Spatial Correlation, Non-Stationarity, and Degrees of Freedom of Holographic Curvature-Reconfigurable Apertures

TL;DR

This paper introduces a holographic curvature-reconfigurable aperture model and a framework to analyze spatial non-stationarity and degrees of freedom, aiding low-altitude antenna system design on nonplanar surfaces.

Contribution

It develops a visibility-aware spatial characterization framework for curvature-reconfigurable holographic apertures, including novel metrics and analysis methods for non-stationarity and spatial degrees of freedom.

Findings

Curvature and propagation support are key factors affecting SnS and DoF.

Array domain SnS influences local statistical stationarity.

DoF limits the number of global spatial modes.

Abstract

Low-altitude wireless platforms increasingly require lightweight, conformal, and densely sampled antenna array apertures with high array gain and spatial selectivity. However, when deployed on nonplanar surfaces, curvature alters the array manifold, local visibility, and propagation support, potentially invalidating spatial-stationarity assumptions. In this paper, we investigate a holographic curvature-reconfigurable aperture (HoloCuRA), modeled as a curvature-controllable holographic surface, and develop a visibility-aware spatial characterization framework for its low-altitude applications. Specifically, the framework jointly quantifies array-domain spatial non-stationarity (SnS), and spatial degrees of freedom (DoF) in line-of-sight, 3GPP non-line-of-sight, and isotropic-scattering propagation environments. For SnS, a novel Power-balanced, Visibility-aware Correlation-Matrix Distance (PoVi-CMD) and a two-stage subarray-screening procedure are introduced. For DoF, the R\'enyi-2 effective rank is adopted, and tractable spatial-correlation expressions under isotropic scattering are developed for efficient DoF analysis. Furthermore, a realizable antenna port mode is introduced to connect SnS with DoF. Numerical results reveal that curvature and propagation support are the primary determinants of both SnS and DoF in HoloCuRA: array domain SnS determines whether subarray statistics can be treated as locally consistent, whereas DoF limits the global spatial modes. The findings provide useful guidance for low-altitude antenna-system design.