On Capacity-Maximizing Angular Densities of Multipath in MIMO Channels

This paper provides a partial answer to the question: "what is the best angular density of multipath in MIMO channels?" using the size-asymptotic theory of Toeplitz matrices for uniform 2-D and 3-D antenna arrays. A Kronecker-type approximation of the array correlation structure is proposed and used to find the angular densities that completely eliminate correlation between any elements of antenna arrays and thus maximize the asymptotic MIMO capacity for a broad class of fading distributions. At half-wavelength spacing, the best angular density is shown to be non-uniform, which implies that the popular Clarke\´s (Jake\´s) model does not represent the best case scenario. The asymptotic results are validated via Monte-Carlo simulations, and a number of practical guidelines for antenna design and optimal orientation are provided.