Performance Bounds for Near-Field Velocity Estimation With Modular Linear Array

Velocity estimation is a cornerstone of the recently introduced near-field predictive beamforming. This letter derives the Cramér-Rao bounds (CRBs) for joint radial and transverse velocity estimation within a predictive beamforming framework employing a modular linear array (MLA). We obtain approximated closed-form CRB expressions that characterize the interplay between array geometry and estimation accuracy, showing that increasing the inter-module separation enlarges the effective aperture and reduces the transverse-velocity CRB, while the radial-velocity CRB remains largely insensitive to this separation. Furthermore, we show that an MLA can achieve the same accuracy as a collocated array with fewer antennas and quantify the relation between inter-module spacing and antenna savings. The derived expressions are validated through simulations by comparing them with the mean-squared error (MSE) of the maximum likelihood estimator (MLE) reported in the literature.