An azimuth-Doppler-delay scattering function: Definition and estimation

In this paper we define a generalized scattering function for the spatio-temporal propagation channel. The definition is free of the restrictive assumption that there is a finite number of scatterers. We derive the time-varying vector channel between the source and the array in a unified manner and define a correlation function and a power spectrum that incorporate the spatial parameter - directly giving rise to the new scattering function of the spatio-temporal channel. In practice, the scattering function can be estimated by applying a well-known non-parametric spectrum estimation method to data obtained from an appropriately designed channel sounding experiment. The Estimator's performance is evaluated theoretically and by simulation.