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

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 Rényi-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.

Figures (14)

• Figure 1: Illustration of a low-altitude HoloCuRA system.
• Figure 2: Geometry and top view of 1D HoloCuRA in 3D space.
• Figure 3: Geometry and the first-layer slice view of 2D HoloCuRA in 3D space.
• Figure 4: Local stable subarray fraction as a function of $\beta$ (rad) for 1D HoloCuRA with $N=128$, $L=0.32~\mathrm{m}$, and $r=2.0~\mathrm{m}$: (a) $\phi=90^\circ$ (VR active) and (b) the $\phi\neq 90^\circ$ region, both plotted versus the number of subarrays $K\in\{2,4,8,16,32,64\}$. Values closer to 1 indicate that a larger fraction of subarrays remains stable for the corresponding curvature/partition setting.
• Figure 5: Local stable subarray fraction as a function of $\beta$ (rad) for 2D HoloCuRA local-SnS at $r=2.0~\mathrm{m}$ for (a) $K=16$ and (b) $K=32$, comparing different partition schemes (X-cut, Z-cut, and 2D grid partitions with the indicated grid sizes). Values closer to 1 indicate that a larger fraction of subarrays remains stable for the corresponding curvature/partition setting.