## Per-symbol-based digital back-propagation approach for PDM-CO-OFDM transmission systems |

Optics Express, Vol. 21, Issue 2, pp. 1547-1554 (2013)

http://dx.doi.org/10.1364/OE.21.001547

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### Abstract

For polarization-division-multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) systems, we propose a per-symbol-based digital back-propagation (DBP) approach which, after cyclic prefix removal, conducts DBP for each OFDM symbol. Compared with previous DBP, this new proposal avoids the use of inefficient overlap-and-add operation and saves one fast Fourier transform (FFT) module, therefore simplifying the hardware implementation. Transmitting a 16-QAM, 42.8-Gb/s PDM-CO-OFDM signal over 960-km standard single mode fiber (SSMF), we compare the previous and the proposed DBP approaches with different receiver’s sampling rates and different step lengths in each DBP iteration, and found that the proposed DBP can achieve a similar performance as that of the previous DBP while enjoying a simpler implementation. We have also specifically introduced a small self-phase modulation (SPM) model for DBP and demonstrated its feasibility with the same experimental setup.

© 2013 OSA

## 1. Introduction

1. M. G. Taylor, “Coherent detection method using DSP for demodulation signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. **16**(2), 674–676 (2004). [CrossRef]

2. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express **16**(2), 880–888 (2008). [CrossRef] [PubMed]

4. D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1217–1226 (2010). [CrossRef]

3. E. Ip, “Nonlinear compensation using back-propagation for polarization-multiplexed transmission” IEEE/OSA,” J. Lightwave Technol. **28**(6), 939–951 (2010). [CrossRef]

## 2. Working principle

3. E. Ip, “Nonlinear compensation using back-propagation for polarization-multiplexed transmission” IEEE/OSA,” J. Lightwave Technol. **28**(6), 939–951 (2010). [CrossRef]

8. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4,160-km SSMF,” IEEE/OSA J. Lightwave Technol. **26**(1), 6–15 (2008). [CrossRef]

9. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express **16**(2), 841–859 (2008). [CrossRef] [PubMed]

2. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express **16**(2), 880–888 (2008). [CrossRef] [PubMed]

3. E. Ip, “Nonlinear compensation using back-propagation for polarization-multiplexed transmission” IEEE/OSA,” J. Lightwave Technol. **28**(6), 939–951 (2010). [CrossRef]

2. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express **16**(2), 880–888 (2008). [CrossRef] [PubMed]

*X*(

*n*) and

*Y*(

*n*) are the NLC input waveforms in X and Y polarizations,

*j*is the imaginary unit,

*α*and

*β*represent the nonlinear coefficients which are functions of the fiber type (effective core area, nonlinear refractive index, and loss etc.), distance, and launch power. After the DBP circuit, a regular OFDM receiver is followed with RF-pilot-based phase noise compensation (PN), cyclic prefix (CP) removal, FFT, channel estimation with training symbols and multiple-input-multiple-output (MIMO) equalization. Notably, in this case the price of nonlinear compensation is the requirement for the extra four blocks of OA-FFT, OA-IFFT, CDC, and NLC.

*N*, the useful size as

_{FFT}*N*(samples not discarded during overlap-and-add method), and the required iterative number as

_{U}*M*, then the total required multiplications for each OFDM symbol in each polarization could be expressed as (assuming

*α*=

*β*and the exponential function implemented with a lookup table):where the first term considers the iterative DBP circuit including OA-FFT/IFFT, CDC, and NLC, and the second considers the regular FFT circuit right before MIMO processing. In the proposed DBP method, if we denote the FFT/IFFT size as

*N*, and the required iterative number as

_{FFT}*M*, then the total required multiplications for each OFDM symbol in each polarization could be expressed as:

## 3. Experimental setup

## 4. Results and discussions

*α*=

*β*which yields the optimum performance according to our observations and the previous reports [5], and present the signal quality in terms of Q factor which is derived from the calculated bit error rate (BER). Only the regular SPM model, i.e. Eq. (1), is used for NLC in Figs. 3 and 4, and both the regular and small SPM models are used in Fig. 5 to compare their performance. Since the proposed method has some hardware benefits over the conventional method, questions might arise such as whether similar performance to that of the conventional one could be maintained with different system parameters. Therefore in the following we investigate performance sensitivities against the receiver sampling rate and used step length per step (required iterations in DBP).

**28**(6), 939–951 (2010). [CrossRef]

4. D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1217–1226 (2010). [CrossRef]

## 5. Conclusion

## Acknowledgment

## References and links

1. | M. G. Taylor, “Coherent detection method using DSP for demodulation signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. |

2. | X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express |

3. | E. Ip, “Nonlinear compensation using back-propagation for polarization-multiplexed transmission” IEEE/OSA,” J. Lightwave Technol. |

4. | D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. |

5. | L. Du, B. Schmidt, and A. J. Lowery, “Efficient digital backpropagation for PDM-CO-OFDM optical transmission systems,” in |

6. | W.-R. Peng, H. Takahashi, I. Morita, and T. Tsuritani, “Per-symbol-based digital back propagation approach for PDM-CO-OFDM transport systems,” in |

7. | G. Agrawal, |

8. | S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4,160-km SSMF,” IEEE/OSA J. Lightwave Technol. |

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

10. | L. R. Rabiner and B. Gold, Theory and application of digital signal processing, Englewood Cliffs, Prentice-Hall, 1975. |

**OCIS Codes**

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

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Subsystems for Optical Networks

**History**

Original Manuscript: October 2, 2012

Revised Manuscript: December 3, 2012

Manuscript Accepted: December 3, 2012

Published: January 15, 2013

**Virtual Issues**

European Conference on Optical Communication 2012 (2012) *Optics Express*

**Citation**

Wei-Ren Peng, Hidenori Takahashi, Itsuro Morita, and Takehiro Tsuritani, "Per-symbol-based digital back-propagation approach for PDM-CO-OFDM transmission systems," Opt. Express **21**, 1547-1554 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1547

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### References

- M. G. Taylor, “Coherent detection method using DSP for demodulation signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004). [CrossRef]
- X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express16(2), 880–888 (2008). [CrossRef] [PubMed]
- E. Ip, “Nonlinear compensation using back-propagation for polarization-multiplexed transmission” IEEE/OSA,” J. Lightwave Technol.28(6), 939–951 (2010). [CrossRef]
- D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron.16(5), 1217–1226 (2010). [CrossRef]
- L. Du, B. Schmidt, and A. J. Lowery, “Efficient digital backpropagation for PDM-CO-OFDM optical transmission systems,” in Proceedings of OFC’2010, paper OTuE2 (2010).
- W.-R. Peng, H. Takahashi, I. Morita, and T. Tsuritani, “Per-symbol-based digital back propagation approach for PDM-CO-OFDM transport systems,” in Proceedings of ECOC’12, paper Th2A6 (2012).
- G. Agrawal, Nonlinear fiber optics, 3rd ed. (Academic Press, 2001).
- S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4,160-km SSMF,” IEEE/OSA J. Lightwave Technol.26(1), 6–15 (2008). [CrossRef]
- W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express16(2), 841–859 (2008). [CrossRef] [PubMed]
- L. R. Rabiner and B. Gold, Theory and application of digital signal processing, Englewood Cliffs, Prentice-Hall, 1975.

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