Abstract

We investigate numerically the influence of fiber splices and fiber connectors to the statistics of mode dependent loss (MDL) and multiple-input multiple-output (MIMO) outage capacity in mode multiplexed multi-mode fiber links. Our results indicate required splice losses much lower than currently feasible to achieve a reasonable outage capacity in long-haul transmission systems. Splice losses as low as 0.03dB may effectively lead to an outage of MIMO channels after only a few hundred kilometers transmission length. In a first approximation, the relative capacity solely depends on the accumulated splice loss and should be less than ≈ 2dB to ensure a relative capacity of 90%. We also show that discrete mode permutation (mixing) within the transmission line may effectively increase the maximum transmission distance by a factor of 5 for conventional splice losses.

© 2012 OSA

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  1. C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).
  2. E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).
  3. R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).
  4. S. Randel, R. Ryf, and A. Gnauck, “Mode-multiplexed 6× 20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.5 (Los Angeles, 2012).
  5. J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).
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  8. P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express19(17), 16680–16696 (2011).
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  9. H. Bulow, H. Al-Hashimi, B. T. Abebe, and B. Schmauss, “Capacity and outage of multimode fiber with statistical bends,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, OW3D.2 (Los Angeles, 2012).
  10. S. Warm and K. Petermann, “Outage capacity for spliced mode multiplexed multi-mode fiber links,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, JW2A.39 (Los Angeles, 2012).
  11. G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multimode fibers,” IEEE Photonics Technol. Lett., 24(21), 1929–1932 (2012).
    [CrossRef]
  12. R. E. Epworth, “Phenomenon of modal noise in fiber systems,” in Optical Fiber Communication (OFC 1979), ThD1 (1979).
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  15. R. Olshansky, “Propagation in glass optical-waveguides,” Rev. Mod. Phys.51(2), 341–367 (1979).
    [CrossRef]
  16. A. A. Juarez, C.-A. Bunge, S. Warm, and K. Petermann, “Perspectives of principal mode transmission in mode-division-multiplex operation,” Opt. Express20(13), 13810–13823 (2012).
    [CrossRef] [PubMed]
  17. G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless pers. commun.6, 311–335 (1998).
    [CrossRef]
  18. K.-P. Ho and J. M. Kahn, “Frequency diversity in mode-division multiplexing systems,” J. Lightwave Technol.29(24), 3719–3726 (2011).
    [CrossRef]
  19. S. Warm and K. Petermann, “Capacity increase in spliced mode-multiplexed transmission systems by using mode mixers,” in IEEE Summer Topical 2012, TuC3.3 (2012).
    [CrossRef]
  20. I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications V B, Systems and Networks5th ed. (Elsevier Inc., 2008).

2012 (2)

G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multimode fibers,” IEEE Photonics Technol. Lett., 24(21), 1929–1932 (2012).
[CrossRef]

A. A. Juarez, C.-A. Bunge, S. Warm, and K. Petermann, “Perspectives of principal mode transmission in mode-division-multiplex operation,” Opt. Express20(13), 13810–13823 (2012).
[CrossRef] [PubMed]

2011 (3)

1998 (1)

G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless pers. commun.6, 311–335 (1998).
[CrossRef]

1980 (2)

E. Rawson, J. Goodman, and R. Norton, “Frequency-dependence of modal noise in multimode optical fibers,” J. Opt. Soc. Am.70(8), 968–976 (1980).
[CrossRef]

K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” IEEE J. Quantum Electron.16(7), 761–770 (1980).
[CrossRef]

1979 (1)

R. Olshansky, “Propagation in glass optical-waveguides,” Rev. Mod. Phys.51(2), 341–367 (1979).
[CrossRef]

Abebe, B. T.

H. Bulow, H. Al-Hashimi, B. T. Abebe, and B. Schmauss, “Capacity and outage of multimode fiber with statistical bends,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, OW3D.2 (Los Angeles, 2012).

Al-Hashimi, H.

H. Bulow, H. Al-Hashimi, B. T. Abebe, and B. Schmauss, “Capacity and outage of multimode fiber with statistical bends,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, OW3D.2 (Los Angeles, 2012).

Awaji, Y.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Bai, N.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Bickham, S.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Bigo, S.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

Bolle, C.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Bulow, H.

H. Bulow, H. Al-Hashimi, B. T. Abebe, and B. Schmauss, “Capacity and outage of multimode fiber with statistical bends,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, OW3D.2 (Los Angeles, 2012).

Bunge, C.-A.

Charlet, G.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

Chung, K. M.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Delbue, R.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Epworth, R. E.

R. E. Epworth, “Phenomenon of modal noise in fiber systems,” in Optical Fiber Communication (OFC 1979), ThD1 (1979).

Esmaeelpour, M.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Essiambre, R.-J.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Foschini, G.

G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless pers. commun.6, 311–335 (1998).
[CrossRef]

Foschini, G. J.

Gans, M.

G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless pers. commun.6, 311–335 (1998).
[CrossRef]

Gnauck, A.

S. Randel, R. Ryf, and A. Gnauck, “Mode-multiplexed 6× 20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.5 (Los Angeles, 2012).

Gnauck, A. H.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Goodman, J.

Ho, K.-P.

Huang, Y.-K.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Imamura, K.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Inaba, H.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Ip, E.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Juarez, A. A.

Kahn, J. M.

Kaminow, I. P.

I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications V B, Systems and Networks5th ed. (Elsevier Inc., 2008).

Kanno, A.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Kawanishi, T.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Klaus, W.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Kobayashi, T.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Koebele, C.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

Lau, A.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Li, G.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Li, M.-J.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Li, T.

I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications V B, Systems and Networks5th ed. (Elsevier Inc., 2008).

Linares, J.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Lingle, R. J.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Lu, C.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Luo, Y.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Mateo, E.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

McCurdy, A.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Milord, L.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

Montero, C.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Moreno, V.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Mukasa, K.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Norton, R.

Olshansky, R.

R. Olshansky, “Propagation in glass optical-waveguides,” Rev. Mod. Phys.51(2), 341–367 (1979).
[CrossRef]

Peckham, D. W.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Peng, G.-D.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Petermann, K.

A. A. Juarez, C.-A. Bunge, S. Warm, and K. Petermann, “Perspectives of principal mode transmission in mode-division-multiplex operation,” Opt. Express20(13), 13810–13823 (2012).
[CrossRef] [PubMed]

G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multimode fibers,” IEEE Photonics Technol. Lett., 24(21), 1929–1932 (2012).
[CrossRef]

K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” IEEE J. Quantum Electron.16(7), 761–770 (1980).
[CrossRef]

S. Warm and K. Petermann, “Outage capacity for spliced mode multiplexed multi-mode fiber links,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, JW2A.39 (Los Angeles, 2012).

S. Warm and K. Petermann, “Capacity increase in spliced mode-multiplexed transmission systems by using mode mixers,” in IEEE Summer Topical 2012, TuC3.3 (2012).
[CrossRef]

Prieto, X.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Pupalaikise, P.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Puttnam, B. J.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Rademacher, G.

G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multimode fibers,” IEEE Photonics Technol. Lett., 24(21), 1929–1932 (2012).
[CrossRef]

Randel, S.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

S. Randel, R. Ryf, and A. Gnauck, “Mode-multiplexed 6× 20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.5 (Los Angeles, 2012).

Rawson, E.

Ryf, R.

S. Randel, R. Ryf, and A. Gnauck, “Mode-multiplexed 6× 20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.5 (Los Angeles, 2012).

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

Sakaguchi, J.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Salsi, M.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

Schmauss, B.

H. Bulow, H. Al-Hashimi, B. T. Abebe, and B. Schmauss, “Capacity and outage of multimode fiber with statistical bends,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, OW3D.2 (Los Angeles, 2012).

Sierra, A.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Sillard, P.

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

Sugizaki, R.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Sureka, A.

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Tam, H.-Y.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Ten, S.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Tse, D.

D. Tse and P. Viswanath, Fundamentals of Wireless Communication (Cambridge University Press, 2005).
[CrossRef]

Tse, V.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

Viswanath, P.

D. Tse and P. Viswanath, Fundamentals of Wireless Communication (Cambridge University Press, 2005).
[CrossRef]

Wada, N.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Warm, S.

A. A. Juarez, C.-A. Bunge, S. Warm, and K. Petermann, “Perspectives of principal mode transmission in mode-division-multiplex operation,” Opt. Express20(13), 13810–13823 (2012).
[CrossRef] [PubMed]

G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multimode fibers,” IEEE Photonics Technol. Lett., 24(21), 1929–1932 (2012).
[CrossRef]

S. Warm and K. Petermann, “Outage capacity for spliced mode multiplexed multi-mode fiber links,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, JW2A.39 (Los Angeles, 2012).

S. Warm and K. Petermann, “Capacity increase in spliced mode-multiplexed transmission systems by using mode mixers,” in IEEE Summer Topical 2012, TuC3.3 (2012).
[CrossRef]

Watanabe, M.

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

Willner, A. E.

I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications V B, Systems and Networks5th ed. (Elsevier Inc., 2008).

Winzer, P. J.

P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express19(17), 16680–16696 (2011).
[CrossRef] [PubMed]

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

Yaman, F.

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

IEEE J. Quantum Electron. (1)

K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” IEEE J. Quantum Electron.16(7), 761–770 (1980).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

G. Rademacher, S. Warm, and K. Petermann, “Analytical description of cross-modal nonlinear interaction in mode multiplexed multimode fibers,” IEEE Photonics Technol. Lett., 24(21), 1929–1932 (2012).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Opt. Express (3)

Rev. Mod. Phys. (1)

R. Olshansky, “Propagation in glass optical-waveguides,” Rev. Mod. Phys.51(2), 341–367 (1979).
[CrossRef]

Wireless pers. commun. (1)

G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless pers. commun.6, 311–335 (1998).
[CrossRef]

Other (11)

S. Warm and K. Petermann, “Capacity increase in spliced mode-multiplexed transmission systems by using mode mixers,” in IEEE Summer Topical 2012, TuC3.3 (2012).
[CrossRef]

I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications V B, Systems and Networks5th ed. (Elsevier Inc., 2008).

R. E. Epworth, “Phenomenon of modal noise in fiber systems,” in Optical Fiber Communication (OFC 1979), ThD1 (1979).

C. Koebele, M. Salsi, L. Milord, R. Ryf, C. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km transmission of five mode division multiplexed data streams at 100Gb/s with low MIMO-DSP complexity,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.3 (Geneva, 2011).

E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Linares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. M. Chung, A. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, and G. Li, “88× 3× 112-Gb/s WDM transmission over 50 km of three-mode fiber with inline few-mode fiber amplifier,” in European Conference on Optical Communication (ECOC) 2011, Th.13.C.2 (Geneva, 2011).

R. Ryf, A. Sierra, R.-J. Essiambre, S. Randel, A. H. Gnauck, C. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikise, A. Sureka, D. W. Peckham, A. McCurdy, and R. J. Lingle, “Mode-equalized distributed raman amplification in 137 km few-mode fiber,” in European Conference on Optical Communication (ECOC) 2011, Th.13.K.5 (Geneva, 2011).

S. Randel, R. Ryf, and A. Gnauck, “Mode-multiplexed 6× 20-GBd QPSK transmission over 1200-km DGD-compensated few-mode fiber,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.5 (Los Angeles, 2012).

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, PDP5C.1 (Los Angeles, 2012).

D. Tse and P. Viswanath, Fundamentals of Wireless Communication (Cambridge University Press, 2005).
[CrossRef]

H. Bulow, H. Al-Hashimi, B. T. Abebe, and B. Schmauss, “Capacity and outage of multimode fiber with statistical bends,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, OW3D.2 (Los Angeles, 2012).

S. Warm and K. Petermann, “Outage capacity for spliced mode multiplexed multi-mode fiber links,” in Optical Fiber Communication Conference and Exposition (OFC), 2012, JW2A.39 (Los Angeles, 2012).

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Figures (14)

Fig. 1
Fig. 1

Spliced linear MIMO MDM transmission system.

Fig. 2
Fig. 2

Mean splice loss α S ¯ as a function of fiber misalignment for fibers with M = {3, 10, 28, 55} modes

Fig. 3
Fig. 3

Overall splice MDL σS,MDL (left) and mean splice MDL difference MDL ¯ S Δ (right) as a function of mean splice loss α S ¯ for fibers with M = {3, 10, 28, 55} modes. The circle-marked values represent a fiber misalignment of σx,y = 0.4μm.

Fig. 4
Fig. 4

Overall link MDL σΣ,MDL as a function of accumulated splice MDL K σ S , MDL for fibers with M = {3, 10, 28, 55} modes and splice MDL values σS,MDL = 0.05dB (left) and σS,MDL = 0.2dB (right). The red reference curve corresponds to i.i.d coupling segments as described in Eq. (11) while the black lines indicate a K (solid) and a Kx (dashed) dependance.

Fig. 5
Fig. 5

Overall link MDL σΣ,MDL (left) and mean link MDL difference MDL ¯ Σ Δ (right) after K = 128 splice points. The circle-marked values represent a fiber misalignment of σx,y = 0.4μm.

Fig. 6
Fig. 6

AWGN model of a spliced MDM transmission system with mode permutation every Kper splices.

Fig. 7
Fig. 7

Overall link MDL σΣ,MDL as a function of accumulated splice MDL K σ S , MDL for a link ensemble without mode permutator and a link ensemble with mode permutation every Kper = {16, 8, 4, 2, 1} splices. The black reference curve corresponds to i.i.d coupling segments as described in Eq. (11). The fiber misalignment is σx,y = 0.4μm. Left) 3-mode MMF with σS,MDL = 0.12dB, right) 55 mode MMF with σS,MDL = 0.08dB.

Fig. 8
Fig. 8

Eigenvalue distribution of H̱H̱ (top left), cumulative distribution function (cdf) of the relative capacity Cr (bottom left) and overall distribution of MDL (right) for fibers guiding M = 3 (dashed) and M = 28 (solid) modes without mode permutation. For both fibers the overall link MDL is σΣ,MDL = 8dB and the number of splices is K = 256.

Fig. 9
Fig. 9

Eigenvalue distribution of H̱H̱ (top left), cumulative distribution function (cdf) of the relative capacity Cr (bottom left) and overall distribution of MDL (right) for fibers guiding M = 3 (dashed) and M = 28 (solid) modes and mode permutation every Kper = 16 splices. For both fibers the overall link MDL is σΣ,MDL = 4dB and the number of splices is K = 256.

Fig. 10
Fig. 10

Relative capacity Cr at outage 10−4 as a function of overall link MDL σΣ,MDL for K={8, 16, 32, 64, 128, 256, 512, 1024} splice points for each fibers with M = 3 (left) and M = 55 modes (right) and varying splice losses.

Fig. 11
Fig. 11

Distribution of the relative capacity Cr for a MMF with M = 28 modes after K = {64, 128, 256} splice points and a mean splice loss α S ¯ of 0.05dB. Gray shaded graphs represent a single MDM link realization, while color shaded graphs represent an ensemble of different link realizations. Gray and color shaded graphs are differently scaled.

Fig. 12
Fig. 12

Relative capacity Cr at outage 10−4 for a MMF with M = 3, M = 10, M = 28 and M = 55 eigenmodes.

Fig. 13
Fig. 13

Relative capacity Cr at outage 10−4 as a function of (left) mean splice loss α S ¯ × K number of splices and (right) mean link loss α Σ S ¯ for fibers with M = {3, 10, 28, 55} modes, different fiber splice losses and different number of splices K.

Fig. 14
Fig. 14

Relative capacity Cr at outage probability 10−4 after 512 splices as a function of splice loss α S ¯ for a link ensemble without mode permutation (no perm.) and a link ensemble with a mode permutator every Kper = {16, 8, 4, 2, 1} splices. Left) a MMF with 3 modes and right) a MMF with 55 modes.

Tables (1)

Tables Icon

Table 1 Multimode fiber parameters at wavelength λ = 1.55μm

Equations (16)

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H _ = k = 1 K T _ k C _ k .
T _ k = diag [ exp ( j ϕ 1 ( k ) ) , , exp ( j ϕ M ( k ) ) ]
c i , j ( k ) = A E i ( k 1 ) ( x , y ) E j ( k ) * ( x + Δ x , y + Δ y ) d A
E l , q ( r , ϕ ) = C l , q ( r w ) l L q ( l ) ( r 2 w 2 ) exp ( r 2 2 w 2 ) { sin ( l ϕ ) cos ( l ϕ )
C r = i = 1 M log 2 ( 1 + λ i E 0 / N 0 ) M log 2 ( 1 + E 0 / N 0 ) .
P out = 0 C o p c ( C ) d C ,
σ Σ , MDL = std ( λ i ( j ) ) ,
MDL Σ Δ , j = max { λ i ( j ) } min { λ i ( j ) } ,
σ Σ , MDL = K σ S , MDL ! = ξ .
σ Σ , MDL = K σ S , MDL .
σ Σ , MDL = ξ 1 + 1 12 ( ξ / γ ) 2 , with γ = 10 / ln ( 10 )
σ Σ , MDL = K x σ S , MDL , with 0.84 > x > 0.77 ,
C _ per = ( 0 1 0 0 0 1 1 0 0 ) .
σ Σ , MDL = K x σ S , MDL , with x 0.65.
SNR a | dB = 58 dB + 0 dBm 5 dB 19 dB 10 log 10 ( 10 ) = 24 dB .
M C = M log 2 ( 1 + SNR a ) = M 4.64 bit / s / Hz

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