Signal power distribution in the azimuth, elevation and time delay domains in urban environments for various elevations of base station antenna

We investigate signal power distribution in the azimuth-of-arrival, elevation-of-arrival and time-of-arrival domains for various positions of the base station antenna located below the rooftop as well as at rooftop level. This article is based on a multiparametric stochastic model we introduced in 2004, as combination of a statistical part, describing an array of buildings randomly distributed at the terrain, and a waveguide model, describing a grid of straight streets with buildings along them. Joint signal power distributions in azimuth-time delay and elevation-azimuth planes are obtained and compared to high-resolution 3-D measurements carried out in downtown Helsinki. A good agreement between theoretical predictions and the measurements is obtained basically, and also regarding the wave-guiding effect and antenna height dependencies. A satisfactory physical explanation,,which accounts for the character of the specific building topography, the height and tilt of the antennas, is found. Finally, we present a numerical experiment of changing the base station antenna height, its directivity, and tilt. By this we show that the proposed stochastic approach allows to predict and control a-priori main parameters of smart antenna based only on knowledge of specific features of built-up terrain.