A Study on Characterization of Near-Field Sub-Regions For Phased-Array Antennas

We characterize three near-field sub-regions for phased array antennas by elaborating on the boundaries {\it Fraunhofer}, {\it radial-focal}, and {\it non-radiating} distances. The {\it Fraunhofer distance} which is the boundary between near and far field has been well studied in the literature on the principal axis (PA) of single-element center-fed antennas, where PA denotes the axis perpendicular to the antenna surface passing from the antenna center. The results are also valid for phased arrays if the PA coincides with the boresight, which is not commonly the case in practice. In this work, we completely characterize the Fraunhofer distance by considering various angles between the PA and the boresight. For the {\it radial-focal distance}, below which beamfocusing is feasible in the radial domain, a formal characterization of the corresponding region based on the general model of near-field channels (GNC) is missing in the literature. We investigate this and elaborate that the maximum-ratio-transmission (MRT) beamforming based on the simple uniform spherical wave (USW) channel model results in a radial gap between the achieved and the desired focal points. While the gap vanishes when the array size $N$ becomes sufficiently large, we propose a practical algorithm to remove this gap in the non-asymptotic case when $N$ is not very large. Finally, the {\it non-radiating} distance, below which the reactive power dominates active power, has been studied in the literature for single-element antennas. We analytically explore this for phased arrays and show how different excitation phases of the antenna array impact it. We also clarify some misconceptions about the non-radiating and Fresnel distances prevailing in the literature.