Signal distribution in the azimuth, elevation, and time-delay domains in urban radio communication links

We investigate the mutual power-spectra distributions in the azimuth, elevation, and time-delay domains in different urban environments with randomly distributed arrays of buildings placed on rough terrain. This is done for various orientations of street guiding structures in the urban scene, and for different elevations of the terminal antenna, the base station, and the subscriber, whether mobile or not, and with respect to the buildings' overlay profile. A combination of the stochastic multi-parametric and crossing-street waveguide models, created earlier, is used to describe a total probability-density function (PDF) of mutual azimuth time-delay, elevation time-delay, and azimuth-elevation distribution of multiply reflected signals arriving at the receiver after multiple reflection, diffraction, and scattering from the numerous obstructions surrounding both terminal antennas. Comparisons with some high-resolution three-dimensional measurements, as well as with the corresponding three-dimensional numerical ray-tracing model, are done to describe directional and spatial-temporal urban channel characteristics, and to predict propagation situations in the urban scene for various locations and directional properties of the terminal antennas.