Characterization of the Near-Field Focusing Region in the Radial Domain For Phased-Array Antennas

As 6G goes toward applying extremely large-scale antenna arrays (ELAAs) as well as very high operating frequencies, the near-field propagation region expands to even hundreds of meters. This provides conventional communication systems with new challenges as well as opportunities. In this context, effectively managing the complexities of near-field communication, and harnessing its unique features require a deep understanding of near-field signal behavior, particularly when initiated from ELAAs. The radial beamfocusing through ELAAs is one of the important unique near-field features which has been less analytically explored and characterized in the literature so far. In this paper, we formally define and characterize the radial focal region and establish the conditions for achieving a near-field focal point in the radial domain. We analytically reveal that employing a maximum ratio beamformer leads to a radial focal gap between the desired and achievable focal points. We analytically prove that when the number of arrays becomes extremely large through ELAAs, the gap is eliminated. In addition, for non-ELAA scenarios where the number of array elements is not very high, we present a beamforming algorithm to remove the gap and precisely create a radial focal point at the desired location. The achieved outcomes are verified through numerical results for single-focal and multi-focal scenarios.