3-D Gaussian Scatter Density Propagation Model Employing a Directional Antenna at BS

In this paper, a propagation model is presented for the land mobile radio cellular systems with 3-D Gaussian distributed scatterers around Mobile Station (MS). The Base Station (BS) equipped with a directional antenna is located outside of the scattering region. The effect of directional antenna is thoroughly observed on spatial and temporal characteristics of the proposed model. General expressions for joint and marginal probability density functions (PDFs) of Angle-of-Arrival (AoA) observed at MS and BS in correspondence with azimuth and elevation angles are derived. Novel expressions for the trivariate and the bivariate density functions for Time-of-Arrival (ToA) / AoA in correspondence with azimuth and elevation angles are derived. Exploiting the proposed model, the theoretical results along with observations are presented to illustrate the effect of directional antenna on the spatio-temporal characteristics of channel. Obtained theoretical results for spatial statistics at BS are compared with an empirical set of measured data, which also demonstrates the validity of proposed model.