On information rates of the fading Wyner cellular model via the thouless formula for the strip

We apply the theory of random Schrödinger operators to the analysis of multi-users communication channels similar to the Wyner model, which are characterized by short-range inter-cell broadcasting. With H the channel transfer matrix, HH
^†
is a narrow-band matrix and in many aspects is similar to a random Schrödinger operator. We relate the per-cell sum-rate capacity of the channel to the integrated density of states of a random Schrödinger 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 explicit results in the high-SNR regime for some particular cases.