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

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, sensing, and localization. With such large arrays, the plane wave approximation is often not accurate because the system may operate in the (radiating) near-field propagation region, namely the Fresnel region, where the electromagnetic field wavefront is spherical. In such a 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 antenna array. In this paper, we study a near-field tracking problem for inferring the position and the velocity of a moving source with an ad-hoc observation model that accounts for the phase-difference profile of a large receiving array. For this tracking problem, we derive the posterior Cramér-Rao Lower Bound (P-CRLB), and we provide insights on how the loss of positioning information outside the Fresnel region results from an increase of the ranging error rather than from inaccuracies of angular estimation. Then, we investigate the accuracy and complexity performance of different Bayesian tracking algorithms in the presence of model parameter mismatches and abrupt trajectory changes. Our results demonstrate the feasibility and high accuracy of most tracking approaches without the need for wideband signals and of any synchronization scheme.