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 Schrodinger 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, H H(dagger) is a narrow band matrix, a fact that does not permit the use of classical random matrices theory. On the other hand, H H(dagger) is in many aspects similar to a random Schrodinger operator. We relate the per-cell sum-rate capacity of the channel to the integrated density of states of a random Schrodinger 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 Schrodinger 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.
random matrices sum-rate capacity distributed antenna array fading channels high-signal-to-noise ratio (snr) characterization wyner cellular uplink