## On the long-memory filtering gain in optical high-order QAM transmission systems |

Optics Express, Vol. 21, Issue 9, pp. 11021-11030 (2013)

http://dx.doi.org/10.1364/OE.21.011021

Acrobat PDF (1642 KB)

### Abstract

In this paper, we verify the effectiveness of the last-stage long memory filter (LMF) in mitigating the long-memory response (LMR) of hardware, i.e. the transmitter and receiver. Based on the experimental results, we draw the following conclusions: 1) LMF can effectively mitigate the LMR impact, such as transmitter reflections, and its efficiency is more significant for high-order QAM signals. 2) Using LMF, a partially-correlated pattern exhibits similar performance to that of an uncorrelated pattern both in back-to-back and after 320-km standard single mode fiber (SSMF) transmission. Moreover, a simple solution to the computational complexity of LMF, effective-tap (ET) LMF, is proposed and demonstrated.

© 2013 OSA

## 1. Introduction

## 2. Working principle

*y*is the output of LMF,

_{k}*k*is the discrete-time sample,

*N*is the tap length of LMF,

_{t}*C*is the tap weights or coefficients, and

_{k}*s*is the input to LMF. The tap coefficients

_{k}*C*are adaptively adjusted by the error vector between the filter output

_{k}*y*and the filter input

_{k}*s*via, for instance, the LMS algorithm [7].

_{k}*N*complex multiplications. Since the memory length of LMR would last over one hundred-symbol duration, the computational cost and consumed power would be too high to be affordable for the receiver digital signal processors. Although such a long tap-length filter could be realized in the frequency domain to reduce the required computations, adaptivity would remain an issue that cannot easily be accommodated in a frequency-domain filter. As a matter of fact, since the LMR results from the hardware which should be relatively stable, only specific taps that correspond to the LMR would really take effect during LMF equalization. Hence, we propose an ET-LMF for LMR equalization, of which the concept is depicted in Fig. 1(b). The ET-LMF identifies and only utilizes the “effective taps” for equalization, where the effective taps are selected if their tap amplitudes after equalization are higher than a predefined threshold, γ. To determine which taps are effective to be used, one possible approach is to perform an offline identification that firstly uses an adaptive FT-LMF and, after convergence, pick up the taps with amplitudes greater than γ for the on-line ET-LMFoperation. Obviously, the effective tap number will be a function of γ and decrease with the increase of γ. Since the LMR would occur only at some specific timing, rather than distributing over the time domain, the required tap number (only the effective ones) of ET-LMF could be much fewer than that of previous FT-LMF, thus greatly saving the required computations. Notably, the ET-LMF would still have a long memory length (but with fewer taps), which is determined by the maximum temporal spacing between any two effective taps. As can be expected, there exists a trade-off between the required tap number and the LMF gain, which will be observed in Section 4.

_{t}## 3. Experimental setup

## 4. Results and discussions

*C*|) after full-tap (401 taps) equalization. To determine the effective taps we define a threshold γ for which the taps are defined as effective and to be used for ET-LMF if |

_{k}*C*| ≥ γ. This method will exclude those ineffective taps for equalization, therefore greatly reducing the tap number while sacrificing limitedly the LMF gain. The ET-LMF gain vs. γ is given in Fig. 7(b), and the required tap number for each polarization is also depicted. We find that the ET-LMF gain is > 0.6 dB with a required tap number of ~66 (at γ = 1.25e-3), and still > 0.5 dB with a tap number of only ~31 (at γ = 2.5e-3). This clearly illustrates the complexity reduction achieved by the proposed ET-LMF.

_{k}## 5. Conclusion

## Acknowledgment

## References and links

1. | A. Sano, T. Kobayashi, S. Yamanaka, A. Matsuura, H. Kawakami, Y. Miyamoto, K. Ishihara, and H. Masuda, “102.3-Tb/s (224x548-Gb/s) C- and extended L-band all-Raman transmission over 240 km using PDM-64QAM single carrier FDM with digital pilot tone,” |

2. | X. Zhou, L. E. Nelson, R. Isaac, P. D. Magill, B. Zhu, D. W. Peckham, P. Borel, and K. Carlson, “4000 km transmission of 50GHz spaced, 10x494.85-Gb/s hybrid 32-64QAM using cascaded equalization and training-assisted phase recovery,” |

3. | J. Yu, Z. Dong, H.-C. Chien, X. Xiao, Z. Jia, and N. Chi, “30-Tb/s (3×12.84-Tb/s) signal transmission over 320km using PDM 64-QAM Modulation,” |

4. | W.-R. Peng, H. Takahashi, T. Tsuritani, and I. Morita, “DAC-free generation and 1200-km transmission of 41-GBd PDM-64QAM using a single I/Q modulator,” |

5. | W.-R. Peng, H. Takahashi, T. Tsuritani, and I. Morita, “50-GHz-spaced, 8x499-Gb/s WDM transmission over 720-km SSMF using per-channel 41.6-GBd PDM-64QAM,” |

6. | D. Chang, F. Yu, Z. Xiao, Y. Li, N. Stojanovic, C. Xie, X. Shi, X. Xu, and Q. Xiong, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10 |

7. | S. Haykin, |

8. | M. J. Ready and R. P. Gooch, “Blind equalization based on radius directed adaptation,” |

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

10. | ITU-T Recommendation G.975.1, Appendix I.9 (2004). |

**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:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 18, 2013

Revised Manuscript: February 24, 2013

Manuscript Accepted: February 24, 2013

Published: April 26, 2013

**Citation**

Wei-Ren Peng, Hidenori Takahashi, Takehiro Tsuritani, and Itsuro Morita, "On the long-memory filtering gain in optical high-order QAM transmission systems," Opt. Express **21**, 11021-11030 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11021

Sort: Year | Journal | Reset

### References

- A. Sano, T. Kobayashi, S. Yamanaka, A. Matsuura, H. Kawakami, Y. Miyamoto, K. Ishihara, and H. Masuda, “102.3-Tb/s (224x548-Gb/s) C- and extended L-band all-Raman transmission over 240 km using PDM-64QAM single carrier FDM with digital pilot tone,” in the Proceedings of OFC’2012, paper PDP5C3 (2012).
- X. Zhou, L. E. Nelson, R. Isaac, P. D. Magill, B. Zhu, D. W. Peckham, P. Borel, and K. Carlson, “4000 km transmission of 50GHz spaced, 10x494.85-Gb/s hybrid 32-64QAM using cascaded equalization and training-assisted phase recovery,” in the Proceedings of OFC’2012, paper PDP5C6 (2012).
- J. Yu, Z. Dong, H.-C. Chien, X. Xiao, Z. Jia, and N. Chi, “30-Tb/s (3×12.84-Tb/s) signal transmission over 320km using PDM 64-QAM Modulation,” in the Proceedings of OFC’2012, paper OM2A4 (2012).
- W.-R. Peng, H. Takahashi, T. Tsuritani, and I. Morita, “DAC-free generation and 1200-km transmission of 41-GBd PDM-64QAM using a single I/Q modulator,” in Proceedings of OECC’2012, paper PDP1–3 (2012).
- W.-R. Peng, H. Takahashi, T. Tsuritani, and I. Morita, “50-GHz-spaced, 8x499-Gb/s WDM transmission over 720-km SSMF using per-channel 41.6-GBd PDM-64QAM,” in Proceedings of ACP’2012, paper AF4C.1 (2012).
- D. Chang, F. Yu, Z. Xiao, Y. Li, N. Stojanovic, C. Xie, X. Shi, X. Xu, and Q. Xiong, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15” in Proceedings of OFC’2011, paper OTuN2 (2011).
- S. Haykin, Adaptive Filter Theory, 4th ed. (Prentice-Hall, 2002), Chap 5.
- M. J. Ready and R. P. Gooch, “Blind equalization based on radius directed adaptation,” in Proceedings of IEEE ICASSP’1990, pp.1699–1702 (1990). [CrossRef]
- T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed-forward carrier recovery for M-QAM constellations,” J. Lightwave Technol.27(8), 989–999 (2009). [CrossRef]
- ITU-T Recommendation G.975.1, Appendix I.9 (2004).

## 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.