A Stochastic Dynamic Model of Rain Attenuation

A dynamic mathematical model of rain attenuation has been developed and is presented in this paper. This model permits the expression of analytic relationships between parameters commonly used to describe the properties of interest for communication. The dynamic model is based on the lognormal distribution of rain attenuation and utilizes a memoryless nonlinear device to transform attenuation and rain intensity into a one-dimensional Gaussian stationary Markov process. Hence, only one parameter is required to introduce the dynamic properties of rain attenuation into the model. Experimental results and the known properties of rain have been used to derive and to verify the model; comparative results are presented and demonstrate good correspondence. The application of the model to the statistical analysis of the performance of communications systems is illustrated in the paper. The use of a dynamic rain attenuation model is necessary in order to analyze radio communication systems with transmit power control to offset the effects of rain attenuation, and where the finite response time of the control system affects the performance. An advantage of the model is the simplicity with which it allows simulation of communication link performance under the influence of rain attenuation. Such simulations are of great interest for complex models of adaptive networks where several deteriorating effects, including finite response times, are present.