Abstract

Mode-division multiplexing (MDM) transmission over few-mode optical fiber has emerged as a promising technology to enhance transmission capacity, in which multiple-input-multiple-output (MIMO) digital signal processing (DSP) after coherent detection is used to demultiplex the signals. Compared with conventional single-mode systems, MIMO-MDM systems suffer non-recoverable signal degradation induced by mode-dependent loss (MDL). In this paper, the MDL-induced signal degradation in orthogonal-frequency-division-multiplexing (OFDM) MDM systems is theoretically quantified in terms of mode-average error vector magnitude (EVM) through frequency domain norm analysis. A novel scalar MDL metric is proposed considering the probability distribution of the practical MDM input signals, and a closed-form expression for EVM measured after zero-force (ZF) MIMO equalization is derived. Simulation results show that the EVM estimations utilizing the novel MDL metric remain unbiased for unrepeated links. For a 6 × 100 km 20-mode MDM transmission system, the estimation accuracy is improved by more than 90% compared with that utilizing traditional condition number (CN) based MDL metric. The proposed MDL metric can be used to predict the MDL-induced SNR penalty in a theoretical manner, which will be beneficial for the design of practical MIMO-MDM systems.

© 2016 Optical Society of America

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References

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  1. D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
    [Crossref]
  2. E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λ× 6× 19-Gbaud wavelength-and mode-division multiplexed transmission over 10× 50-km spans of few-mode fiber with a gain-equalized few-mode EDFA,” J. Lightwave Technol. 32(4), 790–797 (2014).
    [Crossref]
  3. Y. Chen, A. Lobato, Y. Jung, H. Chen, V. Sleiffer, M. Kuschnerov, N. Fontaine, R. Ryf, D. Richardson, B. Lankl, and N. Hanik, “41.6 Tbit/s C-Band SDM OFDM Transmission Through 12 Spatial and Polarization Modes Over 74.17 km Few Mode Fiber,” J. Lightwave Technol. 33(7), 1440–1444 (2015).
    [Crossref]
  4. N. Fontaine, R. Ryf, H. Chen, A. Benitez, B. Guan, R. Scott, B. Ercan, S. Yoo, L. Grüner-Nielsen, Y. Sun, R. Lingle, E. Antonio-Lopez, and R. Amezcua-Correa, “30×30 MIMO Transmission over 15 Spatial Modes,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (Optical Society of America, 2015), paper Th5C.1.
  5. R. Ryf, N. K. Fontaine, H. Chen, B. Guan, B. Huang, M. Esmaeelpour, A. H. Gnauck, S. Randel, S. J. Yoo, A. M. Koonen, R. Shubochkin, Y. Sun, and R. Lingle., “Mode-multiplexed transmission over conventional graded-index multimode fibers,” Opt. Express 23(1), 235–246 (2015).
    [Crossref] [PubMed]
  6. P. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
    [Crossref]
  7. T. Morioka, “Recent progress in space-division multiplexed transmission technologies,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OW4F.2.
    [Crossref]
  8. K. Ho and J. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Lightwave Technol. 32(4), 614–628 (2014).
    [Crossref]
  9. G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
    [Crossref]
  10. R. Ryf, S. Randel, A. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. Burrows, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
    [Crossref]
  11. S. Arik, D. Askarov, and J. Kahn, “MIMO DSP Complexity in Mode-Division Multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th1D.1.
    [Crossref]
  12. B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
    [Crossref] [PubMed]
  13. N. Bai, E. Ip, M. Li, T. Wang, and G. Li, “Experimental demonstration of adaptive frequency-domain equalization for mode-division multiplexed transmission,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OM2C.5.
    [Crossref]
  14. K. P. Ho and J. M. Kahn, “Mode-dependent loss and gain: statistics and effect on mode-division multiplexing,” Opt. Express 19(17), 16612–16635 (2011).
    [Crossref] [PubMed]
  15. A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, and B. Lankl, “Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission,” Opt. Express 20(28), 29776–29783 (2012).
    [Crossref] [PubMed]
  16. C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Criticality of assumptions in the study of performance degradation caused by mode-dependent loss in SDM systems,” in Proceedings of European Conference on Optical Communication (IEEE, 2014), paper P.5.23.
    [Crossref]
  17. A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proceedings of OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology (IEEE, 2014), pp. 234–236.
  18. S. Arık, D. Askarov, and J. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Lightwave Technol. 32(10), 1841–1852 (2014).
    [Crossref]
  19. P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express 19(17), 16680–16696 (2011).
    [Crossref] [PubMed]
  20. A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
    [Crossref]
  21. S. Warm and K. Petermann, “Splice loss requirements in multi-mode fiber mode-division-multiplex transmission links,” Opt. Express 21(1), 519–532 (2013).
    [Crossref] [PubMed]
  22. A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Characterization of Mode-Dependent Loss in SDM Systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Th1J.2.
    [Crossref]
  23. K. Guan, P. Winzer, and M. Shtaif, “BER Performance of MDL-Impaired MIMO-SDM Systems With Finite Constellation Inputs,” IEEE Photonics Technol. Lett. 26(12), 1223–1226 (2014).
    [Crossref]
  24. X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization of Dynamic Evolution of Channel Matrix in Two-mode Fibers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OM2C.3.
    [Crossref]
  25. N. Cvijetic, E. Ip, N. Prasad, M. Li, and T. Wang, “Experimental Time and Frequency Domain MIMO Channel Matrix Characterization versus Distance for 6×28Gbaud QPSK Transmission over 40×25km Few Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Th1J.3.
  26. A. Juarez, E. Krune, S. Warm, C. Bunge, and K. Petermann, “Modeling of Mode Coupling in Multimode Fibers With Respect to Bandwidth and Loss,” J. Lightwave Technol. 32(8), 1549–1558 (2015).
    [Crossref]
  27. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
    [Crossref]
  28. C. Xie, “Polarization-Dependent Loss Induced Penalties in PDM-QPSK Coherent Optical Communication Systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWE6.
    [Crossref]
  29. P. Sillard, “Few-Mode Fibers for Space Division Multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1J.1.
    [Crossref]
  30. A. Lobato, Y. Chen, Y. Jung, H. Chen, B. Inan, M. Kuschnerov, N. K. Fontaine, R. Ryf, B. Spinnler, and B. Lankl, “12-mode OFDM transmission using reduced-complexity maximum likelihood detection,” Opt. Lett. 40(3), 328–331 (2015).
    [Crossref] [PubMed]
  31. B. Inan, Y. Jung, V. Sleiffer, M. Kuschnerov, L. Gruner-Nielsen, S. Adhikari, S. Jansen, D. Richardson, S. Alam, B. Spinnler, and N. Hanik, “Low Computational Complexity Mode Division Multiplexed OFDM Transmission over 130 km of Few Mode Fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OW4F.4.
    [Crossref]
  32. K. Ho and J. Kahn, “Frequency Diversity in Mode-Division Multiplexing Systems,” J. Lightwave Technol. 29(24), 3719–3726 (2011).
    [Crossref]
  33. F. Mezzadri, “How to Generate Random Matrices from the Classical Compact Groups,” Not. Am. Math. Soc. 54(5), 592–604 (2007).
  34. S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: an overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).
    [Crossref]
  35. R. Horn and C. Johnson, Matrix Analysis, 2nd ed. (Cambridge University Press, 2012).
  36. J. Proakis, Digital Communications, 5th ed. (McGraw-Hill, 2007).

2015 (4)

2014 (7)

S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: an overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).
[Crossref]

P. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
[Crossref]

K. Ho and J. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Lightwave Technol. 32(4), 614–628 (2014).
[Crossref]

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λ× 6× 19-Gbaud wavelength-and mode-division multiplexed transmission over 10× 50-km spans of few-mode fiber with a gain-equalized few-mode EDFA,” J. Lightwave Technol. 32(4), 790–797 (2014).
[Crossref]

S. Arık, D. Askarov, and J. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Lightwave Technol. 32(10), 1841–1852 (2014).
[Crossref]

K. Guan, P. Winzer, and M. Shtaif, “BER Performance of MDL-Impaired MIMO-SDM Systems With Finite Constellation Inputs,” IEEE Photonics Technol. Lett. 26(12), 1223–1226 (2014).
[Crossref]

2013 (3)

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

S. Warm and K. Petermann, “Splice loss requirements in multi-mode fiber mode-division-multiplex transmission links,” Opt. Express 21(1), 519–532 (2013).
[Crossref] [PubMed]

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

2012 (4)

2011 (3)

2007 (1)

F. Mezzadri, “How to Generate Random Matrices from the Classical Compact Groups,” Not. Am. Math. Soc. 54(5), 592–604 (2007).

Adhikari, S.

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
[Crossref] [PubMed]

Antonelli, C.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Criticality of assumptions in the study of performance degradation caused by mode-dependent loss in SDM systems,” in Proceedings of European Conference on Optical Communication (IEEE, 2014), paper P.5.23.
[Crossref]

Arik, S.

S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: an overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).
[Crossref]

S. Arık, D. Askarov, and J. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Lightwave Technol. 32(10), 1841–1852 (2014).
[Crossref]

Askarov, D.

Bai, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Becker, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Bennett, K.

Bolle, C.

Bunge, C.

Burrows, E.

Chen, H.

Chen, Y.

Dreschmann, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Esmaeelpour, M.

Essiambre, R.

Ferreira, F.

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, and B. Lankl, “Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission,” Opt. Express 20(28), 29776–29783 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proceedings of OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology (IEEE, 2014), pp. 234–236.

Fini, J.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fontaine, N.

Fontaine, N. K.

Foschini, G. J.

Freude, W.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Gnauck, A.

Gnauck, A. H.

Guan, B.

Guan, K.

K. Guan, P. Winzer, and M. Shtaif, “BER Performance of MDL-Impaired MIMO-SDM Systems With Finite Constellation Inputs,” IEEE Photonics Technol. Lett. 26(12), 1223–1226 (2014).
[Crossref]

Hanik, N.

Hillerkuss, D.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Ho, K.

Ho, K. P.

Hu, J.

Huang, B.

Huang, Y.

Huebner, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Inan, B.

Ip, E.

Jansen, S. L.

Josten, A.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Juarez, A.

Jung, Y.

Kahn, J.

Kahn, J. M.

Koenig, S.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Koonen, A. M.

Koos, C.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Koreshkov, K.

Korolev, A.

Krune, E.

Kuschnerov, M.

A. Lobato, Y. Chen, Y. Jung, H. Chen, B. Inan, M. Kuschnerov, N. K. Fontaine, R. Ryf, B. Spinnler, and B. Lankl, “12-mode OFDM transmission using reduced-complexity maximum likelihood detection,” Opt. Lett. 40(3), 328–331 (2015).
[Crossref] [PubMed]

Y. Chen, A. Lobato, Y. Jung, H. Chen, V. Sleiffer, M. Kuschnerov, N. Fontaine, R. Ryf, D. Richardson, B. Lankl, and N. Hanik, “41.6 Tbit/s C-Band SDM OFDM Transmission Through 12 Spatial and Polarization Modes Over 74.17 km Few Mode Fiber,” J. Lightwave Technol. 33(7), 1440–1444 (2015).
[Crossref]

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, and B. Lankl, “Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission,” Opt. Express 20(28), 29776–29783 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proceedings of OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology (IEEE, 2014), pp. 234–236.

Lankl, B.

Leuthold, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Li, G.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Li, M.

Lingle, R.

Lobato, A.

A. Lobato, Y. Chen, Y. Jung, H. Chen, B. Inan, M. Kuschnerov, N. K. Fontaine, R. Ryf, B. Spinnler, and B. Lankl, “12-mode OFDM transmission using reduced-complexity maximum likelihood detection,” Opt. Lett. 40(3), 328–331 (2015).
[Crossref] [PubMed]

Y. Chen, A. Lobato, Y. Jung, H. Chen, V. Sleiffer, M. Kuschnerov, N. Fontaine, R. Ryf, D. Richardson, B. Lankl, and N. Hanik, “41.6 Tbit/s C-Band SDM OFDM Transmission Through 12 Spatial and Polarization Modes Over 74.17 km Few Mode Fiber,” J. Lightwave Technol. 33(7), 1440–1444 (2015).
[Crossref]

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, and B. Lankl, “Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission,” Opt. Express 20(28), 29776–29783 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proceedings of OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology (IEEE, 2014), pp. 234–236.

Mateo, E.

McCurdy, A.

Mecozzi, A.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Criticality of assumptions in the study of performance degradation caused by mode-dependent loss in SDM systems,” in Proceedings of European Conference on Optical Communication (IEEE, 2014), paper P.5.23.
[Crossref]

Meyer, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Mezzadri, F.

F. Mezzadri, “How to Generate Random Matrices from the Classical Compact Groups,” Not. Am. Math. Soc. 54(5), 592–604 (2007).

Mumtaz, S.

Napoli, A.

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, and B. Lankl, “Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission,” Opt. Express 20(28), 29776–29783 (2012).
[Crossref] [PubMed]

Nebendahl, B.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Nelson, L.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Peckham, D.

Petermann, K.

Rabe, J.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proceedings of OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology (IEEE, 2014), pp. 234–236.

Randel, S.

Richardson, D.

Ryf, R.

Schmogrow, R.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Shtaif, M.

K. Guan, P. Winzer, and M. Shtaif, “BER Performance of MDL-Impaired MIMO-SDM Systems With Finite Constellation Inputs,” IEEE Photonics Technol. Lett. 26(12), 1223–1226 (2014).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Criticality of assumptions in the study of performance degradation caused by mode-dependent loss in SDM systems,” in Proceedings of European Conference on Optical Communication (IEEE, 2014), paper P.5.23.
[Crossref]

Shubochkin, R.

Sierra, A.

Sleiffer, V.

Sleiffer, V. A.

Spinnler, B.

A. Lobato, Y. Chen, Y. Jung, H. Chen, B. Inan, M. Kuschnerov, N. K. Fontaine, R. Ryf, B. Spinnler, and B. Lankl, “12-mode OFDM transmission using reduced-complexity maximum likelihood detection,” Opt. Lett. 40(3), 328–331 (2015).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, and B. Lankl, “Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission,” Opt. Express 20(28), 29776–29783 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proceedings of OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology (IEEE, 2014), pp. 234–236.

Sun, Y.

Tanaka, A.

van den Borne, D.

Warm, S.

Winter, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Winzer, P.

P. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
[Crossref]

K. Guan, P. Winzer, and M. Shtaif, “BER Performance of MDL-Impaired MIMO-SDM Systems With Finite Constellation Inputs,” IEEE Photonics Technol. Lett. 26(12), 1223–1226 (2014).
[Crossref]

R. Ryf, S. Randel, A. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. Burrows, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Criticality of assumptions in the study of performance degradation caused by mode-dependent loss in SDM systems,” in Proceedings of European Conference on Optical Communication (IEEE, 2014), paper P.5.23.
[Crossref]

Winzer, P. J.

Wood, W.

Xia, C.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Yano, Y.

Yoo, S. J.

Zhao, N.

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

Adv. Opt. Photonics (1)

G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (3)

A. Lobato, F. Ferreira, B. Inan, S. Adhikari, M. Kuschnerov, A. Napoli, B. Spinnler, and B. Lankl, “Maximum-likelihood detection in few-mode fiber transmission with mode-dependent loss,” IEEE Photonics Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

K. Guan, P. Winzer, and M. Shtaif, “BER Performance of MDL-Impaired MIMO-SDM Systems With Finite Constellation Inputs,” IEEE Photonics Technol. Lett. 26(12), 1223–1226 (2014).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

J. Lightwave Technol. (7)

K. Ho and J. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Lightwave Technol. 32(4), 614–628 (2014).
[Crossref]

A. Juarez, E. Krune, S. Warm, C. Bunge, and K. Petermann, “Modeling of Mode Coupling in Multimode Fibers With Respect to Bandwidth and Loss,” J. Lightwave Technol. 32(8), 1549–1558 (2015).
[Crossref]

K. Ho and J. Kahn, “Frequency Diversity in Mode-Division Multiplexing Systems,” J. Lightwave Technol. 29(24), 3719–3726 (2011).
[Crossref]

R. Ryf, S. Randel, A. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. Burrows, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λ× 6× 19-Gbaud wavelength-and mode-division multiplexed transmission over 10× 50-km spans of few-mode fiber with a gain-equalized few-mode EDFA,” J. Lightwave Technol. 32(4), 790–797 (2014).
[Crossref]

Y. Chen, A. Lobato, Y. Jung, H. Chen, V. Sleiffer, M. Kuschnerov, N. Fontaine, R. Ryf, D. Richardson, B. Lankl, and N. Hanik, “41.6 Tbit/s C-Band SDM OFDM Transmission Through 12 Spatial and Polarization Modes Over 74.17 km Few Mode Fiber,” J. Lightwave Technol. 33(7), 1440–1444 (2015).
[Crossref]

S. Arık, D. Askarov, and J. Kahn, “Adaptive frequency-domain equalization in mode-division multiplexing systems,” J. Lightwave Technol. 32(10), 1841–1852 (2014).
[Crossref]

Nat. Photonics (2)

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

P. Winzer, “Making spatial multiplexing a reality,” Nat. Photonics 8(5), 345–348 (2014).
[Crossref]

Not. Am. Math. Soc. (1)

F. Mezzadri, “How to Generate Random Matrices from the Classical Compact Groups,” Not. Am. Math. Soc. 54(5), 592–604 (2007).

Opt. Express (6)

Opt. Lett. (1)

Signal Proc. Mag. (1)

S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: an overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).
[Crossref]

Other (14)

R. Horn and C. Johnson, Matrix Analysis, 2nd ed. (Cambridge University Press, 2012).

J. Proakis, Digital Communications, 5th ed. (McGraw-Hill, 2007).

B. Inan, Y. Jung, V. Sleiffer, M. Kuschnerov, L. Gruner-Nielsen, S. Adhikari, S. Jansen, D. Richardson, S. Alam, B. Spinnler, and N. Hanik, “Low Computational Complexity Mode Division Multiplexed OFDM Transmission over 130 km of Few Mode Fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OW4F.4.
[Crossref]

A. Andrusier, M. Shtaif, C. Antonelli, and A. Mecozzi, “Characterization of Mode-Dependent Loss in SDM Systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Th1J.2.
[Crossref]

X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization of Dynamic Evolution of Channel Matrix in Two-mode Fibers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OM2C.3.
[Crossref]

N. Cvijetic, E. Ip, N. Prasad, M. Li, and T. Wang, “Experimental Time and Frequency Domain MIMO Channel Matrix Characterization versus Distance for 6×28Gbaud QPSK Transmission over 40×25km Few Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Th1J.3.

C. Xie, “Polarization-Dependent Loss Induced Penalties in PDM-QPSK Coherent Optical Communication Systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWE6.
[Crossref]

P. Sillard, “Few-Mode Fibers for Space Division Multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1J.1.
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. Winzer, “Criticality of assumptions in the study of performance degradation caused by mode-dependent loss in SDM systems,” in Proceedings of European Conference on Optical Communication (IEEE, 2014), paper P.5.23.
[Crossref]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proceedings of OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology (IEEE, 2014), pp. 234–236.

N. Bai, E. Ip, M. Li, T. Wang, and G. Li, “Experimental demonstration of adaptive frequency-domain equalization for mode-division multiplexed transmission,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OM2C.5.
[Crossref]

N. Fontaine, R. Ryf, H. Chen, A. Benitez, B. Guan, R. Scott, B. Ercan, S. Yoo, L. Grüner-Nielsen, Y. Sun, R. Lingle, E. Antonio-Lopez, and R. Amezcua-Correa, “30×30 MIMO Transmission over 15 Spatial Modes,” in Optical Fiber Communication Conference Post Deadline Papers, OSA Technical Digest (Optical Society of America, 2015), paper Th5C.1.

T. Morioka, “Recent progress in space-division multiplexed transmission technologies,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OW4F.2.
[Crossref]

S. Arik, D. Askarov, and J. Kahn, “MIMO DSP Complexity in Mode-Division Multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th1D.1.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Simulation setup for M × M MIMO-MDM system. PDM-OFDM: polarization division multiplexed OFDM. FM-EDFA: few-mode erbium-doped fiber amplifier. PD-CRX: polarization-diversity coherent receiver.
Fig. 2
Fig. 2 (a) EVM on individual data subcarriers after 3 span transmission. EVM on middle data subcarrier under different SNR after 1 span (b) and 3 span (c) transmission. 6 modes are multiplexed. Per-span MDL is 10 dB. EVM values measured by Monte Carlo simulations are shown as markers: squares for QPSK, circles for 16QAM, crosses for 64QAM. Theoretical EVM estimations are shown as curves: blue solid curve for EVM estimation provided by proposed MDL metric, red dash dot curve for EVM estimation provided by CN-based MDL metric, and green dotted curve for EVM estimation in MDL-free case.
Fig. 3
Fig. 3 Single subcarrier EVM estimation error versus transmitted spans when QPSK is employed. Bar and error bar represent the mean and std. of estimation error. Bars without slashes for EVM estimations provided by proposed MDL metric. Bars with slashes for EVM estimations provided by CN-based MDL metric. 6 modes are multiplexed in (a) and (b). Pre-span MDL is set to be 10 dB in (c) and (d).

Tables (1)

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Table 1 Attenuation and Dispersion of Different Modes in FMFs

Equations (23)

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

H ( i , k ) = H ¯ ( i ) , k = 1 , , K .
Λ ¯ ( i ) = max [ λ ¯ m ( i ) ] min [ λ ¯ m ( i ) ] .
V ( i ) = ( i ) X ( i ) + d Y ( i ) = Y ( i ) + d Y ( i ) .
E ( i ) = - 1 ( i ) V ( i ) = X ( i ) + - 1 ( i ) d Y ( i ) = X ( i ) + d X ( i ) ,
E V M ( i ) Λ ¯ ( i ) 1 S N R ( i ) .
E V M ( i ) = 1 S N R ( i ) ,
( ( i ) ) H ( i ) X ( i ) = α ( i ) X ( i ) ,
( - 1 ( i ) ) H - 1 ( i ) d Y ( i ) = β ( i ) d Y ( i ) ,
( H ¯ ( i ) ) H H ¯ ( i ) ε ¯ m ( i ) = λ ¯ m ( i ) ε ¯ m ( i ) , m = 1 , , M .
X ( i , k ) = m = 1 M a m ( i , k ) ε ¯ m ( i ) .
Y ( i , k ) 2 2 = H ¯ ( i ) X ( i , k ) 2 2 = ( X ( i , k ) ) H ( H ¯ ( i ) ) H H ¯ ( i ) X ( i , k ) = m = 1 M | a m ( i , k ) | 2 λ ¯ m ( i )
Y ( i ) 2 2 = k = 1 K Y ( i , k ) 2 2 = k = 1 K m = 1 M | a m ( i , k ) | 2 λ ¯ m ( i ) = m = 1 M λ ¯ m ( i ) k = 1 K | a m ( i , k ) | 2 = m = 1 M λ ¯ m ( i ) 1 M X ( i ) 2 2 = X ( i ) 2 2 1 M m = 1 M λ ¯ m ( i ) ,
d X ( i ) 2 2 = d Y ( i ) 2 2 1 M m = 1 M 1 λ ¯ m ( i ) .
E V M ( i ) = d X ( i ) 2 2 X ( i ) 2 2 = 1 M m = 1 M λ ¯ m ( i ) 1 M m = 1 M 1 λ ¯ m ( i ) d Y ( i ) 2 2 Y ( i ) 2 2 = Θ ¯ ( i ) 1 S N R ( i ) ,
Θ ¯ ( i ) = λ ¯ m ( i ) m 1 λ ¯ m ( i ) m .
Θ ¯ = Θ ¯ ( i ) i .
Y ( i ) 2 ( i ) 2 X ( i ) 2 ,
d X ( i ) 2 1 ( i ) 2 d Y ( i ) 2 .
d X ( i ) 2 X ( i ) 2 1 ( i ) 2 ( i ) 2 d Y ( i ) 2 Y ( i ) 2 .
1 ( i ) 2 ( i ) 2 = c o n d 2 ( ( i ) ) ,
c o n d 2 ( ( i ) ) = c o n d 2 ( H ¯ ( i ) ) = max [ λ ¯ m ( i ) ] min [ λ ¯ m ( i ) ] = Λ ¯ ( i ) .
d X ( i ) 2 X ( i ) 2 = k = 1 K m = 1 M | d x m ( i , k ) | 2 k = 1 K m = 1 M | x m ( i , k ) | 2 = E V M ( i ) ,
d Y ( i ) 2 Y ( i ) 2 = k = 1 K m = 1 M | d y m ( i , k ) | 2 k = 1 K m = 1 M | y m ( i , k ) | 2 = 1 S N R ( i ) .

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