A Statistical Rain Attenuation Prediction Model With Application to the Advanced Communication Technology Satellite ProjectnII—Theoretical Development of a Dynamic Model and Application to Rain Fade Durations and Tolerable Control Delays for Fade Countermeasures

摘要

A dynamic rain attenuation prediction model is developed for use in obtaining the temporal characteristics, on time scales of minutes or hours, of satellite communication link availability. Analogous to the associated "static" rain attenuation model, which yields yearly attenuation predictions and is the subject of part I of this work (NASA Contractor Report #179498, Sept. 1986), this dynamic model is applicable at any location in the world that is characterized by the static rain attenuation statistics peculiar to the geometry of the satellite link and the rain statistics of the location. Such statistics are calculated by employing the formalism of part I. In fact, the dynamic model presented here is an extension of the static model and reduces to the static model in the appropriate limit. By assuming that rain attenuation is dynamically described by a first-order stochastic differential equation in time and that this random attenuation process is a Markov process, an expression for the associated transition probability is obtained by solving the related forward Kolmogorov equation. This transition probability is then used to obtain such temporal rain attenuation statistics as attenuation dura¬tions and allowable attenuation margins versus control system delay time for specified rain fade control availabilities. The time parameter that enters into the stochastic differential equation, a parameter that is taken to be a temporal characteristic of rain attenuation, is calculated from available experimental data. A coordinated propagation experiment is also specified to obtain this parameter from attenuation observations. Finally, using the atten¬uation statistics found in part I for 59 cities with ACTS links, the dynamic model is used to find fade durations and tolerable control delays for links in these cities.