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

In this paper, we apply the theory of random Schrödinger operators to the analysis of multiusers communication channels similar to the Wyner model, which are characterized by short-range intercell interference. With H the channel transfer matrix, HHf is a narrow band matrix, a fact that does not permit the use of classical random matrices theory. On the other hand, HHf is in many aspects 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 then related to the top Lyapunov exponent of a random sequence of matrices via a version of the Thouless formula. We also derive several bounds on the limiting per-cell sum-rate capacity, some based on the theory of random Schrödinger operators, and some derived from information theoretical considerations. Finally, we get explicit results in the high-signal-to-noise ratio (SNR) regime for some particular cases.

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