Abstract

Conventional large-core multimode fibers (MMFs) are preferred for use in short to medium haul optical fiber links, owing to their tolerance to misalignment and low deployment costs; however, data rates through MMFs are limited by modal dispersion. Digital signal processing with multiple-input multiple-output (MIMO) techniques has offered promising solutions to overcome the dispersion limitations of MMFs, but the impact of the geometry of laser and detector arrays on the achievable data rate is not established. To this end, we use a field-propagation-based model to gauge the impact the geometry of lasers and detectors can have on the achievable ergodic and outage rates of incoherent MIMO-MMF links. Laser and detector array geometries were investigated using a grid-based method to optimize the positions of lasers and detectors for a 1 km MIMO-MMF link. Simulations reveal that systems with appropriately designed laser/detector geometries could improve the achievable rate over the fiber by more than 200% over random laser/detector arrays. The grid-based search technique, however, is limited due to high computational requirements for fine grids. As an alternative, we developed a suboptimal “greedy” selection approach to design detector geometries, which produces detector geometries that attain more than 90% of the rate obtained with an exhaustive search, while requiring less than 0.2% of the computation. The low computation requirements and high performance of the greedy selection approach also motivate the use of dynamically reconfigurable detector arrays to achieve high data rates with reduced signal processing complexity. Methods are also presented for clustering detector elements to obtain more consolidated segmented detectors with better fill factors, while still offering significant data rate benefits. The achievable ergodic rate using these systems is verified to be close to the link’s ergodic capacity.

© 2014 Optical Society of America

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2013 (1)

K. Appaiah, S. Vishwanath, and S. R. Bank, “Vector intensity-modulation and channel state feedback for multimode fiber optic links,” IEEE Trans. Commun., vol.  61, no. 7, pp. 2958–2969, 2013.
[CrossRef]

2012 (4)

H. Bulow, “Optical-mode demultiplexing by optical MIMO filtering of spatial samples,” IEEE Photon. Technol. Lett., vol.  24, no. 12, pp. 1045–1047, 2012.
[CrossRef]

R. Vaze and H. Ganapathy, “Sub-modularity and antenna selection in MIMO systems,” IEEE Commun. Lett., vol.  16, no. 9, pp. 1446–1449, Sept. 2012.
[CrossRef]

M. Blau and D. M. Marom, “Optimization of spatial aperture-sampled mode multiplexer for a three-mode fiber,” IEEE Photon. Technol. Lett., vol.  24, no. 23, pp. 2101–2104, 2012.
[CrossRef]

S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. Monberg, and F. Dimarcello, “WDM/SDM transmission of 10 × 128  Gb/s PDM-QPSK over 2688  km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320  km b/s/Hz,” Opt. Express, vol.  20, no. 2, pp. 706–711, 2012.
[CrossRef]

2011 (4)

2009 (5)

2008 (1)

2007 (1)

2006 (2)

C. Tsekrekos, M. de Boer, A. Martinez, F. Willems, and A. Koonen, “Temporal stability of a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 23, pp. 2484–2486, 2006.
[CrossRef]

C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 22, pp. 2359–2361, 2006.
[CrossRef]

2005 (3)

2004 (1)

2000 (1)

H. R. Stuart, “Dispersive multiplexing in multimode optical fiber,” Science, vol.  289, no. 5477, pp. 281–283, 2000.
[CrossRef]

1999 (1)

E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol.  10, no. 6, pp. 585–595, 1999.
[CrossRef]

1998 (1)

1996 (1)

1995 (1)

E. Zeeb, B. Moller, C. Reiner, M. Ries, T. Hackbarth, and K. Ebeling, “Planar proton implanted VCSEL’s and fiber-coupled 2-D VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron., vol.  1, no. 2, pp. 616–623, 1995.
[CrossRef]

1983 (1)

G. Herskowitz, H. Kobrinski, and U. Levy, “Optical power distribution in multimode fibers with angular-dependent mode coupling,” J. Lightwave Technol., vol.  1, no. 4, pp. 548–554, 1983.
[CrossRef]

1978 (1)

G. Nemhauser, L. Wolsey, and M. Fisher, “An analysis of approximations for maximizing submodular set functions I,” Math. Program., vol.  14, no. 1, pp. 265–294, 1978.
[CrossRef]

1974 (1)

Agrawal, G.

G. Agrawal, Fiber-Optic Communication Systems, vol. 3. New York: Wiley, 1997.

Anderson, A.

N. Bikhazi, M. Jensen, and A. Anderson, “MIMO signaling over the MMF optical broadcast channel with square-law detection,” IEEE Trans. Commun., vol.  57, no. 3, pp. 614–617, 2009.
[CrossRef]

Appaiah, K.

K. Appaiah, S. Vishwanath, and S. R. Bank, “Vector intensity-modulation and channel state feedback for multimode fiber optic links,” IEEE Trans. Commun., vol.  61, no. 7, pp. 2958–2969, 2013.
[CrossRef]

K. Appaiah, S. Vishwanath, and S. R. Bank, “Advanced modulation and multiple-input multiple-output for multimode fiber links,” IEEE Photon. Technol. Lett., vol.  23, no. 20, pp. 1424–1426, 2011.
[CrossRef]

K. Appaiah, R. Salas, S. Vishwanath, and S. R. Bank, “Enhancing data rates in graded-index multimode fibers with offset coupling and multiplexing,” in Optical Fiber Communication Conf., Anaheim, CA, 2013.

K. Appaiah, S. Zisman, S. Vishwanath, and S. R. Bank, “Analysis of laser and detector placement in MIMO multimode optical fiber systems,” in IEEE Int. Conf. on Communications (ICC), June 2012, pp. 2972–2976.

Armstrong, J.

Awaji, Y.

J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

Balemarthy, K.

K. Balemarthy and S. Ralph, “MIMO processing of multi-mode fiber links,” in 19th Annu. Meeting of the IEEE Lasers and Electro-Optics Society (LEOS), Oct.2006, pp. 639–640.

Bank, S. R.

K. Appaiah, S. Vishwanath, and S. R. Bank, “Vector intensity-modulation and channel state feedback for multimode fiber optic links,” IEEE Trans. Commun., vol.  61, no. 7, pp. 2958–2969, 2013.
[CrossRef]

K. Appaiah, S. Vishwanath, and S. R. Bank, “Advanced modulation and multiple-input multiple-output for multimode fiber links,” IEEE Photon. Technol. Lett., vol.  23, no. 20, pp. 1424–1426, 2011.
[CrossRef]

K. Appaiah, R. Salas, S. Vishwanath, and S. R. Bank, “Enhancing data rates in graded-index multimode fibers with offset coupling and multiplexing,” in Optical Fiber Communication Conf., Anaheim, CA, 2013.

K. Appaiah, S. Zisman, S. Vishwanath, and S. R. Bank, “Analysis of laser and detector placement in MIMO multimode optical fiber systems,” in IEEE Int. Conf. on Communications (ICC), June 2012, pp. 2972–2976.

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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

Bikhazi, N.

N. Bikhazi, M. Jensen, and A. Anderson, “MIMO signaling over the MMF optical broadcast channel with square-law detection,” IEEE Trans. Commun., vol.  57, no. 3, pp. 614–617, 2009.
[CrossRef]

Bland-Hawthorn, J.

N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in European Conf. and Exhibition on Optical Communication, Amsterdam, The Netherlands, 2012, paper Th-2.

Blau, M.

M. Blau and D. M. Marom, “Optimization of spatial aperture-sampled mode multiplexer for a three-mode fiber,” IEEE Photon. Technol. Lett., vol.  24, no. 23, pp. 2101–2104, 2012.
[CrossRef]

Bolle, C.

R. Ryf, S. Randel, A. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10  km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB0.

Bolle, C. A.

Boyd, S. P.

Brandt-Pearce, M.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, no. 8, pp. 1402–1412, 2005.
[CrossRef]

Buchali, F.

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,” in 36th European Conf. and Exhibition on Optical Communication (ECOC), 2010, pp. 1–3.

Buelow, H.

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,” in 36th European Conf. and Exhibition on Optical Communication (ECOC), 2010, pp. 1–3.

Bulow, H.

H. Bulow, “Optical-mode demultiplexing by optical MIMO filtering of spatial samples,” IEEE Photon. Technol. Lett., vol.  24, no. 12, pp. 1045–1047, 2012.
[CrossRef]

Burrows, E.

Cao, Q.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, no. 8, pp. 1402–1412, 2005.
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. Monberg, and F. Dimarcello, “WDM/SDM transmission of 10 × 128  Gb/s PDM-QPSK over 2688  km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320  km b/s/Hz,” Opt. Express, vol.  20, no. 2, pp. 706–711, 2012.
[CrossRef]

B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

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Y. Wang, Y. Shao, and N. Chi, “Multiple-inputs multiple-outputs combining center launch and ring launch for high-speed transmission in multimode fiber links,” in Future Wireless Networks and Information Systems. Springer, 2012, pp. 353–360.

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T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Introduction to Algorithms. MIT, 2001.

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de Boer, M.

C. Tsekrekos, M. de Boer, A. Martinez, F. Willems, and A. Koonen, “Temporal stability of a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 23, pp. 2484–2486, 2006.
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S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. W. Peckham, A. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5B-5.

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S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. Monberg, and F. Dimarcello, “WDM/SDM transmission of 10 × 128  Gb/s PDM-QPSK over 2688  km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320  km b/s/Hz,” Opt. Express, vol.  20, no. 2, pp. 706–711, 2012.
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B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

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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,” in 36th European Conf. and Exhibition on Optical Communication (ECOC), 2010, pp. 1–3.

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L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

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E. Zeeb, B. Moller, C. Reiner, M. Ries, T. Hackbarth, and K. Ebeling, “Planar proton implanted VCSEL’s and fiber-coupled 2-D VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron., vol.  1, no. 2, pp. 616–623, 1995.
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R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. W. Peckham, A. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5B-5.

R. Ryf, S. Randel, A. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10  km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB0.

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

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B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

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S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. Monberg, and F. Dimarcello, “WDM/SDM transmission of 10 × 128  Gb/s PDM-QPSK over 2688  km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320  km b/s/Hz,” Opt. Express, vol.  20, no. 2, pp. 706–711, 2012.
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B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

Flower, G.

L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

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N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in European Conf. and Exhibition on Optical Communication, Amsterdam, The Netherlands, 2012, paper Th-2.

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P. Winzer and G. J. Foschini, “Outage calculations for spatially multiplexed fiber links,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper OThO5.

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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,” in 36th European Conf. and Exhibition on Optical Communication (ECOC), 2010, pp. 1–3.

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J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

Gnauck, A.

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

R. Ryf, S. Randel, A. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10  km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB0.

R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. W. Peckham, A. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5B-5.

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Goldsmith, A.

A. Goldsmith, Wireless Communications. Cambridge University, 2005.

Greenberg, M.

Grot, A.

L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

Gruhlke, R.

L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

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E. Zeeb, B. Moller, C. Reiner, M. Ries, T. Hackbarth, and K. Ebeling, “Planar proton implanted VCSEL’s and fiber-coupled 2-D VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron., vol.  1, no. 2, pp. 616–623, 1995.
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G. Herskowitz, H. Kobrinski, and U. Levy, “Optical power distribution in multimode fibers with angular-dependent mode coupling,” J. Lightwave Technol., vol.  1, no. 4, pp. 548–554, 1983.
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Horowitz, M.

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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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

Huijskens, F.

C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 22, pp. 2359–2361, 2006.
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C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Mode group diversity multiplexing transceiver design for graded-index multimode fibres,” in 31st European Conf. on Optical Communication (ECOC), vol. 3, Sept.2005, pp. 727–728.

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J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

Inaba, H.

J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

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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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

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Jansen, S.

S. Jansen, I. Morita, and H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1,000 km of SSMF,” in Optical Fiber Communication Conf., San Diego, CA, 2008, paper PDP2.

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S. L. Jansen, I. Morita, and H. Tanaka, “16×52.5-Gb/s, 50-GHz spaced, POLMUX-CO-OFDM transmission over 4,160 km of SSMF enabled by MIMO processing,” in 33rd European Conf. and Exhibition of Optical Communication, 2007, paper PD1.3.

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N. Bikhazi, M. Jensen, and A. Anderson, “MIMO signaling over the MMF optical broadcast channel with square-law detection,” IEEE Trans. Commun., vol.  57, no. 3, pp. 614–617, 2009.
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Jiang, X.

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. W. Peckham, A. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5B-5.

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Kahn, J. M.

Kanno, A.

J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

Kasahara, K.

Kawai, S.

Kawanishi, T.

J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

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Kirkpatrick, P.

J. Peeters Weem, P. Kirkpatrick, and J. Verdiell, “Electronic dispersion compensation for 10  gigabit communication links over FDDI legacy multimode fiber,” in Optical Fiber Communication Conf., Anaheim, CA, 2005, paper OFO4.

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J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

Kobayashi, T.

J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

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G. Herskowitz, H. Kobrinski, and U. Levy, “Optical power distribution in multimode fibers with angular-dependent mode coupling,” J. Lightwave Technol., vol.  1, no. 4, pp. 548–554, 1983.
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C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 22, pp. 2359–2361, 2006.
[CrossRef]

C. Tsekrekos, M. de Boer, A. Martinez, F. Willems, and A. Koonen, “Temporal stability of a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 23, pp. 2484–2486, 2006.
[CrossRef]

C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Mode group diversity multiplexing transceiver design for graded-index multimode fibres,” in 31st European Conf. on Optical Communication (ECOC), vol. 3, Sept.2005, pp. 727–728.

Kosaka, H.

Law, B.

L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

Leiserson, C.

T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Introduction to Algorithms. MIT, 2001.

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N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in European Conf. and Exhibition on Optical Communication, Amsterdam, The Netherlands, 2012, paper Th-2.

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S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, no. 8, pp. 1402–1412, 2005.
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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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

Li, Y.

Lin, C.-K.

L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

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J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

Suikat, D.

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,” in 36th European Conf. and Exhibition on Optical Communication (ECOC), 2010, pp. 1–3.

Sun, Y.

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. W. Peckham, A. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5B-5.

Sureka, A.

R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. W. Peckham, A. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5B-5.

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

Tan, M.

Tanaka, H.

S. L. Jansen, I. Morita, and H. Tanaka, “16×52.5-Gb/s, 50-GHz spaced, POLMUX-CO-OFDM transmission over 4,160 km of SSMF enabled by MIMO processing,” in 33rd European Conf. and Exhibition of Optical Communication, 2007, paper PD1.3.

S. Jansen, I. Morita, and H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1,000 km of SSMF,” in Optical Fiber Communication Conf., San Diego, CA, 2008, paper PDP2.

Tandon, A.

L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

Tang, L.

L. Tang and D. Miller, “Metallic nanodevices for chip-scale optical interconnects,” J. Nanophoton., vol.  3, no. 1, 030302, 2009.
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Tarighat, A.

Taunay, T.

B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

Taunay, T. F.

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E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol.  10, no. 6, pp. 585–595, 1999.
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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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

Thomsen, B.

B. Thomsen, “MIMO enabled 40 Gb/s transmission using mode division multiplexing in multimode fiber,” in Optical Fiber Communication Conf. (OFC), 2010, paper OThM6.

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D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University, 2005.

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C. Tsekrekos, M. de Boer, A. Martinez, F. Willems, and A. Koonen, “Temporal stability of a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 23, pp. 2484–2486, 2006.
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C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 22, pp. 2359–2361, 2006.
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C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Mode group diversity multiplexing transceiver design for graded-index multimode fibres,” in 31st European Conf. on Optical Communication (ECOC), vol. 3, Sept.2005, pp. 727–728.

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R. Vaze and H. Ganapathy, “Sub-modularity and antenna selection in MIMO systems,” IEEE Commun. Lett., vol.  16, no. 9, pp. 1446–1449, Sept. 2012.
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Verdiell, J.

J. Peeters Weem, P. Kirkpatrick, and J. Verdiell, “Electronic dispersion compensation for 10  gigabit communication links over FDDI legacy multimode fiber,” in Optical Fiber Communication Conf., Anaheim, CA, 2005, paper OFO4.

Vishwanath, S.

K. Appaiah, S. Vishwanath, and S. R. Bank, “Vector intensity-modulation and channel state feedback for multimode fiber optic links,” IEEE Trans. Commun., vol.  61, no. 7, pp. 2958–2969, 2013.
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K. Appaiah, S. Vishwanath, and S. R. Bank, “Advanced modulation and multiple-input multiple-output for multimode fiber links,” IEEE Photon. Technol. Lett., vol.  23, no. 20, pp. 1424–1426, 2011.
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K. Appaiah, R. Salas, S. Vishwanath, and S. R. Bank, “Enhancing data rates in graded-index multimode fibers with offset coupling and multiplexing,” in Optical Fiber Communication Conf., Anaheim, CA, 2013.

K. Appaiah, S. Zisman, S. Vishwanath, and S. R. Bank, “Analysis of laser and detector placement in MIMO multimode optical fiber systems,” in IEEE Int. Conf. on Communications (ICC), June 2012, pp. 2972–2976.

Viswanath, P.

D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University, 2005.

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U. Feige and J. Vondrak, “Approximation algorithms for allocation problems: Improving the factor of 1-1/e,” in 47th Annu. IEEE Symp. on Foundations of Computer Science (FOCS), 2006, pp. 667–676.

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J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

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Y. Li, T. Wang, H. Kosaka, S. Kawai, and K. Kasahara, “Fiber-image-guide-based bit-parallel optical interconnects,” Appl. Opt., vol.  35, no. 35, pp. 6920–6933, 1996.
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Wang, Y.

Y. Wang, Y. Shao, and N. Chi, “Multiple-inputs multiple-outputs combining center launch and ring launch for high-speed transmission in multimode fiber links,” in Future Wireless Networks and Information Systems. Springer, 2012, pp. 353–360.

Watanabe, M.

J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

White, I.

Willems, F.

C. Tsekrekos, M. de Boer, A. Martinez, F. Willems, and A. Koonen, “Temporal stability of a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 23, pp. 2484–2486, 2006.
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Wilson, S. G.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, no. 8, pp. 1402–1412, 2005.
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L. Windover, J. Simon, S. Rosenau, K. Giboney, G. Flower, L. Mirkarimi, A. Grot, B. Law, C.-K. Lin, A. Tandon, R. Gruhlke, H. Xia, G. Rankin, M. Tan, and D. Dolfi, “Parallel-optical interconnects >100 Gb/s,” J. Lightwave Technol., vol.  22, no. 9, pp. 2055–2063, 2004.

J. Simon, L. Windover, S. Rosenau, K. Giboney, B. Law, G. Flower, L. Mirkarimi, A. Grot, C.-K. Lin, A. Tandon, G. Rankin, R. Gruhlke, and D. Dolfi, “Parallel optical interconnect at 10  Gb/s per channel,” in Proc. of 54th Electronic Components and Technology Conf., vol. 1, 2004, pp. 1016–1023.

Winzer, P.

P. Winzer and G. J. Foschini, “Outage calculations for spatially multiplexed fiber links,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper OThO5.

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. W. Peckham, A. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5B-5.

R. Ryf, S. Randel, A. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10  km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB0.

Winzer, P. J.

Wolsey, L.

G. Nemhauser, L. Wolsey, and M. Fisher, “An analysis of approximations for maximizing submodular set functions I,” Math. Program., vol.  14, no. 1, pp. 265–294, 1978.
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Xia, H.

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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

Yan, M.

B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

Yan, M. F.

Zeeb, E.

E. Zeeb, B. Moller, C. Reiner, M. Ries, T. Hackbarth, and K. Ebeling, “Planar proton implanted VCSEL’s and fiber-coupled 2-D VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron., vol.  1, no. 2, pp. 616–623, 1995.
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S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. Monberg, and F. Dimarcello, “WDM/SDM transmission of 10 × 128  Gb/s PDM-QPSK over 2688  km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320  km b/s/Hz,” Opt. Express, vol.  20, no. 2, pp. 706–711, 2012.
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B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

Zisman, S.

K. Appaiah, S. Zisman, S. Vishwanath, and S. R. Bank, “Analysis of laser and detector placement in MIMO multimode optical fiber systems,” in IEEE Int. Conf. on Communications (ICC), June 2012, pp. 2972–2976.

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E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol.  10, no. 6, pp. 585–595, 1999.
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R. Vaze and H. Ganapathy, “Sub-modularity and antenna selection in MIMO systems,” IEEE Commun. Lett., vol.  16, no. 9, pp. 1446–1449, Sept. 2012.
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E. Zeeb, B. Moller, C. Reiner, M. Ries, T. Hackbarth, and K. Ebeling, “Planar proton implanted VCSEL’s and fiber-coupled 2-D VCSEL arrays,” IEEE J. Sel. Top. Quantum Electron., vol.  1, no. 2, pp. 616–623, 1995.
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C. Tsekrekos, M. de Boer, A. Martinez, F. Willems, and A. Koonen, “Temporal stability of a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 23, pp. 2484–2486, 2006.
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M. Blau and D. M. Marom, “Optimization of spatial aperture-sampled mode multiplexer for a three-mode fiber,” IEEE Photon. Technol. Lett., vol.  24, no. 23, pp. 2101–2104, 2012.
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K. Appaiah, S. Vishwanath, and S. R. Bank, “Advanced modulation and multiple-input multiple-output for multimode fiber links,” IEEE Photon. Technol. Lett., vol.  23, no. 20, pp. 1424–1426, 2011.
[CrossRef]

C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett., vol.  18, no. 22, pp. 2359–2361, 2006.
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K. Appaiah, S. Vishwanath, and S. R. Bank, “Vector intensity-modulation and channel state feedback for multimode fiber optic links,” IEEE Trans. Commun., vol.  61, no. 7, pp. 2958–2969, 2013.
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A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, and B. Jalali, “Coherent optical MIMO (COMIMO),” J. Lightwave Technol., vol.  23, no. 8, pp. 2410–2419, 2005.
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D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University, 2005.

B. Thomsen, “MIMO enabled 40 Gb/s transmission using mode division multiplexing in multimode fiber,” in Optical Fiber Communication Conf. (OFC), 2010, paper OThM6.

S. Schöllmann and W. Rosenkranz, “Experimental equalization of crosstalk in a 2 × 2 MIMO system based on mode group diversity multiplexing in MMF systems @ 10.7 Gb/s,” in 33rd European Conf. and Exibition of Optical Communication (ECOC), 2007, pp. 1–2.

Y. Wang, Y. Shao, and N. Chi, “Multiple-inputs multiple-outputs combining center launch and ring launch for high-speed transmission in multimode fiber links,” in Future Wireless Networks and Information Systems. Springer, 2012, pp. 353–360.

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,” in 36th European Conf. and Exhibition on Optical Communication (ECOC), 2010, pp. 1–3.

C. Tsekrekos, A. Martinez, F. Huijskens, and A. Koonen, “Mode group diversity multiplexing transceiver design for graded-index multimode fibres,” in 31st European Conf. on Optical Communication (ECOC), vol. 3, Sept.2005, pp. 727–728.

R. Ryf, S. Randel, A. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10  km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB0.

B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, and F. Dimarcello, “Space-, wavelength-, polarization-division multiplexed transmission of 56  Tb/s over a 76.8  km seven-core fiber,” in Optical Fiber Communication Conf., Los Angeles, CA, 2011, paper PDPB7.

J. Sakaguchi, B. 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 19 × 100 × 172  Gb/s SDM-WDM-PDM-QPSK signals at 305  Tb/s,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-1.

S. Randel, R. Ryf, A. Gnauck, M. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-multiplexed 6 × 20  GBd QPSK transmission over 1200  km DGD-compensated few-mode fiber,” in Nat. Fiber Optic Engineers Conf., Los Angeles, CA, 2012, paper PDP5C-5.

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, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “6×6 MIMO transmission over 50+25+10  km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conf., Los Angeles, CA, 2012, paper OTu2C-4.

S. Jansen, I. Morita, and H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1,000 km of SSMF,” in Optical Fiber Communication Conf., San Diego, CA, 2008, paper PDP2.

S. L. Jansen, I. Morita, and H. Tanaka, “16×52.5-Gb/s, 50-GHz spaced, POLMUX-CO-OFDM transmission over 4,160 km of SSMF enabled by MIMO processing,” in 33rd European Conf. and Exhibition of Optical Communication, 2007, paper PD1.3.

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Figures (18)

Fig. 1.
Fig. 1.

Schematic depicting various components applicable for the model. The launch and detection portions are shown for a single laser and detector, respectively.

Fig. 2.
Fig. 2.

U prop i is a random matrix that describes intermodal coupling within a section. In particular, it transforms a vector containing the weights of each guided mode to provide a vector that has the new weights after the signal has undergone intermodal coupling within the fiber section.

Fig. 3.
Fig. 3.

R i is a random matrix that describes rotation of the polarization of the electric field at section junctions. It rotates the polarization of each mode within the fiber section based upon propagation effects of the fiber.

Fig. 4.
Fig. 4.

M i is a random matrix that describes rotation of the electric field profile due to fiber twists within the i th fiber section.

Fig. 5.
Fig. 5.

Binning approach to evaluate the sum rate achievable over the fiber across all frequency ranges. The frequency response of the fiber channel was split into several bins of 100 MHz each, and the rate was evaluated within each bin assuming a frequency-flat channel response, and added up to get the net rate. This can be thought of as a frequency division multiplexing approach to rate evaluation.

Fig. 6.
Fig. 6.

Beam evolution over 1 km of graded-index MMF. The physical fiber measurement is performed using a beam profiler, while the simulated profile uses one channel realization obtained using the fiber model.

Fig. 7.
Fig. 7.

Multiple lasers and detectors. The devices were assumed to fill 90% of the fiber core area.

Fig. 8.
Fig. 8.

Achievable rate versus SNR for 1 × 1 , 2 × 2 , and 3 × 3 MIMO systems for the best device configuration.

Fig. 9.
Fig. 9.

(a) Achievable rate versus SNR for a 2 × 2 MIMO system for the “best” device configuration that achieves the highest rate and the average over all possible configurations. (b) Configuration of lasers and detectors in the best configuration. The four circles at the bottom represent the fiber cross sections and the laser and detector placements on the cross sections that yielded both the best and the suboptimal configurations.

Fig. 10.
Fig. 10.

(a) Achievable rate versus SNR for a 3 × 3 MIMO system for the “best” device configuration that achieves the highest rate and the average over all possible configurations. (b) Configuration of lasers and detectors in the best configuration.

Fig. 11.
Fig. 11.

Comparing the configurations obtained by the exhaustive search and the greedy search. It can be observed that about 92% of the rate of the optimal exhaustive search can be obtained by the greedy search in this case.

Fig. 12.
Fig. 12.

Similar configurations are observed with both the outage rate and the ergodic rate as metrics for optimizating the laser/detector configurations.

Fig. 13.
Fig. 13.

Laser array utilized with the 50 μm fiber. The lasers have a mode-field diameter of 5 μm and a pitch of 8 μm.

Fig. 14.
Fig. 14.

Detector configurations obtained by the greedy algorithm for detectors of diameter 4 μm for various grid structures. Interestingly, there is a significant preference toward detectors closer to the fiber core, indicating the fact that much of the received power in graded-index MMFs propagates close to the axis.

Fig. 15.
Fig. 15.

Capacity trends obtained with the detector configurations shown in Fig. 14.

Fig. 16.
Fig. 16.

(a) A fiber was analyzed to obtain the best 23 locations to place small circular detectors on a 11 × 11 grid as discussed in Subsection V.C. (b) Clustering these detectors to obtain larger square segments to improve the fill factor. (c) Regular four-element detector array without using the design from the algorithm.

Fig. 17.
Fig. 17.

Comparison of capacity trends for the detector patterns shown in Fig. 16.

Fig. 18.
Fig. 18.

(a) Capacity versus SNR for a 3 × 3 MIMO system for the “best” device configuration that achieves the highest rate and the average over all possible configurations. (b) Configuration of lasers and detectors in the best configuration.

Tables (1)

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Algorithm 1 Greedy Selection Algorithm

Equations (20)

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a p ˜ , q ˜ = E L , E ( p ˜ , q ˜ ) F E L , E L E ( p ˜ , q ˜ ) F , E ( p ˜ , q ˜ ) F , where A , B = R R A ( x , y ) B * ( x , y ) d x d y .
a ̲ L = [ E L , E F 1 E L , E F 2 E L , E F M ] ,
n 2 = n 0 ( x , y ) 2 2 Δ n 0 2 ( r a ) α ,
h j i , k ( t ) = k = 0 2 M a ̲ D j , p ̲ k p ̲ k , a ̲ L i δ ( t τ i ) ,
[ y 1 ( t ) y 2 ( t ) y N D ( t ) ] = H ( t ) [ x 1 ( t ) x 2 ( t ) x N L ( t ) ] + [ n 1 ( t ) n 2 ( t ) n N D ( t ) ] .
C = E [ log 2 det ( I N D + ρ N L HH H ) ] [ b / s / Hz ] ,
R S = log 2 det ( I N D + ρ N D H S H S ) ,
R * ( 1 e 1 ) R S R * .
E [ R S ] = E [ log 2 det ( I N D + ρ N L H S H S ) ]
p out = P [ log 2 det ( I N D + ρ N L HH H ) < R ]
h ( X A B ) + h ( X A B ) h ( X A ) + h ( X B ) A , B { X 1 , X 2 , , X n } .
h ( X A B ) + h ( X A B ) h ( X A ) h ( X B ) = [ h ( X A ) + h ( X B A | X A ) ] + h ( X A B ) h ( X A ) h ( X B ) = h ( X B A | X A ) + h ( X A B ) [ h ( X A B ) h ( X B A | X A B ) ] = h ( X B A | X A ) h ( X B A | X A B ) 0 .
h ( Z S ) = log ( ( π e ) | S | det ( R Z S ) ) = log ( ( π e ) | S | det ( I | S | + ρ N D H S H S ) ) = | S | log ( π e ) + C S .
C S = h ( Z S ) | S | log ( π e ) .
H S { x } = [ H S h x ] ,
C S { x } = log det ( I | S | + 1 + ρ N D [ H S h x ] [ H S h x ] ) = log det ( R Z S { x } ) = h ( Z S { x } ) ( | S | + 1 ) log ( π e ) ,
C S C S { x } ( C T C T { x } ) = h ( Z S { x } ) ( | S | ) log ( π e ) ( h ( Z S ) | S | log ( π e ) ) h ( Z T { x } ) + ( | T | ) log ( π e ) + ( h ( Z T ) | T | log ( π e ) ) = [ h ( Z S { x } ) h ( Z S ) ( h ( Z T { x } ) h ( Z T ) ) ] 0 ( due to the submodularity of entropy ) .
C S { x } = log det ( I | S | + 1 + ρ N D [ H S h x ] [ H S h x ] ) .
C S { x } = log det ( I | S | + 1 + ρ N D [ H S h x ] [ H S h x ] ) = log det ( I N D + ρ N D [ H S h x ] [ H S h x ] ) = log det ( I N D + ρ N D [ H S H S + h x h x ] ) = log det ( I N D + ρ N D H S H S ) + log det ( I N D + ( I N D + ρ N D H S H S ) 1 h x h x ) = log det ( I N D + ρ N D H S H S ) + log ( 1 + h x ( I N D + ρ N D H S H S ) 1 h x ) = C S + log ( 1 + b ) , where b = h x ( I N D + ρ N D H S H S ) 1 h x .
C S { x } = C S + log ( 1 + b ) C S ,