Random Matrix Methods for Wireless Communications

2009 ◽  
Author(s):  
Romain Couillet ◽  
Merouane Debbah
Keyword(s):  
Wireless Communications ◽  
Random Matrix ◽  
Matrix Methods

Design of Reduced-Rank MMSE Multiuser Detectors Using Random Matrix Methods

2004 ◽  
Vol 50 (6) ◽  
pp. 986-1008 ◽  
Author(s):  
L. Li ◽  
A.M. Tulino ◽  
S. Verdu
Keyword(s):  
Random Matrix ◽  
Matrix Methods ◽  
Reduced Rank ◽  
Multiuser Detectors

scholarly journals Large-dimensional random matrix theory and its applications in deep learning and wireless communications

2021 ◽  
pp. 2230001
Author(s):  
Jungang Ge ◽  
Ying-Chang Liang ◽  
Zhidong Bai ◽  
Guangming Pan
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Wireless Communications ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Communication Systems ◽  
Quantum Physics ◽  
Matrix Theory ◽  
Research Field ◽  
Analysis And Design

Large-dimensional (LD) random matrix theory, RMT for short, which originates from the research field of quantum physics, has shown tremendous capability in providing deep insights into large-dimensional systems. With the fact that we have entered an unprecedented era full of massive amounts of data and large complex systems, RMT is expected to play more important roles in the analysis and design of modern systems. In this paper, we review the key results of RMT and its applications in two emerging fields: wireless communications and deep learning. In wireless communications, we show that RMT can be exploited to design the spectrum sensing algorithms for cognitive radio systems and to perform the design and asymptotic analysis for large communication systems. In deep learning, RMT can be utilized to analyze the Hessian, input–output Jacobian and data covariance matrix of the deep neural networks, thereby to understand and improve the convergence and the learning speed of the neural networks. Finally, we highlight some challenges and opportunities in applying RMT to the practical large-dimensional systems.

scholarly journals Optimization of MIMO Systems Capacity Using Large Random Matrix Methods

Entropy ◽  
2012 ◽  
Vol 14 (11) ◽  
pp. 2122-2142
Author(s):  
Florian Dupuy ◽  
Philippe Loubaton
Keyword(s):  
Random Matrix ◽  
Mimo Systems ◽  
Matrix Methods

Random matrices and number theory: some recent themes

2018 ◽  
Author(s):  
Jon P. Keating
Keyword(s):  
Number Theory ◽  
Zeta Function ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Gaussian Random Fields ◽  
Extreme Value Statistics ◽  
Matrix Methods ◽  
Recent Developments ◽  
Riemann Zeta

The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and rather selective introduction to the theory of the Riemann zeta function, in particular to those parts needed to understand the connections with random matrix theory. The second section focuses on the value distribution of the zeta function on its critical line, specifically on recent progress in understanding the extreme value statistics gained through a conjectural link to log–correlated Gaussian random fields and the statistical mechanics of glasses. The third section outlines some number-theoretic problems that can be resolved in function fields using random matrix methods. In this latter case, random matrix theory provides the only route we currently have for calculating certain important arithmetic statistics rigorously and unconditionally.

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