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In this paper we study the spectrum of certain large random Hermitian Jacobimatrices. These matrices are known to describe certain communication setups. Inparticular we are interested in an uplink cellular channel which models mobileusers experiencing a soft-handoff situation under joint multicell decoding.Considering rather general fading statistics we provide a closed formexpression for the per-cell sum-rate of this channel in high-SNR, when anintra-cell TDMA protocol is employed. Since the matrices of interest aretridiagonal, their eigenvectors can be considered as sequences with secondorder linear recurrence. Therefore, the problem is reduced to the study of theexponential 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 andupper bound on the high-SNR power offset of the per-cell sum-rate, which areconsiderably tighter than previously known bounds.

On Certain Large Random Hermitian Jacobi Matrices with Applications to Wireless Communications