Modelling of Non-Stationary Mobile Radio Channels Incorporating the Brownian Mobility Model With Drift

This paper is a pioneering attempt to utilize a Brownian motion (BM) process with drift to model the mobile radio channel under non-stationary conditions. It is assumed that the mobile station (MS) starts moving in a semi-random way, but subject to follow a given direction. This moving scenario is modelled by a BM process with drift (BMD). The starting point of the movement is a fixed point in the twodimensional (2D) propagation area, while its destination is a random point along a predetermined drift. To model the propagation area, we propose a non-centred one-ring scattering model in which the local scatterers are uniformly distributed on a ring that is not necessarily centred on the MS. The semi-random movement of the MS results in local angles-ofarrival (AOAs) and local angles-of-motion (AOMs), which are stochastic processes instead of random variables. We present the first-order density of the AOA and AOM processes in closed form. Subsequently, the local power spectral density (PSD) and autocorrelation function (ACF) of the complex channel gain are provided. The analytical results are simulated, illustrated, and physically explained. It turns out that the targeted Brownian path model results in a statistically non-stationary channel model. The interdisciplinary idea of the paper opens a new perspective on the modelling of non-stationary channels under realistic propagation conditions. Index terms — Channel modelling, Brownian motion, nonstationary channels, local power spectral density, local autocorrelation function.