Non-Stationary Propagation Model for Scattering Volumes With an Application to the Rural LMS Channel

The design of efficient positioning algorithms in navigation satellite systems, like GNSS, operating in land mobile environments demands for detailed models of the radio channel. On the one hand, the models need to accurately describe scattering and shadowing/obstruction caused by vegetation. On the other hand, they have to incorporate the steady change in the propagation constellation due to the receiver displacement. In this paper we propose a model of the non-stationary radio channel in a scenario where a mobile receiver drives past a scattering volume, such as a ball or a cuboid, while the transmitter is elevated, like in satellite positioning applications. Such a volume may represent the canopy of a single tree, the canopies of trees in a grove, or a small forest. Scattering by the volume is characterized by means of multiple point-source scatterers that are assumed to form a marked spatial point process. The system functions of the radio channel are given. An integral form of the time-frequency correlation function of the component in the system functions contributed by the scattering volume is obtained as a direct consequence of Campbell's Theorem. Furthermore, a closed-form approximation of this integral form is derived for time lags corresponding to displacements along the receiver trajectory for which the plane wave assumption holds. The approximation takes into account the steady change in the propagation constellation. The proposed model is validated by means of Monte Carlo simulations and by comparing its prediction capabilities with experimental data in a scenario where a mobile receiver drives past a roadside tree. A good agreement is observed, despite the simplicity of the model.