Massive MIMO and Random Matrix

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Mini Seminar on Massive MIMO and Random Matrix

Department of Electronics & Communication EngineeringNational Institute of Technology, RourkelaVarun Kumar (514EC1005)

Under the supervision of Prof . Sarat Kumar Patra

Massive MIMO and Random Matrix (RMT)Massive MIMO: Massive MIMOmakes a clean break with current practice through the use of a very large number of service antennas (e.g., hundreds or thousands) that are operated fully coherently and adaptively. Extra antennas help by focusing the transmission and reception of signal energy into ever-smaller regions of space.

Random Matrix Theory:A wide range of existing mathematical results that are relevant to the analysis of the statistics of random matrices arising in wireless communications. Complex Gaussian random variables are always circularly symmetric, i.e., with uncorrelated real and imaginary parts, and complex Gaussian vectors are always proper complex.

Most Important Class of Random Matrices:GaussianWignerWishartHaar matricesWe also collect a number of results that hold for arbitrary matrix size.

Wireless Channel Model:

H is fast faded channel matrix. The primary assumption to make mathematical modal are as follows

Gamma Distribution

Some important property of random vector and random matrices

Wigner MatricesLet W be an n n matrix whose (diagonal and upper-triangle) entries are i.i.d. zero-mean Gaussian with unit variance. Then, its p.d.f. is

Some Useful Property of Whishart Matrix:

Other Application:Single-user matched filter De-correlator MMSE Optimum Iterative nonlinear

Conclusion:Random matrix results have been used to characterize the fundamental limits of the various channels that arise in wireless communications.Random matrix theory is very useful to converge the very large matrix size. In stead of solving point to point multiplication addition subtraction and large number of channel realization it easily converge to expected value.

References:A. M. Tulino and S. Verd, Random matrix theory and wireless communications, Foundations Trends Communication. Inf. Theory, vol. 1, no. 1, pp. 1182, June 2004H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, Energy and spectral efficiency of very large multiuser MIMO systems, IEEE Trans. Commun., vol. 61, no. 4, pp. 14361449, Apr. 2013.A Goldsmith, Wireless Communication, Cambridge university press, 2005Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin,`` Bayesian Data Analysis (Chapman & Hall/CRC Texts in Statistical Science) 3rd Edition 2013 M. Matthaiou, M. R. MacKay, P. J. Smith, and J. A. Nossek, On the condition number distribution of complex Wishart matrices, IEEE Trans. Commun., vol. 58, no. 6, pp. 17051717, Jun. 2010G. Stewart, Matrix Algorithms: Basic Decompositions. Philadelphia, PA: SIAM, 1998.

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