Multidimensional Rain Attenuation Stochastic Dynamic Modeling: Application to Earth–Space Diversity Systems

Abstract

A stochastic dynamic model for the induced rain attenuation on multiple radio links is presented in this paper. The model is considered as a generalization of the well-known and wellaccepted Maseng-Bakken model in -dimensions. It incorporates the spatial and time behavior of the rain attenuation phenomena and provides an analytical expression for the transition probability distribution. It consists of a system of stochastic differential equations (SDEs), which, except for the solid mathematical formulation of the correlated rain attenuation stochastic processes, constitutes the general framework for the calculation of other statistical quantities useful for the radio system designers. The long-term statistics and the dynamic properties of rain attenuation are used for the parameterization of the model, without the constraint of any built-in assumptions of the rain field. Finally, the proposed model is used for the generation of correlated rain attenuation time series on multiple satellite communication slant paths and especially to diversity schemes, including site and orbital (angle) diversity. The derived results from the model are tested with respect to experimental long-term statistics for various geometries with very encouraging results. The limitations and the ranges of applicability of the model for Earth-space diversity systems are reported, and the sensitivity of the model on the crucial parameters is discussed.Index Terms-Rain attenuation, satellite link, spatial structure, stochastic differential equations (SDEs).

On the Relationship Between the Spatial Correlation of Point Rain Rate and of Rain Attenuation on Earth-Space Radio Links

“…In site diversity systems, information on the spatial correlation of the rain attenuation as a function of the distance between two or more locations is essential for the proper design of diversity schemes, whose performance improves as the attenuation simultaneously affecting the sites becomes more and more decorrelated [6]. Knowledge of the correlation coefficient is useful also for time series generators and models to be employed in the simulation of satellite networks, where the proper degree of spatial correlation must be maintained in order to generate reliable results [7], [8].…”

Multiple Gateway Transmit Diversity in Q/V Band Feeder Links

“…While the earlier discussion models a single GW to satellite link, the focus of the paper warrants a model for multiple links. Towards this, a n-dimensional generalization was recently proposed in [21] to generate the space-time correlated rain attenuation time series of n links. However, inclusion of spatial correlation makes the analysis intractable and hence we assume spatially independent and identically distributed (i.i.d) links.…”

Interference statistical distribution for cognitive satellite communication systems operating above 10GHz

“…For spatially separated links, rain attenuation time series correlated in spatial domain can be generated through the solution of the multidimensional SDE proposed in [11]. In the latter reference rain attenuation on multiple n links 1 ,...,…”