Duration of Rainfall Fades in GeoSurf Satellite Constellations

We have studied the stochastic processes A and B concerning fade durations due to rain, by simulating attenuation time series A(t) (dB) in the zenith paths of GeoSurf satellite constellations, at sites located in different climatic regions, with the Synthetic Storm Technique. Process B gives the statistics of outages (occurrences) and process A gives the statistics of outage duration (fraction of time), for the same rain attenuation threshold A(t) > S. The two processes are not independent; therefore, we have studied the relationship between their probabilities and defined a uniformity index 0 < U(S) <= 1. U(S) is useful for comparing real cases-fade durations fragmented in many different intervals, with changing S and site-and the limiting case of all fades lasting the same time. As S increases, U(S) increases, approaching 1 at very large thresholds. These results should guide the designers of satellite constellations to consider the impact of A(t) on diverse communications services. Process B (occurrences) impacts mainly on non-real-time services, such as data delivery, more disturbed by the number of outages rather than by their duration. Process A (fraction of time) impacts mainly on real-time services such as television, video conference etc., more disturbed by the duration of the outage.