New View of Learning-Aided Channel Estimation for Movable Antenna Systems

Movable antenna (MA) is an emerging technology with promising potential to enhance communication quality by dynamically adjusting antenna positions to locations with favorable channel conditions. The successful exploitation of spatial selectivity in MA systems depends on the precise knowledge of channel components, such as channel angles and gains. However, current state-of-the-art methods primarily focus on estimating channel components based on measurements from arbitrary MA positions, lacking a theoretical methodology for determining optimal MA positions during the channel estimation period. Additionally, these methods often adopt on-grid approaches, which suffer from inherent resolution limitations. This paper presents a new framework for the joint optimization of MA positions and the channel estimation function. A learning-aided approach driven by a deep neural network is employed. The key to accomplishing joint optimization lies in decomposing the received pilot model into operations identical to those in a neural network layer, where a specific non-linear function is applied after matrix multiplication. The neural network is trained to imitate this decomposed model. Upon completion of training, the entire trained network is divided into optimization solutions: MA positions and a channel angle estimation function. Subsequently, the angles obtained from the network modules are refined in a gridless manner through the proposed MA-alternating minimization refinement (MA-AMR), which are then used to derive channel gains. Numerical results demonstrate that the proposed method surpasses existing methods in terms of estimation accuracy and computational efficiency.