see the performance of DPLL without dynamic FO tracking is degraded significantly as the FO variation rate is increased. The implementation which employs a separate estimation for each block based on the spectrum of the 4th power of the processed symbols [2, 5] is tolerant to FO drifts up to 50 MHz/μs. However, the complexity of this implementation is high. Besides, it does not function well at higher FO variation rate, because the absolute value of the FO in some blocks may exceed the estimation limit of this estimator after FO drifts for a long time. In contrast, with the aid of the proposed FO tracking, FO drifts up to 200 MHz/μs can be compensated with only small degradation. Therefore, by using our FO tracking algorithm the system reliability can be ensured even in an unstable environment where the laser frequency may change abruptly and unpredictably. Moreover, the complexity of the proposed FO tracking is much lower than the implementation using multiple separate estimators.

### 3.2 Experimental validation

16. M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. **36**(5), 605–612 (1988). [CrossRef]

## 4. Conclusion

## References and links

1. | L. Li, Z. Tao, S. Oda, T. Hoshida, and J. C. Rasmussen, “Wide-range, accurate and simple digital frequency offset compensator for optical coherent receivers,” in Proc. OFC’08, Paper OWT4. [CrossRef] |

2. | M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC '09, Paper P3.08. |

3. | J. C. M. Diniz, J. C. R. F. de Oliveira, E. S. Rosa, V. B. Ribeiro, V. E. S. Parahyba, R. da Silva, E. P. da Silva, L. H. H. de Carvalho, A. F. Herbster, and A. C. Bordonalli, “Simple feed-forward wide-range frequency offset estimator for optical coherent receivers,” Opt. Express |

4. | T. Nakagawa, K. Ishihara, T. Kobayashi, R. Kudo, M. Matsui, Y. Takatori, and M. Mizoguchi, “Wide-range and fast-tracking frequency offset estimator for optical coherent receivers,” in Proc. ECOC’10, Paper We.7.A.2. [CrossRef] |

5. | T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Proc. OFC’11, Paper OMJ1. |

6. | X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett. |

7. | A. Leven, N. Kaneda, U. Koc, and Y. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. |

8. | P. Gianni, G. Corral-Briones, C. E. Rodriguez, H. S. Carrer, and M. R. Hueda, “A new parallel carrier recovery architecture for intradyne coherent optical receivers in the presence of laser frequency fluctuations,” in Proc. IEEE GLOBECOM’11, pp. 1–6. [CrossRef] |

9. | S.-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. |

10. | M. Qiu, Q. Zhuge, X. Xu, M. Chagnon, M. Morsy-Osman, and D. V. Plant, “Wide-range, low-complexity frequency offset tracking technique for single carrier transmission systems,” in Proc. OFC’13, Paper OTu3I.8. |

11. | E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. |

12. | T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. |

13. | M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. |

14. | Q. Zhuge, M. Morsy-Osman, X. Xu, M. E. Mousa-Pasandi, M. Chagnon, Z. A. El-Sahn, and D. V. Plant, “Pilot-aided carrier phase recovery for M-QAM using superscalar parallelization based PLL,” Opt. Express |

15. | Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron. |

16. | M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.5060) Fiber optics and optical communications : Phase modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: February 6, 2013

Revised Manuscript: March 16, 2013

Manuscript Accepted: March 18, 2013

Published: March 28, 2013

**Citation**

Meng Qiu, Qunbi Zhuge, Xian Xu, Mathieu Chagnon, Mohamed Morsy-Osman, and David V. Plant, "Simple and efficient frequency offset tracking and carrier phase recovery algorithms in single carrier transmission systems," Opt. Express **21**, 8157-8165 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8157

Sort: Year | Journal | Reset

### References

- L. Li, Z. Tao, S. Oda, T. Hoshida, and J. C. Rasmussen, “Wide-range, accurate and simple digital frequency offset compensator for optical coherent receivers,” in Proc. OFC’08, Paper OWT4. [CrossRef]
- M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC '09, Paper P3.08.
- J. C. M. Diniz, J. C. R. F. de Oliveira, E. S. Rosa, V. B. Ribeiro, V. E. S. Parahyba, R. da Silva, E. P. da Silva, L. H. H. de Carvalho, A. F. Herbster, and A. C. Bordonalli, “Simple feed-forward wide-range frequency offset estimator for optical coherent receivers,” Opt. Express19(26), B323–B328 (2011). [CrossRef] [PubMed]
- T. Nakagawa, K. Ishihara, T. Kobayashi, R. Kudo, M. Matsui, Y. Takatori, and M. Mizoguchi, “Wide-range and fast-tracking frequency offset estimator for optical coherent receivers,” in Proc. ECOC’10, Paper We.7.A.2. [CrossRef]
- T. Nakagawa, M. Matsui, T. Kobayashi, K. Ishihara, R. Kudo, M. Mizoguchi, and Y. Miyamoto, “Non-data-aided wide-range frequency offset estimator for QAM optical coherent receivers,” in Proc. OFC’11, Paper OMJ1.
- X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett.24(1), 82–84 (2012). [CrossRef]
- A. Leven, N. Kaneda, U. Koc, and Y. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007). [CrossRef]
- P. Gianni, G. Corral-Briones, C. E. Rodriguez, H. S. Carrer, and M. R. Hueda, “A new parallel carrier recovery architecture for intradyne coherent optical receivers in the presence of laser frequency fluctuations,” in Proc. IEEE GLOBECOM’11, pp. 1–6. [CrossRef]
- S.-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]
- M. Qiu, Q. Zhuge, X. Xu, M. Chagnon, M. Morsy-Osman, and D. V. Plant, “Wide-range, low-complexity frequency offset tracking technique for single carrier transmission systems,” in Proc. OFC’13, Paper OTu3I.8.
- E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol.25(9), 2675–2692 (2007). [CrossRef]
- T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol.27(8), 989–999 (2009). [CrossRef]
- M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol.27(7), 901–914 (2009). [CrossRef]
- Q. Zhuge, M. Morsy-Osman, X. Xu, M. E. Mousa-Pasandi, M. Chagnon, Z. A. El-Sahn, and D. V. Plant, “Pilot-aided carrier phase recovery for M-QAM using superscalar parallelization based PLL,” Opt. Express20(17), 19599–19609 (2012). [CrossRef] [PubMed]
- Z. Tao, L. Li, L. Liu, W. Yan, H. Nakashima, T. Tanimura, S. Oda, T. Hoshida, and J. C. Rasmussen, “Improvements to digital carrier phase recovery algorithm for high-performance optical coherent receivers,” IEEE J. Sel. Top. Quantum Electron.16(5), 1201–1209 (2010). [CrossRef]
- M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun.36(5), 605–612 (1988). [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.