Abstract

We study an optical space-division multiplexed system where the number of modes that are addressed by the transmitter and receiver is allowed to be smaller than the total number of optical modes supported by the fiber. This situation will be of relevance if, for instance, fibers supporting more modes than can be processed with current multiple-input, multiple-output technology are deployed with the purpose of future-proof installation. We calculate the ergodic capacity and the outage probability of the link and study their dependence on the number of addressed modes at the transmitter and receiver.

© 2012 Optical Society of America

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References

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  1. A. R. Chraplyvy, “The coming capacity crunch,” presented at the European Conference on Optical Communication 2009 (ECOC09), Vienna, Austria, 20–24September2009, plenary talk.
  2. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, Opt. Express 19, 16697 (2011).
    [CrossRef]
  3. P. J. Winzer and G. J. Foschini, Opt. Express 19, 16680 (2011).
    [CrossRef]
  4. K.-P. Ho and J. M. Kahn, J. Lightwave Technol. 29, 3719 (2011).
    [CrossRef]
  5. C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, Opt. Express 20, 11718 (2012).
    [CrossRef]
  6. K.-P. Ho and J. M. Kahn, J. Lightwave Technol. 29, 3119 (2011).
    [CrossRef]
  7. I. E. Telatar, Eur. Trans. Telecommun. 10, 585 (1999).
    [CrossRef]
  8. R. J. Muirhead, Aspects of Multivariate Statistical Theory (Wiley, 1982).
  9. A. Edelman and N. R. Rao, Acta Numerica 14, 233 (1999).
    [CrossRef]
  10. A. Edelman and B. D. Sutton, Found. Comput. Math. 8, 259 (2008).
    [CrossRef]
  11. R. Dar, M. Feder, and M. Shtaif, “The Jacobi MIMO channel” (2012), http://arxiv.org/abs/1202.0305 .
  12. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).

2012 (1)

2011 (4)

2008 (1)

A. Edelman and B. D. Sutton, Found. Comput. Math. 8, 259 (2008).
[CrossRef]

1999 (2)

I. E. Telatar, Eur. Trans. Telecommun. 10, 585 (1999).
[CrossRef]

A. Edelman and N. R. Rao, Acta Numerica 14, 233 (1999).
[CrossRef]

Antonelli, C.

Bolle, C. A.

Chraplyvy, A. R.

A. R. Chraplyvy, “The coming capacity crunch,” presented at the European Conference on Optical Communication 2009 (ECOC09), Vienna, Austria, 20–24September2009, plenary talk.

Edelman, A.

A. Edelman and B. D. Sutton, Found. Comput. Math. 8, 259 (2008).
[CrossRef]

A. Edelman and N. R. Rao, Acta Numerica 14, 233 (1999).
[CrossRef]

Essiambre, R.-J.

Foschini, G. J.

Gnauck, A. H.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).

Ho, K.-P.

Kahn, J. M.

Lingle, R.

McCurdy, A.

Mecozzi, A.

Muirhead, R. J.

R. J. Muirhead, Aspects of Multivariate Statistical Theory (Wiley, 1982).

Peckham, D. W.

Randel, S.

Rao, N. R.

A. Edelman and N. R. Rao, Acta Numerica 14, 233 (1999).
[CrossRef]

Ryf, R.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).

Shtaif, M.

Sierra, A.

Sutton, B. D.

A. Edelman and B. D. Sutton, Found. Comput. Math. 8, 259 (2008).
[CrossRef]

Telatar, I. E.

I. E. Telatar, Eur. Trans. Telecommun. 10, 585 (1999).
[CrossRef]

Winzer, P. J.

Acta Numerica (1)

A. Edelman and N. R. Rao, Acta Numerica 14, 233 (1999).
[CrossRef]

Eur. Trans. Telecommun. (1)

I. E. Telatar, Eur. Trans. Telecommun. 10, 585 (1999).
[CrossRef]

Found. Comput. Math. (1)

A. Edelman and B. D. Sutton, Found. Comput. Math. 8, 259 (2008).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (3)

Other (4)

A. R. Chraplyvy, “The coming capacity crunch,” presented at the European Conference on Optical Communication 2009 (ECOC09), Vienna, Austria, 20–24September2009, plenary talk.

R. J. Muirhead, Aspects of Multivariate Statistical Theory (Wiley, 1982).

R. Dar, M. Feder, and M. Shtaif, “The Jacobi MIMO channel” (2012), http://arxiv.org/abs/1202.0305 .

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1980).

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Figures (2)

Fig. 1.
Fig. 1.

Ergodic capacity normalized by C(1,1,1;ρ)=log(1+ρ2) versus ρ2 for various combinations of mt×mr with m=6.

Fig. 2.
Fig. 2.

Outage probability versus the normalized rate r. The number of supported modes is m=6 and ρ2=20dB.

Equations (9)

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y̲=ρH11x̲+z̲,
H=[H11H12H21H22].
C(mt,mr,m;ρ)=E[i=1mminlog(1+ρ2λi)],
C(mt,mr,m;ρ)=01log(1+λρ2)×λα(1λ)βk=0mmin1bk,α,β1[Pk(α,β)(12λ)]2dλ,
bk,α,β=12k+α+β+1(2k+α+βk)(2k+α+βk+α)1.
C(mt,mr,m;ρ)=(mt+mrm)C(1,1,1;ρ)+C(mmr,mmt,m;ρ),
Pout(mt,mr,m;R)=Pr[logdet(Imt+ρ2H11H11)<R].
Pout(mt,mr,m;R)=Kmt,mr,m1Bi=1mminλi|mrmt|×(1λi)mmrmti<j(λiλj)2dλ,
Pout(mt,mr,m;rlog(1+ρ2))=Pout(mmr,mmt,m;r˜log(1+ρ2)),

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