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

TL;DR

This paper investigates how array geometry affects near-field beamfocusing and spatial degrees of freedom in high-frequency wireless systems, deriving new metrics and designing a polar codebook that improves channel estimation.

Contribution

It introduces the effective beamfocusing Rayleigh distance (EBRD) for generalized URAs and analyzes how geometry influences near-field beamdepth and DoF, leading to optimized array designs.

Findings

Elongated arrays like ULAs have narrower beamdepth than square URAs.

The array geometry significantly impacts beamdepth under fixed element count.

The proposed polar codebook improves channel estimation NMSE by 2 dB.

Abstract

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.