Multipaths’ statistics for scatterers with inverted elliptic–parabolic spatial density around the mobile

Abstract

The joint and marginal probability densities of multipaths’ angles-of-arrival (AOA) and times-of-arrival (TOA) at the cellular base station are developed in closed form in this paper. Unlike the general simplification assumption in the open literature in which the scatterers are assumed to be located in a circular region for non-uniform spatial densities, the scatterers in this paper are assumed to be located in an elliptical region to properly model the elliptical footprint around the mobile station from the elevated base station with directional antenna. The inverted elliptic–parabolic spatial density was adopted to model the non-uniform distribution of the scatterers around the mobile. The uplink’s AOA–TOA joint distributions, AOA and TOA marginal distributions were analytically derived in closed form. How the eccentricity of the elliptical scatterer region affects the probability density functions is discussed. Furthermore, the derived AOA marginal distribution is compared to that of the elliptic conic and inverted parabolic models. The proposed model is shown to have better least-squares fit to some empirical AOA data compared to the elliptic conic and inverted parabolic models.