Abstract

The capacity of mode-division multiplexing (MDM) systems is limited, for a given outage probability, by mode-dependent loss (MDL) and gain. Modal degrees of freedom may be exploited to increase transmission rate (multiplexing gain) or lower outage probability (diversity gain), but there is a fundamental tradeoff between the achievable multiplexing and diversity gains. In this Letter, we present the diversity-multiplexing tradeoff in MDM systems for the first time, studying the impact of signal-to-noise ratio, MDL, and frequency diversity order on the tradeoff in the strong-mode-coupling regime.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. J. Essiambre and R. W. Tkach, Proc. IEEE 100, 1035 (2012).
    [CrossRef]
  2. T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
    [CrossRef]
  3. K.-P. Ho and J. M. Kahn, Opt. Express 19, 16612 (2011).
    [CrossRef]
  4. K.-P. Ho and J. M. Kahn, in Optical Fiber Telecommunications VI, I. P. Kaminow, T. Li, and A. E. Willner, eds., (Elsevier, 2013), pp. 491–568.
  5. P. J. Winzer and G. J. Foschini, Opt. Express 19, 16680 (2011).
    [CrossRef]
  6. P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
    [CrossRef]
  7. Z. Lizhong and D. Tse, IEEE Trans. Inf. Theory 49, 1073 (2003).
    [CrossRef]
  8. L. Zhao, W. Mo, Y. Ma, and Z. Wang, IEEE Trans. Inf. Theory 53, 1549 (2007).
    [CrossRef]
  9. R. Narasimhan, IEEE Trans. Inf. Theory 52, 3965 (2006).
    [CrossRef]
  10. A. Medles and D. Slock, in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2005), pp. 1813–1817.
  11. D. Tse, P. Viswanath, and L. Zheng, IEEE Trans. Inf. Theory 50, 1859 (2004).
    [CrossRef]
  12. S. Ö. Arik, J. M. Kahn, and K.-P. Ho, IEEE Signal Process. Mag. 31(2), 25 (2014).
    [CrossRef]
  13. S. Ö. Arik, D. Askarov, and J. M. Kahn, J. Lightwave Technol. 31, 423 (2013).
    [CrossRef]
  14. S. Mumtaz, R. Essiambre, and G. Agrawal, J. Lightwave Technol. 31, 398 (2013).
    [CrossRef]
  15. R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol. 28, 662 (2010).
    [CrossRef]
  16. K.-P. Ho, J. Lightwave Technol. 30, 3603 (2012).
    [CrossRef]
  17. K.-P. Ho and J. M. Kahn, J. Lightwave Technol. 29, 3719 (2011).
    [CrossRef]
  18. C. Marco, D. Dardari, and M. K. Simon, IEEE Trans. Wirel. Commun. 2, 840 (2003).
    [CrossRef]

2014

S. Ö. Arik, J. M. Kahn, and K.-P. Ho, IEEE Signal Process. Mag. 31(2), 25 (2014).
[CrossRef]

2013

2012

K.-P. Ho, J. Lightwave Technol. 30, 3603 (2012).
[CrossRef]

R. J. Essiambre and R. W. Tkach, Proc. IEEE 100, 1035 (2012).
[CrossRef]

T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
[CrossRef]

2011

2010

2007

L. Zhao, W. Mo, Y. Ma, and Z. Wang, IEEE Trans. Inf. Theory 53, 1549 (2007).
[CrossRef]

2006

R. Narasimhan, IEEE Trans. Inf. Theory 52, 3965 (2006).
[CrossRef]

P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
[CrossRef]

2004

D. Tse, P. Viswanath, and L. Zheng, IEEE Trans. Inf. Theory 50, 1859 (2004).
[CrossRef]

2003

C. Marco, D. Dardari, and M. K. Simon, IEEE Trans. Wirel. Commun. 2, 840 (2003).
[CrossRef]

Z. Lizhong and D. Tse, IEEE Trans. Inf. Theory 49, 1073 (2003).
[CrossRef]

Agrawal, G.

Arik, S. Ö.

S. Ö. Arik, J. M. Kahn, and K.-P. Ho, IEEE Signal Process. Mag. 31(2), 25 (2014).
[CrossRef]

S. Ö. Arik, D. Askarov, and J. M. Kahn, J. Lightwave Technol. 31, 423 (2013).
[CrossRef]

Askarov, D.

Awaji, Y.

T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
[CrossRef]

Dardari, D.

C. Marco, D. Dardari, and M. K. Simon, IEEE Trans. Wirel. Commun. 2, 840 (2003).
[CrossRef]

Elia, P.

P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
[CrossRef]

Essiambre, R.

Essiambre, R. J.

Foschini, G. J.

Goebel, B.

Ho, K.-P.

S. Ö. Arik, J. M. Kahn, and K.-P. Ho, IEEE Signal Process. Mag. 31(2), 25 (2014).
[CrossRef]

K.-P. Ho, J. Lightwave Technol. 30, 3603 (2012).
[CrossRef]

K.-P. Ho and J. M. Kahn, J. Lightwave Technol. 29, 3719 (2011).
[CrossRef]

K.-P. Ho and J. M. Kahn, Opt. Express 19, 16612 (2011).
[CrossRef]

K.-P. Ho and J. M. Kahn, in Optical Fiber Telecommunications VI, I. P. Kaminow, T. Li, and A. E. Willner, eds., (Elsevier, 2013), pp. 491–568.

Kahn, J. M.

S. Ö. Arik, J. M. Kahn, and K.-P. Ho, IEEE Signal Process. Mag. 31(2), 25 (2014).
[CrossRef]

S. Ö. Arik, D. Askarov, and J. M. Kahn, J. Lightwave Technol. 31, 423 (2013).
[CrossRef]

K.-P. Ho and J. M. Kahn, J. Lightwave Technol. 29, 3719 (2011).
[CrossRef]

K.-P. Ho and J. M. Kahn, Opt. Express 19, 16612 (2011).
[CrossRef]

K.-P. Ho and J. M. Kahn, in Optical Fiber Telecommunications VI, I. P. Kaminow, T. Li, and A. E. Willner, eds., (Elsevier, 2013), pp. 491–568.

Kramer, G.

Kumar, K. R.

P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
[CrossRef]

Kumar, P. V.

P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
[CrossRef]

Lizhong, Z.

Z. Lizhong and D. Tse, IEEE Trans. Inf. Theory 49, 1073 (2003).
[CrossRef]

Lu, H.

P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
[CrossRef]

Ma, Y.

L. Zhao, W. Mo, Y. Ma, and Z. Wang, IEEE Trans. Inf. Theory 53, 1549 (2007).
[CrossRef]

Marco, C.

C. Marco, D. Dardari, and M. K. Simon, IEEE Trans. Wirel. Commun. 2, 840 (2003).
[CrossRef]

Medles, A.

A. Medles and D. Slock, in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2005), pp. 1813–1817.

Mo, W.

L. Zhao, W. Mo, Y. Ma, and Z. Wang, IEEE Trans. Inf. Theory 53, 1549 (2007).
[CrossRef]

Morioka, T.

T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
[CrossRef]

Mumtaz, S.

Narasimhan, R.

R. Narasimhan, IEEE Trans. Inf. Theory 52, 3965 (2006).
[CrossRef]

Pawar, S. A.

P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
[CrossRef]

Poletti, F.

T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
[CrossRef]

Richardson, D.

T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
[CrossRef]

Ryf, R.

T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
[CrossRef]

Simon, M. K.

C. Marco, D. Dardari, and M. K. Simon, IEEE Trans. Wirel. Commun. 2, 840 (2003).
[CrossRef]

Slock, D.

A. Medles and D. Slock, in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2005), pp. 1813–1817.

Tkach, R. W.

R. J. Essiambre and R. W. Tkach, Proc. IEEE 100, 1035 (2012).
[CrossRef]

Tse, D.

D. Tse, P. Viswanath, and L. Zheng, IEEE Trans. Inf. Theory 50, 1859 (2004).
[CrossRef]

Z. Lizhong and D. Tse, IEEE Trans. Inf. Theory 49, 1073 (2003).
[CrossRef]

Viswanath, P.

D. Tse, P. Viswanath, and L. Zheng, IEEE Trans. Inf. Theory 50, 1859 (2004).
[CrossRef]

Wang, Z.

L. Zhao, W. Mo, Y. Ma, and Z. Wang, IEEE Trans. Inf. Theory 53, 1549 (2007).
[CrossRef]

Winzer, P. J.

Zhao, L.

L. Zhao, W. Mo, Y. Ma, and Z. Wang, IEEE Trans. Inf. Theory 53, 1549 (2007).
[CrossRef]

Zheng, L.

D. Tse, P. Viswanath, and L. Zheng, IEEE Trans. Inf. Theory 50, 1859 (2004).
[CrossRef]

IEEE Commun. Mag.

T. Morioka, Y. Awaji, R. Ryf, P. J. Winzer, D. Richardson, and F. Poletti, IEEE Commun. Mag. 50(2), 31 (2012).
[CrossRef]

IEEE Signal Process. Mag.

S. Ö. Arik, J. M. Kahn, and K.-P. Ho, IEEE Signal Process. Mag. 31(2), 25 (2014).
[CrossRef]

IEEE Trans. Inf. Theory

P. Elia, K. R. Kumar, S. A. Pawar, P. V. Kumar, and H. Lu, IEEE Trans. Inf. Theory 52, 3869 (2006).
[CrossRef]

Z. Lizhong and D. Tse, IEEE Trans. Inf. Theory 49, 1073 (2003).
[CrossRef]

L. Zhao, W. Mo, Y. Ma, and Z. Wang, IEEE Trans. Inf. Theory 53, 1549 (2007).
[CrossRef]

R. Narasimhan, IEEE Trans. Inf. Theory 52, 3965 (2006).
[CrossRef]

D. Tse, P. Viswanath, and L. Zheng, IEEE Trans. Inf. Theory 50, 1859 (2004).
[CrossRef]

IEEE Trans. Wirel. Commun.

C. Marco, D. Dardari, and M. K. Simon, IEEE Trans. Wirel. Commun. 2, 840 (2003).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Proc. IEEE

R. J. Essiambre and R. W. Tkach, Proc. IEEE 100, 1035 (2012).
[CrossRef]

Other

K.-P. Ho and J. M. Kahn, in Optical Fiber Telecommunications VI, I. P. Kaminow, T. Li, and A. E. Willner, eds., (Elsevier, 2013), pp. 491–568.

A. Medles and D. Slock, in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2005), pp. 1813–1817.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Distribution of single-frequency capacity C1 for D=6, 12, 20, and 30 using 107 channel realizations for SNR=9dB and ξ=10dB.

Fig. 2.
Fig. 2.

Accumulated rms MDL ξ versus single-frequency multiplexing gain r1 using 2×107 channel realizations for SNR=9dB and D=12 modes.

Fig. 3.
Fig. 3.

SNR versus single-frequency multiplexing gain r1 using 2×107 channel realizations for ξ=10dB and D=12 modes.

Fig. 4.
Fig. 4.

Single-frequency diversity gain d1(r1,SNR) versus SNR for different values of single-frequency multiplexing gain r1 using 2×107 channel realizations for ξ=10dB and D=12 modes.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

Mtot(Ω)=exp(i2Ω2β2Ltot)·k=1KsecV(k)Λ(Ω)U(k)H.
Λ(Ω)=diag[exp(g12iΩτ1)exp(gD2iΩτD)],
C1=j=1Dlog2(1+SNR1Dk=1DE{λk2}λj2),
ξ=Ksecσg.
r=Clog2(1+SNR).
log2j=1D(1+SNR·λj21Dk=1DE{λk2})E{log2j=1D(1+SNR·λj21Dk=1Dλk2)}E{log2j=1D(1+SNR)}=Dlog2(1+SNR).
Pout,1(r1,SNR)=Prob[C1<r1log2(1+SNR)],
d1(r1,SNR)=log(Pout,1(r1,SNR))log(SNR).
FD[(CavgCout,1)/(CavgCout,FD)]2,
Pout,1exp((CavgCout,1)2/σC2)/12,
Pout,FDexp((CavgCout,FD)2FD/σC2)/12.
dFD(rFD,SNR)=log(Pout,FD(rFD,SNR))log(SNR).
dFD(r,SNR)FD·d1(r,SNR).

Metrics