Path integral analysis of paraxial radiowave propagation over a cliff edge

The attenuation function is derived with respect to the the free space field for waves propagating over a perfectly conducting cliff edge. The general case of having a raised transmitter and receiver is considered. Based on physical arguments and the Feynman path integral, the exact propagator describing propagation over a ground plane which is the elementary building block of a cliff edge is derived. The total propagator for the cliff-edge geometry is derived using Markov´s property of the paraxial wave equation propagator. The result reduces to that obtained using the compensation theorem, when both the source and the observation points are set at ground level. The validity of the result is confirmed by laboratory experiments