ESTIMATION OF RADAR TARGET REFLECTIVITY IN ULTRAWIDEBAND REGIME – A GROUP THEORETIC APPROACH

Abstract

This paper presents a fundamentally new mathematical framework based on the group representation theory for the modeling and processing of signals in ultrawideband (UWB) regime. A group theoretical approach is motivated by the fact that in UWB regime, the underlying mathematical structure of the inverse scattering is governed by the affine group. In particular, received echo can be viewed as the affine Fourier transform of the range-Doppler image evaluated at the transmitted waveform. Based on group representation theory and a novel Wiener filtering method over the affine group, we derived a regularized closed form analytical estimate of the range-Doppler target reflectivity density in the presence of nonstationary noise and clutter in UWB regime. This estimate also leads to a method of data fusion to form synthetic UWB high resolution images from multiple radars with narrowband transmission. 1