Modeling Ka-band scintillation as a fractal process

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