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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8157–8165
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Simple and efficient frequency offset tracking and carrier phase recovery algorithms in single carrier transmission systems

Meng Qiu, Qunbi Zhuge, Xian Xu, Mathieu Chagnon, Mohamed Morsy-Osman, and David V. Plant  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8157-8165 (2013)
http://dx.doi.org/10.1364/OE.21.008157


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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

The FO estimator in our algorithm is capable of tracking the FO between the transmit laser and the LO. It includes two parts: a) the initial FO estimation; and b) FO drift tracking. The initial FO estimation gives the overall frequency mismatch of the received sequence. To achieve this we use the training-symbol-aided method described in [6

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]

]. This algorithm gives a FO estimation range of [−Rs/2, Rs/2], where Rs is the symbol rate. This wide estimation range is essential especially when a large global FO exists between the transmit laser and the LO.

In addition to a reduction in complexity, the proposed FO tracking algorithm has other benefits. Firstly, our estimator can compensate the FO dynamically. By doing this, the residual FO is always minimized such that it can be tolerated by CPR algorithms even in the presence of FO drifts. Next, the tracking algorithm estimates the FO increment rather than measure the absolute FO. Therefore, if the initial FO can be estimated within [−Rs/2, Rs/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 [−Rs/2, Rs/2]. This benefit is crucial when we use a low-cost laser source with large end-of-life frequency inaccuracy.

In high data rate systems parallelization and pipelining are used [12

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

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

]. Specifically, received sequences are de-multiplexed into multiple parallel streams and each stream is processed individually. We note that the parallelization process not only enhances phase noise induced impairments [12

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]

] but also amplifies the influence of the FO and its drift. Specifically, if the degree of parallelism is denoted by P, then for a certain stream, one symbol is extracted every P symbols from the original sequence, as shown in Fig. 2
Fig. 2 The implementation of parallelization.
[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]

]. Therefore, the FO-induced phase shift between adjacent symbols is increased by 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.

3. Setup, results and discussions

3.1 Simulation evaluation

First we investigate the regime without parallelization. In this simulation, a 28-Gbaud QPSK sequence with 1.12 × 106 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. 104 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.

Figure 5(a)
Fig. 5 (a) FO evolution and the estimations using the proposed tracking algorithm. (b) BER versus FO drift rate for systems with different tracking strategies.
shows a specific case when the initial FO is 1 GHz, the FO drift rate is 2 MHz/μs and the block length is 104 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]

]. Figure 5(b) demonstrates our algorithm’s tolerance to a very high FO drift rate assuming the FO drifts linearly in each simulation. The bit error rates (BER) in this figure are obtained under the optimized parameters of the DPLL and 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

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.

, 5

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.

] 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

The received symbols are interleaved into 8 streams and processed in parallel for the carrier recovery. In the 5th stream, the FO tracking is performed using the proposed FO estimator, and the CPR and symbol decision is achieved through a DPLL and differential coding/decoding. After the FO and carrier phase errors are obtained in the 5th stream, they are shared to recover the other 7 streams. We obtained a serial sequence containing 7.02 × 106 symbols in total, corresponding to a time duration of 250.71 μs in the 28 Gbaud system. The block length is 2000 in each parallel stream, which enables a time resolution of 0.571 μs considering the degree of parallelism is 8. The value of K is 50, which means we calculate the phase increment every 50 symbols.

Figure 9 (a)
Fig. 9 (a) Estimated FO versus time and (b) BER versus sequence length for systems with and without FO tracking.
depicts the estimated FO variation based on the proposed algorithm. During the time duration of 250 μs, the FO drifts approximately 88 MHz, which amounts to an average drift rate of approximately 0.35 MHz/μs. The black stars represent the FO estimations of the discrete data sections which are estimated based on the spectrum of the 4th power of the processed symbols. From the comparison, we can see the results based on our approach match the values given by the spectral approach. However, the complexity of the proposed algorithm is much lower.

Finally the BER of the different parallel streams are compared, which is shown in Fig. 10
Fig. 10 BER of different parallel streams when the degree of parallelism is (a) 8, (b) 16 and (c) 32.
. The cases with parallelism degree equal to 8, 16 and 32 are investigated using the data above. In these three cases, the FO tracking and the DPLL-based CPR are employed in the 5th stream, the 9th stream and the 17th stream, respectively. The BER level without parallel processing is also plotted as a reference. As a result of parallelization, the performance of each stream is degraded slightly compared with the serial case as shown in Fig. 10, because the effects of the FO and phase noise are enhanced in each stream after interleaving. However, a similar performance among the different streams is observed, thus validating the proposed parallel processing scheme up to a parallelism degree of 32.

4. Conclusion

In this paper, we propose a low-complexity and efficient carrier recovery algorithm for the optical coherent receiver in single carrier systems. Working as a frequency offset (FO) estimator, it is capable of tracking the FO variation with low complexity. In simulation, it gives accurate FO estimations with small errors, and FO drifts up to 200 MHz/μs can be compensated effectively for QPSK signals. Experimentally we successfully recovered a data sequence having >80 MHz FO drift in a 112 Gb/s DP-QPSK system. We show that the algorithm maintains good system performance in the presence of FO drift, which is in contrast with the significant degradation in the configuration without tracking mechanisms. In the regime with parallelization, we also demonstrate that the carrier information in one stream can be shared with other parallel streams. This further reduces the overall complexity for both the FO tracking and carrier phase recovery (CPR).

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 19(26), B323–B328 (2011). [CrossRef] [PubMed]

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. 24(1), 82–84 (2012). [CrossRef]

7.

A. Leven, N. Kaneda, U. Koc, and Y. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007). [CrossRef]

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. 29(13), 1997–2004 (2011). [CrossRef]

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. 25(9), 2675–2692 (2007). [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]

13.

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

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]

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(5), 1201–1209 (2010). [CrossRef]

16.

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

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


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References

  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. Express19(26), B323–B328 (2011). [CrossRef] [PubMed]
  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.24(1), 82–84 (2012). [CrossRef]
  7. A. Leven, N. Kaneda, U. Koc, and Y. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007). [CrossRef]
  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.29(13), 1997–2004 (2011). [CrossRef]
  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.25(9), 2675–2692 (2007). [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]
  13. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol.27(7), 901–914 (2009). [CrossRef]
  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. Express20(17), 19599–19609 (2012). [CrossRef] [PubMed]
  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(5), 1201–1209 (2010). [CrossRef]
  16. M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun.36(5), 605–612 (1988). [CrossRef]

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