Movable Intelligent Surface (MIS) for Wireless Communications: Architecture, Modeling, Algorithm, and Prototyping

Reconfigurable intelligent surfaces enhance wireless systems by reshaping propagation environments. However, dynamic metasurfaces (MSs) with numerous phase-shift elements incur undesired control and hardware costs. In contrast, static MSs (SMSs), configured with static phase shifts pre-designed for specific communication demands, offer a cost-effective alternative by eliminating element-wise tuning. Nevertheless, SMSs typically support a single beam pattern with limited flexibility. In this paper, we propose a novel Movable Intelligent Surface (MIS) technology that enables dynamic beamforming while maintaining static phase shifts. Specifically, we design a MIS architecture comprising two closely stacked transmissive MSs: a larger fixed-position MS 1 and a smaller movable MS 2. By differentially shifting MS 2's position relative to MS 1, the MIS synthesizes distinct beam patterns. Then, we model the interaction between MS 2 and MS 1 using binary selection matrices and padding vectors and formulate a new optimization problem that jointly designs the MIS phase shifts and selects shifting positions for worst-case signal-to-noise ratio maximization. This position selection, equal to beam pattern scheduling, offers a new degree of freedom for RIS-aided systems. To solve the intractable problem, we develop an efficient algorithm that handles unit-modulus and binary constraints and employs manifold optimization methods. Finally, extensive validation results are provided. We implement a MIS prototype and perform proof-of-concept experiments, demonstrating the MIS's ability to synthesize desired beam patterns that achieve one-dimensional beam steering. Numerical results show that by introducing MS 2 with a few elements, MIS effectively offers beamforming flexibility for significantly improved performance. We also draw insights into the optimal MIS configuration and element allocation strategy.

Two-Timescale Design for Movable Antennas Enabled-Multiuser MIMO Systems

Movable antennas (MAs), which can be swiftly repositioned within a defined region, offer a promising solution to the limitations of fixed-position antennas (FPAs) in adapting to spatial variations in wireless channels, thereby improving channel conditions and communication between transceivers. However, frequent MA position adjustments based on instantaneous channel state information (CSI) incur high operational complexity, making real-time CSI acquisition impractical, especially in fast-fading channels. To address these challenges, we propose a two-timescale transmission framework for MA-enabled multiuser multiple-input-multiple-output (MU-MIMO) systems. In the large timescale, statistical CSI is exploited to optimize MA positions for long-term ergodic performance, whereas, in the small timescale, beamforming vectors are designed using instantaneous CSI to handle short-term channel fluctuations. Within this new framework, we analyze the ergodic sum rate and develop efficient MA position optimization algorithms for both maximum-ratio-transmission (MRT) and zero-forcing (ZF) beamforming schemes. These algorithms employ alternating optimization (AO), successive convex approximation (SCA), and majorization-minimization (MM) techniques, iteratively optimizing antenna positions and refining surrogate functions that approximate the ergodic sum rate. Numerical results show significant ergodic sum rate gains with the proposed two-timescale MA design over conventional FPA systems, particularly under moderate to strong line-of-sight (LoS) conditions. Notably, MA with ZF beamforming consistently outperforms MA with MRT, highlighting the synergy between beamforming and MAs for superior interference management in environments with moderate Rician factors and high user density, while MA with MRT can offer a simplified alternative to complex beamforming designs in strong LoS conditions.