Flexible intelligent metasurface (FIM) technology has emerged as a promising technology for enhancing wireless communication performance by dynamically reshaping the propagation environment. Compared with conventional rigid reconfigurable intelligent surfaces (RIS), an FIM is composed of multiple electromagnetic (EM) scattering units, each of which can flexibly modify its displacement in the direction normal to the surface, thereby cooperatively morphing the overall surface shape. This additional degree of freedom (DoF) enables improved beamforming and interference mitigation, particularly in complex multicell scenarios. In this paper, an optimization problem for maximizing the weighted sum-rate (WSR) in a multicell multi-user multiple-input single-output (MU-MISO) system assisted by an FIM deployed at the cell boundary is investigated. We jointly optimize the transmit beamforming at the base station (BS), the phase shift matrix, and the FIM surface shape, subject to constraints on the transmit power budget, unit-modulus reflection coefficients, and surface shape morphing range. Due to the non-convex objective function with highly coupled variables, solving the formulated optimization problem is challenging. To tackle this challenge, we propose an efficient alternating optimization framework that leverages 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, the Riemannian conjugate gradient (RCG) algorithm is leveraged to optimize the phase shift matrix, while the projected gradient descent (PGD) method is adopted to optimize the surface shape of the FIM. Additionally, the optimal beamforming vectors are obtained in closed form.

翻译：柔性智能超表面（FIM）技术因其动态重塑传播环境的能力，已成为增强无线通信性能的前瞻性技术。与传统刚性可重构智能超表面（RIS）相比，FIM由多个电磁散射单元构成，每个单元可灵活改变其法向位移，从而协同调整整体表面形态。这种额外的自由度使波束成形和干扰抑制性能得到提升，尤其在复杂的多小区场景中。本文研究了部署于小区边界的FIM辅助多小区多用户多输入单输出（MU-MISO）系统中，最大化加权和速率（WSR）的优化问题。我们在发射功率预算、单位模反射系数及表面形态变形范围的约束条件下，联合优化基站（BS）的发射波束成形、相移矩阵及FIM表面形态。由于目标函数非凸且变量高度耦合，求解该优化问题极具挑战。为此，我们提出一种高效的交替优化框架，利用加权最小均方误差（WMMSE）方法重构问题，并采用块坐标下降（BCD）算法迭代更新变量。具体而言，采用黎曼共轭梯度（RCG）算法优化相移矩阵，利用投影梯度下降（PGD）方法优化FIM表面形态，同时以闭式形式获得最优波束成形向量。