Bending Beam for THz Wireless Networks: Fundamental, Design Issue, and Prototype

Bending beams, characterized by their non diffracting and self-healing properties in the near field, offer a new approach to bypass blockage in terahertz (THz) wireless communication and sensing. However, the investigations of bend ing beams in the context of wireless communications still remain at an early stage. This article provides a state-of-the-art review of the fundamentals and key application scenarios of bending beams in THz wireless communications and sensing. We first present and compare the existing beamforming design and practical hardware implementation methods for bending beams. Next, we discuss potential applications of bending beams in wireless communica tions and sensing and identify their associated challenges, such as blocked channel modeling, bending beam training, codebook design, etc. Finally, a hardware demonstration of bending beam over THz frequency bands is presented, validating the advantages of bending beam over conventional beamfocusing.

Deep Learning-Empowered Movable-Antenna Position Optimization with Partial CSI

Movable antennas (MAs) are a promising technology to improve wireless data rates by dynamically adjusting their positions to avoid deep fading. However, finding the optimal MA positions requires full channel state information (CSI) for all possible locations within the movement region, creating massive channel estimation overhead. This paper proposes a deep neural network (DNN)-based learning framework to predict the optimal positions of multiple transmit MAs in a multi-user multiple-input single-output (MISO) system, entirely bypassing explicit channel estimation.First, we analyze a single-user MISO case, revealing a complex, highly nonlinear mapping between the optimal MA positions and the channel power gains from a specific subset of locations in the transmit region to the user. Because this mapping cannot be mathematically characterized for practical channel models, we train a DNN via supervised learning to capture it. The pre-trained DNN can then determine optimized MA positions in real-time relying only on partial power measurements from the transmit region.Extending this to multi-user scenarios is challenging due to complex rate expressions and the lack of globally optimal position solutions to use as training labels. To overcome this, we develop an unsupervised training framework that directly maximizes the multi-user sum-rate. This framework utilizes an attention-based architecture to extract latent features from the partial channel measurements and effectively manage inter-user interference. Simulation results show that our proposed approach achieves near-optimal performance in single-user systems and surpasses conventional CSI-based alternating optimization algorithms in multi-user environments.

Unlocking the Potential of Movable Antennas: General and Practical Antenna Position Optimization

Recently, movable antenna (MA) has attracted wide attention in wireless communications due to its potential in enhancing wireless communication performance via local movement within a confined region. However, antenna position optimization (APO) has emerged as a major challenge for MAs, due to the lack of a tractable, analytical, and accurate channel model in terms of antenna positions. Although existing works have developed various algorithms for APO, most of them are based on simplified theoretical channel models, which limit their generality. To address this challenge, in this article, we present more general and effective APO algorithms for different purposes, categorized as continuous APO and discrete APO, respectively. Continuous APO is mainly applied for flexible array signal processing to boost large-scale communication performance, while discrete APO is applied for small-scale multi-path channel reshaping. Specifically, the discrete APO discretizes the antenna movement region into multiple sampling points and employs discrete algorithms to determine the optimal MA positions based on the point-wise channel state information (CSI), without the need for an analytical channel model. To reduce the overhead for CSI acquisition, we also present more efficient learning-based APO algorithms that operate without requiring full point-wise CSI. Finally, we compare the application scenarios of the proposed algorithms and validate their effectiveness with numerical results.

Mixture-of-Experts Diffusion Models for Adaptive Massive MIMO Channel Estimation via Variational Bayesian Inference

Channel estimation is essential to massive multiple-input multiple-output (MIMO) systems. While recent generative model-based approaches using lightweight diffusion models (DMs) have achieved superior performance, they typically rely on a single data-driven prior, which limits their adaptability to varying channel distributions in real-world scenarios. To address this deficiency, we propose a mixture-of-experts (MoE) diffusion model (DM) framework combined with variational Bayesian inference. Specifically, our approach employs multiple pre-trained DMs, with each trained on a specific type of propagation channels. We then propose a probabilistic graphical model in which the channel is modeled as a latent variable drawn from one of these candidate generative priors with a certain probability. By integrating variational Bayesian inference with DM-based data priors, the underlying channel along with the expert indicator variable are jointly inferred, thus enabling automatic model adaptation for channel estimation. The effectiveness of our approach is evaluated on 3GPP CDL channels. Simulation results demonstrate that our proposed approach achieves a clear performance improvement over the standard DM-based method that employs a single prior trained on aggregated data from all channel types, particularly when the channel samples from different propagation environments are imbalanced.

Joint Communication and Trajectory Design for Movable Antenna Systems

Movable antennas (MAs) have attracted significant attention in wireless communications due to their ability to reconfigure channel conditions by flexibly adjusting the antenna positions within a confined region. However, MA movement generally incurs a non-negligible delay, which may significantly limit the data transmission time at optimized positions. To tackle this challenge, this paper investigates a new joint communication and trajectory optimization problem, where each MA transmits while moving along an optimized trajectory to prolong the effective data transmission time. Focusing on a single-MA system, our goal is to maximize the average data rate by optimizing the MA's positions over time, subject to its maximum velocity constraints. However, this continuous-time antenna position optimization problem is highly non-convex and challenging to solve. To tackle this challenge, we first consider a special case with two channel paths and derive the optimal MA trajectory in closed form. For other general cases, we ingeniously reformulate the average rate maximization problem into a fixed-hop shortest path problem in graph theory by sampling the antenna movement region into a multitude of discrete points, and solve it optimally. Simulation results demonstrate that our proposed algorithm can significantly improve the data rate compared to other baseline schemes.

Terahertz Beam Squint Mitigation via Six-Dimensional Movable Antennas

Analog beamforming holds great potential for future terahertz (THz) communications due to its ability to generate high-gain directional beams with low-cost phase shifters. However, conventional analog beamforming may suffer substantial performance degradation in wideband systems due to the beam squint effect. Instead of relying on high-cost true-time delayers, we propose an efficient six-dimensional movable antenna (6DMA) architecture to mitigate the beam-squint effect. In particular, we study a wideband wide-beam coverage problem in this paper, aiming to maximize the minimum beamforming gain over a given range of azimuth/elevation angles and frequencies by jointly optimizing the analog beamforming vector, the MA positions within a two-dimensional (2D) region, and the three-dimensional (3D) rotation angles of the antenna array. However, this problem is non-convex and intractable to solve optimally due to the coupling of the spatial and frequency domains and that of the antenna weights, positions and rotation. To tackle this problem, we first derive an optimal solution to it in a special case with azimuth or elevation angle coverage only. It is shown that rotating a uniform linear array (ULA) is sufficient to achieve global optimality and eliminate beam-squint effects. While for other general cases, an alternating optimization (AO) algorithm is proposed to obtain a high-quality suboptimal solution, where the antennas' beamforming weights, positions, and rotation angles are alternately optimized by combining successive convex approximation (SCA), sequential update with Gibbs sampling (GS), and hybrid coarse- and fine-grained search. Simulation results demonstrate that our proposed scheme can significantly outperform conventional antenna arrays without antenna movement or rotation, thus offering a cost-effective solution for wideband transmission over THz bands.

Indirect and Direct Multiuser Hybrid Beamforming for Far-Field and Near-Field Communications: A Deep Learning Approach

Hybrid beamforming for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging in the near field because the channel depends jointly on angle and distance, and the multiuser interference (MUI) is strong. Existing deep learning methods typically follow either a decoupled design that optimizes analog beamforming without explicitly accounting for MUI, or an end-to-end (E2E) joint analog-digital optimization that can be unstable under nonconvex constant-modulus (CM), pronounced analog-digital coupling, and gradient pattern of sum-rate loss. To address both issues, we develop a complex-valued E2E framework based on a variant minimum mean square error (variant-MMSE) criterion, where the digital precoder is eliminated in closed form via Karush-Kuhn-Tucker (KKT) conditions so that analog learning is trained with a stable objective. The network employs a grouped complex-convolution sensing front-end for uplink (UL) measurements, a shared complex multi-layer perceptron (MLP) for per-user feature extraction, and a merged constant-modulus head to output the analog precoder. In the indirect mode, the network designs hybrid beamformers from estimated channel state information (CSI). In the direct mode where explicit CSI is unavailable, the network learns the sensing operator and the analog mapping from short pilots, after which additional pilots estimate the equivalent channel and enable a KKT closed-form digital precoder. Simulations show that the indirect mode approaches the performance of iterative variant-MMSE optimization with a complexity reduction proportional to the antenna number. In the direct mode, the proposed method improves spectral efficiency over sparse-recovery pipelines and recent deep learning baselines under the same pilot budget.

Integrated Channel Estimation and Sensing for Near-Field ELAA Systems

In this paper, we study the problem of uplink channel estimation for near-filed orthogonal frequency division multiplexing (OFDM) systems, where a base station (BS), equipped with an extremely large-scale antenna array (ELAA), serves multiple users over the same time-frequency resource block. A non-orthogonal pilot transmission scheme is considered to accommodate a larger number of users that can be supported by ELAA systems without incurring an excessive amount of training overhead. To facilitate efficient multi-user channel estimation, we express the received signal as a third-order low-rank tensor, which admits a canonical polyadic decomposition (CPD) model for line-of-sight (LoS) scenarios and a block term decomposition (BTD) model for non-line-of-sight (NLoS) scenarios. An alternating least squares (ALS) algorithm and a non-linear least squares (NLS) algorithm are employed to perform CPD and BTD, respectively. Channel parameters are then efficiently extracted from the recovered factor matrices. By exploiting the geometry of the propagation paths in the estimated channel, users' positions can be precisely determined in LoS scenarios. Moreover, our uniqueness analysis shows that the proposed tensor-based joint multi-user channel estimation framework is effective even when the number of pilot symbols is much smaller than the number of users, revealing its potential in training overhead reduction. Simulation results demonstrate that the proposed method achieves markedly higher channel estimation accuracy than compressed sensing (CS)-based approaches.

Movable Antenna-Enhanced Near-Field Flexible Beamforming: Performance Analysis and Optimization

As an emerging wireless communication technology, movable antennas (MAs) offer the ability to adjust the spatial correlation of steering vectors, enabling more flexible beamforming compared to fixed-position antennas (FPAs). In this paper, we investigate the use of MAs for two typical near-field beamforming scenarios: beam nulling and multi-beam forming. In the first scenario, we aim to jointly optimize the positions of multiple MAs and the beamforming vector to maximize the beam gain toward a desired direction while nulling interference toward multiple undesired directions. In the second scenario, the objective is to maximize the minimum beam gain among all the above directions. However, both problems are non-convex and challenging to solve optimally. To gain insights, we first analyze several special cases and show that, with proper positioning of the MAs, directing the beam toward a specific direction can lead to nulls or full gains in other directions in the two scenarios, respectively. For the general cases, we propose a discrete sampling method and an alternating optimization algorithm to obtain high-quality suboptimal solutions to the two formulated problems. Furthermore, considering the practical limitations in antenna positioning accuracy, we analyze the impact of position errors on the performance of the optimized beamforming and MA positions, by introducing a Taylor series approximation for the near-field beam gain at each target. Numerical results validate our theoretical findings and demonstrate the effectiveness of our proposed algorithms.

Movable Antenna Enhanced Multi-Region Beam Coverage: A Multi-Notch-Filter-Inspired Design

Movable antenna (MA) has emerged as a promising technology to enhance wireless communication performance by exploiting the new degree of freedom (DoF) via antenna position optimization. In this letter, we investigate the MA-enhanced wide beam coverage over multiple subregions in the spatial domain. Specifically, we aim to maximize the minimum beam gain over the desired subregions by jointly optimizing the transmit beamforming and antenna position vector (APV). Although this problem is non-convex, we propose an efficient algorithm to solve it by leveraging the similarity between the considered multi-region coverage and classical multi-notch filter (MNF) design. In particular, we construct a spatial MNF-based transmit beamforming vector by assuming a continuous amplitude and phase-shift profile within the antenna movement region. Based on this continuous profile, we propose a sequential update algorithm to select an optimal subset of MA positions for multi-region coverage, jointly with a Gibbs sampling (GS) procedure to avoid undesired local optimum. Numerical results show that our proposed algorithm can significantly outperform conventional fixed position antennas (FPAs) and achieve a comparable performance to the alternating optimization (AO) algorithm with dramatically lower complexity.