Paper Info
Title
Coulomb Gas Analogy: A Statistical Physics Approach to Performance Analysis of MIMO Systems
Abstract
In this correspondence, by adopting the Coulomb gas analogy that is an analytical approach from statistical physics, we derive a closed-form approximation of the cumulative distribution function (CDF) of the largest eigenvalue of a random Gram matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \boldsymbol {H}^{H} \boldsymbol {H}$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol {H}$</tex-math></inline-formula> denotes the channel matrix of a multiple-input multiple-output (MIMO) system. The expression of approximation has a simple structure in terms of several elementary functions, which is derived by assuming that the entries of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol {H}$</tex-math></inline-formula> have Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> distributed amplitude with an independent phase. This assumption is made because it applies in two common cases of the Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> distributions, i.e., with a uniformly distributed phase and a complex signal model. Simulation results indicate that the theoretical expression also provides a good approximation to the CDF for Rice and Hoyt distributions when the CDF is within a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">near-one</italic> range. This range takes the form of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(P_{no}, 1)$</tex-math></inline-formula> , where we assume <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P_{no} = 10^{-3}$</tex-math></inline-formula> by default in this study. The derived approximation can find many uses for the performance analysis of MIMO beamforming and singular value decomposition MIMO systems, e.g., evaluating the outage probability for these systems.
Year
DOI
Venue
2019
10.1109/TVT.2018.2889332
IEEE Transactions on Vehicular Technology
Keywords
Field
DocType
MIMO communication,Eigenvalues and eigenfunctions,Rayleigh channels,Physics,Performance analysis,Array signal processing
Statistical physics,Singular value decomposition,Matrix (mathematics),Computer science,Elementary function,MIMO,Nakagami distribution,Cumulative distribution function,Gramian matrix,Eigenvalues and eigenvectors
Journal
Volume
Issue
ISSN
68
2
0018-9545
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Yuan Qi12415.41
Rongrong Qian24913.30
Na Li3327.78