Stochastic-Deterministic Assessment of Electric Field Radiated by Base Station Antenna above a Two-Layered Ground

The paper deals with stochastic-deterministic modelling of radiated electric field by base station antennas (BSAs) operating in GSM frequency range. Within the framework of deterministic analysis, the total electric field above a two-layered lossy ground is obtained by considering the incident and reflected ray in the far field zone. The influence of nonhomogeneous lower medium is taken into account via two approaches: Fresnel plane wave reflection coefficient (FRM) and simplified reflection coefficient stemming from Modified Image Theory (MIT). Antenna height, relative conductivity, and permittivity of each ground layer, as well as the thickness of the upper ground layer, are considered as input parameters with inherent uncertainty. To quantify the uncertainty of output electric field, deterministic models are treated as black boxes by two stochastic methods, Monte Carlo (MC) and Stochastic Collocation (SC), respectively. Stochastic mean and standard deviation of the output are computed, and sensitivity analysis is carried out in order to analyze the impact of input parameters’ variations on the resulting electric field variance. The presented results expose weakness and strength of the two stochastic methods, particularly identifying the cases when the preferred SC method fails to converge. Furthermore, sensitivity analysis reveals that despite the smallest variation around its respective average value, the antenna height has the highest impact on the output variance at observation points in the vicinity of the antenna. However, as the distance from the antenna increases, the 1st layer depth and its relative electric permittivity become the most significant parameters.