## Nonlinearity mitigation for high-speed optical OFDM transmitters using digital pre-distortion |

Optics Express, Vol. 21, Issue 6, pp. 7354-7361 (2013)

http://dx.doi.org/10.1364/OE.21.007354

Acrobat PDF (2179 KB)

### Abstract

Optical orthogonal frequency-division multiplexing (OOFDM) signal is sensitive to nonlinear distortions induced by optical modulators. We propose and experimentally demonstrate a digital pre-distortion (DPD) algorithm to linearize the optical modulators including electro-absorption modulated lasers (EML) and Mach-Zehnder modulators (MZM) used in high-speed OOFDM transmitters. By using an adaptive DPD algorithm with a learning structure, the inverse transfer function of a modulator, which is based on a polynomial model, has been obtained. In the experiment, the performance improvements with and without considering the memory effects of the DPD model are illustrated. The two typical kinds of high-speed OOFDM signals with a bit rate up to 30-Gb/s have been implemented experimentally. The results show that the nonlinear distortion induced by optical modulators can be compensated by using the DPD algorithm to substantially improve the optical modulation index.

© 2013 OSA

## 1. Introduction

1. D. Z. Hsu, C. C. Wei, H. Y. Chen, J. Chen, M. C. Yuang, S. H. Lin, and W. Y. Li, “21 Gb/s after 100 km OFDM long-reach PON transmission using a cost-effective electro-absorption modulator,” Opt. Express **18**(26), 27758–27763 (2010). [CrossRef] [PubMed]

2. W. R. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (>100-Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol. **30**(12), 2025–2034 (2012). [CrossRef]

1. D. Z. Hsu, C. C. Wei, H. Y. Chen, J. Chen, M. C. Yuang, S. H. Lin, and W. Y. Li, “21 Gb/s after 100 km OFDM long-reach PON transmission using a cost-effective electro-absorption modulator,” Opt. Express **18**(26), 27758–27763 (2010). [CrossRef] [PubMed]

2. W. R. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (>100-Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol. **30**(12), 2025–2034 (2012). [CrossRef]

## 2. OOFDM transmitter and polynomial-based DPD algorithm

*λ*

_{1}to

*λ*.

_{N}**E**||

^{2}[6

6. D. R. Morgan, Z. Ma, J. Kim, M. G. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process. **54**(10), 3852–3860 (2006). [CrossRef]

6. D. R. Morgan, Z. Ma, J. Kim, M. G. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process. **54**(10), 3852–3860 (2006). [CrossRef]

**means packing all the polynomials of**

_{polynomial}**w**which consists of

*w*and

_{mk}*w*is coefficients vector of

_{mkl}*M*,

_{sml}*K*are the memory tap and nonlinear order index array in single memory layer and

_{sml}*M*,

_{cml}*K*are for cross memory layer, respectively.

_{cml}*L*is the memory distances of cross memory terms. Thus, in vector form of

_{cml}**E**||

^{2}iswhere (•)

^{H}represents complex conjugate transpose. To lower the estimation error, the DPD coefficients can be trained adaptively with a step size of

*μ*and the iteration function is written as follows [6

6. D. R. Morgan, Z. Ma, J. Kim, M. G. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process. **54**(10), 3852–3860 (2006). [CrossRef]

**w**

_{0}= 0 and

*μ*<1. When Eq. (3) converges, the output of DPD block is as follows,

### Comment on the cost and complexity of DPD algorithm

## 3. Experimental setup and results

^{15}-1) is parallelized and mapped into 16/32/64 QAM symbols. The subcarrier size is 512 and CP overhead is 1/32. The OFDM samples are generated offline in a MATLAB program and uploaded into an arbitrary waveform generator (Tektronix AWG 7122B) which is operated at 12-GS/s. The total bit rates of CVOFDM and RVOFDM signals are 30-Gb/s and 20-Gb/s, respectively. The bandwidth of LPF is 5.5-GHz and up-conversion frequency of CVOFDM signal is 9.3-GHz. The commercial EML and MZM are used as modulators under test in the experiments, respectively. The variable optical attenuator (VOA) is used to control the optical power for PD detection and the signal is then sampled by a real time oscilloscope (Tektronix DSA 72004B) at 50GS/s and 1M samples are recorded each time.

**X**and corresponding output

*S*and

_{r}*S*are respectively received and transmitted symbols; OMI = (

_{t}*V*)

_{in}*/(*

_{RMS}*V*/2), where (

_{max}*V*)

_{in}*is root mean square of the electric input to the optical modulators and*

_{RMS}*V*is maximum input voltage swing of EML, or switch voltage of MZM (

_{max}*V*).

_{π}### 3.1 Experimental results of 30-Gb/s EML-based CVOFDM transmitter

*μ*and memory effect are two key factors to improve the efficacy of the DPD algorithm. Here, the parameters of Eq. (3) chosen were

*M*= {0,1,2,3},

_{sml}*K*= {0,1, …, 5},

_{sml}*M*= {0,1},

_{cml}*K*= {2,4} and

_{cml}*L*= {1,2,3}. If a particular polynomial coefficient is too small, this order and memory product can be ignored. Figure 4(a) shows measured EVM from transmitted 16QAM CVOFDM signal after several iterations under different values of

_{cml}*μ*. Obviously, Eq. (3) with larger

*μ*converges fast but may be unstable and may even cause errors, while small

*μ*reduces error, however converges slowly. Therefore, we chose

*μ*= 0.7 as a tradeoff between the stability and converging speed.

*M*= {0},

_{sml}*K*= {0,1,…,5},

_{sml}*M*,

_{cml}*K*and

_{cml}*L*are null. Then, the different performances with memory or memoryless DPD algorithms can be obtained. Figure 4(b) shows the measured EVMs of the transmitted 16/64QAM OOFDMsignal with the memoryless DPD and memory DPD algorithms. EVMs of 16/32/64QAM OOFDM signals vs. OMI with and without memory DPD algorithms are shown in Fig. 4(c). Here, the OMI range is selected from 18% to 34.5%. From Fig. 4(c), we can see that both the memoryless DPD and memory DPD algorithm can compensate for the nonlinearities of the EML. However, the performance of memory DPD algorithm is better than memoryless DPD. It can also be found that the memory DPD algorithm can improve the OMI over 16.5% to achieve the same EVM of 16/32/64QAM OOFDM signals.

_{cml}### 3.2 Experimental results of 20-Gb/s MZM-based RVOFDM transmitter

*V*, there is a moderate nonlinear distortion and can be compensated by DPD algorithm. However, if the driving voltage is larger than

_{π}*V*, the cosine transfer function leads to severe nonlinear distortion that the output peak signal is not clipped but reversed, which means that the signal falls into a forbidden region. In this case, the proposed DPD algorithm based on polynomials is not capable of modeling its inverse function, which is different from EML. The measured EVM with and without using the DPD algorithm are shown in Fig. 7(b) in which the different regions can be divided based on the improvement of the DPD algorithm. Noise influence can be found in the linear region (blue circles) when OMI is too small. Fortunately, the experimental result also shows that the OMI can be improved from about 9% to 16%.

_{π}## 4. Conclusion

## Acknowledgments

## References and links

1. | D. Z. Hsu, C. C. Wei, H. Y. Chen, J. Chen, M. C. Yuang, S. H. Lin, and W. Y. Li, “21 Gb/s after 100 km OFDM long-reach PON transmission using a cost-effective electro-absorption modulator,” Opt. Express |

2. | W. R. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (>100-Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol. |

3. | Y. T. Moon, J. W. Jang, W. K. Choi, and Y. W. Choi, “Simultaneous noise and distortion reduction of a broadband optical feedforward transmitter for multi-service operation in radio-over-fiber systems,” Opt. Express |

4. | Y. Shen, B. Hraimel, X. Zhang, G. E. R. Cowan, K. Wu, and T. Liu, “A novel analog broadband RF predistortion circuit to linearize electro-absorption modulators in multiband OFDM radio-over-fiber systems,” IEEE Trans. Microw. Theory Tech. |

5. | B. Hraimel and X. Zhang, “A low cost broadband predistortion linearized single drive x-cut Mach-Zehnder modulator for radio-over-fiber systems,” IEEE Photon. Technol. Lett. |

6. | D. R. Morgan, Z. Ma, J. Kim, M. G. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process. |

7. | L. Ding, G. T. Zhou, D. R. Morgan, Z. Ma, J. S. Kenney, J. Kim, and C. R. Giardina, “A robust digital baseband predistorter constructed using memory polynomials,” IEEE Trans. Commun. |

8. | D. J. F. Barros and J. M. Kahn, “Optical modulator optimization for orthogonal frequency-division multiplexing,” J. Lightwave Technol. |

9. | Z. Liu, M. A. Violas, and N. B. Carvalho, “Digital predistortion for RSOAs as external modulators in radio over fiber systems,” Opt. Express |

10. | T. Alves, J. Morgado, and A. Cartaxo, “Linearity improvement of directly modulated PONs by digital pre-distortion of coexisting OFDM-based signals,” in |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(230.4110) Optical devices : Modulators

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: December 28, 2012

Revised Manuscript: March 4, 2013

Manuscript Accepted: March 4, 2013

Published: March 15, 2013

**Citation**

Yuan Bao, Zhaohui Li, Jianping Li, Xinhuan Feng, Bai-ou Guan, and Guifang Li, "Nonlinearity mitigation for high-speed optical OFDM transmitters using digital pre-distortion," Opt. Express **21**, 7354-7361 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-7354

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### References

- D. Z. Hsu, C. C. Wei, H. Y. Chen, J. Chen, M. C. Yuang, S. H. Lin, and W. Y. Li, “21 Gb/s after 100 km OFDM long-reach PON transmission using a cost-effective electro-absorption modulator,” Opt. Express18(26), 27758–27763 (2010). [CrossRef] [PubMed]
- W. R. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (>100-Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol.30(12), 2025–2034 (2012). [CrossRef]
- Y. T. Moon, J. W. Jang, W. K. Choi, and Y. W. Choi, “Simultaneous noise and distortion reduction of a broadband optical feedforward transmitter for multi-service operation in radio-over-fiber systems,” Opt. Express15(19), 12167–12173 (2007). [CrossRef] [PubMed]
- Y. Shen, B. Hraimel, X. Zhang, G. E. R. Cowan, K. Wu, and T. Liu, “A novel analog broadband RF predistortion circuit to linearize electro-absorption modulators in multiband OFDM radio-over-fiber systems,” IEEE Trans. Microw. Theory Tech.58(11), 3327–3335 (2010). [CrossRef]
- B. Hraimel and X. Zhang, “A low cost broadband predistortion linearized single drive x-cut Mach-Zehnder modulator for radio-over-fiber systems,” IEEE Photon. Technol. Lett.24(18), 1571–1573 (2012). [CrossRef]
- D. R. Morgan, Z. Ma, J. Kim, M. G. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process.54(10), 3852–3860 (2006). [CrossRef]
- L. Ding, G. T. Zhou, D. R. Morgan, Z. Ma, J. S. Kenney, J. Kim, and C. R. Giardina, “A robust digital baseband predistorter constructed using memory polynomials,” IEEE Trans. Commun.52(1), 159–165 (2004). [CrossRef]
- D. J. F. Barros and J. M. Kahn, “Optical modulator optimization for orthogonal frequency-division multiplexing,” J. Lightwave Technol.27(13), 2370–2378 (2009). [CrossRef]
- Z. Liu, M. A. Violas, and N. B. Carvalho, “Digital predistortion for RSOAs as external modulators in radio over fiber systems,” Opt. Express19(18), 17641–17646 (2011). [CrossRef] [PubMed]
- T. Alves, J. Morgado, and A. Cartaxo, “Linearity improvement of directly modulated PONs by digital pre-distortion of coexisting OFDM-based signals,” in Proceedings of Advanced Photonics Congress, (Optical Society of America, 2012), paper AW4A.2.

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