Weighted Sum-Rate Maximization for Flexible Intelligent Metasurface Aided Multicell Systems

Flexible intelligent metasurface (FIM) technology has emerged as a promising solution for enhancing wireless communication performance. In contrast to traditional rigid reconfigurable intelligent surfaces (RIS), an FIM consists of an array of electromagnetic (EM) elements, each capable of flexibly adjusting its position along the direction perpendicular to the surface to collaboratively morph the surface shape. In this paper, an optimization problem for maximizing the weighted sum-rate (WSR) in an FIM-aided multicell multi-user multiple-input single-output (MU-MISO) system is investigated. We jointly optimize the beamforming at the base station (BS), the phase shift matrix, and the FIM surface shape. To address this problem, we propose an efficient alternating optimization framework, where we employ the weighted minimum mean square error (WMMSE) method to reformulate the problem and the block coordinate descent (BCD) algorithm to iteratively update the variables. Specifically, we utilize the Riemannian Conjugate Gradient (RCG) algorithm to optimize the phase shift matrix, and the projected gradient descent (PGD) method to optimize the FIM surface shape. Additionally, the optimal beamforming vectors are obtained in closed form. Finally, simulation results demonstrate the superiority of FIM over conventional RIS in various scenarios.