Degrees of Freedom of Spatial Multiplexing in Distance Domain of Arbitrary Continuous-Aperture Array in Near-Field Region

2025-07-01

AI Summary

This study investigates the fundamental limit—namely, the theoretical upper bound on distance-domain spatial degrees of freedom (DoF)—for near-field ultra-large aperture arrays to achieve multi-user spatial multiplexing solely via range differences at identical angular directions. For a line-of-sight channel between a two-dimensional continuous transmit aperture and a linear receive array, we formulate an integral operator model based on a Hermite convolution kernel and employ Fourier analysis to derive a closed-form expression for the DoF. We first reveal that the distance-domain DoF is governed by the physical boundaries of the array—not its internal structure—and propose a projection transformation method to equivalently map non-broadside configurations to broadside cases. Extending this framework to modular arrays, we demonstrate that modularization enhances DoF within a fixed physical length. These results provide critical theoretical foundations and design principles for high-density, near-field multi-user communication systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Non-convex Optimization
• Application Domains: Mobility, Driving & Flight

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Security and Privacy: Large-scale security measurements

Abstract

Extremely large aperture array operating in the near-field regime unlocks additional spatial resources that can be exploited to simultaneously serve multiple users even when they share the same angular direction, a capability not achievable in conventional far-field systems. A fundamental question, however, remains: What is the maximum spatial degree of freedom (DoF) of spatial multiplexing in the distance domain? In this paper, we address this open problem by investigating the spatial DoF of a line-of-sight (LoS) channel between a large two-dimensional transmit aperture and a linear receive array with collinearly-aligned elements (i.e., at the same angular direction) but located at different distances from the transmit aperture. We assume that both the aperture and linear array are continuous-aperture (CAP) arrays with an infinite number of elements and infinitesimal spacing, which establishes an upper bound for the spatial degrees of freedom (DoF) in the case of finite elements. First, we assume an ideal case where the transmit array is a single piece and the linear array is on the broad side of the transmit array. By reformulating the channel as an integral operator with a Hermitian convolution kernel, we derive a closed-form expression for the spatial DoF via the Fourier transform. Our analysis shows that the spatial DoF in the distance domain is predominantly determined by the extreme boundaries of the array rather than its detailed interior structure. We further extend the framework to non-broadside configurations by employing a projection method, which effectively converts the spatial DoF to an equivalent broadside case. Finally, we extend our analytical framework to the modular array, which shows the spatial DoF gain over the single-piece array given the constraint of the physical length of the array.

Problem

• Determines maximum spatial DoF in near-field distance domain
• Analyzes DoF for continuous-aperture arrays with collinear receivers
• Extends framework to modular arrays for DoF gains

Innovation

• Continuous-aperture arrays for near-field spatial multiplexing
• Fourier transform to derive closed-form DoF expression
• Projection method for non-broadside configurations