Numerical Analysis: Coarse graining of stochastic differential equations with application to wireless channel modeling
Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In Multipath Fading Channel (MFC) models the signal reception is modeled by a sum of wave path contributions, and and Clarke’s model  is an important example of such which has been widely accepted in many wireless applications.
In this project we propose an extension of Clarke’s model that includes time-varying stochastic MFC model with scatterers that driven by a Poisson process randomly flip on and off. A limit Gaussian process model is derived from our model extension, when the number of active wave paths tends to infinity. Statistical properties of our MFC model are analyzed and shown to fit well with those of real signal measurements.
A second focus of this project is to analyze and perform numerical studies of the error and computational cost of generating signal realizations by our proposed MFC and Gaussian process models.
 R. H. Clarke. A statistical theory of mobile-radio reception. Bell Sys. Tech., vol. 47, pp. 957-1000, 1968.