Analytically derived uplink/downlink TOA and 2D-DOA distributions with scatterers in a 3D 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 land mobile cellular wireless communication system\´s uplink and downlink multipaths\´ time-of-arrival (TOA) and two-dimensional (2D) direction-of-arrival (DOA), rigorously derived via thorough mathematics based on a "geometrical" model of the three-dimensional (3D) spatial relationships among the mobile-station (MS), the scatterers, and the base-station (BS). The scatterers are herein modeled to have a uniform 3D spatial distribution in an above-ground hemisphere with a flat circular base (or alternatively, within a sphere) centered at the mobile.