Distance-Domain Degrees of Freedom in Near-Field Region

TL;DR

This paper investigates the distance-domain degrees of freedom in near-field large aperture arrays, deriving a closed-form expression and analyzing how array shape and configuration affect spatial resource utilization.

Contribution

It introduces a novel analytical framework for assessing distance-domain DoF in near-field arrays, including non-broadside and modular array configurations.

Findings

Distance-domain DoF is mainly influenced by array boundaries.

Closed-form expression for DoF derived via Fourier transform.

Modular arrays can achieve higher DoF than single-piece arrays.

Abstract

Extremely large aperture arrays operating in the near-field regime unlock additional spatial resources, which can be exploited to simultaneously serve multiple users even when they share the same angular direction. This work investigates the distance-domain degrees of freedom (DoF), defined as the DoF when a user varies only its distance to the base station and not the angle. To obtain the distance-domain DoF, we investigate a line-of-sight (LoS) channel between a base station (source) and observation region representing users. The base station is modeled as a large two-dimensional transmit (Tx) array with an arbitrary shape. The observation region is modeled as an arbitrarily long linear receive (Rx) array, where elements are collinearly aligned but located at varying distances from the Tx array. We assume that both the Tx and Rx arrays have continuous apertures with an infinite number of elements and infinitesimal spacing, which establishes an upper bound for the distance-domain DoF in the case of a finite number of elements. First, we analyze an ideal case where the Tx array is a single piece and the Rx array is on the broadside of the Tx array. By reformulating the channel as an integral operator with a Hermitian convolution kernel, we derive a closed-form expression for the distance-domain DoF via the Fourier transform. Our analysis shows that the distance-domain DoF is predominantly determined by the extreme boundaries of both the Tx and Rx arrays rather than their detailed interior structure. We further extend the framework to non-broadside configurations by employing a projection method that converts the problem to an equivalent broadside case. Finally, we extend the analytical framework to modular arrays and show the distance-domain DoF gain over a single-piece array under a fixed total physical length.