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

Authors:
Nathan Levy;Ofer Zeitouni;Shlomo Shamai
Affiliations:
Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel and Département de Mathématiques et Applications, Ecole Normale Supérieure, Paris, Franc ...;Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel and School of Mathematics, University of Minnesota, Minneapolis, MN;Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 6
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Random matrix theory and wireless communications

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

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Capacity-achieving input covariance for single-user multi-antenna channels

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Shannon-theoretic approach to a Gaussian cellular multiple-access channel with fading

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High-SNR power offset in multiantenna communication

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

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On certain large random Hermitian Jacobi matrices with applications to wireless communications

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Information theoretic aspects of users' activity in a Wyner-like cellular model

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Multi-cell MIMO cooperative networks: a new look at interference

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Abstract

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, HH† is a narrow band matrix, a fact that does not permit the use of classical random matrices theory. On the other hand, HH† 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.