Mode-dependent loss and gain: statistics and effect on mode-division multiplexing.

In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the small-MDL region that is expected to be of interest for practical long-haul transmission. Information-theoretic channel capacities of mode-division-multiplexed systems in the presence of MDL are studied, including average and outage capacities, with and without channel state information.

[1]  R. Bellman.  Limit theorems for non-commutative operations. I. , 1954 .

[2]  E. Wigner.  Characteristic Vectors of Bordered Matrices with Infinite Dimensions I , 1955 .

[3]  H. Furstenberg,et al.  Products of Random Matrices , 1960 .

[4]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[5]  D. Gloge.  Weakly guiding fibers. , 1971, Applied optics.

[6]  D. Gloge,et al.  Optical power flow in multimode fibers , 1972 .

[7]  R. Olshansky,et al.  Mode Coupling Effects in Graded-index Optical Fibers. , 1975, Applied optics.

[8]  M. Berger.  Central limit theorem for products of random matrices , 1984 .

[9]  Charles M. Newman,et al.  The Stability of Large Random Matrices and Their Products , 1984 .

[10]  R. E. Wagner,et al.  Phenomenological approach to polarisation dispersion in long single-mode fibres , 1986 .

[11]  D. Voiculescu.  Limit laws for Random matrices and free products , 1991 .

[12]  Alexandru Nica,et al.  Free random variables , 1992 .

[13]  A. Crisanti,et al.  Products of random matrices in statistical physics , 1993 .

[14]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[15]  I. White,et al.  An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links , 1998 .

[16]  J. Le Bihan,et al.  Multichannel transmission of a multicore fiber coupled with vertical-cavity surface-emitting lasers , 1999 .

[17]  A. Robert Calderbank,et al.  Space-time block coding for wireless communications: performance results , 1999, IEEE J. Sel. Areas Commun..

[18]  Stuart,et al.  Dispersive multiplexing in multimode optical fiber , 2000, Science.

[19]  Lih-Yuan Deng,et al.  Orthogonal Arrays: Theory and Applications , 1999, Technometrics.

[20]  Keang-Po Ho,et al.  Statistical properties of stimulated Raman crosstalk in WDM systems , 2000, Journal of Lightwave Technology.

[21]  H. Kogelnik,et al.  PMD fundamentals: polarization mode dispersion in optical fibers. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[22]  H. Bercovici,et al.  Limit laws for products of free and independent random variables , 2000 .

[23]  Xiaoyi Bao,et al.  Statistical distribution of polarization-dependent loss in the presence of polarization-mode dispersion in single-mode fibers , 2001 .

[24]  H. Kogelnik,et al.  Polarization-Mode Dispersion , 2002 .

[25]  A. Mecozzi,et al.  The statistics of polarization-dependent loss in optical communication systems , 2002, IEEE Photonics Technology Letters.

[26]  A. Edelman,et al.  Matrix models for beta ensembles , 2002, math-ph/0206043.

[27]  Bojun Yang,et al.  Polarization mode dispersion in WDM systems , 2002 .

[28]  L. Palmieri,et al.  The exact statistics of polarization-dependent loss in fiber-optic links , 2003, IEEE Photonics Technology Letters.

[29]  Jean Armstrong,et al.  Effects of phase noise on performance of OFDM systems using an ICI cancellation scheme , 2003, IEEE Trans. Broadcast..

[30]  Branka Vucetic,et al.  Space-Time Coding , 2003 .

[31]  Antonia Maria Tulino,et al.  Random Matrix Theory and Wireless Communications , 2004, Found. Trends Commun. Inf. Theory.

[32]  Yeheskel Bar-Ness,et al.  OFDM systems in the presence of phase noise: consequences and solutions , 2004, IEEE Transactions on Communications.

[33]  Ross D. Murch,et al.  Layered space-frequency equalization in a single-carrier MIMO system for frequency-selective channels , 2004, IEEE Transactions on Wireless Communications.

[34]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[35]  Alan F. Benner,et al.  Exploitation of optical interconnects in future server architectures , 2005 .

[36]  Mike Ignatowski,et al.  Exploitation of optical interconnects in future server architectures , 2005, IBM J. Res. Dev..

[37]  B. Jalali,et al.  Coherent optical MIMO (COMIMO) , 2005, Journal of Lightwave Technology.

[38]  Ali Esmaili,et al.  Probability and Random Processes , 2005, Technometrics.

[39]  Alexandru Nica,et al.  Lectures on the Combinatorics of Free Probability , 2006 .

[40]  V. Kargin.  The norm of products of free random variables , 2006, math/0611593.

[41]  Ali H. Sayed,et al.  Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links , 2006, IEEE Communications Letters.

[42]  Ali H. Sayed,et al.  Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links - eScholarship , 2007 .

[43]  A. Agmon,et al.  Coherent Transmission Direct Detection MIMO Over Short-Range Optical Interconnects and Passive Optical Networks , 2008, Journal of Lightwave Technology.

[44]  Y Tang,et al.  Coherent optical OFDM: theory and design. , 2008, Optics express.

[45]  Yasuhiro Koike,et al.  Plastic optical fibers: Technologies and communication links , 2008 .

[46]  F. Götze,et al.  Limit theorems in free probability theory II , 2008 .

[47]  T. Tao,et al.  From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices , 2008, 0810.2994.

[48]  V. Kargin.  Limit theorems in free probability theory , 2008 .

[49]  W. Shieh,et al.  21.4 Gbit/s transmission over 200 km multimode fibre using coherent optical OFDM , 2008 .

[50]  William Shieh,et al.  Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing. , 2008, Optics express.

[51]  Chongjin Xie,et al.  WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation. , 2009, Optics express.

[52]  J. Kahn,et al.  Principal Modes in Graded-Index Multimode Fiber in Presence of Spatial- and Polarization-Mode Coupling , 2009, Journal of Lightwave Technology.

[53]  B. Zhu,et al.  Seven-core multicore fiber transmissions for passive optical network. , 2010, Optics express.

[54]  Henning Bülow.  Coherent Multi Channel Transmission over Multimode-Fiber and Related Signal Processing , 2010 .

[55]  S. Bigo,et al.  Nonlinear effects in long-haul transmission over bimodal optical fibre , 2010, 36th European Conference and Exhibition on Optical Communication.

[56]  William Shieh,et al.  Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber , 2011 .

[57]  William Shieh,et al.  Equalization-enhanced phase noise induced timing jitter. , 2011, Optics letters.

[58]  Massimiliano Salsi,et al.  Transmission at 2×100Gb/s, over two modes of 40km-long prototype few-mode fiber, using LCOS-based mode multiplexer and demultiplexer , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[59]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[60]  Keang-Po Ho,et al.  Statistics of Group Delays in Multimode Fiber With Strong Mode Coupling , 2011, Journal of Lightwave Technology.

[61]  Peter J. Winzer,et al.  Outage calculations for spatially multiplexed fiber links , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[62]  K. Ho.  Central Limit for the Product of Free Random Variables , 2011, 1101.5220.

[63]  A. Gnauck,et al.  Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.