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

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.