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The objective of this paper is to describe recent activities carried out in the field of Earth-Space propagation for ESA and CNES or in the framework of European projects. In a first part, the temporal behaviour of the propagation channel is briefly addressed thanks to the development and validation of time series synthesisers. In a second part, which is the main core of the paper, it is shown how space variation of propagation impairments can be described with the development of generators of rain attenuation fields from two studies carried out by Politecnico di Milano for ESA and by ONERA for CNES. Then, the "hot topic" of the space-time variability of the propagation channel is dealt with, thanks to current research activity carried out by ONERA and Politecnico di Milano.