Angle of arrival statistics for 3-D macrocell environment using directional antenna at BS

Angle of Arrival (AoA) statistics at base station (BS) are observed for 3-D macrocell environment that assume uniform distribution of scatterers confined in a semispheroid with a directional antenna employed at elevated BS. Closed-form expressions for joint probability density function (PDF) and marginal PDFs in correspondence to azimuth and elevation angles seen at BS are derived. Furthermore, theoretical results along with observations are shown to illustrate the effect of directional antenna on spatial characteristics. Comparison of proposed model is made with some notable models found in literature which also validates the generalization of proposed model.