Near-field Tracking with Large Antenna Arrays: Fundamental Limits and Practical Algorithms

Abstract: Applications towards 6G have brought a huge interest towards arrays with a high number of antennas and operating within the millimeter and sub-THz bandwidths for joint communication and localization. With such large arrays, the plane wave approximation is often not accurate because the system may operate in the near-field propagation region (Fresnel region) where the electromagnetic field wavefront is spherical. In this case, the curvature of arrival (CoA) is a measure of the spherical wavefront that can be used to infer the source position using only a single large array. In this paper, we study a near-field tracking problem for inferring the state (i.e., the position and velocity) of a moving source with an ad-hoc observation model that accounts for the phase profile of a large receiving array. For this tracking problem, we derive the posterior Cram\'er-Rao Lower Bound (P-CRLB) and show the effects when the source moves inside and outside the Fresnel region. We provide insights on how the loss of positioning information outside Fresnel comes from an increase of the ranging error rather than from inaccuracies of angular estimation. Then, we investigate the performance of different Bayesian tracking algorithms in the presence of model mismatches and abrupt trajectory changes. Our results demonstrate the feasibility and high accuracy for most of the tracking approaches without the need of wideband signals and of any synchronization scheme. signals and of any synchronization scheme.