Abstract

In this paper, closed-form analytical bounds on PMD-induced symbol error rate and outage probability in high-speed long-haul optical orthogonal frequency division multiplexed (OFDM) systems are derived, evaluated, and verified experimentally in order to assess the PMD tolerance of this modulation format. To obtain the analytical results, the PMD channel is modeled as a linear time-invariant system, whose end-to-end transfer function is used to upper-bound symbol error and outage probabilities in IM/DD optical OFDM transmission. The symbol error rate bounds predicted by the general analytical model are verified experimentally on a 10-Gb/s OFDM system with instantaneous DGD ranging between $\Delta\tau = 0$ and 120 ps. The outage probability bounds indicate that, if no RF guard bands are required, OFDM enables high-speed transmission with at least twice the PMD tolerance provided by an equivalent uncompensated OOK-based system at system outage probabilities $P_{{\rm out,\ sys}}<10^{-5}$. If RF guard bands are required to mitigate effects of other distortions, it is shown that a penalty in the system PMD tolerance proportional to the intermediate RF subcarrier frequency, $f_{{\rm RF}}$, is exerted. Consequently, a tolerance tradeoff exists in IM/DD OFDM systems, wherein $f_{\rm RF}$ as well as baseband constellation size may be viewed as design parameters that can be optimized depending on specific system requirements.

© 2008 IEEE

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  1. C. Poole, R. Tkach, A. Chraplyvy, D. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
  2. F. Buchali, H. Bülow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightw. Technol. 22, 1116-1126 (2004).
  3. C. Xie, L. Möller, H. Haunstein, S. Hunsche, "Comparison of system tolerance to polarization-mode dispersion between different modulation formats," IEEE Photon. Techol. Lett. 15, 1168-1170 (2003).
  4. H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, P. Andrekson, "A comparison between different PMD compensation techniques," J. Lightw. Technol. 20, 368-378 (2002).
  5. O. E. Agazzi, "Maximum-likelihood sequence estimation in dispersive optical channels," J. Lightw. Technol. 23, 749-763 (2005).
  6. M. Jäger, T. Rankl, J. Spiegel, H. Bülow, F. Buchali, "Performance of turbo equalizers for optical PMD channels," J. Lightw. Technol. 24, 1226-1236 (2006).
  7. A. J. Lowery, J. Armstrong, "Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems," OSA Opt. Exp. 14, 2079-2084 (2006).
  8. W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 134-136 (2006).
  9. N. Cvijetic, L. Xu, T. Wang, "Adaptive PMD compensation using OFDM in long-haul 10 Gb/s DWDM systems," IEEE/OSA Opt. Fiber Conf. (2007) OTuA5.
  10. I. B. Djordjevic, "PMD compensation in fiber-optic communication systems with direct detection using LDPC-coded OFDM," OSA Opt. Exp. 15, (2007).
  11. A. J. Lowery, L. B. Du, J. Armstrong, "Performance of optical OFDM in ultralong-haul WDM lightwave systems," J. Lightw. Technol. 25, 131-138 (2007).
  12. W. Shieh, X. Yi, Y. Tang, "Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber," IEEE Electron. Lett. 43, 183-185 (2007).
  13. W. Shieh, X. Yi, Y. Ma, Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems.," OSA Opt. Exp. 15, 9936-9947 (2007).
  14. S. L. Jansen, I. Morita, H. Tanaka, "16$\,\times\,$52.5-Gb/s, 50-GHz spaced, POLMUX-CO-OFDM transmission over 4 160-km SSMF enabled by MIMO processing," Eur. Conf. Optical Communications (2007).
  15. H. Bülow, "Electronic dispersion compensation," IEEE/OSA Optical Fiber Conf. (2007).
  16. H. Bülow, "System outage probability due to first- and second-order PMD," IEEE Photon. Techol. Lett. 10, 696-698 (1998).
  17. E. Forestieri, G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system," J. Lightw. Technol. 22, 988-996 (2004).
  18. G. Biondini, W. L. Kath, C. R. Menyuk, "Importance sampling for polarization-mode dispersion," IEEE Photon. Technol. Lett. 14, (2002).
  19. M. Secondini, E. Forestieri, "All-order PMD outage probability evaluation by Markov chain Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1417-1419 (2005).
  20. P. J. Winzer, H. Kogelnik, K. Ramanan, "Precise outage specifications for 1st-order PMD," IEEE Photon. Technol. Lett. 16, 449-451 (2004).
  21. J. Kissing, T. Gravemann, E. Voges, "Analytical probability density function for the Q factor due to PMD and noise," IEEE Photon. Techol. Lett. 15, 611-613 (2003).
  22. A. Djupsjöbacka, "Calculation of signal outage due to polarization mode dispersion," IEEE Photon. Techol. Lett. 13, 660-662 (2001).
  23. I. B. Djordjevic, B. Vasic, "100 Gb/s transmission using orthogonal frequency-division multiplexing," IEEE Photon. Technol. Lett. 18, 1576-1578 (2006).
  24. G. J. Foschini, C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightw. Technol. 9, 1439-1456 (1991).
  25. M. Cvijetic, Optical Transmission Systems Engineering (Artech House, 2004).
  26. R. Hui, C. Allen, K. Demarest, "PMD-insensitive SCM optical receiver using polarization diversity," IEEE Phot. Technol. Lett. 14, (2002).
  27. S. G. Wilson, Digital Modulation and Coding. (Prentice-Hall, 1995).

2007

I. B. Djordjevic, "PMD compensation in fiber-optic communication systems with direct detection using LDPC-coded OFDM," OSA Opt. Exp. 15, (2007).

A. J. Lowery, L. B. Du, J. Armstrong, "Performance of optical OFDM in ultralong-haul WDM lightwave systems," J. Lightw. Technol. 25, 131-138 (2007).

W. Shieh, X. Yi, Y. Tang, "Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber," IEEE Electron. Lett. 43, 183-185 (2007).

W. Shieh, X. Yi, Y. Ma, Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems.," OSA Opt. Exp. 15, 9936-9947 (2007).

2006

M. Jäger, T. Rankl, J. Spiegel, H. Bülow, F. Buchali, "Performance of turbo equalizers for optical PMD channels," J. Lightw. Technol. 24, 1226-1236 (2006).

A. J. Lowery, J. Armstrong, "Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems," OSA Opt. Exp. 14, 2079-2084 (2006).

W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 134-136 (2006).

I. B. Djordjevic, B. Vasic, "100 Gb/s transmission using orthogonal frequency-division multiplexing," IEEE Photon. Technol. Lett. 18, 1576-1578 (2006).

2005

M. Secondini, E. Forestieri, "All-order PMD outage probability evaluation by Markov chain Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1417-1419 (2005).

O. E. Agazzi, "Maximum-likelihood sequence estimation in dispersive optical channels," J. Lightw. Technol. 23, 749-763 (2005).

2004

F. Buchali, H. Bülow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightw. Technol. 22, 1116-1126 (2004).

P. J. Winzer, H. Kogelnik, K. Ramanan, "Precise outage specifications for 1st-order PMD," IEEE Photon. Technol. Lett. 16, 449-451 (2004).

E. Forestieri, G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system," J. Lightw. Technol. 22, 988-996 (2004).

2003

J. Kissing, T. Gravemann, E. Voges, "Analytical probability density function for the Q factor due to PMD and noise," IEEE Photon. Techol. Lett. 15, 611-613 (2003).

C. Xie, L. Möller, H. Haunstein, S. Hunsche, "Comparison of system tolerance to polarization-mode dispersion between different modulation formats," IEEE Photon. Techol. Lett. 15, 1168-1170 (2003).

2002

H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, P. Andrekson, "A comparison between different PMD compensation techniques," J. Lightw. Technol. 20, 368-378 (2002).

G. Biondini, W. L. Kath, C. R. Menyuk, "Importance sampling for polarization-mode dispersion," IEEE Photon. Technol. Lett. 14, (2002).

R. Hui, C. Allen, K. Demarest, "PMD-insensitive SCM optical receiver using polarization diversity," IEEE Phot. Technol. Lett. 14, (2002).

2001

A. Djupsjöbacka, "Calculation of signal outage due to polarization mode dispersion," IEEE Photon. Techol. Lett. 13, 660-662 (2001).

1998

H. Bülow, "System outage probability due to first- and second-order PMD," IEEE Photon. Techol. Lett. 10, 696-698 (1998).

1991

C. Poole, R. Tkach, A. Chraplyvy, D. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).

G. J. Foschini, C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightw. Technol. 9, 1439-1456 (1991).

J. Lightw. Technol.

F. Buchali, H. Bülow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightw. Technol. 22, 1116-1126 (2004).

IEEE Phot. Technol. Lett.

R. Hui, C. Allen, K. Demarest, "PMD-insensitive SCM optical receiver using polarization diversity," IEEE Phot. Technol. Lett. 14, (2002).

IEEE Electron. Lett.

W. Shieh, X. Yi, Y. Tang, "Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber," IEEE Electron. Lett. 43, 183-185 (2007).

IEEE Photon. Technol. Lett.

C. Poole, R. Tkach, A. Chraplyvy, D. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).

IEEE Photon. Technol. Lett.

M. Secondini, E. Forestieri, "All-order PMD outage probability evaluation by Markov chain Monte Carlo simulations," IEEE Photon. Technol. Lett. 17, 1417-1419 (2005).

IEEE Photon. Technol. Lett.

P. J. Winzer, H. Kogelnik, K. Ramanan, "Precise outage specifications for 1st-order PMD," IEEE Photon. Technol. Lett. 16, 449-451 (2004).

I. B. Djordjevic, B. Vasic, "100 Gb/s transmission using orthogonal frequency-division multiplexing," IEEE Photon. Technol. Lett. 18, 1576-1578 (2006).

G. Biondini, W. L. Kath, C. R. Menyuk, "Importance sampling for polarization-mode dispersion," IEEE Photon. Technol. Lett. 14, (2002).

W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 134-136 (2006).

IEEE Photon. Techol. Lett.

J. Kissing, T. Gravemann, E. Voges, "Analytical probability density function for the Q factor due to PMD and noise," IEEE Photon. Techol. Lett. 15, 611-613 (2003).

IEEE Photon. Techol. Lett.

A. Djupsjöbacka, "Calculation of signal outage due to polarization mode dispersion," IEEE Photon. Techol. Lett. 13, 660-662 (2001).

C. Xie, L. Möller, H. Haunstein, S. Hunsche, "Comparison of system tolerance to polarization-mode dispersion between different modulation formats," IEEE Photon. Techol. Lett. 15, 1168-1170 (2003).

H. Bülow, "System outage probability due to first- and second-order PMD," IEEE Photon. Techol. Lett. 10, 696-698 (1998).

J. Lightw. Technol.

E. Forestieri, G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system," J. Lightw. Technol. 22, 988-996 (2004).

M. Jäger, T. Rankl, J. Spiegel, H. Bülow, F. Buchali, "Performance of turbo equalizers for optical PMD channels," J. Lightw. Technol. 24, 1226-1236 (2006).

J. Lightw. Technol.

O. E. Agazzi, "Maximum-likelihood sequence estimation in dispersive optical channels," J. Lightw. Technol. 23, 749-763 (2005).

J. Lightw. Technol.

H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, P. Andrekson, "A comparison between different PMD compensation techniques," J. Lightw. Technol. 20, 368-378 (2002).

A. J. Lowery, L. B. Du, J. Armstrong, "Performance of optical OFDM in ultralong-haul WDM lightwave systems," J. Lightw. Technol. 25, 131-138 (2007).

G. J. Foschini, C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightw. Technol. 9, 1439-1456 (1991).

OSA Opt. Exp.

I. B. Djordjevic, "PMD compensation in fiber-optic communication systems with direct detection using LDPC-coded OFDM," OSA Opt. Exp. 15, (2007).

A. J. Lowery, J. Armstrong, "Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems," OSA Opt. Exp. 14, 2079-2084 (2006).

OSA Opt. Exp.

W. Shieh, X. Yi, Y. Ma, Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems.," OSA Opt. Exp. 15, 9936-9947 (2007).

Other

S. L. Jansen, I. Morita, H. Tanaka, "16$\,\times\,$52.5-Gb/s, 50-GHz spaced, POLMUX-CO-OFDM transmission over 4 160-km SSMF enabled by MIMO processing," Eur. Conf. Optical Communications (2007).

H. Bülow, "Electronic dispersion compensation," IEEE/OSA Optical Fiber Conf. (2007).

N. Cvijetic, L. Xu, T. Wang, "Adaptive PMD compensation using OFDM in long-haul 10 Gb/s DWDM systems," IEEE/OSA Opt. Fiber Conf. (2007) OTuA5.

M. Cvijetic, Optical Transmission Systems Engineering (Artech House, 2004).

S. G. Wilson, Digital Modulation and Coding. (Prentice-Hall, 1995).

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