Path Integral Analysis of Paraxial Radiowave Propagation Over a Building with a Wedged Roof

Abstract

A technique for solving paraxial propagation problems is presented in which the propagation path is first divided into a number of basic regions. Then a closed form expression for the propagator over such an elementary region is found by employing a high frequency asymptotic approximation to the path integral formulation of the problem. The propagator over the complete path is formulated by cascading the propagators over the elementary regions. The technique is illustrated by deriving an attenuation function for the problem of radiowave propagation over a building with a wedged roof, situated over a flat ground. A random simulation is performed and the statistical results are shown to be in good agreement with those obtained from experimental data. It is found that the mean of the received signal in dB's varies with total distance D from the transmitter as α + 101og(D^P), with p = -3.7 and α is a constant. The cumulative distribution of the attenuation in dB's at an arbitrary distance from the transmitter is shown to be that of a normal probability density function. Therefore, the attenuation exhibits a log-normal distribution, which is in agreement with the distribution obtained by experiment. It is also found that the signal 5 to 95% variability, about its mean value, is 20 dB.