We propose a model that describes the signal fading process due to scintillation in the presence of rain. We analyzed a data set of uplink (30 GHz) and downlink (20 GHz) attenuation values averaged over 1 s intervals. The data are samples relative to ten significant events, for a total of 180 000 s recorded at the Spino d'Adda (North of Italy) station using the Olympus satellite. Our analysis is based on the fact that the plot of attenuation versus time recalls the behavior of a self-similar process. We then make various considerations, and propose a fractional Brownian motion model for the scintillation process. We describe the model in detail, with pictures showing the apparent self-similarity of the measured data. We then show that the Hurst parameter of the process is a simple function of the rain fade. We describe a method for producing random data that interpolate the measured samples, while preserving some of their interesting statistical properties. This method can be used for simulating fade countermeasure systems. As a possible application of the model, we show how to optimize fade measurement times for fade countermeasure systems.