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

Central limit theorem and large deviations of the fading Wyner cellular model via product of... 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 P(|C m − C| > ɛ) ≤ e −mα with α = α(ɛ) > 0 and C = $$\mathop {\lim }\limits_{m \to \infty }$$ C m , as opposed to the rate $$e^{ - m^2 \alpha }$$ in classical random matrix theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

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

, Volume 45 (1) – Apr 30, 2009
18 pages

Publisher
Springer Journals
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946009010025
Publisher site
See Article on Publisher Site

### 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 P(|C m − C| > ɛ) ≤ e −mα with α = α(ɛ) > 0 and C = $$\mathop {\lim }\limits_{m \to \infty }$$ C m , as opposed to the rate $$e^{ - m^2 \alpha }$$ in classical random matrix theory.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 30, 2009

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