We apply the theory of random Schrodinger operators to the analysis of multi-users communication channels similar to the Wyner model, that are characterized by short-range intra-cell broadcasting. With $H$ the channel transfer matrix, $HH^dagger$ is
a narrow-band matrix and in many aspects is 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 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 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-SNR regime for some particular cases.
In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular we are interested in an uplink cellular channel which models mobile users experien
cing a soft-handoff situation under joint multicell decoding. Considering rather general fading statistics we provide a closed form expression for the per-cell sum-rate of this channel in high-SNR, when an intra-cell TDMA protocol is employed. Since the matrices of interest are tridiagonal, their eigenvectors can be considered as sequences with second order linear recurrence. Therefore, the problem is reduced to the study of the exponential growth of products of two by two matrices. For the case where $K$ users are simultaneously active in each cell, we obtain a series of lower and upper bound on the high-SNR power offset of the per-cell sum-rate, which are considerably tighter than previously known bounds.
