Reflection from Random Surfaces-a Wigner Function Approach

Diffusive reflection of wave-fields from rough surfaces is ubiquitous in applications, providing an important propagation mechanism in wireless communication systems, for example. We describe this phenomenon here using the formalism of Wigner functions, which allows us to represent incoherent incident and reflected wave fields in a form that has a natural limit as phase-space densities of rays. A propagator of Wigner functions, such as described in this paper, can therefore effectively be used to incorporate intrinsically interference-dominated rough surface reflection into practical simulation algorithms for ray tracing. We demonstrate this approach by incorporating the Wigner propagator into an application of the Dynamical Energy Analysis (DEA) method, which allows efficient calculation of ray densities in enclosed, multi-reflective environments.