Modeling of Reverberant Radio Channels Using Propagation Graphs

In measurements of in-room radio channel responses, an avalanche effect can be observed: earliest signal components, which appear well separated in delay, are followed by an avalanche of components arriving with increasing rate of occurrence, gradually merging into a diffuse tail with exponentially decaying power. We model the channel as a propagation graph in which vertices represent transmitters, receivers, and scatterers, while edges represent propagation conditions between vertices. The recursive structure of the graph accounts for the exponential power decay and the avalanche effect. We derive a closed-form expression for the graph's transfer matrix. This expression is valid for any number of interactions and is straightforward to use in numerical simulations. We discuss an example where time dispersion occurs only due to propagation in between vertices. Numerical experiments reveal that the graph's recursive structure yields both an exponential power decay and an avalanche effect.