A Random Walk Model of Wave Propagation

This paper shows that a reasonably accurate description of propagation loss in small urban cells can be obtained with a simple stochastic model based on the theory of random walks, that accounts for only two parameters: the amount of clutter and the amount of absorption in the environment. Despite the simplifications of the model, the derived analytical solution correctly describes the smooth transition of power attenuation from an inverse square law with the distance to the transmitter, to an exponential attenuation as this distance is increased - as it is observed in practice. Our analysis suggests using a simple exponential path loss formula as an alternative to the empirical formulas that are often used for prediction. Results are validated by comparison with experimental data collected in a small urban cell.