Optimal waveforms for wideband radar imaging

In this paper, we study the problem of optimal radar range-Doppler imaging. Unlike traditional approaches that start from a given echo processing method, we identify a radar ima`in` procedure by minimizing a distance measure between the reconstructed target reflectivity function and the actual reflectivity function. We show that in the absence of observation noise, optimal imaging is achieved by transmitting a set of waveforms derived from a kernel corresponding to the tar`et reflectivity function. Reconstruction is equivalent to computing the wavelet transforms of each received echo with respect to its corresponding transmitted waveform, and summing the results. We study invariances of the optimal set of imaging waveforms. Using these invariances, we develop the concept of a target class. A target class is a set of targets that can be optimally imaged with a single library of waveforms. We conclude by showin` that in the presence of observation noise, optimal imaging depends on both the noise intensity and the distribution of the singular values corresponding to the kernel derived from the tar`et reflectivity function. ©1998 The Franklin Institute. Published by Elsevier Science Ltd.