A fractal attenuation model for the Ka band

We propose a model that describes the rain attenuation process, which can be useful for designing atmospheric fade countermeasure systems for satellite communications. We analyzed a data set of uplink (30 GHz) and down-link (20 GHz) attenuation values averaged over I second intervals. The data are samples relative to 10 significant events, for a total of 180,000 s, recorded at the Spine 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 behaviour of a self-similar process. Starting from this observation, we make various considerations and propose a fractional Brownian motion model for modeling the attenuation process. We describe the model in detail, with pictures showing the apparent self-similarity of the measured data, then we show that the Hurst parameter of the process is a simple function of the attenuation. In order to produce useful data for simulating fade countermeasure systems, one needs to interpolate the measured attenuation traces, which have I s granularity, so we describe a method for producing random data that interpolate the measured samples, while preserving some of their interesting statistical properties. We conclude by suggesting a possible application for such a model, which is the subject of current research.