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Abstract

The thesis presents novel models for the prediction of rain attenuation statistics in Earth-satellite multiple-site diversity systems using copula functions. Site diversity systems are adopted to compensate for severe rain attenuation and thereby increase system availability. The proposed models can therefore be used for the accurate and reliable design of site diversity systems operating at high frequencies, thus enabling high data rates in Earth-satellite communications.

The first proposed model is based on the Gaussian copula, and the joint statistics of rain attenuation are calculated by taking into account the rain attenuation statistics for particular Earth-satellite slant paths and the separation distance between the Earth stations. The proposed model outperforms the existing ITU-R P.618 model for two-site diversity and the model based on the Clayton copula. The proposed model can be used for multi-site diversity with an arbitrary number of sites, which was not adequately supported by state-of-the-art models.
To improve accuracy, a further prediction model based on the Gaussian copula is proposed. This model takes into account not only the separation distance but also two other geometric characteristics of the site diversity system, namely the baseline orientation angle and the elevation angle. A comparison of total error performance shows that the second model performs better than the first for two- and three-site diversity configurations. The only disadvantage of the Gaussian-copula-based models is their computational complexity.
Considering that Archimedean copulas are generally simpler, and following an extensive analysis of several families, we found that the hyperbolic cosecant copula is appropriate for predicting the joint statistics of rain attenuation. Two multi-site prediction models are proposed: one that takes into account only the distance between the stations and another that also includes the dependence on the baseline orientation and elevation angles.
The error performance of the four models was investigated by comparing their predictions with experimental data using a database of 56 two-site diversity experiments from different regions of the world and 11 three-site diversity experiments from Europe and the USA. The results show that, for two-site diversity systems, the proposed models perform notably better than the ITU-R model and slightly better than the Clayton model. The Gaussian models generally exhibit the smallest errors. However, the performance of each model varies depending on the region and experimental conditions considered.
More specifically, the Gaussian model that accounts only for distance performs best for European experiments in both two- and three-site diversity configurations. For two-site experiments in the USA, Canada, and Japan, and three-site experiments in the USA, the hyperbolic cosecant copula-based model that accounts for the dependence on distance, elevation angle, and baseline orientation angle exhibits the best performance. In two-site diversity systems, the Gaussian model that takes into account distance, elevation angle, and baseline orientation angle outperforms the other models notably when the distance exceeds 10 km and the baseline orientation angle is greater than 45°.