Stacked intelligent metasurfaces (SIMs) have recently gained attention as a paradigm for wave-domain signal processing with reduced reliance on costly radio-frequency (RF) chains. However, conventional SIMs rely on uniform inter-layer spacing and require deep stacking to ensure processing capability, resulting in severe power attenuation in practice. To address this issue, we propose a flexible intelligent layered metasurface (FILM) architecture consisting of two shape-controllable flexible metasurface layers. By replacing rigid metasurfaces with flexible ones in both layers, the transmission coefficient matrix can be dynamically adjusted, significantly decreasing the number of required layers while maintaining signal processing performance. Firstly, we develop a two-layer FILM-assisted multi-user multiple-input single-output (MU-MISO) system, wherein we formulate a channel fitting problem aimed at reducing the difference between the FILM-induced and target channels. Then, we solve this non-convex problem by employing an alternating optimization (AO) method, featuring closed-form phase shift updates and a gradient descent-based shape optimization. Furthermore, we analyze the upper bound on sum-rate and the complexity of computation to provide insights into design trade-offs. Finally, simulation results demonstrated that the proposed transmissive FILM architecture achieves over 200\% improvement in sum-rate and more than 7 dB bit-error rate (BER) gain compared to the conventional seven-layer SIMs.

翻译：堆叠智能超表面（SIMs）作为一种依赖较少昂贵射频（RF）链的波域信号处理范式，近来受到关注。然而，传统SIMs依赖均匀的层间间距，并需要深度堆叠以确保处理能力，导致实际应用中严重的功率衰减。为解决此问题，我们提出了一种柔性智能分层超表面（FILM）架构，由两个形状可控的柔性超表面层组成。通过将两层中的刚性超表面替换为柔性超表面，传输系数矩阵可动态调整，在保持信号处理性能的同时显著减少所需层数。首先，我们开发了一个双层FILM辅助的多用户多输入单输出（MU-MISO）系统，其中我们构建了一个信道拟合问题，旨在减小FILM诱导信道与目标信道之间的差异。然后，我们采用交替优化（AO）方法解决这一非凸问题，该方法具有闭式相移更新和基于梯度下降的形状优化。此外，我们分析了和速率的上界和计算复杂度，以提供设计权衡的见解。最后，仿真结果表明，与传统七层SIMs相比，所提出的透射式FILM架构在和速率上实现了超过200%的提升，并在误码率（BER）上获得了超过7 dB的增益。