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 Probl. Peredachi Inf., 2009, Volume 45, Issue 1, Pages 8–26 (Mi ppi1255)

Information Theory

Central limit theorem and large deviations of the fading Wyner cellular model via product of random matrices theory

N. Levyab, O. Zeitounicd, Sh. Shamai (Shitz)a

a Technion, Haifa, Israel
b Ècole Normale Supérieure, Paris, France
c University of Minnesota
d Weizmann Institute of Science, Rehovot, Israel

Abstract: We apply the theory of products of random matrices to the analysis of multi-user communication channels similar to the Wyner model, which are characterized by short-range intra-cell broadcasting. We study fluctuations of the per-cell sum-rate capacity in the non-ergodic regime and provide results of the type of the central limit theorem (CLT) and large deviations (LD). Our results show that CLT fluctuations of the per-cell sum-rate $C_m$ are of order $1/\sqrt m$, where $m$ is the number of cells, whereas they are of order $1/m$ in classical random matrix theory. We also show an LD regime of the form $\mathbf P(|C_m-C|>\varepsilon)\le e^{-m\alpha}$ with $\alpha=\alpha(\varepsilon)>0$ and $C=\lim\limits_{m\to\infty}C_m$, as opposed to the rate $e^{-m^2\alpha}$ in classical random matrix theory.

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English version:
Problems of Information Transmission, 2009, 45:1, 5–22

Bibliographic databases:

UDC: 621.391.1:519.2
Revised: 24.11.2008

Citation: N. Levy, O. Zeitouni, Sh. Shamai (Shitz), “Central limit theorem and large deviations of the fading Wyner cellular model via product of random matrices theory”, Probl. Peredachi Inf., 45:1 (2009), 8–26; Problems Inform. Transmission, 45:1 (2009), 5–22

Citation in format AMSBIB
\Bibitem{LevZeiSha09} \by N.~Levy, O.~Zeitouni, Sh.~Shamai (Shitz) \paper Central limit theorem and large deviations of the fading Wyner cellular model via product of random matrices theory \jour Probl. Peredachi Inf. \yr 2009 \vol 45 \issue 1 \pages 8--26 \mathnet{http://mi.mathnet.ru/ppi1255} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2513159} \transl \jour Problems Inform. Transmission \yr 2009 \vol 45 \issue 1 \pages 5--22 \crossref{https://doi.org/10.1134/S0032946009010025} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000265776300002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65549092709} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Gesbert D., Hanly S., Huang H., Shitz Sh.Sh., Simeone O., Yu W., “Multi-cell MIMO cooperative networks: a new look at interference”, IEEE Journal on Selected Areas in Communications, 28:9 (2010), 1380–1408
2. Levy N., Zeitouni O., Shamai S., “On information rates of the fading Wyner cellular model via the thouless formula for the strip”, IEEE Trans. Inform. Theory, 56:11 (2010), 5495–5514
3. Levy N., Shamai Sh., “Information theoretic aspects of users' activity in a Wyner-like cellular model”, IEEE Trans. Inform. Theory, 56:5 (2010), 2241–2248
4. Simmons D.E., Coon J.P., Warsi N., “Capacity and Power Scaling Laws For Finite Antenna Mimo Amplify-and-Forward Relay Networks”, IEEE Trans. Inf. Theory, 62:4 (2016), 1993–2008
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