Spatial Correlation and Degrees of Freedom in Arched HMIMO Arrays: A Closed-Form Analysis

Abstract: This paper presents a closed-form analysis of spatial correlation and degrees of freedom (DoF) for arched holographic multiple-input multiple-output (HMIMO) arrays, which can be viewed as a special form of fluid antenna systems (FAS) when their geometry is fluidically adaptable. Unlike traditional planar configurations, practical HMIMO surfaces may exhibit curvature, significantly influencing their spatial characteristics and performance. We derive exact correlation expressions for both arched uniform linear arrays and arched uniform rectangular arrays, capturing curvature effects under far field propagation. Our results reveal that isotropic scattering results in DoF being dominated by the maximum span of the HMIMO array, such that shape effects are weakened, and bending does not significantly reduce the available spatial DoF. Numerical simulations validate the accuracy of the closed-form formulas and demonstrate the robustness of DoF against curvature variations, supporting flexible array designs. These findings offer fundamental insights into geometry-aware optimization for next-generation HMIMO/FAS systems and pave the way for practical implementations of curved HMIMO arrays.