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