Cross-correlation of scattered GNSS signals

Navigation signals reflected by the Earth surface, collected by a receiver in relative movement with respect to the source and the surface, can exhibit temporal fluctuations. Their features are related to the characteristics of the surface roughness and they can be observed even in the presence of almost flat surfaces with gentle undulations, i.e., those whose horizontal scale can be comparable with the impinging wavelength. In this work, a full-wave solution of the scattering based on the Kirchhoff approximation is implemented to characterize the temporal variability of scattered signals of opportunity. A numerical solution is compared with a simple closed-form expression achieved considering omnidirectional sources. The analysis can provide useful information for the interpretation of GNSS data, especially those collected by means of satellite platforms, which presents an intrinsic variability that can significantly affect the retrieval of bio-geophysical parameters.