## Investigation of PMD in direct-detection optical OFDM with zero padding |

Optics Express, Vol. 21, Issue 18, pp. 20851-20856 (2013)

http://dx.doi.org/10.1364/OE.21.020851

Acrobat PDF (935 KB)

### Abstract

We investigate the polarization-mode dispersion (PMD) effect of zero padding OFDM (ZP-OFDM) in direct-detection optical orthogonal frequency division multiplexing (DDO-OFDM) systems. We first study the conventional equalization method for ZP-OFDM. Then an equalization method based on sorted QR decomposition is proposed to further improve the performance. It is found that the performance improvement of ZP-OFDM is due to the frequency domain oversampling (FDO) induced inter-carrier interference (ICI). Numerical simulation results show that compared with cyclic prefix OFDM (CP-OFDM), ZP-OFDM has a significantly higher tolerance to PMD in DDO-OFDM systems when the channel spectral nulls occur at certain differential group delay (DGD) values.

© 2013 OSA

## 1. Introduction

3. X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. **19**(12), 919–921 (2007). [CrossRef]

3. X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. **19**(12), 919–921 (2007). [CrossRef]

6. C.-Y. Wang, C.-C. Wei, C.-T. Lin, and S. Chi, “Direct-detection polarization division multiplexed orthogonal frequency-division multiplexing transmission systems without polarization tracking,” Opt. Lett. **37**(24), 5070–5072 (2012). [PubMed]

7. N. Cvijetic, S. G. Wilson, and D. Qian, “System Outage Probability Due to PMD in High-Speed Optical OFDM Transmission,” J. Lightwave Technol. **26**(14), 2118–2127 (2008). [CrossRef]

8. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Impact of PMD in single-receiver and polarization-diverse direct-detection optical OFDM,” J. Lightwave Technol. **27**(14), 2792–2799 (2009). [CrossRef]

*, (·)*

^{T}*and (·)*

^{H}^{†}represent transpose, Hermitian and pseudoinverse operators;

**F**

*represents a unitary*

_{M}*M*×

*M*DFT matrix; Diag(

**) stands for a diagonal matrix whose diagonal is vector**

*x***; Bold letters denote vectors and matrices.**

*x*## 2. Channel equalization for ZP-OFDM

10. B. Muquet, Z. Wang, G. B. Giannakis, M. de Courville, and O. Duhaamel, “Cyclic prefixing or zero padding for wireless multicarrier transmissions?” IEEE Trans. Commun. **50**(12), 2136–2148 (2002). [CrossRef]

*i-*th OFDM symbol in frequency domain is denoted by a

*N*× 1 vector

*P = N + D*. We define a

*P*×

*N*matrix

*L*

^{th}-order (

*L*≤

*D*) FIR filter with channel impulse response being a

*P*× 1 vector

*P*× 1 vector which can be expressed as:where

**H**is a

*P*×

*P*circulant matrix with first column

**h**;

**H**

_{ISI}is a

*P*×

*P*upper triangular Toeplitz matrix with first row

*P*× 1 noise vector. For ZP-OFDM, the ISI can be eliminated since

**H**

_{ISI}

**F**

_{zp}= 0. Then (1) can be rewritten as

**M**

*in (5) is a full column rank matrix as long as*

_{U}*U*>

*N*. Since the QR decomposition [11] can be applied to the full column matrix, (4) can be re-written aswhere the

**Q**has orthogonal columns with unit form and the

**R**is upper triangular. Multiplying

**Q**

*, then (7) can be re-written asDue to the upper triangular structure of*

^{H}**R**, the

*k*-th element of

*k*-th subcarrier

**M**

*to arrange the diagonal elements in matrix*

_{U}**R**in ascending order. We refer to the equalization method based on sorted QR decomposition in (9) and (10) as “ZP-OFDM-sQR”.

## 3. Simulation results and discussions

8. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Impact of PMD in single-receiver and polarization-diverse direct-detection optical OFDM,” J. Lightwave Technol. **27**(14), 2792–2799 (2009). [CrossRef]

12. OptiSystem Version 10.0 Available: http://www.optiwave.com/.

_{(Eb/N0)}. As shown in Fig. 2, the simulation parameters are as follows: 1) input state of polarization angle 𝜃 = π/4, corresponding to the worst case [8

8. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Impact of PMD in single-receiver and polarization-diverse direct-detection optical OFDM,” J. Lightwave Technol. **27**(14), 2792–2799 (2009). [CrossRef]

*N*is 64 and all the subcarriers are filled with data; 3) the CP or ZP size is set to be 8; 4) the sampling rate of DAC is 20GSamples/s; 5) the up-conversion RF frequency is 20 GHz; 6) 1600ps/nm of chromatic dispersion is added; 7) 20 training symbols are used for every 300 data symbols for channel estimation. Therefore, the total transmission bit rate is 20GSa/s × 64/ (64 + 8) × 2b/Sa × 300/ (300 + 20) = 33.3 Gb/s.

*U*=

*P*= 72 versus

*E*/

_{b}*N*

_{0}for different DGD values is shown in Fig. 3(a). With the interference cancellation in each step, ZP-OFDM-sQR shows the best performance among the three cases. At DGD values of 15 ps and the 7% forward error coding (FEC) threshold (3.8 × 10

^{−3}), ZP-OFDM-sQR shows ~1.6 dB

*E*/

_{b}*N*

_{0}improvement than CP-OFDM. It can be seen that the performance improvement of ZP-OFDM (ZP-OFDM-sQR) is more significant at DGD of 20 and 100 ps than 15 ps. This is because the spectral null is more obvious at larger DGD values as shown in Fig. 3 (b)-(e). The spectral dips occur at

*f*= (2

_{n}*k*+ 1)/2𝛥𝜏 (

*k*is a non-negative integer), which confirms the PMD analytical results [7

7. N. Cvijetic, S. G. Wilson, and D. Qian, “System Outage Probability Due to PMD in High-Speed Optical OFDM Transmission,” J. Lightwave Technol. **26**(14), 2118–2127 (2008). [CrossRef]

**27**(14), 2792–2799 (2009). [CrossRef]

*E*/

_{b}*N*

_{0}≥25dB . However, CP-OFDM shows a clear BER floor and cannot achieve error free transmission with FEC at the corresponding DGD values.

*U*= 68, 72 and 128 versus

*E*/

_{b}*N*

_{0}for DGD values of 20 and 100 ps, respectively. The BER performances of ZP-OFDM with all three

*U*values are better than that of CP-OFDM. The performance is slightly improved with an increase in

*U*, but the difference is negligible at the

*E*/

_{b}*N*

_{0}of 25 dB. Therefore, the equalizer with

*U*= 68 can recover the signal effectively with lower computation complexity.

*E*/

_{b}*N*

_{0}of 30 dB versus DGD are shown in Fig. 5. As shown in Fig. 5, the BER performance of ZP-OFDM (ZP-OFDM-sQR) can achieve 7% FEC threshold when DGD varies from20ps to 120ps. This means that ZP-OFDM (ZP-OFDM-sQR) can always achieve error free transmission with FEC. However CP-OFDM cannot achieve error free transmission even with FEC in the range of 20ps to 120ps. The BER fluctuation in Fig. 5 can be explained as the frequency spacing between the subcarriers and channel notches is varied at different DGD values. When some subcarriers are located exactly at the channel spectral nulls, the OSNR of those subcarriers will be close to zero, resulting in a significant increase in BER.

## 4. Conclusion

## Acknowledgments

## References and links

1. | W. Shieh and I. B. Djordjevic, OFDM for Optical Communications. New York: Academic, 2010. |

2. | W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express |

3. | X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. |

4. | W.-R. Peng, H. Takahashi, I. Morita, and H. Tanaka, “Transmission of a 214-Gb/s single-polarization direct-detection optical OFDM superchannel over 720-km standard single mode fiber with EDFA-only amplification,” European Conference on Optical Communications, Paper PDP 2.5.Turin, Italy (2010). |

5. | 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. |

6. | C.-Y. Wang, C.-C. Wei, C.-T. Lin, and S. Chi, “Direct-detection polarization division multiplexed orthogonal frequency-division multiplexing transmission systems without polarization tracking,” Opt. Lett. |

7. | N. Cvijetic, S. G. Wilson, and D. Qian, “System Outage Probability Due to PMD in High-Speed Optical OFDM Transmission,” J. Lightwave Technol. |

8. | B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Impact of PMD in single-receiver and polarization-diverse direct-detection optical OFDM,” J. Lightwave Technol. |

9. | M. Mayrock and H. Haunstein, “PMD tolerant direct-detection optical OFDM System”, European Conference on Optical Communications, Paper Tu.5.2.5, Berlin, Germany (2007). |

10. | B. Muquet, Z. Wang, G. B. Giannakis, M. de Courville, and O. Duhaamel, “Cyclic prefixing or zero padding for wireless multicarrier transmissions?” IEEE Trans. Commun. |

11. | G. Golub and C. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ, Press, 1996. |

12. | OptiSystem Version 10.0 Available: http://www.optiwave.com/. |

**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: May 22, 2013

Revised Manuscript: July 15, 2013

Manuscript Accepted: August 12, 2013

Published: August 29, 2013

**Citation**

Xiang Li, Arokiaswami Alphones, Wen-De Zhong, and Changyuan Yu, "Investigation of PMD in direct-detection optical OFDM with zero padding," Opt. Express **21**, 20851-20856 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20851

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### References

- W. Shieh and I. B. Djordjevic, OFDM for Optical Communications. New York: Academic, 2010.
- W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express16(9), 6378–6386 (2008). [CrossRef] [PubMed]
- X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett.19(12), 919–921 (2007). [CrossRef]
- W.-R. Peng, H. Takahashi, I. Morita, and H. Tanaka, “Transmission of a 214-Gb/s single-polarization direct-detection optical OFDM superchannel over 720-km standard single mode fiber with EDFA-only amplification,” European Conference on Optical Communications, Paper PDP 2.5.Turin, Italy (2010).
- 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]
- C.-Y. Wang, C.-C. Wei, C.-T. Lin, and S. Chi, “Direct-detection polarization division multiplexed orthogonal frequency-division multiplexing transmission systems without polarization tracking,” Opt. Lett.37(24), 5070–5072 (2012). [PubMed]
- N. Cvijetic, S. G. Wilson, and D. Qian, “System Outage Probability Due to PMD in High-Speed Optical OFDM Transmission,” J. Lightwave Technol.26(14), 2118–2127 (2008). [CrossRef]
- B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Impact of PMD in single-receiver and polarization-diverse direct-detection optical OFDM,” J. Lightwave Technol.27(14), 2792–2799 (2009). [CrossRef]
- M. Mayrock and H. Haunstein, “PMD tolerant direct-detection optical OFDM System”, European Conference on Optical Communications, Paper Tu.5.2.5, Berlin, Germany (2007).
- B. Muquet, Z. Wang, G. B. Giannakis, M. de Courville, and O. Duhaamel, “Cyclic prefixing or zero padding for wireless multicarrier transmissions?” IEEE Trans. Commun.50(12), 2136–2148 (2002). [CrossRef]
- G. Golub and C. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ, Press, 1996.
- OptiSystem Version 10.0 Available: http://www.optiwave.com/ .

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