## A simple peak-to-average power ratio reduction scheme for all optical orthogonal frequency division multiplexing systems with intensity modulation and direct detection

Optics Express, Vol. 17, Issue 18, pp. 15614-15622 (2009)

http://dx.doi.org/10.1364/OE.17.015614

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### Abstract

This paper fundamentally investigates the peak-to-average power ratio (PAPR) theory in all optical orthogonal frequency division multiplexing (OFDM) systems which employ intensity modulation-direct detection (IM-DD) scheme. We propose a low-complexity PAPR reduction scheme based on phase pre-emphasis. Simulations show that the proposed scheme brings about a 3.74 dB PAPR reduction and better nonlinear impairment tolerance in a 16×10Gb/s IM-DD all optical OFDM system.

© 2009 Optical Society of America

## 1. Introduction

1. J. Armstrong, “OFDM for Optical Communications,” J. Lightwave. Technol. **27**, 189–204 (2009).
[CrossRef]

4. K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express **16**, 4023–4028 (2008).
[CrossRef] [PubMed]

4. K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express **16**, 4023–4028 (2008).
[CrossRef] [PubMed]

5. E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori1, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, “Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1Tb/s (50×88.8-Gb/s) DWDM Link over 800 km SMF Including 50-GHz Spaced ROADM Nodes,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP8.

8. Y. Tang, K. P. Ho, and W. Shieh, “Coherent Optical OFDM Transmitter Design Employing Predistortion,” IEEE Photon. Tech. Lett. **20**,954–956 (2008).
[CrossRef]

4. K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express **16**, 4023–4028 (2008).
[CrossRef] [PubMed]

## 2. All optical OFDM system configuration

## 3. PAPR theory in IM-DD all optical OFDM systems

*x*can be expressed by Eq. (1).

_{n}*X*denotes the kth modulated phase shift keying (PSK) or quadrature amplitude modulation (QAM) symbol.

_{k}*X*can be written as

_{k}*X*=

_{k}*a*+

_{k}*jb*, where

_{k}*a*and

_{k}*b*indicate the real component and imaginary component of

_{k}*X*, respectively. Assuming that

_{k}*a*and

_{k}*b*are independent with each other, the statistical characteristics of

_{k}*a*and

_{k}*b*are given in Eq. (2) and Eq. (3).

_{k}^{2}is the variation of

*a*and

_{k}*b*. Setting

_{k}*x*=

_{n}*x*

_{n,I}+

*jx*

_{n,Q},

*x*

_{n,I}and

*x*

_{n,Q}respectively indicate the real component and imaginary component of

*x*. Calculating Eq. (1)~(3) and applying the central limit theorem for large N [11], the probability distributions of

_{n}*x*

_{n,I}and

*x*

_{n,Q}follow the Gaussian distribution. Therefore, the complementary cumulative distribution function (CCDF) of PAPR can be written as Eq.(4) [12].

*X*follows 0–1 distribution. Consequently, Eq.(2) and (3) should be modified to Eq. (5) and (6).

_{k}*x*

_{n,I}and

*x*

_{n,Q}don’t satisfy the Linderberg condition any more. So they have no analytical probability distribution functions. Consequently, Eq. (4) is not suitable for IM-DD all optical OFDM systems. Numerical simulation is the only way to investigate PAPR characteristics under this condition.

## 4. A novel simple PAPR reduction scheme

*x*

_{0},

*x*

_{1},…,

*x*

_{N-1}), lining up in sequence in time domain. Because

*X*follows 0–1 distribution, it’s clear that

_{k}*x*| reaches a maximum when n=0. This means that

_{n}*X*(k=0,1,…,N-1) are multiplexed by the same phase factor. Because the value of |

_{k}*x*| always reaches its maximum when n=0, PAPR will be reduced if the in-phase condition (when n=0) is eliminated. In our PAPR reduction scheme, different phase pre-emphasises are introduced and Eq. (1) is converted to Eq. (7) and (8).

_{n}*φ*is the kth phase pre-emphasis. Chosen suitable values for

_{k}*φ*, the in-phase condition (when n=0) can be eliminated and PAPR will be reduced.

_{k}## 5. 16×10Gb/s IM-DD all optical OFDM application

^{™}V7.6 to simulate a 16×10Gb/s IM-DD all optical OFDM system, the configuration of which is shown in Fig.1. In this simulation, the ODFT and OIDFT are based on a phase shifter array and a delay line array. The optical signal eye diagrams transmitted into the fiber are given in Fig.6 and Fig.7. Under the condition of no phase pre-emphasis, the eye diagram shows a power peak at the central of an OFDM symbol, as shown in Fig.6. This is consistent with the aforementioned PAPR characteristics in IM-DD all optical OFDM systems. When phase pre-emphasis is applied, no obvious power peak appears in the eye diagram, as shown in Fig.7. This means that with phase pre-emphasis, the peak power is dispersed to the whole OFDM symbol cycle. As a result, the corresponding PAPR will be significantly lower.

## 6. Conclusions

^{-9}and1×10

^{-12}, respectively. Therefore, system tolerance of nonlinear impairment increases significantly, owing to the contribution of the proposed PAPR reduction scheme.

## Acknowledgement

## References and links

1. | J. Armstrong, “OFDM for Optical Communications,” J. Lightwave. Technol. |

2. | W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Exp. |

3. | J. Armstrong, “OFDM: From Copper and Wireless to Optical,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMM1. |

4. | K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express |

5. | E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori1, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, “Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1Tb/s (50×88.8-Gb/s) DWDM Link over 800 km SMF Including 50-GHz Spaced ROADM Nodes,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP8. |

6. | Y. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, “Dual-Polarization 2×2 IFFT/FFT Optical Signal Processing for 100-Gb/s QPSK-PDM All-Optical OFDM,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuM4. |

7. | K. Takiguchi, M. Oguma, T. Shibata, and H. Takahashi, “Optical OFDM Demultiplexer Using Silica PLC Based Optical FFT Circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWO3. |

8. | Y. Tang, K. P. Ho, and W. Shieh, “Coherent Optical OFDM Transmitter Design Employing Predistortion,” IEEE Photon. Tech. Lett. |

9. | J. Armstrong, “New OFDM peak-to-average power reduction scheme,” in Proceedings of IEEE on Vehicular Technology , (IEEE, 2001), pp 756–760. |

10. | K. Tanaka and S. Norimatsu, “Transmission Performance of WDM/OFDM Hybrid Systems over Optical Fibers,” Electronics and Communications in Japan , Part 1, |

11. | N. Shiryaev, |

12. | S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” Wireless Communications IEEE |

**OCIS Codes**

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

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

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(070.7145) Fourier optics and signal processing : Ultrafast processing

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 5, 2009

Revised Manuscript: July 8, 2009

Manuscript Accepted: July 22, 2009

Published: August 19, 2009

**Citation**

Xiaojun Liang, Wei Li, Weidong Ma, and Kai Wang, "A simple peak-to-average power ratio reduction scheme for all optical orthogonal frequency division multiplexing systems with intensity modulation and direct detection," Opt. Express **17**, 15614-15622 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-18-15614

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### References

- J. Armstrong, "OFDM for Optical Communications," J. Lightwave. Technol. 27, 189-204 (2009). [CrossRef]
- W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt. Express 16, 841-859 (2006). [CrossRef]
- J. Armstrong, "OFDM: From Copper and Wireless to Optical," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMM1.
- K. Lee, T. T. Chan and J. K. Rhee, "All optical discrete Fourier transform processor for 100 Gbps OFDM transmission," Opt. Express 16, 4023-4028 (2008). [CrossRef] [PubMed]
- E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori1, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, "Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1Tb/s (50 x 88.8-Gb/s) DWDM Link over 800 km SMF Including 50-GHz Spaced ROADM Nodes," in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP8.
- Y. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, "Dual-Polarization 2x2 IFFT/FFT Optical Signal Processing for 100-Gb/s QPSK-PDM All-Optical OFDM," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuM4.
- K. Takiguchi, M. Oguma, T. Shibata, and H. Takahashi, "Optical OFDM Demultiplexer Using Silica PLC Based Optical FFT Circuit," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWO3.
- Y. Tang, K. P. Ho, and W. Shieh, "Coherent Optical OFDM Transmitter Design Employing Predistortion," IEEE Photon. Tech. Lett. 20, 954-956 (2008). [CrossRef]
- J. Armstrong, "New OFDM peak-to-average power reduction scheme," in Proceedings of IEEE on Vehicular Technology, (IEEE, 2001), pp 756-760.
- K. Tanaka and S. Norimatsu, "Transmission Performance of WDM/OFDM Hybrid Systems over Optical Fibers," Electron. Commun. Japan, Part 1, 90, 14-24(2007). [CrossRef]
- N. Shiryaev, Probability (New York, springer-verlag, 1996).
- S. H. Han and J. H. Lee, "An overview of peak-to-average power ratio reduction techniques for multicarrier transmission," Wireless Commun. IEEE 12(2), 56-65 (2005).

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