Estimation of Overspread Scattering Functions

In many radar scenarios, the radar target or the medium is assumed to possess randomly varying parts. The properties of the target are described by a random process known as the spreading function. Its second order statistics under the WSSUS assumption are given by the scattering function. Recent developments in operator sampling theory suggest novel channel sounding procedures that allow for the determination of the spreading function given complete statistical knowledge of the operator echo from a single sounding by a weighted pulse train. We construct and analyze a novel estimator for the scattering function based on these findings. Our results apply whenever the scattering function is supported on a compact subset of the time-frequency plane. We do not make any restrictions either on the geometry of this support set, or on its area. Our estimator can be seen as a generalization of the averaged periodogram estimator for the case of a non-rectangular geometry of the support set of the scattering function.