A Stochastic Differential Equation for Wireless Channels Based on Jakes' Model with Time-Varying Phases

A stochastic differential equation for describing the dynamics of a scattered electric field at a moving receiver for a wireless channel is derived. The derivation is based on an extension of Jakes' model where the Doppler shifts are described as usual but where the phases are time-varying and described by Wiener processes. An approximation to this stochastic differential equation that is easier to work with is also given. The approximation, whose parameters can be interpreted physically, facilitates simulations since only one complex valued signal needs to be generated. A numerical example for illustrating its degree of validity is presented.