Estimation of radar target reflectivity in ultrawideband regime - a group theoretic approach

The paper presents a fundamentally new mathematical framework based on group representation theory for the modeling and processing of signals in the ultrawideband (UWB) regime. A group theoretical approach is motivated by the fact that in the UWB regime, the underlying mathematical structure of the inverse scattering is governed by the affine group. In particular, a 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 derive a regularized closed form analytical estimate of the range-Doppler target reflectivity density in the presence of nonstationary noise and clutter in the 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.