Cramer Rao bound computation for velocity estimation in the broad-band case using the Mellin transform

The author presents explicit expressions of the Cramer-Rao bounds (CRBs) for estimating the velocity and the radial position of a target illuminated by a signal which does not satisfy Woodward´s conditions (small relative bandwidth and reasonable time-bandwidth product). Classically, the variance lower bounds of estimates are obtained by inverting the Fisher information matrix (FIM) built according to the classical maximum likelihood (ML) estimation theory. The direct application of this procedure to broadband situations has so far not been performed for technical reasons. It is shown that the use of the Mellin transform allows a simple computation of the FIM and leads to a clear interpretation of its elements in the time-frequency plane.<>