## Adaptive nonlinear Volterra equalizer for mitigation of chirp-induced distortions in cost effective IMDD OFDM systems |

Optics Express, Vol. 21, Issue 22, pp. 26527-26532 (2013)

http://dx.doi.org/10.1364/OE.21.026527

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### Abstract

We report experimental validations of an adaptive 2^{nd} order Volterra equalization scheme for cost effective IMDD OFDM systems. This equalization scheme was applied to both uplink and downlink transmission. Downlink settings were optimized for maximum bitrate where we achieved 34Gb/s over 10km of SSMF using an EML with 10GHz bandwidth. For the uplink, maximum reach was optimized achieving 14Gb/s using a low-cost DML with 2.5GHz bandwidth.

© 2013 OSA

## 1. OFDM for optical access systems

2. X. Q. Jin, E. Hugues-Salas, R. P. Giddings, J. L. Wei, J. Groenewald, and J. M. Tang, “First real-time experimental demonstrations of 11.25Gb/s optical OFDMA PONs with adaptive dynamic bandwidth allocation,” Opt. Express **19**(21), 20557–20570 (2011). [CrossRef] [PubMed]

3. P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Communications **43**(2), 773–775 (1995). [CrossRef]

4. C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett. **36**(2), 151–153 (2011). [CrossRef] [PubMed]

**m**) on a Directly Modulated Laser (DML).

**m**≈10% [5

5. J. L. Wei, C. Sánchez, R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Significant improvements in optical power budgets of real-time optical OFDM PON systems,” Opt. Express **18**(20), 20732–207459 (2010). [CrossRef] [PubMed]

8. C. Xia and W. Rosenkranz, “Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering,” J. Lightwave Technol. **25**(4), 996–1001 (2007). [CrossRef]

## 2. Nonlinear distortions in OFDM IMDD transmission

## 3. Nonlinear Volterra equalizer

^{nd}order. The signal vector

*y⃗*at the output of the filter is calculated as: where

*u⃗*=

*x⃗*[

*n*−

*N*/2 + 1;

*n*+

*N*/2] and

*x⃗*being a vector representing the downsampled received signal,

*L⃗*is the linear FIR filter with size

*N*and

*M*(

*M*+ 1)/2. The schematic of the Volterra equalizer can be seen in Fig. 2. Filter coefficients can be optimized using the Least Mean Squares (LMS) or Recursive Least Squares (RLS) algorithms [8

8. C. Xia and W. Rosenkranz, “Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering,” J. Lightwave Technol. **25**(4), 996–1001 (2007). [CrossRef]

**r**samples per symbol. Although less samples per symbol are available, filter memory for a given number of considered symbols is now smaller improving convergence.

## 4. Experimental set-up

**m**≈60%) and laser bias was set to 16mA, optimizing bitrate for 10km SSMF transmission. The DML biasing was set at 1.1V (41mA), with

**m**≈60% allowing large power budget optimizing reach for a 38km SSMF transmission.

**r**=4 this led to N=8 and M=18.

**r**=3 and

**r**=4, leading to: N=9, M=6 and N=12, M=8, respectively. The latter has shown to lead to 1dB improvement in terms of Received Optical Power (ROP). The results reported in the following were obtained using

**r**=4.

*VPItransmissionMaker Optical Systems*.

## 5. Experimental results

^{−3}we successfully transmitted a bitrate of 34Gb/s (net 30.5Gb/s). After performing Volterra equalization, the system shows improvement when compared to the unequalized system. Although limited, there is improvement for mostly all sub-carriers as seen in Fig. 4(diamonds). This small improvement is expected as the dominating impairment is not SSII but noise.

**m**≈60%, which drives the laser out of the linear regime, thus increasing chirp. Nevertheless 11.63Gb/s (net 10.17Gb/s) transmission was achieved. After Volterra equalization Fig. 5(diamonds), there is an improvement for higher frequency sub-carriers. Lower frequency sub-carriers are affected by receiver noise alone, whereas sub-carriers in the upper half of the frequency range are mostly affected by SSII [6]. At this point, power loading was performed to maintain a flat BER Fig. 5(crosses), where approximately three decades of improvement in terms of average BER are seen when compared to the non-equalized system Fig. 5(squares vs. crosses).

^{−5}) we achieve an increase of ≈22.6% from a bitrate of 11.63Gb/s (net 10.17Gb/s) to a bitrate of 14.25Gb/s (net 12.4Gb/s).

## 6. Conclusion

## Acknowledgments

## References and links

1. | W. Shieh and I. Djordjevic, |

2. | X. Q. Jin, E. Hugues-Salas, R. P. Giddings, J. L. Wei, J. Groenewald, and J. M. Tang, “First real-time experimental demonstrations of 11.25Gb/s optical OFDMA PONs with adaptive dynamic bandwidth allocation,” Opt. Express |

3. | P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Communications |

4. | C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett. |

5. | J. L. Wei, C. Sánchez, R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Significant improvements in optical power budgets of real-time optical OFDM PON systems,” Opt. Express |

6. | W. Yan, B. Liu, L. Li, Z. Tao, T. Takahara, and J. C. Rasmussen, “Nonlinear Distortion and DSP-based Compensation in Metro and Access Networks using Discrete Multi-tone,” in Proceedings of ECOC’2012 (Mo1B2). |

7. | D. Hsu, C. Wei, H. Chen, C. Song, I. Lu, and J. Chen, “74.4% SSII Cancellation in an EAM-based OFDM-IMDD Transmission System,” in Proceedings of OFC/NFOEC’2013 (OM2C7). |

8. | C. Xia and W. Rosenkranz, “Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering,” J. Lightwave Technol. |

9. | W. Yan, T. Tanaka, B. Liu, M. Nishihara, L. Li, T. Takahara, Z. Tao, J. C. Rasmussen, and T. Drenski, “100 Gb/s Optical IM-DD Transmission with 10G-Class Devices Enabled by 65 GSamples/s CMOS DAC Core,” in Proceedings of OFC/NFOEC’2013 (OM3H1). |

**OCIS Codes**

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

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 19, 2013

Revised Manuscript: September 30, 2013

Manuscript Accepted: October 2, 2013

Published: October 28, 2013

**Citation**

Nuno Sequeira André, Kai Habel, Hadrien Louchet, and André Richter, "Adaptive nonlinear Volterra equalizer for mitigation of chirp-induced distortions in cost effective IMDD OFDM systems," Opt. Express **21**, 26527-26532 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26527

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### References

- W. Shieh and I. Djordjevic, OFDM for Optical Communications (Academic Press, 2009).
- X. Q. Jin, E. Hugues-Salas, R. P. Giddings, J. L. Wei, J. Groenewald, and J. M. Tang, “First real-time experimental demonstrations of 11.25Gb/s optical OFDMA PONs with adaptive dynamic bandwidth allocation,” Opt. Express19(21), 20557–20570 (2011). [CrossRef] [PubMed]
- P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Communications43(2), 773–775 (1995). [CrossRef]
- C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett.36(2), 151–153 (2011). [CrossRef] [PubMed]
- J. L. Wei, C. Sánchez, R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Significant improvements in optical power budgets of real-time optical OFDM PON systems,” Opt. Express18(20), 20732–207459 (2010). [CrossRef] [PubMed]
- W. Yan, B. Liu, L. Li, Z. Tao, T. Takahara, and J. C. Rasmussen, “Nonlinear Distortion and DSP-based Compensation in Metro and Access Networks using Discrete Multi-tone,” in Proceedings of ECOC’2012 (Mo1B2).
- D. Hsu, C. Wei, H. Chen, C. Song, I. Lu, and J. Chen, “74.4% SSII Cancellation in an EAM-based OFDM-IMDD Transmission System,” in Proceedings of OFC/NFOEC’2013 (OM2C7).
- C. Xia and W. Rosenkranz, “Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering,” J. Lightwave Technol.25(4), 996–1001 (2007). [CrossRef]
- W. Yan, T. Tanaka, B. Liu, M. Nishihara, L. Li, T. Takahara, Z. Tao, J. C. Rasmussen, and T. Drenski, “100 Gb/s Optical IM-DD Transmission with 10G-Class Devices Enabled by 65 GSamples/s CMOS DAC Core,” in Proceedings of OFC/NFOEC’2013 (OM3H1).

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