## Study on dispersion-induced phase noise in an optical OFDM radio-over-fiber system at 60-GHz band |

Optics Express, Vol. 18, Issue 20, pp. 20774-20785 (2010)

http://dx.doi.org/10.1364/OE.18.020774

Acrobat PDF (1235 KB)

### Abstract

Abstract: While coherency between an RF-tone and OFDM signals in RoF systems at 60 GHz is de-correlated by fiber dispersion, both phase rotation term (PRT) on each subcarrier and inter-carrier interference (ICI) between subcarriers are induced at a receiver. We analytically calculate the powers of PRT and ICI under different parameters, such as subcarrier number, modulation format, laser linewidth and transmission distance. Moreover, dispersion-induced ICI is shown to be non-Gaussian distributed by its kurtosis, and its distribution depends on system parameters. Therefore, using only the power of ICI cannot predict accurate bit error rate (BER) and corresponding power penalty. We propose to use *t*-distribution to fit the distribution of ICI, and it can be used to compute BER precisely.

© 2010 OSA

## 1. Introduction

1. M. Sauer, A. Kobyakov, and J. George, “Radio over fiber for picocellular network architectures,” J. Lightwave Technol. **25**(11), 3301–3320 (2007). [CrossRef]

2. A. M. J. Koonen and L. M. Garcia, “Radio-over-MMF techniques – part II: microwave to millimeter-wave systems,” J. Lightwave Technol. **26**(15), 2396–2408 (2008). [CrossRef]

4. H.-C. Chien, A. Chowdhury, Z. Jia, Y.-T. Hsueh, and G.-K. Chang, “60 GHz millimeter-wave gigabit wireless services over long-reach passive optical network using remote signal regeneration and upconversion,” Opt. Express **17**, 3016–3024 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe- 17-5-3016.

7. C.-T. Lin, J. Chen, P.-T. Shih, W.-J. Jiang, and S. Chi, “Ultra-high data-rate 60 GHz radio-over-fiber systems employing optical frequency multiplication and OFDM formats,” J. Lightwave Technol. **28**(16), 2296–2306 (2010). [CrossRef]

8. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. **27**(3), 189–204 (2009). [CrossRef]

4. H.-C. Chien, A. Chowdhury, Z. Jia, Y.-T. Hsueh, and G.-K. Chang, “60 GHz millimeter-wave gigabit wireless services over long-reach passive optical network using remote signal regeneration and upconversion,” Opt. Express **17**, 3016–3024 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe- 17-5-3016.

7. C.-T. Lin, J. Chen, P.-T. Shih, W.-J. Jiang, and S. Chi, “Ultra-high data-rate 60 GHz radio-over-fiber systems employing optical frequency multiplication and OFDM formats,” J. Lightwave Technol. **28**(16), 2296–2306 (2010). [CrossRef]

10. W.-R. Peng, J. Chen, and S. Chi, “On the phase noise impact in direct-detection optical OFDM transmission,” IEEE Photon. Technol. Lett. **22**(9), 649–651 (2010). [CrossRef]

10. W.-R. Peng, J. Chen, and S. Chi, “On the phase noise impact in direct-detection optical OFDM transmission,” IEEE Photon. Technol. Lett. **22**(9), 649–651 (2010). [CrossRef]

*t*-distribution is a suitable candidate, it can be used to compute BER precisely under different parameters, such as subcarrier number, modulation format and transmission distance.

## 2. System model

11. C.-T. Lin, P.-T. Shih, J. Chen, W.-Q. Xue, P.-C. Peng, and S. Chi, “Optical millimeter-wave signal generation using frequency quadrupling technique and no optical filtering,” IEEE Photon. Technol. Lett. **20**(12), 1027–1029 (2008). [CrossRef]

12. P.-T. Shih, J. Chen, C.-T. Lin, W.-J. Jiang, H.-S. Huang, P.-C. Peng, and S. Chi, “Optical millimeter-wave signal generation via frequency 12-tupling,” J. Lightwave Technol. **28**(1), 71–78 (2010). [CrossRef]

13. K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. **37**(8), 515–516 (2001). [CrossRef]

7. C.-T. Lin, J. Chen, P.-T. Shih, W.-J. Jiang, and S. Chi, “Ultra-high data-rate 60 GHz radio-over-fiber systems employing optical frequency multiplication and OFDM formats,” J. Lightwave Technol. **28**(16), 2296–2306 (2010). [CrossRef]

*q*th subcarrier in an OFDM symbol without transmission is given as, where

*q*th subcarrier. Since the proper cyclic prefix is added at the transmitter, CD of fiber only affects the phase of the channel response. However, the PN induced by different group delays is not considered in Eq. (1). Since the subcarrier number of OFDM signals,

*N*, is usually large to make each subcarrier bandwidth small, in order to be tolerant to uneven frequency response, each subcarrier can be treated as a monochromatic carrier for simplicity, as shown in Fig. 2 . Consequently, while the RF-tone and the OFDM subcarriers propagate in fiber with different group velocities, the phase difference between the RF-tone and the

*q*th subcarrier can be simply approximated as

14. M. S. El-Tanany, Y. Wu, and L. Hazy, “Analytical modeling and simulation of phase noise interference in OFDM-based digital television terrestrial broadcasting systems,” IEEE Trans. Broadcast **47**(1), 20–31 (2001). [CrossRef]

*q*th subcarrier. Hence,

*β*is the 3-dB laser linewidth. Considering the discrete frequency component of

*q*th subcarrier by

10. W.-R. Peng, J. Chen, and S. Chi, “On the phase noise impact in direct-detection optical OFDM transmission,” IEEE Photon. Technol. Lett. **22**(9), 649–651 (2010). [CrossRef]

15. X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM systems,” J. Lightwave Technol. **26**(10), 1309–1316 (2008). [CrossRef]

*q*th subcarrier, and

## 3. The properties of PRT and ICI

14. M. S. El-Tanany, Y. Wu, and L. Hazy, “Analytical modeling and simulation of phase noise interference in OFDM-based digital television terrestrial broadcasting systems,” IEEE Trans. Broadcast **47**(1), 20–31 (2001). [CrossRef]

*A*is a random variable, the

*c*is the light speed,

*L*is the transmission distance, and the frequency difference between the first (last) subcarrier and the RF-tone is

*β*of 1 MHz. The OFDM signals over fewer subcarriers show lower ICI power but higher PRT power, and the PRT power increases faster than ICI power as CD increasing. Therefore, both of them have to be considered to evaluate the transmission performance. Furthermore, while the relative group delay is small and

17. E. Costa and S. Pupolin, “M-QAM-OFDM system performance in the presence of a nonlinear amplifier and phase noise,” IEEE Trans. Commun. **50**(3), 462–472 (2002). [CrossRef]

*N*= 32 in Figs. 4(a) and (b), because

*q = N/*2 are plotted in Fig. 5 . For ICI, fewer subcarriers and higher dispersion will result in higher kurtosis and more deviation from a normal distribution. Moreover, since

*M*-ary QAM (

**22**(9), 649–651 (2010). [CrossRef]

*N*= 128 shows higher error, compared with the case of

*N*= 32, due to larger

*N*= 32 to

*N*= 128 for 64-QAM owing to the reduction of

**22**(9), 649–651 (2010). [CrossRef]

## 4. Using *t*-distribution to simulate ICI

18. K. Pearson, “Contributions to the mathematical theory of evolution. II. skew variation in homogeneous material,” Philos. Trans. Roy. Soc. London Ser. A **186**(0), 343–414 (1895). [CrossRef]

*t*-distribution, of which the normalized probability density function (pdf) is, and

*ν*approaches infinity, kurtosis excess is zero and it becomes a normal distribution. By setting

*t*-distribution are plotted by the dashed lines in Fig. 6(b), and the

*t*-distributions have good agreement with the numerical results. To further examine the similarity between the

*t*-distribution and ICI distribution, Eq. (10) is used to calculate BER curves, and the theoretical BER becomes Eq. (6) after replacing

18. K. Pearson, “Contributions to the mathematical theory of evolution. II. skew variation in homogeneous material,” Philos. Trans. Roy. Soc. London Ser. A **186**(0), 343–414 (1895). [CrossRef]

*A*and

*B*are two independent real random variable with the means of zero, the variances of

*A*and

*B*represents ICI and white noise, respectively, the modified parameter,

*t*-distibution can fit the simulation results well. Figures 8 -11 exhibit the SNR penalty at the BER of 10

^{−3}. Only ICI is considered in Figs. 8-11(b), and only PRT is considered in Figs. 8-11(c), while both of them are included in Figs. 8-11(a). Figures 8-11(c) depict that the penalty induced by PRT can be estimated well by Eq. (6) by setting

*t*-distribution, it shows estimation error of < 1 dB with or without considering PRT. However, if the laser linewidth is wider and/or the higher order QAM is adopted, the maximum transmission distance and the accumulated CD are lower, and the corresponding power and kurtosis of ICI are also lower resulting in smaller estimation error by Gaussian approximation, such as the case shown in Figs. 11(a) and (b). In conclusion,

*t*-distribution offers a simple and reasonable way to estimate the BER and the maximum transmission distance limited by dispersion-induced PN, especially when the subcarrier number is low and the accumulated CD is high.

## 5. Conclusions

*t*-distribution is adopted to approach the exact distribution of ICI owing to its adjustable kurtosis. Compared with the numerical results, the approximation of

*t*-distribution can provide a simple way to calculate the BER with estimation error of < 1 dB under different laser linewidths, subcarrier numbers, modulation formats, and transmission distances.

## References and links

1. | M. Sauer, A. Kobyakov, and J. George, “Radio over fiber for picocellular network architectures,” J. Lightwave Technol. |

2. | A. M. J. Koonen and L. M. Garcia, “Radio-over-MMF techniques – part II: microwave to millimeter-wave systems,” J. Lightwave Technol. |

3. | Y. X. Guo, B. Luo, C. S. Park, L. C. Ong, M.-T. Zhou, and S. Kato, “60 GHz radio-over-fiber for Gbps transmission,” in Proc. Global Symp. Millimeter Waves (GSMM), 41–43 (2008). |

4. | H.-C. Chien, A. Chowdhury, Z. Jia, Y.-T. Hsueh, and G.-K. Chang, “60 GHz millimeter-wave gigabit wireless services over long-reach passive optical network using remote signal regeneration and upconversion,” Opt. Express |

5. | C. T. Lin, E. Z. Wong, W. J. Jiang, P. T. Shih, J. Chen, and S. Chi, “28‐Gb/s 16‐QAM OFDM radio‐over‐fiber system within 7‐GHz license‐free band at 60 GHz employing all-optical up-conversion,” in |

6. | Z. Jia, J. Yu, Y.-T. Hsueh, A. Chowdhury, H.-C. Chien, J. A. Buck, and G.-K. Chang, “Multiband signal generation and dispersion-tolerant transmission based on photonic frequency tripling technology for 60-GHz radio-over-fiber systems,” IEEE Photon. Technol. Lett. |

7. | C.-T. Lin, J. Chen, P.-T. Shih, W.-J. Jiang, and S. Chi, “Ultra-high data-rate 60 GHz radio-over-fiber systems employing optical frequency multiplication and OFDM formats,” J. Lightwave Technol. |

8. | J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. |

9. | Z. Zan, M. Premaratne, and A. J. Lowery, “Laser RIN and linewidth requirements for direct detection optical OFDM,” in |

10. | W.-R. Peng, J. Chen, and S. Chi, “On the phase noise impact in direct-detection optical OFDM transmission,” IEEE Photon. Technol. Lett. |

11. | C.-T. Lin, P.-T. Shih, J. Chen, W.-Q. Xue, P.-C. Peng, and S. Chi, “Optical millimeter-wave signal generation using frequency quadrupling technique and no optical filtering,” IEEE Photon. Technol. Lett. |

12. | P.-T. Shih, J. Chen, C.-T. Lin, W.-J. Jiang, H.-S. Huang, P.-C. Peng, and S. Chi, “Optical millimeter-wave signal generation via frequency 12-tupling,” J. Lightwave Technol. |

13. | K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. |

14. | M. S. El-Tanany, Y. Wu, and L. Hazy, “Analytical modeling and simulation of phase noise interference in OFDM-based digital television terrestrial broadcasting systems,” IEEE Trans. Broadcast |

15. | X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM systems,” J. Lightwave Technol. |

16. | D. Petrovic, W. Rave, and G. Fettweis, “Properties of the intercarrier interference due to phase noise in OFDM,” in |

17. | E. Costa and S. Pupolin, “M-QAM-OFDM system performance in the presence of a nonlinear amplifier and phase noise,” IEEE Trans. Commun. |

18. | K. Pearson, “Contributions to the mathematical theory of evolution. II. skew variation in homogeneous material,” Philos. Trans. Roy. Soc. London Ser. A |

**OCIS Codes**

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

(060.5625) Fiber optics and optical communications : Radio frequency photonics

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 11, 2010

Revised Manuscript: September 7, 2010

Manuscript Accepted: September 7, 2010

Published: September 15, 2010

**Citation**

Chia Chien Wei and Jason (Jyehong) Chen, "Study on dispersion-induced phase noise in an optical OFDM radio-over-fiber system at 60-GHz band," Opt. Express **18**, 20774-20785 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-20774

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### References

- M. Sauer, A. Kobyakov, and J. George, “Radio over fiber for picocellular network architectures,” J. Lightwave Technol. 25(11), 3301–3320 (2007). [CrossRef]
- A. M. J. Koonen and L. M. Garcia, “Radio-over-MMF techniques – part II: microwave to millimeter-wave systems,” J. Lightwave Technol. 26(15), 2396–2408 (2008). [CrossRef]
- Y. X. Guo, B. Luo, C. S. Park, L. C. Ong, M.-T. Zhou, and S. Kato, “60 GHz radio-over-fiber for Gbps transmission,” in Proc. Global Symp. Millimeter Waves (GSMM), 41–43 (2008).
- H.-C. Chien, A. Chowdhury, Z. Jia, Y.-T. Hsueh, and G.-K. Chang, “60 GHz millimeter-wave gigabit wireless services over long-reach passive optical network using remote signal regeneration and upconversion,” Opt. Express 17, 3016–3024 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe- 17-5-3016.
- C. T. Lin, E. Z. Wong, W. J. Jiang, P. T. Shih, J. Chen, and S. Chi, “28‐Gb/s 16‐QAM OFDM radio‐over‐fiber system within 7‐GHz license‐free band at 60 GHz employing all-optical up-conversion,” in Proc. CLEO 2009, Maryland, Baltimore, CPDA8 (2009).
- Z. Jia, J. Yu, Y.-T. Hsueh, A. Chowdhury, H.-C. Chien, J. A. Buck, and G.-K. Chang, “Multiband signal generation and dispersion-tolerant transmission based on photonic frequency tripling technology for 60-GHz radio-over-fiber systems,” IEEE Photon. Technol. Lett. 20(17), 1470–1472 (2008). [CrossRef]
- C.-T. Lin, J. Chen, P.-T. Shih, W.-J. Jiang, and S. Chi, “Ultra-high data-rate 60 GHz radio-over-fiber systems employing optical frequency multiplication and OFDM formats,” J. Lightwave Technol. 28(16), 2296–2306 (2010). [CrossRef]
- J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]
- Z. Zan, M. Premaratne, and A. J. Lowery, “Laser RIN and linewidth requirements for direct detection optical OFDM,” in Proc. CLEO’08, San Jose, CWN2 (2008).
- W.-R. Peng, J. Chen, and S. Chi, “On the phase noise impact in direct-detection optical OFDM transmission,” IEEE Photon. Technol. Lett. 22(9), 649–651 (2010). [CrossRef]
- C.-T. Lin, P.-T. Shih, J. Chen, W.-Q. Xue, P.-C. Peng, and S. Chi, “Optical millimeter-wave signal generation using frequency quadrupling technique and no optical filtering,” IEEE Photon. Technol. Lett. 20(12), 1027–1029 (2008). [CrossRef]
- P.-T. Shih, J. Chen, C.-T. Lin, W.-J. Jiang, H.-S. Huang, P.-C. Peng, and S. Chi, “Optical millimeter-wave signal generation via frequency 12-tupling,” J. Lightwave Technol. 28(1), 71–78 (2010). [CrossRef]
- K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001). [CrossRef]
- M. S. El-Tanany, Y. Wu, and L. Hazy, “Analytical modeling and simulation of phase noise interference in OFDM-based digital television terrestrial broadcasting systems,” IEEE Trans. Broadcast 47(1), 20–31 (2001). [CrossRef]
- X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM systems,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]
- D. Petrovic, W. Rave, and G. Fettweis, “Properties of the intercarrier interference due to phase noise in OFDM,” in Proc. ICC’05, 2605–2610 (2005)
- E. Costa and S. Pupolin, “M-QAM-OFDM system performance in the presence of a nonlinear amplifier and phase noise,” IEEE Trans. Commun. 50(3), 462–472 (2002). [CrossRef]
- K. Pearson, “Contributions to the mathematical theory of evolution. II. skew variation in homogeneous material,” Philos. Trans. Roy. Soc. London Ser. A 186(0), 343–414 (1895). [CrossRef]

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