On marginal and joint Gaussian and hyperbolic angle-of-arrival probability density functions in multi-path mobile environment

Abstract

In mobile environment, derivation of the angle-of-arrival (AoA) probability density function (pdf) of signals transmitted from a user equipment's antenna (UE) to a base station (BS) by modeling random scatterers between them using an appropriate distribution is an important task. Gaussian and hyperbolic distributions have been successfully employed to derive the corresponding Gaussian and hyperbolic AoA marginal pdfs. In general, the AoA is assumed to be between -90o and +90o. This paper proposes the Gaussian and hyperbolic distributions to model the scatterers, resulting in joint Gaussian and hyperbolic AoA pdfs. Approximate marginal and joint Gaussian and hyperbolic AoA pdfs when the AoA is small and when it is large are derived. The entropy of these pdfs is then estimated to determine the effectiveness of the Gaussian and hyperbolic distributions in modeling the scatterers. Relative merits of the Gaussian and hyperbolic AoA pdfs are discussed. Comparisons between joint AoA pdfs and marginal AoA pdfs are made. Future work is also outlined.