A Novel Non-Stationary Channel Model Utilizing Brownian Random Paths

Abstract

This paper proposes a non-stationary channel model in which real-time dynamics of the mobile station (MS) aretaken into account. We utilize Brownian motion (BM) processes to model targeted and non-targeted dynamics of the MS. Theproposed trajectory model consists of both drift and random components to capture both targeted and non-targeted motionsof the MS. The Brownian trajectory model is then employed to provide a non-stationary channel model, in which thescattering effects of the propagation area are modelled by a non-centred one-ring geometric scattering model. The startingpoint of the motion is a fixed point in the propagation environment, whereas its terminating point is a random pointalong a predetermined drift. The drift component can be controlled by a so-called drift parameter. Tracking the MS on theproposed Brownian path allows us to derive the local angles-of-arrival (AOAs) and local angles-of-motion (AOMs), whichare expressed by stochastic processes rather than random variables. We compute the first-order densities of the AOA andAOM processes in closed form. The local power spectral density (PSD) of the Doppler frequencies and the autocorrelationfunction (ACF) of the complex channel gain are also provided. Given a walking speed scenario, the analytical results aredemonstrated and explained in depth. It turns out that the proposed Brownian path model results in a non-stationarynon-isotropic channel model. The proposed geometry-based channel model is very useful for the performance analysis ofmobile communication systems under non-stationary conditions.