Abstract

When an electronic equalizer is used to compensate the modal dispersion in a mode-division multiplexed system, receiver phase noise induces interference to the multi-input- multi-output (MIMO) receiver. Based on the statistics of the modal dispersion in the strong coupling regime, the interference variance is evaluated analytically based on an exact model, a semicircle asymptotic for large number of modes, and a first-order approximation.

© 2013 IEEE

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  1. A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, W. Shieh, "Reception of dual-spatial-mode CO-OFDM signal over a two-mode fiber," J. Lightw. Technol. 30, 634-640 (2012).
  2. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, R. Lingle, "Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing," J. Lightw. Technol. 30, 521-531 (2012).
  3. L. Gruner-Nielsen, Y. Sun, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, B. Palsdottir, "Few mode transmission fiber with low DGD, low mode coupling, and low loss," J. Lightw. Technol. 30, 3693-3698 (2012).
  4. C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Margoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer," Opt. Exp. 19, 16593-16600 (2011).
  5. K.-P. Ho, J. M. Kahn, Optical Fiber Telecommunications VIB (Academic, 2013) pp. 491-568.
  6. W. Shieh, K. P. Ho, "Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing," Opt. Exp. 16, 15718-15727 (2008).
  7. C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Exp. 17, 4815-4823 (2009).
  8. A. P. T. Lau, T. S. R. Shen, W. Shieh, K. P. Ho, "Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection," Opt. Exp. 18, 17239-17251 (2010).
  9. Q. B. Zhuge, C. Chen, D. V. Plant, "Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission," Opt. Exp. 19, 4472-4484 (2011).
  10. W. Shieh, "Interaction of laser phase noise with differential-mode-delay in few-mode fibre based MIMO systems," Proc. OFC/NFOEC '12 (2012).
  11. K.-P. Ho, J. M. Kahn, "Frequency diversity in mode-division multiplexing systems," J. Lightw. Technol. 29, 3719-3726 (2011).
  12. K. P. Ho, J. M. Kahn, "Statistics of group delays in multimode fiber with strong mode coupling," J. Lightw. Technol. 29, 3119-3128 (2011).
  13. K. P. Ho, J. M. Kahn, "Delay-spread distribution for multimode fiber with strong mode coupling," IEEE Photon. Technol. Lett. 24, 1906-1909 (2012).
  14. S. Ö. Arik, D. Askarov, J. M. Kahn, "Effect of mode coupling on signal processing complexity in mode-division multiplexing," J. Lightw. Technol. 31, 423-431 (2013).
  15. K.-P. Ho, J. M. Kahn, "Mode-dependent loss and gain: Statistics and effect on mode-division multiplexing," Opt. Exp. 19, 16612-16635 (2011).
  16. A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, B. Lankl, "Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission," Opt. Exp. 20, 29776-29783 (2012).
  17. S. Warm, K. Petermann, "Splice loss requirements in multi-mode fiber mode-division-multiplex transmission links," Opt. Exp. 21, 519-532 (2013).
  18. A. Mecozzi, C. Antonelli, M. Shtaif, "Coupled Manakov equations in multimode fibers with strongly coupled groups of modes," Opt. Exp. 20, 23436-23441 (2012).
  19. S. Fan, J. M. Kahn, "Principal modes in multimode waveguides," Opt. Lett. 20, 135-137 (2006).
  20. P. J. Winzer, G. J. Foschini, "MIMO capacities and outage probabilities in spatially multiplexed optical transport systems," Opt. Exp. 19, 16680-16696 (2011).
  21. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).
  22. E. Wigner, "Characteristic vectors of bordered matrices with infinite dimensions," Ann. Math. 62, 548-564 (1955).
  23. T. Tao, V. H. Vu, "From the Littlewood-Offord problem to the circular law: Universality of the spectral distribution of random matrices," Bull. Am. Math. Soc. 46, 337-396 (2009).
  24. G. N. Watson, A Treatise of the Theory of Bessel Functions (Cambridge Univ. Press, 1922).
  25. Y. L. Yuke, Mathematical Functions and Their Applications (Academic, 1975).
  26. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1979).
  27. L. J. Slater, Generalized Hypergeometric Functions (Cambridge Univ. Press, 1966).
  28. K.-P. Ho, "Effects of homodyne crosstalk on dual-polarization QPSK signals," J. Lightw. Technol. 29, 124-131 (2011).
  29. M. B. Shemirani, J. M. Kahn, "Higher-order modal dispersion in graded-index multimode fiber," J. Lightw. Technol. 27, 5461-5468 (2009).
  30. A. Heck, Introduction to Maple (Springer, 2003).
  31. M. Creutz, "On invariant integration over SU(N)," J. Math. Phys. 19, 2043-2046 (1978).
  32. P. A. Mello, "Averages on the unitary group and applications to the problem of disordered conductors," J. Phys., A: Math. Gen. 23, 4061-4080 (1990).
  33. C. W. J. Beenaker, "Random-matrix theory of quantum transport," Rev. Mod. Phys. 69, 731-808 (1997).
  34. M. L. Mehta, Random Matrices (Elsevier, 2004).

2013 (2)

S. Ö. Arik, D. Askarov, J. M. Kahn, "Effect of mode coupling on signal processing complexity in mode-division multiplexing," J. Lightw. Technol. 31, 423-431 (2013).

S. Warm, K. Petermann, "Splice loss requirements in multi-mode fiber mode-division-multiplex transmission links," Opt. Exp. 21, 519-532 (2013).

2012 (6)

A. Mecozzi, C. Antonelli, M. Shtaif, "Coupled Manakov equations in multimode fibers with strongly coupled groups of modes," Opt. Exp. 20, 23436-23441 (2012).

K. P. Ho, J. M. Kahn, "Delay-spread distribution for multimode fiber with strong mode coupling," IEEE Photon. Technol. Lett. 24, 1906-1909 (2012).

A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, B. Lankl, "Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission," Opt. Exp. 20, 29776-29783 (2012).

A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, W. Shieh, "Reception of dual-spatial-mode CO-OFDM signal over a two-mode fiber," J. Lightw. Technol. 30, 634-640 (2012).

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, R. Lingle, "Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing," J. Lightw. Technol. 30, 521-531 (2012).

L. Gruner-Nielsen, Y. Sun, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, B. Palsdottir, "Few mode transmission fiber with low DGD, low mode coupling, and low loss," J. Lightw. Technol. 30, 3693-3698 (2012).

2011 (7)

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Margoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer," Opt. Exp. 19, 16593-16600 (2011).

Q. B. Zhuge, C. Chen, D. V. Plant, "Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission," Opt. Exp. 19, 4472-4484 (2011).

K.-P. Ho, J. M. Kahn, "Frequency diversity in mode-division multiplexing systems," J. Lightw. Technol. 29, 3719-3726 (2011).

K. P. Ho, J. M. Kahn, "Statistics of group delays in multimode fiber with strong mode coupling," J. Lightw. Technol. 29, 3119-3128 (2011).

K.-P. Ho, J. M. Kahn, "Mode-dependent loss and gain: Statistics and effect on mode-division multiplexing," Opt. Exp. 19, 16612-16635 (2011).

P. J. Winzer, G. J. Foschini, "MIMO capacities and outage probabilities in spatially multiplexed optical transport systems," Opt. Exp. 19, 16680-16696 (2011).

K.-P. Ho, "Effects of homodyne crosstalk on dual-polarization QPSK signals," J. Lightw. Technol. 29, 124-131 (2011).

2010 (1)

A. P. T. Lau, T. S. R. Shen, W. Shieh, K. P. Ho, "Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection," Opt. Exp. 18, 17239-17251 (2010).

2009 (3)

C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Exp. 17, 4815-4823 (2009).

M. B. Shemirani, J. M. Kahn, "Higher-order modal dispersion in graded-index multimode fiber," J. Lightw. Technol. 27, 5461-5468 (2009).

T. Tao, V. H. Vu, "From the Littlewood-Offord problem to the circular law: Universality of the spectral distribution of random matrices," Bull. Am. Math. Soc. 46, 337-396 (2009).

2008 (1)

W. Shieh, K. P. Ho, "Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing," Opt. Exp. 16, 15718-15727 (2008).

2006 (1)

S. Fan, J. M. Kahn, "Principal modes in multimode waveguides," Opt. Lett. 20, 135-137 (2006).

1997 (1)

C. W. J. Beenaker, "Random-matrix theory of quantum transport," Rev. Mod. Phys. 69, 731-808 (1997).

1990 (1)

P. A. Mello, "Averages on the unitary group and applications to the problem of disordered conductors," J. Phys., A: Math. Gen. 23, 4061-4080 (1990).

1978 (1)

M. Creutz, "On invariant integration over SU(N)," J. Math. Phys. 19, 2043-2046 (1978).

1955 (1)

E. Wigner, "Characteristic vectors of bordered matrices with infinite dimensions," Ann. Math. 62, 548-564 (1955).

Ann. Math. (1)

E. Wigner, "Characteristic vectors of bordered matrices with infinite dimensions," Ann. Math. 62, 548-564 (1955).

Bull. Am. Math. Soc. (1)

T. Tao, V. H. Vu, "From the Littlewood-Offord problem to the circular law: Universality of the spectral distribution of random matrices," Bull. Am. Math. Soc. 46, 337-396 (2009).

IEEE Photon. Technol. Lett. (1)

K. P. Ho, J. M. Kahn, "Delay-spread distribution for multimode fiber with strong mode coupling," IEEE Photon. Technol. Lett. 24, 1906-1909 (2012).

J. Lightw. Technol. (1)

K. P. Ho, J. M. Kahn, "Statistics of group delays in multimode fiber with strong mode coupling," J. Lightw. Technol. 29, 3119-3128 (2011).

J. Lightw. Technol. (4)

A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, W. Shieh, "Reception of dual-spatial-mode CO-OFDM signal over a two-mode fiber," J. Lightw. Technol. 30, 634-640 (2012).

L. Gruner-Nielsen, Y. Sun, J. W. Nicholson, D. Jakobsen, K. G. Jespersen, R. Lingle, B. Palsdottir, "Few mode transmission fiber with low DGD, low mode coupling, and low loss," J. Lightw. Technol. 30, 3693-3698 (2012).

K.-P. Ho, "Effects of homodyne crosstalk on dual-polarization QPSK signals," J. Lightw. Technol. 29, 124-131 (2011).

M. B. Shemirani, J. M. Kahn, "Higher-order modal dispersion in graded-index multimode fiber," J. Lightw. Technol. 27, 5461-5468 (2009).

J. Lightw. Technol. (3)

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, R. Lingle, "Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing," J. Lightw. Technol. 30, 521-531 (2012).

K.-P. Ho, J. M. Kahn, "Frequency diversity in mode-division multiplexing systems," J. Lightw. Technol. 29, 3719-3726 (2011).

S. Ö. Arik, D. Askarov, J. M. Kahn, "Effect of mode coupling on signal processing complexity in mode-division multiplexing," J. Lightw. Technol. 31, 423-431 (2013).

J. Math. Phys. (1)

M. Creutz, "On invariant integration over SU(N)," J. Math. Phys. 19, 2043-2046 (1978).

J. Phys., A: Math. Gen. (1)

P. A. Mello, "Averages on the unitary group and applications to the problem of disordered conductors," J. Phys., A: Math. Gen. 23, 4061-4080 (1990).

Opt. Exp. (4)

K.-P. Ho, J. M. Kahn, "Mode-dependent loss and gain: Statistics and effect on mode-division multiplexing," Opt. Exp. 19, 16612-16635 (2011).

W. Shieh, K. P. Ho, "Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing," Opt. Exp. 16, 15718-15727 (2008).

C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Exp. 17, 4815-4823 (2009).

Q. B. Zhuge, C. Chen, D. V. Plant, "Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission," Opt. Exp. 19, 4472-4484 (2011).

Opt. Exp. (6)

A. P. T. Lau, T. S. R. Shen, W. Shieh, K. P. Ho, "Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection," Opt. Exp. 18, 17239-17251 (2010).

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Margoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, G. Charlet, "Two mode transmission at 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer," Opt. Exp. 19, 16593-16600 (2011).

A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, B. Lankl, "Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission," Opt. Exp. 20, 29776-29783 (2012).

S. Warm, K. Petermann, "Splice loss requirements in multi-mode fiber mode-division-multiplex transmission links," Opt. Exp. 21, 519-532 (2013).

A. Mecozzi, C. Antonelli, M. Shtaif, "Coupled Manakov equations in multimode fibers with strongly coupled groups of modes," Opt. Exp. 20, 23436-23441 (2012).

P. J. Winzer, G. J. Foschini, "MIMO capacities and outage probabilities in spatially multiplexed optical transport systems," Opt. Exp. 19, 16680-16696 (2011).

Opt. Lett. (1)

S. Fan, J. M. Kahn, "Principal modes in multimode waveguides," Opt. Lett. 20, 135-137 (2006).

Rev. Mod. Phys. (1)

C. W. J. Beenaker, "Random-matrix theory of quantum transport," Rev. Mod. Phys. 69, 731-808 (1997).

Other (9)

M. L. Mehta, Random Matrices (Elsevier, 2004).

G. N. Watson, A Treatise of the Theory of Bessel Functions (Cambridge Univ. Press, 1922).

Y. L. Yuke, Mathematical Functions and Their Applications (Academic, 1975).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1979).

L. J. Slater, Generalized Hypergeometric Functions (Cambridge Univ. Press, 1966).

A. Heck, Introduction to Maple (Springer, 2003).

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).

K.-P. Ho, J. M. Kahn, Optical Fiber Telecommunications VIB (Academic, 2013) pp. 491-568.

W. Shieh, "Interaction of laser phase noise with differential-mode-delay in few-mode fibre based MIMO systems," Proc. OFC/NFOEC '12 (2012).

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