Probability distributions of rain attenuation obtainable with linear combining techniques in space-to-Earth links using time diversity

The purpose of this paper is to show how the complementary probability distribution of rain attenuation is drastically changed in the lower rain attenuation range by applying linear combining techniques, namely, equal-gain combining and the maximal-ratio combining, discussed in the historical paper by Brennan in 1959. These combing techniques can also be applied to the Automatic Repeat Request techniques. Defined the instantaneous processing gain and the equivalent attenuation in the 3 cases, we show examples of time series of the various parameters, based on the experimental rain attenuation time series recorded with the ITALSAT 18.7 GHz beacon, in a 37.8° slant path in Spino d'Adda (Italy). Then, we report long-term complementary probability distribution functions of the instantaneous gain and equivalent attenuation, by simulating rain attenuation time series at 19.7 and 39.4 GHz, path elevation angle 35.5°, with the Synthetic Storm Technique, using on-site measured rain rate time series of 10 years, by simulating the ALPHASAT link at Spino d'Adda. Similar results are also found at different frequencies and elevation angles in Tampa (Advanced Communications Technology Satellite, ACTS result test), the Isle of Guam, and Prague. The main conclusions are as follows: (1) As expected, the instantaneous time diversity gain can be large when the delay time is large and rain attenuation is large; (2) scintillation affects time diversity links as the direct links; (3) equal-gain and maximal-ratio combining can add up to 3 dB to the selection diversity gain when the time diversity gain is very small; and (4) equal-gain and maximal-ratio combining reduce the fraction of time of rain attenuation in an average year to a value less than the probability of exceeding 3 dB in the link without diversity.