Microcellular systems, random walks, and wave propagation

A new, simple model of wave propagation for microcellular systems is applied to predict the path loss of a wireless channel. The model does not rely on the classical theory of electromagnetic wave propagation, but it is entirely based on probability theory. We consider the canonical scenario of a random environment of partially absorbing scatterers and model the trajectory of each photon in the system as a random walk. This model leads to a path loss formula that rather accurately (in comparison to other models and experimental data) 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. This result can justify empirical formulas that are often used for path loss prediction, characterized by a breakpoint distance at which the exponent of a power law is increased from a value of approximately 2 to a value in the range of 4 to 10. Theoretical predictions of the model are validated by showing agreement with experimental data collected in the city of Rome, Italy.