General Expression for Azimuthal Angle Distribution of Various Elliptical-Shaped Geometry-Based Stochastic Channel Models

Geometry-based stochastic channel models with differently distributed scatterers within elliptical-shaped scattering region, become more and more popular due to their applicability for modeling different propagation scenarios in the emerging 5 G networks. However, to date, their spatial and temporal characteristics are usually provided in integral forms, which are not appropriate for analytical manipulations. In this paper, it is shown that the azimuthal angles of arrival and departure for elliptical (two-dimensional) and ellipsoidal (three-dimensional) channel models, with (non)uniformly distributed scatterers and arbitrary chosen positions of the transmitter and the receiver, has the same statistics as N-dimensional channel model with homogeneously distributed scatterers within hyperellipsoidal-shaped scattering region. Thus, the azimuthal angle distributions of N-dimensional channel model with homogeneously distributed scatterers within hyperellipsoidal-shaped scattering region are derived as closed-form expressions, providing for the first time in literature the azimuthal angles of arrival and departure distributions for various existing elliptical-shaped geometry-based stochastic channel models and for a whole new class of 2-D and 3-D channel models with nonuniformly distributed scatterers.