Analytically Derived Uplink/Downlink TOA and 2-D-DOA Distributions With Scatterers in a 3-D Hemispheroid Surrounding the Mobile

This paper presents the open literature's first closed-form explicit expressions of the trivariate joint and marginal distributions of a landmobile cellular wireless communication system's uplink and downlink multipaths' time of arrival and two-dimensional direction of arrival, rigorously derived via thorough mathematics based on a "geometrical" model of the three-dimensional (3-D) spatial relationships among the mobile station, the scatterers, and the base station. The scatterers are herein modeled to have a uniform 3-D spatial distribution in an aboveground hemisphere with a flat circular base (or alternatively, within a sphere) centered at the mobile