Deep learning based Channel Estimation and Beamforming in Movable Antenna Systems

Movable antenna (MA) has emerged as a promising technology for future wireless systems. Compared with traditional fixed-position antennas, MA improves system performance by antenna movement to optimize channel conditions. For multiuser wideband MA systems, this paper proposes deep learning-based framework integrating channel estimation (CE), antenna position optimization, and beamforming, with a clear workflow and enhanced efficiency. Specifically, to obtain accurate channel state information (CSI), we design a two-stage CE mechanism: first reconstructing the channel matrix from limited measurements via compressive sensing, then introducing a Swin-Transformer-based denoising network to refine CE accuracy for subsequent optimization. Building on this, we address the joint optimization challenge by proposing a Transformer-based network that intelligently maps CSI sequences of candidate positions to optimal MA positions while combining a model-driven weighted minimum mean square error (WMMSE) beamforming approach to achieve better performance. Simulation results demonstrate that the proposed methods achieve superior performance compared with existing counterparts under various conditions. The codes about this work are available at https://github.com/ZiweiWan/Code-4-DL-MA-CE-BF.

💡 Research Summary

The paper tackles the emerging concept of movable antennas (MAs) for next‑generation wireless networks, where each antenna element can physically relocate within a predefined area to improve channel conditions. While MA technology promises reduced hardware cost and enhanced spectral efficiency compared with conventional fixed‑position massive MIMO, its practical deployment is hampered by the difficulty of acquiring accurate channel state information (CSI) and by the need to jointly optimize antenna positions and beamforming vectors.

To address these challenges, the authors propose an end‑to‑end deep‑learning framework that integrates three key modules: (1) a two‑stage channel estimation (CE) procedure, (2) a transformer‑based antenna position selection network, and (3) a model‑driven weighted minimum mean‑square error (WMMSE) beamforming network.

Stage 1 – Compressive‑Sensing‑Based Initial CE.
During pilot transmission, only a small subset (J) of the (N) possible antenna locations is visited ( (J \ll N) ) to keep training overhead low. The received pilot signals are stacked and expressed as a linear measurement model ( \mathbf{y}= \mathbf{B}{\text{ce}}\bar{\mathbf{A}}\bar{\mathbf{x}} + \mathbf{z}), where (\bar{\mathbf{A}}) is a dictionary built from a fine angular grid (size (G^2)). The authors enforce a common support set across all OFDM sub‑carriers and solve the simultaneous sparse recovery problem using the simultaneous orthogonal matching pursuit (SOMP) algorithm. This yields an initial estimate (\hat{\mathbf{h}}{\text{ini}}