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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 17 — Aug. 15, 2011
  • pp: 16680–16696

MIMO capacities and outage probabilities in spatially multiplexed optical transport systems

Peter J. Winzer and Gerard J. Foschini  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 16680-16696 (2011)
http://dx.doi.org/10.1364/OE.19.016680


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Abstract

With wavelength-division multiplexing (WDM) rapidly nearing its scalability limits, space-division multiplexing (SDM) seems the only option to further scale the capacity of optical transport networks. In order for SDM systems to continue the WDM trend of reducing energy and cost per bit with system capacity, integration will be key to SDM. Since integration is likely to introduce non-negligible crosstalk between multiple parallel transmission paths, multiple-input multiple output (MIMO) signal processing techniques will have to be used. In this paper, we discuss MIMO capacities in optical SDM systems, including related outage considerations which are an important part in the design of such systems. In order to achieve the low-outage standards required for optical transport networks, SDM transponders should be capable of individually addressing, and preferably MIMO processing all modes supported by the optical SDM waveguide. We then discuss the effect of distributed optical noise in MIMO SDM systems and focus on the impact of mode-dependent loss (MDL) on system capacity and system outage. Through extensive numerical simulations, we extract scaling rules for mode-average and mode-dependent loss and show that MIMO SDM systems composed of up to 128 segments and supporting up to 128 modes can tolerate up to 1 dB of per-segment MDL at 90% of the system’s full capacity at an outage probability of 10−4.

© 2011 OSA

OCIS Codes
(060.4230) Fiber optics and optical communications : Multiplexing
(060.4510) Fiber optics and optical communications : Optical communications

ToC Category:
Capacity Limits

History
Original Manuscript: June 6, 2011
Revised Manuscript: August 4, 2011
Manuscript Accepted: August 9, 2011
Published: August 15, 2011

Virtual Issues
Space Multiplexed Optical Transmission (2011) Optics Express

Citation
Peter J. Winzer and Gerard J. Foschini, "MIMO capacities and outage probabilities in spatially multiplexed optical transport systems," Opt. Express 19, 16680-16696 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-16680


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References

  1. R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–10 (2010). [CrossRef]
  2. J. Gray and P. Shenoy, “Rules of thumb in data engineering,” Microsoft Research Technical Report MS-TR-99-100 (2000).
  3. J. L. Hennessy and D. A. Patterson, Computer Architectures: A Quantitative Approach (Morgan Kaufmann, 2003).
  4. http://top500.org/lists/2010/06/performance_development
  5. F. B. Shepherd and P. J. Winzer, “Selective randomized load balancing and mesh networks with changing demands,” J. Opt. Netw. 5(5), 320–339 (2006). [CrossRef]
  6. P. J. Winzer, “Beyond 100G ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010). [CrossRef]
  7. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]
  8. A. R. Chraplyvy, “The coming capacity crunch,” European Conference on Optical Communication (ECOC’09), plenary talk (2009).
  9. P. J. Winzer and R.-J. Essiambre, “Advanced optical modulation formats,” in Optical Fiber Telecommunications V B , I. Kaminow, T. Li, and A. Willner (eds.), (Academic, 2008), ch. 2, pp. 23–94.
  10. P. J. Winzer, “Modulation and multiplexing in optical communication systems,” IEEE-LEOS Newsletter , Feb.2009, http://photonicssociety.org/newsletters/feb09/modulation.pdf .
  11. P. J. Winzer, “Energy-efficient optical transport capacity scaling through spatial multiplexing,” IEEE Photon. Technol. Lett. 23(13), 851–853 (2011). [CrossRef]
  12. R. J. Essiambre, “Impact of fiber parameters on nonlinear fiber capacity,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’11), OTuJ1 (2011).
  13. T. Morioka, “New generation optical infrastructure technologies: EXAT initiative towards 2020 and beyond,” Proc. Optoelectronics and Communications Conference (OECC’09), FT4 (2009).
  14. Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009). [CrossRef]
  15. C. R. Doerr and T. F. Taunay, “Silicon photonics core-, wavelength-, and polarization-diversity receiver,” IEEE Photon. Technol. Lett. 23(9), 597–599 (2011). [CrossRef]
  16. P. J. Winzer, A. H. Gnauck, A. Konczykowska, F. Jorge, and J.-Y. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” Proc. European Conference on Optical Communication (ECOC’11), Tu.5.B.7 (2011).
  17. G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Tech. J. 1(2), 41–59 (1996). [CrossRef]
  18. J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, and M. Watanabe, “109-Tb/s (7x97x172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi-core fiber,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’11), PDPB6 (2011).
  19. B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, F. V. Dimarcello, K. Abedin, P. W. Wisk, D. W. Peckham, and P. Dziedzic, “Space-, wavelength-, polarization-division multiplexed transmission of 56-Tb/s over a 76.8-km seven-core fiber,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’11), PDPB7 (2011).
  20. R. Ryf, R.-J. Essiambre, S. Randel, A. H. Gnauck, P. J. Winzer, T. Hayashi, T. Taru, and T. Sasaki, “MIMO-based crosstalk suppression in spatially multiplexed 56-Gb/s PDM-QPSK signals in strongly-coupled 3-core fiber,” accepted for publication in IEEE Photon. Technol. Lett. (2011).
  21. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6x6 MIMO processing,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’11), PDPB10 (2011).
  22. M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over two modes of 40-km-long prototype few-mode fiber, using LCOS-based mode multiplexer and demultiplexer,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’11), PDPB9 (2011).
  23. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’11), PDPB8 (2011).
  24. S. Berdague and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21(11), 1950–1955 (1982). [CrossRef] [PubMed]
  25. H. R. Stuart, “Dispersive multiplexing in multimode optical fiber,” Science 289(5477), 281–283 (2000). [CrossRef] [PubMed]
  26. S. Murshid, B. Grossman, and P. Narakorn, “Spatial domain multiplexing: a new dimension in fiber optic multiplexing,” Opt. Laser Technol. 40(8), 1030–1036 (2008). [CrossRef]
  27. A. Tarighat, R. C. J. Hsu, A. R. Shah, A. H. Sayed, and B. Jalali,“Fundamentals and challenges of optical multiple-input-multiple-output multimode fiber links,” IEEE Commun. Mag. , 57–63 (2007). [CrossRef]
  28. S. Schoellmann, N. Schrammar, and W. Rosenkranz, “Experimental realisation of 3x3 MIMO system with mode group diversity multiplexing limited by modal noise,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’08), JWA68 (2008).
  29. M. Nazarathy and A. Agmon, “Coherent transmission direct detection MIMO over short-range optical interconnects and passive optical networks,” J. Lightwave Technol. 26, 2037–2045 (2008). [CrossRef]
  30. B. Franz, D. Suikat, R. Dischler, F. Buchali, and H. Buelow, “High speed OFDM data transmission over 5 km GI-multimode fiber using spatial multiplexing with 2 × 4 MIMO processing,” Proc. European Conference on Optical Communication (ECOC’10), Tu.3.C.4 (2010).
  31. P. J. Winzer and G. J. Foschini, “Outage calculations for spatially multiplexed fiber links,” Proc. Optical Fiber Communications Conference (OFC/NFOEC’11), OThO5 (2011).
  32. C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in long-haul transmission over bimodal optical fibre,” Proc. European Conference on Optical Communication (ECOC’10), Mo.2.C.6 (2010).
  33. H. Bölcskei, D. Gesbert, and A. J. Paulraj, “On the capacity of OFDM-based spatial multiplexing systems,” IEEE Trans. Commun. 50(2), 225–234 (2002). [CrossRef]
  34. A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bölcskei, “An overview of MIMO communications—a key to Gigabit wireless,” Proc. IEEE 92(2), 198 –218 (2004). [CrossRef]
  35. H. Kogelnik, L. E. Nelson, and R. M. Jopson, “Polarization mode dispersion,” in Optical Fiber Telecommunications IV B , I. P. Kaminow and T. Li (eds.), San Diego: Academic, ch. 15, 725–861 (2002).
  36. M. Brodsky, N. J. Frigo, and M. Tur, “Polarization mode dispersion,” in Optical Fiber Telecommunications V A , I. P. Kaminow, T. Li, and A. E. Willner (eds.), (Academic, 2008), ch. 17, pp. 605–670.
  37. C. Xie, “Polarization-mode-dispersion impairments in 112-Gb/s PDM-QPSK coherent systems,” Proc. European Conference on Optical Communication (ECOC’10), Th.10.E.6 (2010).
  38. F. Mezzadri, “How to generate random matrices from the classical compact groups,” Notices of the AMS 54, 592–604 (2007).
  39. B. Wedding and C. N. Haslach, “Enhanced PMD mitigation by polarization scrambling and forward error correction,” Proc. Optical Fiber Communication Conference (OFC’01), WAA1 (2001).
  40. X. Liu, C. R. Giles, X. Wei, A. J. van Wijngaarden, Y.-H. Kao, C. Xie, L. Moller, and I. Kang, “Demonstration of broad-band PMD mitigation in the presence of PDL through distributed fast polarization scrambling and forward-error correction,” IEEE Photon. Technol. Lett. 17(5), 1109–1111 (2005). [CrossRef]
  41. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]
  42. A. Nafta, E. Meron, and M. Shtaif, “Capacity limitations in fiber-optic communications systems as a result of polarization dependent loss,” Opt. Lett. 34(23), 3613–3615 (2009). [CrossRef] [PubMed]
  43. E. Meron, A. Andrusier, M. Feder, and M. Shtaif, “Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization dependent loss,” Opt. Lett. 35(21), 3547–3549 (2010). [CrossRef] [PubMed]
  44. A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14(3), 313–315 (2002). [CrossRef]
  45. Y. Fukada, “Probability density function of polarization dependent loss (PDL) in optical transmission system composed of passive devices and connecting fibers,” J. Lightwave Technol. 20(6), 953–964 (2002). [CrossRef]
  46. M. Yu, C. Kan, M. Lewis, and A. Sizmann, “Statistics of polarization-dependent loss, insertion loss, and signal power in optical communication systems,” IEEE Photon. Technol. Lett. 14(12), 1695–1697 (2002). [CrossRef]
  47. A. Mecozzi and M. Shtaif, “Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization,” J. Lightwave Technol. 22(8), 1856–1871 (2004). [CrossRef]
  48. L. E. Nelson, C. Antonelli, A. Mecozzi, M. Birk, P. Magill, A. Schex, and L. Rapp, “Statistics of polarization dependent loss in an installed long-haul WDM system,” Opt. Express 19(7), 6790–6796 (2011) [CrossRef] [PubMed]
  49. A. Steinkamp, S. Vorbeck, and E. I. Voges, “Polarization mode dispersion and polarization dependent loss in optical fiber systems,” Proc. SPIE 5596, 243–254 (2004). [CrossRef]
  50. A. El Amari, N. Gisin, B. Perny, H. Zbinden, and C. W. Zimmer, “Statistical prediction and experimental verification of concatenations of fiber optic components with polarization dependent loss,” J. Lightwave Technol. 16(3), 332–339 (1998). [CrossRef]
  51. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L.L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010). [CrossRef]
  52. A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and its Applications (Academic, 1979).
  53. J. B. Lasserre, “A trace inequality for matrix product,” IEEE Trans. Autom. Control 40(8), 1500–1501 (1995). [CrossRef]

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