An effective low-grazing reflection coefficient for modeling groundwave propagation over randomly rough terrain

For propagation over a rough terrain, the physical statistical properties of the ground surface have a direct impact on the statistics of the propagating signal. When the transmitter and receiver are close, the LOS (line-of-sight) space wave from the transmitting antenna, when it exists, provides the primary contribution to the total received signal, as the coherent reflection from the underlying rough surface is reduced by the random scattering effects. However, over a long distance, as the propagation path approaches the grazing condition, in accordance with the Rayleigh criterion, the surface appears electrically smooth again and coherent cancellation between the direct and ground scattered signals is re-established. These qualitative observations are consistent with numerical simulation results presented in previous works [1, 2]; specifically, as it has been shown in [1], for fixed transmitter and receiver locations, the far field propagation loss increases with the surface rms height as expected but also shows considerable dependence on the two-point surface correlation length. Furthermore, at grazing propagation, it is no longer proper to calculate coherent signal statistics by a complete replacement of the rough surface with a smooth surface positioned at the original surface's physical mean height, for now the effective height is a function of both rms height and correlation length. Although numerical models such as those prescribed in [1, 2] have proven to be efficient simulators in dealing with the near-ground channel, it is also convenient to quantitatively capture the aforementioned observations—which have not been sufficiently addressed and explained in existing literature—in analytical formulations.