Analytically derived TOA-DOA distributions of uplink/downlink wireless-cellular multipaths arisen from scatterers with an inverted-parabolic spatial distribution around the mobile

This letter presents the joint/marginal distributions of the uplink (downlink) multipaths\´ azimuth angles of arrival and times of arrival at the cellular base station (mobile). These closed-form explicit densities are rigorously derived based on a new "geometrical model" wherein omnidirectional scatterers are modeled as spatially distributed at an inverted parabolic spatial distribution on a two-dimensional disc centered at the mobile. This "inverted parabolic" density, in contrast to the uniform disc density or the rim density, indirectly accounts for scattering power loss. This new model better least-squares-fit some empirical data than its competing models can.