Calculation of the Dynamic Input Parameter for a Stochastic Model Simulating Rain Attenuation: A Novel Mathematical Approach

The Maseng-Bakken model simulates rain attenuation induced on a microwave link, and it accepts as input three parameters: the first two coincide with the parameters belonging to the conditional lognormal cumulative distribution of rain attenuation while the third one-called the dynamic parameter hereafter-should be assigned appropriately so that the model reflects some particular dynamic properties of rain attenuation. Thus far, the dynamic parameter has been calculated with emphasis on the simulation of the spectral density function of rain attenuation. This in turn, does not necessarily imply that the Maseng-Bakken model also simulates other crucial statistical features of rain attenuation such as Fade/Inter-Fade Duration Statistics. In this paper, we demonstrate a novel mathematical algorithm that gives the optimum value for the dynamic parameter so that the Maseng-Bakken model approximates simultaneously both second-order and hitting time statistics, with the latter being quite similar to Fade/Interfade durations. The algorithm is exemplified through the simulation of rain attenuation affecting a satellite channel which operates at 20 GHz and connects Athens with Hellas-Sat 2. The results show that the optimum value for the dynamic parameter is much more "sensitive" to hitting time statistics-and probably to fade durations statistics as well-than it is to the spectral density function of rain attenuation.