Applications of Large Random Matrices in Communications Engineering
Abstract
This work gives an overview of analytic tools for the design, analysis, and modelling of communication systems which can be described by linear vector channels such as y = Hx+z where the number of components in each vector is large. Tools from probability theory, operator algebra, and statistical physics are reviewed. The survey of analytical tools is complemented by examples of applications in communications engineering. Asymptotic eigenvalue distributions of many classes of random matrices are given. The treatment includes the problem of moments and the introduction of the Stieltjes transform. Free probability theory, which evolved from noncommutative operator algebras, is explained from a probabilistic point of view in order to better fit the engineering community. For that purpose freeness is defined without reference to noncommutative algebras. The treatment includes additive and multiplicative free convolution, the Rtransform, the Stransform, and the free central limit theorem. The replica method developed in statistical physics for the purpose of analyzing spin glasses is reviewed from the viewpoint of its applications in communications engineering. Correspondences between free energy and mutual information as well as energy functions and detector metrics are established. These analytic tools are applied to the design and the analysis of linear multiuser detectors, the modelling of scattering in communication channels with dual antennas arrays, and the analysis of optimal detection for communication via codedivision multipleaccess and/or dual antenna array channels.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.5479
 Bibcode:
 2013arXiv1310.5479M
 Keywords:

 Computer Science  Information Theory
 EPrint:
 arXiv admin note: text overlap with arXiv:0706.1169 by other authors