Abstract

In the regime of strong mode coupling, the modal gains and losses and the modal group delays of a multimode fiber are known to have well-defined statistical properties. In mode-division multiplexing, mode-dependent gains and losses are known to cause fluctuations in the channel capacity, so that the capacity at finite outage probability can be substantially lower than the average capacity. Mode-dependent gains and losses, when frequency-dependent, have a coherence bandwidth that is inversely proportional to the modal group delay spread. When mode-division-multiplexed signals occupy a bandwidth far larger than the coherence bandwidth, the mode-dependent gains and losses are averaged over frequency, causing the outage capacity to approach the average capacity. The difference between the average and outage capacities is found to be inversely proportional to the square-root of a diversity order that is given approximately by the ratio of the signal bandwidth to the coherence bandwidth.

© 2011 IEEE

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  35. F. Yaman, N. Bai, B. Zhu, T. Wang, G. Li, "Long distance transmission in few-mode fibers," Opt. Expr. 18, 13250-13257 (2010).
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2011 (6)

A. Al Amni, A. Li, S. Chen, X. Chen, G. Gao, W. Shieh, "Dual-LP$_{11}$ mode 4$\,\times\,$4 MIMO-OFDM transmission over a two-mode fiber," Opt. Expr. 19, 16672--16678 (2011).

S. Randel, R. Ryf, A. Sierra, P. Winzer, A. H. Gnuack, C. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, R. Lingle, "6$\,\times\,$56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6$\,\times\,$6 MIMO equalization," Opt. Expr. 19, 16697-16707 (2011).

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$\,\times\,$100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer," Opt. Expr. 19, 16593-16600 (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. Expr. 19, 16612-16635 (2011).

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

2010 (2)

R. E. Freund, C.-A. Bunge, N. N. Ledentsov, D. Molin, C. Caspar, "High-speed transmission in multimode fibers," J. Lightw. Technol. 28, 569-586 (2010).

F. Yaman, N. Bai, B. Zhu, T. Wang, G. Li, "Long distance transmission in few-mode fibers," Opt. Expr. 18, 13250-13257 (2010).

2009 (2)

M. B. Shemirani, W. Mao, R. A. Panicker, J. M. Kahn, "Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling," J. Lightw. Technol. 27, 1248-1261 (2009).

K.-P. Ho, "Subband equaliser for chromatic dispersion of optical fibre," Electron. Lett. 45, 1224-1226 (2009).

2008 (2)

E. Ip, A. P. T. Lau, D. J. F. Barros, J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Expr. 16, 753-791 (2008).

M. Nazarathy, A. Agmon, "Coherent transmission direct detection MIMO over short-range optical interconnects and passive optical networks," J. Lightw. Technol. 26, 2037-2045 (2008).

2007 (1)

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, B. Jalali, "Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links," IEEE Commun. Mag. 57-63 (2007).

2006 (1)

R. M. Gray, "Toeplitz and circulant matrices: A review," Foundation Trends Commun. Inf. Theory 2, 155-239 (2006).

2005 (1)

A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, B. Jalali, "Coherent optical MIMO (COMIMO)," J. Lightw. Technol. 23, 2410-2419 (2005).

2004 (3)

K. Liu, T. Kadous, A. K. Sayeed, "Orthogonal time-frequency signaling over doubly dispersive channels," IEEE Trans. Inf. Theory 50, 2583-2602 (2004).

X. Zhu, R. D. Murch, "Layered space-frequency equalization in a single-carrier MIMO system for frequency-selective channels," IEEE Trans. Wireless Commun. 3, 701-708 (2004).

A. M. Tulino, S. Verdú, "Random matrix theory and wireless communications," Foundation Trends Commun. Inf. Theory 1, 1-182 (2004).

2003 (2)

X. Ma, G. B. Giannakis, "Maximum-diversity transmissions over doubly selective wireless channels," IEEE Trans. Inf. Theory 49, 1832-1840 (2003).

P. K. Pepeljugoski, D. M. Kuchta, "Design of optical communications data links," IBM J. Res. Dev. 47, 223-237 (2003).

2001 (2)

N. Al-Dhahir, "Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels," IEEE Commun. Lett. 5, 304-306 (2001).

M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightw. Technol. 19, 324-331 (2001).

2000 (1)

H. R. Stuart, "Dispersive multiplexing in multimode optical fiber," Science 289, 281-283 (2000).

1999 (1)

V. Tarokh, H. Jafarkhani, A. R. Calderbank, "Space-time block codes from orthogonal designs," IEEE Trans. Inf. Theory 45, 1456-1467 (1999).

1998 (1)

D. A. Nolan, M. J. Li, "Fiber spin-profile designs for producing fibers with low polarization mode dispersion," Opt. Lett. 23, 1659-1661 (1998).

1995 (2)

H. Sari, G. Karam, I. Jeanclaude, "Transmission techniques for digital terrestrial TV broadcasting," IEEE Commun. Mag. 100-109 (1995).

W. Y. Zou, Y. Wu, "COFDM: An overview," IEEE Trans. Broadcast. 41, 1-8 (1995).

1982 (1)

1980 (1)

K.-I. Kitayama, S. Sikai, N. Uchida, "Impulse response prediction based on experimental mode-coupling coefficient in a 10-km long graded-index fiber," J. Quantum Electron. QE-16, 356-362 (1980).

1975 (1)

R. Olshansky, "Mode-coupling effects in graded-index optical fibers," App. Opt. 14, 935-945 (1975).

1972 (2)

D. Gloge, "Optical power flow in multimode fibers," Bell System Tech. J. 51, 1767-1780 (1972).

R. M. Gray, "On the asymptotic eigenvalue distribution of Toeplitz matrices," IEEE Trans. Inf. Theory IT-18, 725-730 (1972).

1970 (1)

App. Opt. (1)

R. Olshansky, "Mode-coupling effects in graded-index optical fibers," App. Opt. 14, 935-945 (1975).

Appl. Opt. (2)

Bell System Tech. J. (1)

D. Gloge, "Optical power flow in multimode fibers," Bell System Tech. J. 51, 1767-1780 (1972).

Electron. Lett. (1)

K.-P. Ho, "Subband equaliser for chromatic dispersion of optical fibre," Electron. Lett. 45, 1224-1226 (2009).

Foundation Trends Commun. Inf. Theory (1)

A. M. Tulino, S. Verdú, "Random matrix theory and wireless communications," Foundation Trends Commun. Inf. Theory 1, 1-182 (2004).

Foundation Trends Commun. Inf. Theory (1)

R. M. Gray, "Toeplitz and circulant matrices: A review," Foundation Trends Commun. Inf. Theory 2, 155-239 (2006).

IBM J. Res. Dev. (1)

P. K. Pepeljugoski, D. M. Kuchta, "Design of optical communications data links," IBM J. Res. Dev. 47, 223-237 (2003).

IEEE Commun. Mag. (1)

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, B. Jalali, "Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links," IEEE Commun. Mag. 57-63 (2007).

IEEE Trans. Broadcast. (1)

W. Y. Zou, Y. Wu, "COFDM: An overview," IEEE Trans. Broadcast. 41, 1-8 (1995).

IEEE Trans. Inf. Theory (1)

X. Ma, G. B. Giannakis, "Maximum-diversity transmissions over doubly selective wireless channels," IEEE Trans. Inf. Theory 49, 1832-1840 (2003).

IEEE Commun. Lett. (1)

N. Al-Dhahir, "Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels," IEEE Commun. Lett. 5, 304-306 (2001).

IEEE Commun. Mag. (1)

H. Sari, G. Karam, I. Jeanclaude, "Transmission techniques for digital terrestrial TV broadcasting," IEEE Commun. Mag. 100-109 (1995).

IEEE Trans. Inf. Theory (2)

K. Liu, T. Kadous, A. K. Sayeed, "Orthogonal time-frequency signaling over doubly dispersive channels," IEEE Trans. Inf. Theory 50, 2583-2602 (2004).

R. M. Gray, "On the asymptotic eigenvalue distribution of Toeplitz matrices," IEEE Trans. Inf. Theory IT-18, 725-730 (1972).

IEEE Trans. Inf. Theory (1)

V. Tarokh, H. Jafarkhani, A. R. Calderbank, "Space-time block codes from orthogonal designs," IEEE Trans. Inf. Theory 45, 1456-1467 (1999).

IEEE Trans. Wireless Commun. (1)

X. Zhu, R. D. Murch, "Layered space-frequency equalization in a single-carrier MIMO system for frequency-selective channels," IEEE Trans. Wireless Commun. 3, 701-708 (2004).

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. (5)

A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, B. Jalali, "Coherent optical MIMO (COMIMO)," J. Lightw. Technol. 23, 2410-2419 (2005).

M. Nazarathy, A. Agmon, "Coherent transmission direct detection MIMO over short-range optical interconnects and passive optical networks," J. Lightw. Technol. 26, 2037-2045 (2008).

R. E. Freund, C.-A. Bunge, N. N. Ledentsov, D. Molin, C. Caspar, "High-speed transmission in multimode fibers," J. Lightw. Technol. 28, 569-586 (2010).

M. Karlsson, "Probability density functions of the differential group delay in optical fiber communication systems," J. Lightw. Technol. 19, 324-331 (2001).

M. B. Shemirani, W. Mao, R. A. Panicker, J. M. Kahn, "Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling," J. Lightw. Technol. 27, 1248-1261 (2009).

J. Quantum Electron. (1)

K.-I. Kitayama, S. Sikai, N. Uchida, "Impulse response prediction based on experimental mode-coupling coefficient in a 10-km long graded-index fiber," J. Quantum Electron. QE-16, 356-362 (1980).

Opt. Expr. (2)

F. Yaman, N. Bai, B. Zhu, T. Wang, G. Li, "Long distance transmission in few-mode fibers," Opt. Expr. 18, 13250-13257 (2010).

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

Opt. Lett. (1)

D. A. Nolan, M. J. Li, "Fiber spin-profile designs for producing fibers with low polarization mode dispersion," Opt. Lett. 23, 1659-1661 (1998).

Opt. Expr. (5)

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

A. Al Amni, A. Li, S. Chen, X. Chen, G. Gao, W. Shieh, "Dual-LP$_{11}$ mode 4$\,\times\,$4 MIMO-OFDM transmission over a two-mode fiber," Opt. Expr. 19, 16672--16678 (2011).

S. Randel, R. Ryf, A. Sierra, P. Winzer, A. H. Gnuack, C. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, R. Lingle, "6$\,\times\,$56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6$\,\times\,$6 MIMO equalization," Opt. Expr. 19, 16697-16707 (2011).

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$\,\times\,$100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS based mode multiplexer and demultiplexer," Opt. Expr. 19, 16593-16600 (2011).

E. Ip, A. P. T. Lau, D. J. F. Barros, J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Expr. 16, 753-791 (2008).

Science (1)

H. R. Stuart, "Dispersive multiplexing in multimode optical fiber," Science 289, 281-283 (2000).

Other (11)

E. Lindskog, A. Paulraj, "A transmit diversity scheme for delay spreads channel," Proc. IEEE ICC (2000) pp. 207-311.

K. F. Lee, D. B. Williams, "A space-frequency transmitter diversity techniques for OFDM systems," IEEE GlobeCom (2000) pp. 1473-1477.

T. S. Rappaport, Wireless Communications: Principles & Practice (Prentice Hall, 2002).

Y. Koike, S. Takahashi, Optical Fiber Telecommunications VB: Systems and Networks (Elsevier Academic, 2008).

I. T. Jolliffe, Principal Component Analysis (Springer, 2002).

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (Wiley-IEEE, 1987).

M. Vetterli, J. Kovačević, Wavelets and Subband Coding (Prentice Hall, 1995).

G. R. Grimmett, D. R. Stirzaker, Probability and Random Processes (Oxford Univ. Press, 1992).

D. Tse, P. Viswanath, Fundamentals of Wireless Communication (Cambridge Univ. Press, 2005).

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Natl. Acad. Sci. (2000) pp. 4541-4550.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, 1974).

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