The use of a finite-element method to predict the scattering of UHF signals off terrain

Close to a high-power UK television station operating at frequencies around 800 MHz, reception difficulties were experienced by viewers owing to adverse height¿gain characteristics up to 10 m above ground level, Most of the terrain between the station and the viewers was uncluttered and fully illuminated by the transmitting antenna within a radius of 4 km and so computer modelling of the soil scatter was undertaken by finite-element summation, avoiding any diffraction analysis, to predict the theoretical height¿gain characteristics. The terrain was modelled as a two-dimensional cross-section between transmitter and receiver containing 40 000 soil elements each 0·25¿ wide. The illumination from the highly-directional transmitting antenna, comprising 32 radiating elements in a 40 vertical stack, was modelled as an approximation to a true spherical wavefront emanating from each individual antenna element. Nearly 1·3 million phasor summations were required to illuminate the terrain at each frequency considered. Height-gain characteristics at any given receiving range were predicted by summing 40 000 scatter terms at each spot height. The predictions were compared with measurements to determine which parts of the terrain were contributing to the scatter. Further insight was obtained by plotting histograms of the individual contributions predicted from 160 facets of soil, each 25 m (65¿) wide, along the 4 km path profile.