## Fast dispersion estimation in coherent optical 16QAM fast OFDM systems |

Optics Express, Vol. 21, Issue 2, pp. 2500-2505 (2013)

http://dx.doi.org/10.1364/OE.21.002500

Acrobat PDF (1034 KB)

### Abstract

Fast channel estimation is crucial to increase the payload efficiency which is of particular importance for optical packet networks. In this paper, we propose a novel least-square based dispersion estimation method in coherent optical fast OFDM (F-OFDM) systems. Additionally, we experimentally demonstrate for the first time a 37.5 Gb/s 16QAM coherent F-OFDM system with 480 km transmission using the proposed scheme. The results show that this method outperforms the conventional channel estimation methods in minimizing the overhead load. A single training symbol can achieve near-optimum channel estimation without any prior information of the transmission distance. This makes optical F-OFDM a very promising scheme for the future burst-mode applications.

© 2013 OSA

## 1. Introduction

8. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s-1 line-rate superchannel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics **5**(6), 364–371 (2011). [CrossRef]

2. B. Inan, S. Adhikari, O. Karakaya, P. Kainzmaier, M. Mocker, H. von Kirchbauer, N. Hanik, and S. L. Jansen, “Real-time 93.8-Gb/s polarization-multiplexed OFDM transmitter with 1024-point IFFT,” Opt. Express **19**(26), B64–B68 (2011). [CrossRef] [PubMed]

4. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express **16**(26), 21944–21957 (2008). [CrossRef] [PubMed]

5. B. Liu, L. Zhang, X. Xin, and J. Yu, “None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying,” Opt. Express **20**(20), 22878–22885 (2012). [CrossRef] [PubMed]

10. J. Zhao and A. D. Ellis, “Advantage of optical fast OFDM over OFDM in residual frequency offset compensation,” IEEE Photon. Technol. Lett. **24**(24), 2284–2287 (2012). [CrossRef]

10. J. Zhao and A. D. Ellis, “Advantage of optical fast OFDM over OFDM in residual frequency offset compensation,” IEEE Photon. Technol. Lett. **24**(24), 2284–2287 (2012). [CrossRef]

11. J. Zhao and A. D. Ellis, “Transmission of 4-ASK optical fast OFDM with chromatic dispersion compensation,” IEEE Photon. Technol. Lett. **24**(1), 34–36 (2012). [CrossRef]

## 2. Principle

*H*(

*ω*), at frequency

*ω*can be written as:where

_{i}*H*(

_{s}*ω*) represents the static response at

_{i}*ω*regardless of the transmission paths of the packets, including the transfer functions of the modulator, drive amplifier, and receiver.

_{i}*A*and

*D*are the channel gain/loss and the accumulated CD value respectively. These parameters are unknown and may vary packet by packet.

_{a}*H*(

*ω*) may be obtained using TSs. Because

*H*(

_{s}*ω*) is fixed for all received packets and can be readily obtained beforehand, we define the estimated normalized frequency response,

_{i}*H*

_{m}(

*ω*), at frequency

*ω*by using

_{i}*m*TSs as:where

*d*(

_{j}*ω*) and

_{i}*a*

_{j}(

*ω*) are the received and transmitted data at frequency

_{i}*ω*for the

_{i}*j*

^{th}F-OFDM symbol. In Eq. (2), the number,

*m*, should be sufficient to mitigate the noise effect on

*H*(

_{m}*ω*), which however increases the overhead or reduces the payload efficiency.

_{i}*A*and

*D*, that require rapid estimation for each packet. The proposed method finds the parameter values for the model Eq. (1) that best fit

_{a}*H*(

_{m}*ω*) with the minimal overhead. We define the sum of the squares of the errors between

_{i}*H*(

_{m}*ω*) and the fitted values provided by Eq. (1),

_{i}*S*(

*A*,

*D*), as:where

_{a}*N*represents the number of subcarriers in the TS used for the parameter estimation.

*A*and

*D*are estimated by minimizing

_{a}*S*(

*A*,

*D*) and setting the gradient to zero:Equations (3)-(4) result in a nonlinear least-square problem, which can be solved by choosing initial values for

_{a}*A*and

*D*and then refining the parameters iteratively. Assuming the initial values are

_{a}*A*and

_{1}*D*, we linearize the model by using the first-order Taylor series expansion:

_{a,1}*A*and

*D*: where

_{a}*k*is the iteration number. Typically, near-optimal parameter values can be obtained after only several iterations. The initial values of

*A*and

*D*depend on the amount of prior information. In this paper, we assume that no prior information is available, and set

_{a}*A*as |

_{1}*H*(

_{m}*ω*)|. The initial value,

_{1}*D*, is set as:As Eq. (8) is only used to obtain the initial coarse estimate of

_{a,1}*D*, it does not require extensive search with fine resolutions. The principle of this method can be extended to polarization multiplexed systems where the channel gain/loss should be replaced by a 2 × 2 matrix.

_{a}## 3. Experimental setup

*V*

_{π}to avoid nonlinear distortion. The generated optical signal was amplified by an erbium doped fiber amplifier (EDFA), filtered by a 0.8-nm optical band-pass filter (OBPF), and transmitted over a recirculating loop comprising 60-km single-mode fiber (SMF) with 14-dB fiber loss. The noise figure of the EDFA was 5 dB and another 0.8-nm OBPF was used in the loop to suppress the amplified spontaneous emission noise. The launch power per span was around −5.5 dBm.

*H*(

_{m}*ω*) was further averaged over multiple adjacent subcarriers. The subcarrier number for averaging was 5, which was verified by additional results to obtain the near-optimum performance; 3) the proposed method where

_{i}*H*(

_{m}*ω*) was employed to estimate

_{i}*A*and

*D*that were then used to reconstruct the channel response based on Eq. (1). 2400 F-OFDM symbols were measured, giving a total number of measured 16QAM symbols of 240,000.

_{a}## 4. Experimental results

^{−3}was ~16 dB, and the penalties after 360 km and 480 km were around 1 dB and 2 dB respectively. This penalty may have been caused by the de-polarization during transmission. When the number of TSs was reduced to one, the estimated channel response was highly distorted by the noise, resulting in significantly degraded performance when the conventional method (pluses) was applied. ISFA improved the performance but still exhibited large performance penalties. On the other hand, the proposed method with

*m*= 1 could achieve similar performance as that with

*m*= 20. Insets of Fig. 2(a) illustrate the constellation diagrams of the 16QAM F-OFDM at 19.6 dB OSNR and confirm the performance advantage of the proposed method. Figure 2(b) shows the BER versus the transmission distance for three aforementioned methods when single TS was used. The OSNR values for 0, 120, 240, 360 and 480 km were 18.4, 19, 19, 19.2, and 19.6 dB respectively. It can be seen that the conventional method resulted in the poorest performance, with BER of ~10

^{−2}for all distances. ISFA mitigated the noise effect by averaging

*H*(

_{m}*ω*) over multiple subcarriers. When the proposed method was applied, the performance was the best with more than one order of magnitude BER improvement when compared to the conventional method.

_{i}*m*= 1. The curve for the ISFA method is smoother due to the reduced noise effect. In the proposed method,

*A*and

*D*can be well estimated from an over-determined system, in which the subcarrier number of the TSs is more than the unknowns. The solid curves in Fig. 3 are actually the fitting curves of

_{a}*H*(

_{1}*ω*) based on the model of Eq. (1) that greatly reduce the noise effect.

_{i}*A*

_{1}and

*D*

_{a,1}. Figure 4(b) shows the BER versus the iteration number. The OSNR values for 360 and 480 km were 19.2 and 19.6 dB, respectively. It can be seen that one iteration could obtain the optimal BER for both distances.

## 5. Conclusions

## Acknowledgments:

## References and links

1. | L. A. Neto, A. Gharba, P. Chanclou, N. Genay, B. Charbonnier, M. Ouzzif, C. A. Berthelemot, and J. L. Masson, “High bit rate burst mode optical OFDM for next generation passive optical networks,” in |

2. | B. Inan, S. Adhikari, O. Karakaya, P. Kainzmaier, M. Mocker, H. von Kirchbauer, N. Hanik, and S. L. Jansen, “Real-time 93.8-Gb/s polarization-multiplexed OFDM transmitter with 1024-point IFFT,” Opt. Express |

3. | Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express |

4. | X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express |

5. | B. Liu, L. Zhang, X. Xin, and J. Yu, “None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying,” Opt. Express |

6. | L. Liu, X. Yang, and W. Hu, “Chromatic dispersion compensation using two pilot tones in optical OFDM systems,” in |

7. | H. Chen, M. Chen, and S. Xie, “All-optical sampling orthogonal frequency division multiplexing scheme for high speed transmission system,” J. Lightwave Technol. |

8. | D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s-1 line-rate superchannel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics |

9. | J. E. Simsarian, J. Gripp, A. H. Gnauck, G. Raybon, and P. J. Winzer, “Fast tuning 224-Gb/s intra-dyne receiver for optical packet networks,” |

10. | J. Zhao and A. D. Ellis, “Advantage of optical fast OFDM over OFDM in residual frequency offset compensation,” IEEE Photon. Technol. Lett. |

11. | J. Zhao and A. D. Ellis, “Transmission of 4-ASK optical fast OFDM with chromatic dispersion compensation,” IEEE Photon. Technol. Lett. |

12. | C. Lei, H. Chen, M. Chen, and S. Xie, “A high spectral efficiency optical OFDM scheme based on interleaved multiplexing,” Opt. Express |

13. | E. Giacoumidis, S. K. Ibrahim, J. Zhao, J. M. Tang, A. D. Ellis, and I. Tomos, “Experimental and theoretical investigations of intensity modulation and direct detection optical fast OFDM over MMF links,” IEEE Photon. Technol. Lett. |

**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: December 3, 2012

Revised Manuscript: January 10, 2013

Manuscript Accepted: January 17, 2013

Published: January 25, 2013

**Citation**

J. Zhao and H. Shams, "Fast dispersion estimation in coherent optical 16QAM fast OFDM systems," Opt. Express **21**, 2500-2505 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-2500

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### References

- L. A. Neto, A. Gharba, P. Chanclou, N. Genay, B. Charbonnier, M. Ouzzif, C. A. Berthelemot, and J. L. Masson, “High bit rate burst mode optical OFDM for next generation passive optical networks,” in Proc. European Conference on Optical Communication (2010), paper Tu.3.B.5.
- B. Inan, S. Adhikari, O. Karakaya, P. Kainzmaier, M. Mocker, H. von Kirchbauer, N. Hanik, and S. L. Jansen, “Real-time 93.8-Gb/s polarization-multiplexed OFDM transmitter with 1024-point IFFT,” Opt. Express19(26), B64–B68 (2011). [CrossRef] [PubMed]
- Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express20(3), 2379–2385 (2012). [CrossRef] [PubMed]
- X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express16(26), 21944–21957 (2008). [CrossRef] [PubMed]
- B. Liu, L. Zhang, X. Xin, and J. Yu, “None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying,” Opt. Express20(20), 22878–22885 (2012). [CrossRef] [PubMed]
- L. Liu, X. Yang, and W. Hu, “Chromatic dispersion compensation using two pilot tones in optical OFDM systems,” in Proc. Asia Communications and Photonics Conference (2011), paper 830937.1–6.
- H. Chen, M. Chen, and S. Xie, “All-optical sampling orthogonal frequency division multiplexing scheme for high speed transmission system,” J. Lightwave Technol.27(21), 4848–4854 (2009). [CrossRef]
- D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s-1 line-rate superchannel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011). [CrossRef]
- J. E. Simsarian, J. Gripp, A. H. Gnauck, G. Raybon, and P. J. Winzer, “Fast tuning 224-Gb/s intra-dyne receiver for optical packet networks,” Optical Fiber Communication Conference (2010), paper PDPB5.
- J. Zhao and A. D. Ellis, “Advantage of optical fast OFDM over OFDM in residual frequency offset compensation,” IEEE Photon. Technol. Lett.24(24), 2284–2287 (2012). [CrossRef]
- J. Zhao and A. D. Ellis, “Transmission of 4-ASK optical fast OFDM with chromatic dispersion compensation,” IEEE Photon. Technol. Lett.24(1), 34–36 (2012). [CrossRef]
- C. Lei, H. Chen, M. Chen, and S. Xie, “A high spectral efficiency optical OFDM scheme based on interleaved multiplexing,” Opt. Express18(25), 26149–26154 (2010). [CrossRef] [PubMed]
- E. Giacoumidis, S. K. Ibrahim, J. Zhao, J. M. Tang, A. D. Ellis, and I. Tomos, “Experimental and theoretical investigations of intensity modulation and direct detection optical fast OFDM over MMF links,” IEEE Photon. Technol. Lett.24, 52–54 (2012).

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