Movable Intelligent Surface-Enabled Wireless Communications: Static Phase Shifts with Mechanical Reconfigurability

Intelligent surfaces that reshape electromagnetic waves are regarded as disruptive technologies for wireless networks. However, existing designs sit at two costly extremes: dynamic reconfigurable intelligent surfaces (RISs) offer fine beam control but require dense cabling, continuous power consumption, and substantial signaling overhead, whereas low-cost static surfaces require no control lines or electronics but are limited to a single beam pattern. This disparity leaves a practical gap for quasi-static environments, such as industrial Internet-of-things and smart agriculture scenarios, where channels are stable with user demands changing only occasionally or periodically, and neither extreme is sufficiently economical or flexible. To bridge this gap, we propose a novel movable intelligent surface (MIS) architecture, whose beam patterns are switched not by electronic phase tuning but by mechanically sliding a small, pre-phased secondary metasurface layer across a larger, likewise static primary layer. We develop an MIS signal model that characterizes the interaction between static phase elements with dynamic geometry via binary selection matrices. Based on this model, we formulate a new type of optimization problems that jointly design static phase shifts and the overlapping position selection of MS2 (equal to beam pattern scheduling). Efficient algorithms based on the penalty method, block coordinate descent, and Riemannian manifold optimization are proposed to tackle these mixed-integer non-convex problems. Simulation results demonstrate that the proposed MIS architecture substantially narrows the performance gap between single-layer static surfaces and dynamic RISs, providing a practical and flexible solution for quasi-static wireless applications.