Mutual-Coupling-Aware Movable and Fluid Antennas on Holographic Surfaces: A Wavenumber-Domain Circuit-Field Unification

RESUMO

Movable and fluid antenna systems turn antenna position into a design variable. At sub-wavelength spacings, however, their behavior is governed by mutual coupling, modeled today by two disjoint traditions: circuit-theoretic impedance matrices with element-level constants, and field-theoretic kernels with norm-type power constraints. This paper unifies the two. Starting from the impedance kernel of a holographic surface, a Poynting-anchored balance identifies its resistive part with ohmic plus radiated power and its reactive part with stored-energy imbalance, and a circuit-field equivalence shows that the multiport impedance matrix is the kernel sampled at the port separations, in a single closed spherical-Hankel form. In the wavenumber domain the resistive kernel asymptotically diagonalizes in the aperture size: visible modes radiate at closed-form prices, evanescent modes only dissipate, and a flexible port becomes a constant-modulus codeword whose coupling is the pullback of the spectral weight. Coupling-aware multi-user sum-rate maximization over precoders and port positions is then formulated under physical power and voltage constraints and solved by weighted-MMSE and projected-gradient steps with closed-form gradients. A modal relaxation upper-bounds every port configuration and seeds the search by FFT-based codeword projection. A half-wavelength corollary and a superdirectivity margin quantify when coupling hurts, and when it helps.