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

• Authors:
• N. Levy;O. Zeitouni;S. Shamai (Shitz)

• Affiliations:
• Department of Electrical Engineering, Technion, Haifa, Israel;Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel and School of Mathematics, University of Minnesota, Minneapolis, USA;Department of Electrical Engineering, Technion, Haifa, Israel

• Venue:
• Problems of Information Transmission
• Year:
• 2009
• IEEE Transactions on Information Theory

• IEEE Transactions on Information Theory

• IEEE Transactions on Information Theory

• IEEE Transactions on Information Theory

• IEEE Transactions on Information Theory

• IEEE Journal on Selected Areas in Communications - Special issue on cooperative communications in MIMO cellular networks

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### 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.