Large deviation approach to the outage optical MIMO capacity

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. The lack of back-scattering necessitates the modeling of the transmission coefficients between modes as elements of a unitary matrix. Also, due to the scattering between modes the channel is modeled as a random Haar unitary matrix between Nt transmitting and Nr receiving modes. In this paper, we apply a large-deviations approach from random matrix theory to obtain the outage capacity for Haar matrices in the low outage limit, which is appropriate for fiber-optical communications. This methodology is based on the Coulomb gas method for the eigenvalues of a matrix developed in statistical physics. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.

[1]  Hesham El Gamal,et al.  The Throughput–Reliability Tradeoff in Block-Fading MIMO Channels , 2007, IEEE Transactions on Information Theory.

[2]  J. Speidel,et al.  Analytical performance of MIMO MMSE receivers in correlated Rayleigh fading environments , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[3]  B. Zhu,et al.  Statistics of crosstalk in bent multicore fibers. , 2010, Optics express.

[4]  Toshio Morioka,et al.  Enhancing optical communications with brand new fibers , 2012, IEEE Communications Magazine.

[5]  M. Debbah,et al.  Second-order statistics of large isometric matrices and applications to MMSE SIR , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[6]  Kunimasa Saitoh,et al.  An Investigation on Crosstalk in Multi-Core Fibers by Introducing Random Fluctuation along Longitudinal Direction , 2011, IEICE Trans. Commun..

[7]  Robert W. Tkach,et al.  Scaling optical communications for the next decade and beyond , 2010, Bell Labs Technical Journal.

[8]  S. Majumdar,et al.  Large deviations of the maximum eigenvalue in Wishart random matrices , 2007, cond-mat/0701371.

[9]  Philippe Loubaton,et al.  MMSE analysis of certain large isometric random precoded systems , 2003, IEEE Trans. Inf. Theory.

[10]  Ronen Dar,et al.  The Jacobi MIMO Channel , 2013, IEEE Transactions on Information Theory.

[11]  S. Simon,et al.  Crossover from conserving to lossy transport in circular random-matrix ensembles. , 2005, Physical review letters.

[12]  I. G. MacDonald,et al.  Symmetric functions and Hall polynomials , 1979 .

[13]  Thomas L. Marzetta,et al.  Capacity of Differential Versus Nondifferential Unitary Space–Time Modulation for MIMO Channels , 2005, IEEE Transactions on Information Theory.

[14]  Bahram Jalali,et al.  Coherent optical MIMO (Invited Paper) , 2005, SPIE Defense + Commercial Sensing.

[15]  P. Forrester.  Log-Gases and Random Matrices , 2010 .

[16]  C. Beenakker.  Random-matrix theory of quantum transport , 1996, cond-mat/9612179.

[17]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[18]  Peter J. Winzer,et al.  MIMO capacities and outage probabilities in spatially multiplexed optical transport systems. , 2011, Optics express.

[19]  Martin,et al.  Wave-packet approach to noise in multichannel mesoscopic systems. , 1992, Physical review. B, Condensed matter.

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

[21]  Mérouane Debbah,et al.  Random Beamforming Over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach , 2010, IEEE Transactions on Information Theory.

[22]  J. Conway,et al.  Functions of a Complex Variable , 1964 .

[23]  T. Sasaki,et al.  Ultra-low-crosstalk multi-core fiber realizing space-division multiplexed ultra-long-haul transmission , 2012, 2012 Conference on Lasers and Electro-Optics (CLEO).

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

[25]  S. Majumdar,et al.  Large deviations of the maximal eigenvalue of random matrices , 2010, 1009.1945.

[26]  Satya N. Majumdar,et al.  Course 4 Random matrices, the ulam problem, directed polymers & growth models, and sequence matching , 2007, cond-mat/0701193.

[27]  Oriol Bohigas,et al.  Distributions of conductance and shot noise and associated phase transitions. , 2008, Physical review letters.

[28]  Matthew R. McKay,et al.  Coulumb Fluid, Painlevé Transcendents, and the Information Theory of MIMO Systems , 2012, IEEE Transactions on Information Theory.

[29]  Ali H. Sayed,et al.  Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications] , 2007, IEEE Communications Magazine.

[30]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[31]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[32]  S. Majumdar,et al.  Extreme value statistics of eigenvalues of Gaussian random matrices. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Giuseppe Caire,et al.  Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity , 2009, IEEE Transactions on Information Theory.

[34]  Lizhong Zheng,et al.  Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels , 2003, IEEE Trans. Inf. Theory.

[35]  F. Dyson.  Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .