Abstract

Few-mode fiber transmission systems are typically impaired by mode-dependent loss (MDL). In an MDL-impaired link, maximum-likelihood (ML) detection yields a significant advantage in system performance compared to linear equalizers, such as zero-forcing and minimum-mean square error equalizers. However, the computational effort of the ML detection increases exponentially with the number of modes and the cardinality of the constellation. We present two methods that allow for near-ML performance without being afflicted with the enormous computational complexity of ML detection: improved reduced-search ML detection and sphere decoding. Both algorithms are tested regarding their performance and computational complexity in simulations of three and six spatial modes with QPSK and 16QAM constellations.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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  16. F. Ferreira, D. Fonseca, A. Lobato, B. Inan, and H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” IEEE Photon. Technol. Lett. 25(12), 1091–1094 (2013).
    [Crossref]
  17. S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.
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    [Crossref]
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    [Crossref]
  20. K. Honjo and T. Ohtsuki, “Computational complexity reduction of MLD based on SINR in MIMO spatial multiplexing systems,” IEICE transactions on communications 89(3), 914–921 (2006).
    [Crossref]
  21. M. Chouayakh, A. Knopp, and B. Lankl, “Low-effort near maximum likelihood MIMO detection with optimum hardware resource exploitation,” Electron. Lett. 43(20), 1104–1106 (2007).
    [Crossref]
  22. J. Jaldén and B. Ottersten, “On the complexity of sphere decoding in digital communications,” IEEE Trans. Signal Process. 53(4), 1474–1484 (2005).
    [Crossref]
  23. N. Tax and B. Lankl, “Fixed effort sphere decoder for MIMO OFDM systems,” in Proc. of WCSP’13, 2013.
  24. Ll. N. Trefethen and D. Bau, Numerical Linear Algebra (Society for Industrial and Applied Mathematics, 1997).
    [Crossref]
  25. E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices,” IEEE Trans. Inf. Theory. 48(8), 2201–2214, (2002).
    [Crossref]
  26. B. Hassibi and H. Vikalo, “On the expected complexity of integer least-squares problems,” in Proc. of ICASSP’02, 2002.
    [Crossref]
  27. X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization and analysis of few-mode fiber channel dynamics,” IEEE Photon. Technol. Lett. 25(18), 1819–1822 (2013).
    [Crossref]

2014 (1)

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

2013 (4)

V. A. J. M. Sleiffer, H. Chen, Y. Jung, P. Leoni, M. Kuschnerov, A. Simperler, H. Fabian, H. Schuh, F. Kub, D. J. Richardson, S. U. Alam, L. Grner-Nielsen, Y. Sun, A. M. J. Koonen, and H. de Waardt, “Field demonstration of mode-division multiplexing upgrade scenarios on commercial networks,” Opt. Express 21(25), 31036–31046 (2013).
[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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, and H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” IEEE Photon. Technol. Lett. 25(12), 1091–1094 (2013).
[Crossref]

X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization and analysis of few-mode fiber channel dynamics,” IEEE Photon. Technol. Lett. 25(18), 1819–1822 (2013).
[Crossref]

2012 (1)

2011 (3)

2010 (1)

J.-S. Kim, S.-H. Moon, and I. Lee, “A new reduced complexity ML detection scheme for MIMO systems,” IEEE Trans. Commun.,  58(4), 1302–1310 (2010).
[Crossref]

2007 (1)

M. Chouayakh, A. Knopp, and B. Lankl, “Low-effort near maximum likelihood MIMO detection with optimum hardware resource exploitation,” Electron. Lett. 43(20), 1104–1106 (2007).
[Crossref]

2006 (1)

K. Honjo and T. Ohtsuki, “Computational complexity reduction of MLD based on SINR in MIMO spatial multiplexing systems,” IEICE transactions on communications 89(3), 914–921 (2006).
[Crossref]

2005 (1)

J. Jaldén and B. Ottersten, “On the complexity of sphere decoding in digital communications,” IEEE Trans. Signal Process. 53(4), 1474–1484 (2005).
[Crossref]

2002 (1)

E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices,” IEEE Trans. Inf. Theory. 48(8), 2201–2214, (2002).
[Crossref]

1999 (1)

E. Viterbo and J. Boutros, “A universal lattice code decoder for fading channels,” IEEE Trans. Inf. Theory. 45(5), 1639–1642 (1999).
[Crossref]

1985 (1)

U. Fincke and M. Pohst, “Improved methods for calculating vectors of short length in a lattice, including a complexity analysis,” Mathematics of computation 44(170), 463–471 (1985).
[Crossref]

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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. Sleiffer, M. Kuschnerov, N. Hanik, and S. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(9), 10859–10869 (2012).
[Crossref] [PubMed]

Agrell, E.

E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices,” IEEE Trans. Inf. Theory. 48(8), 2201–2214, (2002).
[Crossref]

Alam, S.

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Grüner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express 19(26), B952–B957 (2011).
[Crossref]

Alam, S. U.

Bau, D.

Ll. N. Trefethen and D. Bau, Numerical Linear Algebra (Society for Industrial and Applied Mathematics, 1997).
[Crossref]

Biglieri, E.

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. J. Paulraj, and V. H. Poor, MIMO Wireless Communications (Cambridge University, 2007).
[Crossref]

Bigo, S.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Bigot, L.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Bland-Hawthorn, J.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

Bolle, C.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Boutros, J.

E. Viterbo and J. Boutros, “A universal lattice code decoder for fading channels,” IEEE Trans. Inf. Theory. 45(5), 1639–1642 (1999).
[Crossref]

Burrows, E.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Calderbank, R.

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. J. Paulraj, and V. H. Poor, MIMO Wireless Communications (Cambridge University, 2007).
[Crossref]

Chandrasekhar, S.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Charlet, G.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Chen, H.

Chen, X.

X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization and analysis of few-mode fiber channel dynamics,” IEEE Photon. Technol. Lett. 25(18), 1819–1822 (2013).
[Crossref]

Chouayakh, M.

M. Chouayakh, A. Knopp, and B. Lankl, “Low-effort near maximum likelihood MIMO detection with optimum hardware resource exploitation,” Electron. Lett. 43(20), 1104–1106 (2007).
[Crossref]

M. Chouayakh, A. Knopp, and B. Lankl, “Fixed effort MIMO decoders for wireless indoor channels: Theory and practical field trials,” in Proc. of PIMRC’08, 2008.

Constantinides, A.

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. J. Paulraj, and V. H. Poor, MIMO Wireless Communications (Cambridge University, 2007).
[Crossref]

Corbett, B.

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

Corteselli, S.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

de Waardt, H.

Delbue, R.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Dhar, A.

Ercan, B.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

Eriksson, T.

E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices,” IEEE Trans. Inf. Theory. 48(8), 2201–2214, (2002).
[Crossref]

Essiambre, R.-J.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

Fabian, H.

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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, and H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” IEEE Photon. Technol. Lett. 25(12), 1091–1094 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. Sleiffer, M. Kuschnerov, N. Hanik, and S. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(9), 10859–10869 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Mode scramblers and reduced search maximum likelihood detection for mode-dependent-loss-impaired transmission,” in Proc. of ECOC’13 (Optical Society of America, 2014), paper Th.2.C.3.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proc. of OECC/ACOFT’14 (Optical Society of America, 2014), paper TU4B-3.

Fincke, U.

U. Fincke and M. Pohst, “Improved methods for calculating vectors of short length in a lattice, including a complexity analysis,” Mathematics of computation 44(170), 463–471 (1985).
[Crossref]

Fonseca, D.

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, and H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” IEEE Photon. Technol. Lett. 25(12), 1091–1094 (2013).
[Crossref]

Fontaine, N. K.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

Foschini, G. J.

Giles, D.

Giles, I. P.

Gnauck, A. H.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Goldsmith, A.

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. J. Paulraj, and V. H. Poor, MIMO Wireless Communications (Cambridge University, 2007).
[Crossref]

Grner-Nielsen, L.

V. A. J. M. Sleiffer, H. Chen, Y. Jung, P. Leoni, M. Kuschnerov, A. Simperler, H. Fabian, H. Schuh, F. Kub, D. J. Richardson, S. U. Alam, L. Grner-Nielsen, Y. Sun, A. M. J. Koonen, and H. de Waardt, “Field demonstration of mode-division multiplexing upgrade scenarios on commercial networks,” Opt. Express 21(25), 31036–31046 (2013).
[Crossref]

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Grüner-Nielsen, L.

Guan, B.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Hanik, N.

Hassibi, B.

B. Hassibi and H. Vikalo, “On the expected complexity of integer least-squares problems,” in Proc. of ICASSP’02, 2002.
[Crossref]

He, J.

X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization and analysis of few-mode fiber channel dynamics,” IEEE Photon. Technol. Lett. 25(18), 1819–1822 (2013).
[Crossref]

Ho, K.-P.

Honjo, K.

K. Honjo and T. Ohtsuki, “Computational complexity reduction of MLD based on SINR in MIMO spatial multiplexing systems,” IEICE transactions on communications 89(3), 914–921 (2006).
[Crossref]

Inan, B.

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, and H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” IEEE Photon. Technol. Lett. 25(12), 1091–1094 (2013).
[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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. Sleiffer, M. Kuschnerov, N. Hanik, and S. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(9), 10859–10869 (2012).
[Crossref] [PubMed]

Jaldén, J.

J. Jaldén and B. Ottersten, “On the complexity of sphere decoding in digital communications,” IEEE Trans. Signal Process. 53(4), 1474–1484 (2005).
[Crossref]

Jansen, S.

Jensen, R. V.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Jung, Y.

Kahn, J. M.

Kang, Q.

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

Kim, J.-S.

J.-S. Kim, S.-H. Moon, and I. Lee, “A new reduced complexity ML detection scheme for MIMO systems,” IEEE Trans. Commun.,  58(4), 1302–1310 (2010).
[Crossref]

Knopp, A.

M. Chouayakh, A. Knopp, and B. Lankl, “Low-effort near maximum likelihood MIMO detection with optimum hardware resource exploitation,” Electron. Lett. 43(20), 1104–1106 (2007).
[Crossref]

M. Chouayakh, A. Knopp, and B. Lankl, “Fixed effort MIMO decoders for wireless indoor channels: Theory and practical field trials,” in Proc. of PIMRC’08, 2008.

Koonen, A. M. J.

Kub, F.

Kuschnerov, M.

V. A. J. M. Sleiffer, H. Chen, Y. Jung, P. Leoni, M. Kuschnerov, A. Simperler, H. Fabian, H. Schuh, F. Kub, D. J. Richardson, S. U. Alam, L. Grner-Nielsen, Y. Sun, A. M. J. Koonen, and H. de Waardt, “Field demonstration of mode-division multiplexing upgrade scenarios on commercial networks,” Opt. Express 21(25), 31036–31046 (2013).
[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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. Sleiffer, M. Kuschnerov, N. Hanik, and S. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(9), 10859–10869 (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 Proc. of OECC/ACOFT’14 (Optical Society of America, 2014), paper TU4B-3.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Mode scramblers and reduced search maximum likelihood detection for mode-dependent-loss-impaired transmission,” in Proc. of ECOC’13 (Optical Society of America, 2014), paper Th.2.C.3.

Lankl, B.

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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

M. Chouayakh, A. Knopp, and B. Lankl, “Low-effort near maximum likelihood MIMO detection with optimum hardware resource exploitation,” Electron. Lett. 43(20), 1104–1106 (2007).
[Crossref]

N. Tax and B. Lankl, “Fixed effort sphere decoder for MIMO OFDM systems,” in Proc. of WCSP’13, 2013.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proc. of OECC/ACOFT’14 (Optical Society of America, 2014), paper TU4B-3.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Mode scramblers and reduced search maximum likelihood detection for mode-dependent-loss-impaired transmission,” in Proc. of ECOC’13 (Optical Society of America, 2014), paper Th.2.C.3.

M. Chouayakh, A. Knopp, and B. Lankl, “Fixed effort MIMO decoders for wireless indoor channels: Theory and practical field trials,” in Proc. of PIMRC’08, 2008.

Le Cocq, G.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Lee, I.

J.-S. Kim, S.-H. Moon, and I. Lee, “A new reduced complexity ML detection scheme for MIMO systems,” IEEE Trans. Commun.,  58(4), 1302–1310 (2010).
[Crossref]

Leoni, P.

Leon-Saval, S. G.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

Li, A.

X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization and analysis of few-mode fiber channel dynamics,” IEEE Photon. Technol. Lett. 25(18), 1819–1822 (2013).
[Crossref]

Li, Z.

Lingle, R.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Liu, C.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

Lobato, 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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, and H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” IEEE Photon. Technol. Lett. 25(12), 1091–1094 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. Sleiffer, M. Kuschnerov, N. Hanik, and S. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(9), 10859–10869 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Mode scramblers and reduced search maximum likelihood detection for mode-dependent-loss-impaired transmission,” in Proc. of ECOC’13 (Optical Society of America, 2014), paper Th.2.C.3.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proc. of OECC/ACOFT’14 (Optical Society of America, 2014), paper TU4B-3.

Mestre, M. A.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Moon, S.-H.

J.-S. Kim, S.-H. Moon, and I. Lee, “A new reduced complexity ML detection scheme for MIMO systems,” IEEE Trans. Commun.,  58(4), 1302–1310 (2010).
[Crossref]

Mumtaz, S.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

Neilson, D. T.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

OCallaghan, J.

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

Ohtsuki, T.

K. Honjo and T. Ohtsuki, “Computational complexity reduction of MLD based on SINR in MIMO spatial multiplexing systems,” IEICE transactions on communications 89(3), 914–921 (2006).
[Crossref]

Ottersten, B.

J. Jaldén and B. Ottersten, “On the complexity of sphere decoding in digital communications,” IEEE Trans. Signal Process. 53(4), 1474–1484 (2005).
[Crossref]

Palou, X.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Paulraj, A. J.

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. J. Paulraj, and V. H. Poor, MIMO Wireless Communications (Cambridge University, 2007).
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Peyrot, D.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Pohst, M.

U. Fincke and M. Pohst, “Improved methods for calculating vectors of short length in a lattice, including a complexity analysis,” Mathematics of computation 44(170), 463–471 (1985).
[Crossref]

Poletti, F.

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Grüner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express 19(26), B952–B957 (2011).
[Crossref]

Poor, V. H.

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. J. Paulraj, and V. H. Poor, MIMO Wireless Communications (Cambridge University, 2007).
[Crossref]

Pupalaikis, P.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Quiquempois, Y.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

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 Proc. of OECC/ACOFT’14 (Optical Society of America, 2014), paper TU4B-3.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Mode scramblers and reduced search maximum likelihood detection for mode-dependent-loss-impaired transmission,” in Proc. of ECOC’13 (Optical Society of America, 2014), paper Th.2.C.3.

Randel, S.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Richardson, D.

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

Richardson, D. J.

Ryf, R.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

Sahu, J.

Y. Jung, Q. Kang, J. Sahu, B. Corbett, J. OCallaghan, F. Poletti, S. Alam, and D. Richardson, “Reconfigurable modal gain control of a few-mode EDFA supporting 6 spatial modes,” IEEE Photon. Technol. Lett. 26(11), 1100–1103 (2014).
[Crossref]

Sahu, J. K.

SalazarGil, J. R.

N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. SalazarGil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, “Few-mode fiber wavelength selective switch with spatial-diversity and reduced-steering angle,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper Th4A.7.

Salsi, M.

M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. of ECOC’12 (Optical Society of America, 2012), paper Th.3.A.6.

Schmidt, C.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

Schuh, H.

Shieh, W.

X. Chen, J. He, A. Li, J. Ye, and W. Shieh, “Characterization and analysis of few-mode fiber channel dynamics,” IEEE Photon. Technol. Lett. 25(18), 1819–1822 (2013).
[Crossref]

Sierra, A.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

Silva, H.

F. Ferreira, D. Fonseca, A. Lobato, B. Inan, and H. Silva, “Reach improvement of mode division multiplexed systems using fiber splices,” IEEE Photon. Technol. Lett. 25(12), 1091–1094 (2013).
[Crossref]

Simperler, A.

Sleiffer, V.

Sleiffer, V. A. J. M.

Spinnler, B.

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 Photon. Technol. Lett. 25(12), 1095–1098 (2013).
[Crossref]

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. Sleiffer, M. Kuschnerov, N. Hanik, and S. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(9), 10859–10869 (2012).
[Crossref] [PubMed]

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Mode scramblers and reduced search maximum likelihood detection for mode-dependent-loss-impaired transmission,” in Proc. of ECOC’13 (Optical Society of America, 2014), paper Th.2.C.3.

A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, “Enhanced performance for MDL-impaired few-mode fiber transmission,” in Proc. of OECC/ACOFT’14 (Optical Society of America, 2014), paper TU4B-3.

Sun, Y.

V. A. J. M. Sleiffer, H. Chen, Y. Jung, P. Leoni, M. Kuschnerov, A. Simperler, H. Fabian, H. Schuh, F. Kub, D. J. Richardson, S. U. Alam, L. Grner-Nielsen, Y. Sun, A. M. J. Koonen, and H. de Waardt, “Field demonstration of mode-division multiplexing upgrade scenarios on commercial networks,” Opt. Express 21(25), 31036–31046 (2013).
[Crossref]

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Sureka, A.

R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grner-Nielsen, R. V. Jensen, and R. Lingle, “708-km combined WDM/SDM transmission over few-mode fiber supporting 12 spatial and polarization modes,” in Proc. of ECOC’13 (Optical Society of America, 2013), paper We.2.D.1.

Tax, N.

N. Tax and B. Lankl, “Fixed effort sphere decoder for MIMO OFDM systems,” in Proc. of WCSP’13, 2013.

Trefethen, Ll. N.

Ll. N. Trefethen and D. Bau, Numerical Linear Algebra (Society for Industrial and Applied Mathematics, 1997).
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Tulino, A.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

van den Borne, D.

Vardy, A.

E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lattices,” IEEE Trans. Inf. Theory. 48(8), 2201–2214, (2002).
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Vikalo, H.

B. Hassibi and H. Vikalo, “On the expected complexity of integer least-squares problems,” in Proc. of ICASSP’02, 2002.
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Viterbo, E.

E. Viterbo and J. Boutros, “A universal lattice code decoder for fading channels,” IEEE Trans. Inf. Theory. 45(5), 1639–1642 (1999).
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Winzer, P.

S. Randel, A. Sierra, S. Mumtaz, A. Tulino, R. Ryf, P. Winzer, C. Schmidt, and R.-J. Essiambre, “Adaptive MIMO signal processing for mode-division multiplexing,” in Proc. of OFC/NFOEC’14 (Optical Society of America, 2014), paper OW3D.5.

Winzer, P. J.

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Figures (7)

Fig. 1
Fig. 1 Block diagram of the simulated system. Nt: Number of tributaries, MS: mode scrambler, (D)MUX: (de)multiplexer, ASE: amplified spontaneous emission noise.
Fig. 2
Fig. 2 Block diagram of the (a) transmitter and (b) receiver front end.
Fig. 3
Fig. 3 The IRSML two-stage algorithm.
Fig. 4
Fig. 4 (a) OSNR penalty at a TBER of 1E-3 for different detection schemes and (b) MDL as a function of the distance for three modes and QPSK.
Fig. 5
Fig. 5 Average reach at an OSNR penalty of 1 dB. Solid markers corresponds to a reach greater than 95 % of the SD/ML reach.
Fig. 6
Fig. 6 Number of complex multiplications needed for the detection of one bit for one subcarrier.
Fig. 7
Fig. 7 SD complexity as a function of the distance. (a) Average complexity, (b) maximum registered complexity, (c) average and maximum γ for three modes, (d) average and maximum γ for six modes.

Equations (20)

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r = Hs + η ,
G MMSE = ( H H H + σ η 2 σ s 2 I N t ) 1 H H
y MMSE = G MMSE r
s ^ ML = arg min s A N t r Hs 2
s ^ IRSML = arg min s S r Hs 2
δ μ , i = | y MMSE i s μ , i | ,
arg min s μ , i δ μ , i
s ^ SD = arg min s S R ( r , H ) r Hs 2 .
S R ( r , H ) = { s A N t , r Hs 2 R 2 }
s ^ SD = arg min s S R ( w , R ) w Rs 2 .
S R ( w , R ) = { s A N t , w Rs 2 R 2 }
Q H r Rs 2 = k = 1 N t | q k H r l = 1 N t R k l s l | 2 ,
Q H r Rs 2 = k = N t 1 | q k H y l = k N t R k l s l | 2 .
e = [ R 1 w ] = [ R 1 Q H r ]
N t 3 3 + N t 2 = : c 1
1 N f ( c 1 + 2 N t 3 ) + N t 2 N t log 2 M = : c 2
M N t N t 2 N t log 2 M
c 2 + N max N t 2 N t log 2 M
2 N t 3 3 = : c 3
c 3 + c 1 N f + B N t log 2 M

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