Simulation of Multipath Reflections from Planetary Bodies: Theory and Application to the Lunar South Pole

— This article describes a new simulation model to estimate multipath reflections from planetary bodies in the solar system for which a digital elevation map (DEM) is available, but its spatial resolution is significantly larger than the carrier wavelength. To account for uncertainty in the terrain roughness within a DEM facet, we assume that its surface can be modeled as a two-dimensional Gaussian random process and derive its radar cross-section (RCS) under the high-frequency approximation (Geometric Optics). Our solution extends the range of validity of these approximations to low-incidence angles, shows that the RCS can be decomposed into a coherent and non-coherent term, and obtains closed-form expressions for polygonal facets with any number of sides. Once the simulation model has been presented, we apply it to a downlink between a rover on the lunar South Pole and a Deep Space Network (DSN) station. We show that the model produces sensible results, increasing the amount of reflected power when the elevation angle subtended by Earth in the lunar sky decreases. We also show how the model can be coupled with orbital simulators to obtain a full characterization of the multipath environment using the delay and Doppler spread.