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

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3 Author(s)
Nathan Levy ; Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa, Israel ; Ofer Zeitouni ; Shlomo Shamai

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.

Published in:

IEEE Transactions on Information Theory  (Volume:56 ,  Issue: 11 )