Analyzing URA Geometry for Enhanced Near-Field Beamfocusing and Spatial Degrees of Freedom

With the deployment of large antenna arrays at high-frequency bands, future wireless communication systems are likely to operate in the radiative near-field. Unlike far-field beam steering, near-field beams can be focused on a spatial region with a finite depth, enabling spatial multiplexing in the range dimension. Moreover, in the line-of-sight MIMO near-field, multiple spatial degrees of freedom (DoF) are accessible, akin to a scattering- rich environment. In this paper, we derive the beamdepth for a generalized uniform rectangular array (URA) and investigate how the array geometry influences near-field beamdepth and its limits. We define the effective beamfocusing Rayleigh distance (EBRD), to present a near-field boundary with respect to beamfocusing and spatial multiplexing gains for the generalized URA. Our results demonstrate that under a fixed element count constraint, the array geometry has a strong impact on beamdepth, whereas this effect diminishes under a fixed aperture length constraint. Moreover, compared to uniform square arrays, elongated configurations such as uniform linear arrays (ULAs) yield narrower beamdepth and extend the effective near-field region defined by the EBRD. Building on these insights, we design a polar codebook for compressed-sensing-based channel estimation that leverages our findings. Simulation results show that the proposed polar codebook achieves a 2 dB NMSE improvement over state-of-the-art methods. Additionally, we present an analytical expression to quantify the effective spatial DoF in the near-field, revealing that they are also constrained by the EBRD. Notably, the maximum spatial DoF is achieved with a ULA configuration, outperforming a square URA in this regard.