Effect of directional antenna on the spatial characteristics of 3-D macrocell environment

In this paper, a geometrically based 3-D propagation model is presented for macrocellular land mobile radio channel with a mobile station (MS) located at the center of a 3-D scattering semi-spheroid and a base station (BS) employing a directional antenna located outside of the semi-spheroid. The effect of directional antenna is thoroughly observed on the spatial characteristics seen at MS. Closed-form expressions for joint and marginal probability density functions (PDFs) of Angle of Arrival (AoA) seen at MS in correspondence with azimuth and elevation angles are derived. Moreover, the theoretical results along with observations are shown that illustrate the effect of directional antenna on the spatial statistics of the proposed 3-D model. Finally, the theoretical results obtained are compared with some notable 2-D and 3-D scattering models found in literature, which validates the proposed scattering model.