FSIM: Fluid Element Stacked Intelligent Metasurface for Multiuser Downlink Networks

Tsung-Yu Wei, Li-Hsiang Shen, Kai-Ten Feng, Lie-Liang Yang

A fluid element (FE)-aided stacked intelligent metasurface (FSIM) for multiple-input single-output (MISO) communication system is investigated, where a multi-antenna base station (BS) serves multiple single-antenna users through FSIM. Unlike conventional SIM with fixed meta-atom deployment, the architecture allows the meta-atoms in each layer to move within a predefined fluidic region to further increase the spatial diversity. By jointly optimizing the two-dimensional meta-atom positions, BS transmit beamforming, and FSIM phase-shifts, the cascaded BS-FSIM-user channels can be flexibly reconfigured to enhance the desired signals and suppress multiuser interference. The proposed sum-rate maximization problem is highly non-convex and nonlinear due to the coupled solutions of element position, beamforming, and phase-shift. To address this challenge, an alternating optimization (AO) algorithm is developed to iteratively update these variables. The beamforming and FSIM phase-shift subproblems are transformed into semi-definite programming problems and solved by using successive convex approximation (SCA), first-order Taylor approximation, and penalty-based rank-one relaxation, whilst the FE position subproblem is handled through a projected gradient-based update. Simulation results reveal that a compact FSIM with a small inter-layer thickness is preferable, as increasing the thickness weakens inter-layer coupling and degrades the achievable sum rate. Results also demonstrate that the proposed FSIM significantly outperforms conventional SIMs with fixed positions, patch-based structures, partial fluidity, restricted fluid regions, and existing flexible intelligent metasurfaces. Furthermore, the proposed AO-based algorithm achieves superior rate performance compared to sub-schemes, metaheuristic methods, and conventional beamforming benchmarks.