Movable antenna (MA) is a new technology capable of dynamically adjusting antenna positions, allowing the full exploitation of spatial degrees of freedom (DoFs). The successful realization of the spatial potential from MA systems critically depends on precise knowledge of channel components. However, existing MA channel estimation methods are primarily concerned with identifying these components from observations at arbitrarily placed MAs, without providing an efficient strategy for MA position optimization. Furthermore, conventional gridless refinement methods suffer from high computational complexity and lack explicit parameter pairing, limiting estimation accuracy. To overcome these issues, this paper proposes a learning-driven framework that jointly optimizes MA positions and the channel estimation function in MA-aided wideband systems. The core principle involves decomposing the system model into operations analogous to those in a deep neural network layer, wherein a non-linear function is applied after matrix multiplication. A neural network is trained to emulate this decomposed model. After training, the network is partitioned into three modules representing the optimized Tx-MA positions, Rx-MA positions, and the channel parameter estimation function, which collectively enable the estimation of paired channel angles and delays. In addition, a low-complexity refinement algorithm, termed stepwise alternating optimization (SWAO), is introduced to sequentially refine the initial angle and delay estimates. Simulation results confirm the superiority of the proposed method in estimation accuracy and computational complexity.

Accurate channel state information is fundamental for fully unleashing the potential of millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, two primary challenges hinder its acquisition. The first challenge is the insufficient research on hybrid beamformer design during the channel estimation period, contrasted with the extensive focus on the data transmission period. Secondly, conventional channel estimation schemes overlook practical effects present in mmWave wideband systems, namely beam squint. To tackle these obstacles, this paper presents a learning-aided joint optimization framework for beamformers and the geometric parameter estimation function, customized for specific environments. Inspired by the analogous operations between a neural network and a reshaped signal model, the early stages of the network are trained to emulate the reshaped signal model. After completing training, the early weight matrices are extracted to shape the beamformers, while the remainder constitutes the function. Essentially, joint optimization is accomplished by decomposing a single trained network into multiple components under specific constraints. Following the initial search for geometric parameters facilitated by these components, they undergo beam squint-specialized refinement for precise channel reconstruction. Numerical results demonstrate the adaptability of the proposed beamformers to the environment through heightened effective SNR levels. Furthermore, the superior performance of the proposed method over existing methods in channel estimation is proven.

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.

Accurate channel state information is paramount for fully harnessing the benefits of massive antennas in communication systems. However, two primary challenges impede its acquisition. Firstly, conventional far-field assumption-based channel estimation schemes become impractical in near-field dominant future communication systems. In contrast to the far-field assumption, which relies solely on angle-dependent channels, the near-field introduces location-dependency. The second challenge involves limited research on hybrid beamformer design during the channel estimation period, unlike the extensive focus on the data transmission period. To overcome these hurdles, this paper presents a neural network-aided joint optimization of the beamformer and localization function for near-field channel estimation, customized to the specific environment. Inspired by the similarity between operations in a neural network and a signal model, the initial network weights emulate the beamforming matrix during training. Subsequently, these weights are extracted for beamformer design, while the remainder of the network serves as the localization function. Following localization, the location parameters undergo refinement, paving the way for precise channel reconstruction. Unlike prevailing near-field channel estimation methods that solely exploit range information from array response, our approach additionally leverages range-dependent frequency selectivity characteristics. Simulation results prove the adaptability of the proposed beamformer to given environments and demonstrate the superior performance of the proposed method in channel estimation.