Modelling of non-stationary mobile radio channels using two-dimensional brownian motion processes

The interdisciplinary idea of this paper is to employ a two-dimensional (2D) Brownian motion (BM) process to model non-stationary mobile fading channels. It is assumed that the mobile station (MS) starts moving from a fixed point along a random path in the 2D plane. We model such a moving scenario by a 2D BM process, in which the variance of the process determines the deviation of the MS from its starting point. The propagation area is modelled by a non-centred one-ring scattering model, where the local scatterers are uniformly distributed on a ring centred not necessarily on the MS. The random movement of the MS in the proposed scattering model results in local angles-of-arrival (AOAs) and local angles-of-motion (AOMs) characterized by stochastic processes rather than random variables. We derive the first-order density of the AOA and AOM processes in closed form. The local power spectral density (PSD) of the Doppler frequencies and the local autocorrelation function (ACF) of the complex channel gain are also provided. The numerical results show that the proposed non-targeted Brownian path model results in a non-stationary non-isotropic channel model. The proposed trajectory model is very useful for characterizing irregular movements of mobile users. Furthermore, the pioneering idea of the paper provides a new method for the modelling of mobile radio channels under non-stationary conditions.