On Information Rates of the Fading Wyner Cellular Model via the Thouless Formula for the Strip

Abstract: We apply the theory of random Schr\"odinger operators to the analysis of multi-users communication channels similar to the Wyner model, that are characterized by short-range intra-cell broadcasting. With $H$ the channel transfer matrix, $HH^\dagger$ is a narrow-band matrix and in many aspects is similar to a random Schr\"odinger operator. We relate the per-cell sum-rate capacity of the channel to the integrated density of states of a random Schr\"odinger operator; the latter is related to the top Lyapunov exponent of a random sequence of matrices via a version of the Thouless formula. Unlike related results in classical random matrix theory, limiting results do depend on the underlying fading distributions. We also derive several bounds on the limiting per-cell sum-rate capacity, some based on the theory of random Schr\"odinger operators, and some derived from information theoretical considerations. Finally, we get explicit results in the high-SNR regime for some particular cases.