Estimation of Overspread Scattering Functions

TL;DR

This paper introduces a new estimator for the scattering function in radar systems, leveraging operator sampling theory to handle arbitrary support geometries without restrictions on size or shape.

Contribution

It develops a novel, generalized estimator for the scattering function based on recent operator sampling advances, applicable to arbitrary support sets in the time-frequency domain.

Findings

Estimator works for any compact support of the scattering function

No restrictions on the support set's geometry or area

Generalizes the averaged periodogram for non-rectangular supports

Abstract

In many radar scenarios, the radar target or the medium is assumed to possess randomly varying parts. The properties of a 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 an averaged periodogram estimator for the case of a non-rectangular geometry of the support set of the scattering function.