Element Coefficient and Position Optimization for Flexible Intelligent Metasurface-Aided Movable Antenna Communications

In addition to the adjustable element excitation coefficients of the base station (BS) and the reflecting coefficient of the reconfigurable intelligent metasurface, we explore the potential of flexible-geometry array configurations. Specifically, we investigate the adaptive optimization of element positions to provide additional degrees of freedom in flexible intelligent metasurface (FIM)-aided movable antenna (MA) systems. To maximize the achievable communication rate, we formulate a joint optimization problem that coordinating these three key parameters. The optimization variables are partitioned into two distinct subsets corresponding to the BS and FIM, enabling alternating optimization strategy. Within this framework, closed-form expressions for the BS beamforming vectors and FIM phase shifts are analytically derived to facilitate position optimization for both the BS and FIM. Notably, the position optimization subproblem can be simplified through analytical solutions for the element excitation coefficients. Simulation results demonstrate that the proposed flexible-position design achieves a 48.59% improvement in spectral efficiency compared to conventional fixed-position configurations.