Abstract

Channel matrix plays a critical role in receiver design and ultimate channel performance. To fully describe the channel matrix of a few-mode fiber (FMF), we choose the generalized high-dimensional Gell-Mann matrices, an equivalent of the 2-dimensional Pauli matrices used for a single-mode fiber (SMF), as the basis for the channel matrix decomposition. The frequency dependence of channel matrix can be studied in terms of the autocorrelation function (ACF), showing how fast channel changes in frequency domain. In this paper, we derive a canonical stochastic differential equation (SDE) for the FMF channel matrix in the regime of strong coupling. With the SDE, we develop an analytical form for the ACF of FMF channel matrix, from which the channel correlation bandwidth is obtained.

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References

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    [CrossRef]

2012

2011

2002

2001

2000

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

1998

M. Hsieh and C. Wei, “Channel estimation for OFDM systems based in comb-type pilot arrangement in frequency selective fading channels,” IEEE Trans. Consum. Electron.44(1), 217–225 (1998).
[CrossRef]

1997

S. Weigert, “Baker-Campbell-Hausdorff relation for special unitary groups SU(N),” J. Phys. Math. Gen.30(24), 8739–8749 (1997).
[CrossRef]

1996

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fiber with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
[CrossRef]

1991

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol.9(11), 1439–1456 (1991).
[CrossRef]

1975

D. C. Cox and R. Leck, “Correlation bandwidth and delay spread multipath propagation statistics for 91-MHz urban mobile radio channels,” IEEE Trans. Commun.23(11), 1271–1280 (1975).
[CrossRef]

R. Olshansky, “Mode-coupling effects in graded-index optical fibers,” Appl. Opt.14(4), 935–945 (1975).
[CrossRef] [PubMed]

1962

M. Gell-Man, “Symmetries of Baryons and Mesons,” Phys. Rev.125(3), 1067–1084 (1962).
[CrossRef]

Al Amin, A.

Antonelli, C.

Bai, N.

Bickham, S.

Bolle, C.

Bononi, A.

Burrows, E. C.

Chen, S.

Chen, X.

Cox, D. C.

D. C. Cox and R. Leck, “Correlation bandwidth and delay spread multipath propagation statistics for 91-MHz urban mobile radio channels,” IEEE Trans. Commun.23(11), 1271–1280 (1975).
[CrossRef]

Esmaeelpour, M.

Essiambre, R.

Foschini, G. J.

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol.9(11), 1439–1456 (1991).
[CrossRef]

Gao, G.

Gell-Man, M.

M. Gell-Man, “Symmetries of Baryons and Mesons,” Phys. Rev.125(3), 1067–1084 (1962).
[CrossRef]

Gnauck, A. H.

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Ho, K.-P.

Hsieh, M.

M. Hsieh and C. Wei, “Channel estimation for OFDM systems based in comb-type pilot arrangement in frequency selective fading channels,” IEEE Trans. Consum. Electron.44(1), 217–225 (1998).
[CrossRef]

Huang, Y. K.

Ip, E.

Kahn, J. M.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Lau, A. P. T.

Leck, R.

D. C. Cox and R. Leck, “Correlation bandwidth and delay spread multipath propagation statistics for 91-MHz urban mobile radio channels,” IEEE Trans. Commun.23(11), 1271–1280 (1975).
[CrossRef]

Li, A.

Li, G.

Li, M. J.

Liñares, J.

Lingle, R.

Lu, C.

Luo, Y.

Man Chung, K.

Mateo, E.

McCurdy, A. H.

Mecozzi, A.

Menyuk, C. R.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fiber with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
[CrossRef]

Montero, C.

Moreno, V.

Mumtaz, S.

Olshansky, R.

Peckham, D. W.

Peng, G. D.

Poole, C. D.

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol.9(11), 1439–1456 (1991).
[CrossRef]

Prieto, X.

Randel, S.

Ryf, R.

Shieh, W.

Shtaif, M.

Sierra, A.

Tam, H. Y.

Ten, S.

Tse, V.

Vannucci, A.

Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fiber with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
[CrossRef]

Wang, T.

Wei, C.

M. Hsieh and C. Wei, “Channel estimation for OFDM systems based in comb-type pilot arrangement in frequency selective fading channels,” IEEE Trans. Consum. Electron.44(1), 217–225 (1998).
[CrossRef]

Weigert, S.

S. Weigert, “Baker-Campbell-Hausdorff relation for special unitary groups SU(N),” J. Phys. Math. Gen.30(24), 8739–8749 (1997).
[CrossRef]

Winzer, P. J.

Yaman, F.

Appl. Opt.

IEEE Trans. Commun.

D. C. Cox and R. Leck, “Correlation bandwidth and delay spread multipath propagation statistics for 91-MHz urban mobile radio channels,” IEEE Trans. Commun.23(11), 1271–1280 (1975).
[CrossRef]

IEEE Trans. Consum. Electron.

M. Hsieh and C. Wei, “Channel estimation for OFDM systems based in comb-type pilot arrangement in frequency selective fading channels,” IEEE Trans. Consum. Electron.44(1), 217–225 (1998).
[CrossRef]

J. Lightwave Technol.

J. Phys. Math. Gen.

S. Weigert, “Baker-Campbell-Hausdorff relation for special unitary groups SU(N),” J. Phys. Math. Gen.30(24), 8739–8749 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

M. Gell-Man, “Symmetries of Baryons and Mesons,” Phys. Rev.125(3), 1067–1084 (1962).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Other

C. Antonelli, A. Mecozzi, and M. Shtaif, “Modeling of linear and nonlinear coupling in multiple-mode fiber optic transmission with MIMO signal processing,” Signals, Systems and Computers (Asilomar, 2012), 645–649.

L. Arnold, Stochastic Differential Equations Theory and Application (Wiley 1974).

T. C. Gard, Introduction to Stochastic Differential Equations (Marcel Dekker, INC. 1988).

B. Øksendal, Stochastic Differential Equation (Springer-Verlag Berlin Heidelberg 1989).

A. Li, A. A. Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” OFC/NFOEC2011, PDPB8 (2011).

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Figures (1)

Fig. 1
Fig. 1

The comparison of the analytical and simulation result for the ACF of the FMF channel matrix with 2 to 4 spatial modes.

Equations (1)

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Λ k = 2 k(k+1) [ 1 1 k 0 0 ]( k=1 to n1 ).

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