Radial-Angular Resolution Framework for Near-Field Communications

Near-field beamfocusing confines radiated power into a localized three-dimensional focal spot, making the analytical characterization of radial and angular resolution critical for sixth-generation (6G) multi-user systems, yet existing models treat the focal resolution as a fixed geometric outcome rather than a tunable design variable. Based on the Angular Representation (ASR) approach, this paper presents a resolution framework to design contiguous focal regions across both the radial and angular domain for steered multi-user systems. By extending the definition of a tunable inter-beam overlap ρ, we derive closed-form expressions for the radial and angular focal boundaries and extents, alongside the steering-dependent minimum focal distance d 0, min and maximum steering angle θ max. Using these boundaries, iterative synthesis algorithms are developed to construct uniform and non-uniform radial and angular beam arrangements. Finally, by analyzing both isolated and joint radial-angular configurations, we quantify the fundamental trade-offs between ρ, achievable user capacity, inter-user interference, and system sum-rate across varying steering angles.