Effect of Directional Antenna on the Doppler Spectrum in 3-D Mobile Radio Propagation Environment

In this paper, an analytical model is proposed for a macrocellular communication system with directional antennas at elevated base station (BS) to quantify the effect of directivity of the radiated waves from antennas on the Doppler spectrum in a 3-D radio propagation environment. The impacts of antenna beamwidth and motion of mobile station (MS) are thoroughly investigated on the statistical distribution of the power Doppler spectrum. Closed-form expressions for trivariate probability density functions (pdfs) of propagation path distance, power, and Doppler shift are derived. Furthermore, general expressions for joint and marginal pdfs of elevation angle of arrival, power, and Doppler shift are established. Finally, the obtained theoretical results, along with the observations that illustrate the effect of directivity of the antenna beamwidth and the direction of the MS's motion on the distribution characteristics of the power Doppler spectrum, are presented. It is established that for motion of the MS in all directions, the spread in distribution of the Doppler shift observed is significantly reduced due to the use of a directional antenna at the BS with a narrow beam directed toward the desired user. It is also observed that, for a sharp azimuthal beam of directional antenna, the multipath components corresponding to the scatterers in the elevation plane result in the reduction of Doppler shift with an increase in their vertical distance from the MS.