Blockage-aware Hierarchical Codebook Design for RIS-Assisted Movable Antenna Systems

Abstract

In this paper, we propose a novel blockage-aware hierarchical beamforming framework for movable antenna (MA) systems operating at millimeter-wave (mm-Wave) frequencies. While existing works on MA systems have demonstrated performance gains over conventional systems, they often neglect the design of specialized codebooks to leverage MA's unique capabilities and address the challenges of increased energy consumption and latency inherent to MA systems. To address these aspects, we first integrate blockage detection into the codebook design process based on the Gerchberg-Saxton (GS) algorithm, significantly reducing inefficiencies due to beam evaluations done in blocked directions. Then, we use a two-stage approach to reduce the complexity of the joint beamforming and Reconfigurable Intelligent Surfaces (RIS) optimization problem. The simulations demonstrate that the proposed adaptive codebook successfully improves the Energy Efficiency (EE) and reduces the beam training overhead, substantially boosting the practical deployment potential of RIS-assisted MA systems in future wireless networks.

Figures (11)

• Figure 1: System model of MA-BS and RIS-assisted communication illustrating signal obstructions and beam rotation, where $\triangle \phi$ is the beam rotation angle.
• Figure 2: Illustration of blockage geometry.
• Figure 3: Illustration of beam rotation.
• Figure 4: Binary-tree structured hierarchical codebook.
• Figure 5: Empirical convergence of the blockage-aware GS algorithm under different blockage densities. The figure shows the normalized masked residual $r_t = E_t / E_0$ versus iteration index $t$ for blockage densities of $\{0\%, 10\%, 30\%, 50\%\}$. Solid lines represent mean trajectories, while shaded regions depict the Interquartile Range (IQR) across multiple random blockage pattern realizations for each density level. The vertical dashed line marks the conservative iteration cap $I_{\max}{=}40$. All curves exhibit the characteristic GS convergence profile—rapid initial decrease followed by a plateau—indicating stable convergence across scenarios.