Dual-Layer Fluid Three-Dimensional Antenna Arrays for MIMO Communications

Abstract

This work proposes a novel dual-layer fluid three-dimensional (3D) antenna array architecture for enhancing spatial sampling capability beyond conventional planar topologies. This physically realizable structure, in contrast to abstract volumetric models, makes use of spatially stratified fluid layers to enable 3D beamforming while carefully taking into consideration realistic constraints such as inter-layer anti-blockage, mutual coupling, and local port boundaries. An analytical framework is developed by deriving a closed-form spherical-harmonic series representation of the 3D spatial correlation function (SCF), which decomposes correlation into magnitude-dependent and direction-dependent components. Based on the derived SCF, a Jensen-type upper bound on the ergodic capacity is established, linking the capacity behavior to the eigenvalue structure of the transmit and receive spatial correlation matrices. To address the nonconvexity of the joint design problem, an alternating optimization (AO) framework is developed. The approach employs hyperbolic tangent mapping and a log-sum-exp (LSE) approximation to confine antenna movements, enforce minimum spacing, and avoid inter-layer blockage. Within this framework, the transmit covariance matrix is optimized via singular value decomposition-based water-filling, while the fluid antenna geometry is updated through gradient ascent. Extensive numerical simulations verify that the proposed fluid 3D array achieves capacity enhancements of approximately 24.83% over fixed dual-layer arrays and 45.48% over single-layer extended arrays, demonstrating robust performance even in sparse scattering and rank-deficient propagation environments.