Physics-Informed Spatial-Temporal Transformer for Terahertz Near-Field Beam Tracking

Terahertz (THz) ultra-massive multiple-input multiple-output (UM-MIMO) promises ultra-high throughput, while its highly directional beams demand rapid and accurate beam tracking driven by precise user-state estimation. Moreover, large array apertures at high frequencies induce near-field propagation effects, where far-field modeling becomes inaccurate and near-field parametric channel estimation is costly. Bypassing near-field codebook, PAST-TT is proposed to bridge near-field tracking with low-overhead far-field codebook probing by exploiting parallax, amplified by widely spaced subarrays. With comb-type frequency-division multiplexing pilots, each subarray yields frequency-affine phase signatures whose frequency and temporal increments encode propagation delay and its variation between frames. Building on these signatures, a Parallax-Aware Spatial Transformer (PAST) compresses them and outputs per-frame position estimates with token reliability to downweight bad frames, regularized by a physics-in-the-loop consistency loss. A causal Temporal Transformer (TT) then performs reliability-aware filtering and prediction over a sliding window to initialize the beam of the next frame. Acting on short token sequences, PAST-TT avoids a monolithic spatial-temporal network over raw pilots, which keeps the model lightweight with a critical path latency of 0.61 ms. Simulations show that at 15 dB signal-to-noise ratio, PAST achieves 7.81 mm distance RMSE and 0.0588° angle RMSE. Even with a bad-frame rate of 0.1, TT reduces the distance and angle prediction RMSE by 23.1% and 32.8% compared with the best competing tracker.

Near-field Boundary Distance in mmWave and THz Communications with Misaligned Antenna Arrays

Wireless communications in the millimeter wave (mmWave) and terahertz (THz) spectrum allow harnessing large frequency bands, thus achieving ultra-high data rates. However, the inherently short wavelengths of mmWave and THz signals lead to an extended radiative near-field region, where certain canonical far-field assumptions fail. Most prior works aimed to characterize this radiative near-field region either do not consider antenna arrays on both communicating nodes or, if they do, assume perfect alignment between the arrays. However, such assumptions break down in many realistic deployments, where both sides must employ large-scale mmWave/THz antenna arrays to maintain the desired communication range, while perfect antenna alignment cannot be guaranteed particularly under nodes mobility. In this work, a generalized mathematical framework is presented to characterize the radiative near-field distance in directional mmWave and THz communication systems under various realistic array rotations and misalignments. With the use of the developed framework, compact closed-form expressions are derived for the near-field boundary distance in a wide range of antenna configurations, including array-to-array and array-to-point setups, considering both linear and planar arrays. Our numerical study reveals that the presence of antenna misalignment may significantly adjust the boundaries of the near-field region in mmWave and THz communication systems.

Airy Beam Engineering in Near-field Communications: A Tractable Closed-Form Analysis in the Terahertz Band

Terahertz (THz) communication can offer terabit-per-second rates in future wireless systems, thanks to the ultra-wide bandwidths, but require large antenna arrays. As antenna apertures expand and we enter the near-field scenarios, the conventional binary classification of communication links as either Line-of-Sight (LoS) or Non-Line-of-Sight (NLoS) becomes insufficient. Instead, quasi-LoS scenarios, where the LoS path is partially obstructed, are increasingly prevalent, posing significant challenges for traditional LoS focusing and steering beams. The Airy beam serves as a promising alternative, utilizing its non-diffracting and curved trajectory properties to mitigate such blockages. However, while existing electromagnetics literature primarily explores their physical patterns without practical generation schemes, recent communication-oriented designs predominantly rely on learning-based frameworks lacking interpretable closed-form solutions. To address this issue, this paper investigates a closed-form Airy beam design to efficiently synthesize Airy beam phase profiles based on the positions of the transceivers and obstacles. Specifically, rigorous analytical derivations of the electric field and trajectory are presented to establish a deterministic closed-form design for ULA Airy beamforming. Leveraging 3D wavefront separability, this framework is extended to uniform planar arrays (UPAs) with two operation modes: the hybrid focusing-Airy mode and the dual Airy mode. Simulation results verify the effectiveness of our derived trajectory equations and demonstrate that the proposed closed-form design significantly outperforms conventional beamforming schemes in quasi-LoS scenarios. Furthermore, the proposed method achieves performance comparable to exhaustive numerical searches with low computational complexity and enhanced physical interpretability.

Joint and Streamwise Distributed MIMO Satellite Communications with Multi-Antenna Ground Users

We consider a low Earth orbit downlink communication, where multiple satellites jointly serve multi-antenna ground users, transmitting multiple spatial streams per user. Using a line-of-sight-dominant satellite channel model with statistical channel state information, including angular information and large-scale fading, we study two distributed transmission modes with different fronthaul requirements. First, for joint transmission, where all satellites transmit all user streams, we formulate a sum spectral efficiency (SE) maximization problem under general convex power constraints and address the intractability of the exact ergodic SE expression by adopting a tractable approximation. Exploiting the equivalence between sum SE maximization and weighted sum mean square error minimization, we derive a novel iterative transceiver design. Second, to reduce fronthaul load, we propose streamwise transmission, where each stream is sent by a single satellite, and develop an eigenmode-based stream-satellite association using participation factors and a maximum-weight bipartite matching problem solved by the Hungarian algorithm. Numerical simulations evaluate the validity of the SE approximation, demonstrate conditions under which streamwise transmission performs nearly optimally or trades SE for lower overhead, highlight the impact of stream/user loading, and show substantial performance gains over conventional benchmarks.

A Primer on Evolutionary Frameworks for Near-Field Multi-Source Localization

This paper introduces a novel class of model-driven evolutionary frameworks for near-field multi-source localization, addressing the major limitations of grid-based subspace methods such as MUSIC and data-dependent deep learning approaches. To this end, we develop two complementary evolutionary localization frameworks that operate directly on the continuous spherical-wave signal model and support arbitrary array geometries without requiring labeled data, discretized angle--range grids, or architectural constraints. The first framework, termed NEar-field MultimOdal DE (NEMO-DE) associates each individual in the evolutionary population to a single source and optimizes a residual least-squares objective in a sequential manner, updating the data residual and enforcing spatial separation to estimate multiple source locations. To overcome the limitation of NEMO-DE under large power imbalances among the sources, we propose the second framework, named NEar-field Eigen-subspace Fitting DE (NEEF-DE), which jointly encodes all source locations and minimizes a subspace-fitting criterion that aligns a model-based array response subspace with the received signal subspace. Although the proposed frameworks are algorithm-agnostic and compatible with various evolutionary optimizers, differential evolution (DE) is adopted in this work as a representative search strategy due to its simplicity, robustness, and strong empirical performance. We provide extensive numerical experiments to evaluate the performance of the proposed frameworks under different system configurations. This work establishes evolutionary computation as a powerful and flexible paradigm for model-based near-field localization, paving the way for future innovations in this domain.

Quantized Precoding for Maximizing Sum Rate in MU-MIMO Systems with Constrained Fronthaul

This paper studies a downlink multi-user multiple-input multiple-output (MU-MIMO) system, where the precoding matrix is computed at a baseband unit (BBU) and then transmitted to the remote antenna array over a limited-capacity digital fronthaul. The limited bit resolution of the fronthaul introduces quantization effects that are explicitly modeled. We propose a novel sum rate maximization framework that directly incorporates the quantizer's constraints into the precoding design. The resulting maximization problem, a non-convex mixed-integer program, is addressed using a new iterative algorithm inspired by the weighted minimum mean square error (WMMSE) methodology. The precoding optimization subproblem is reformulated as an integer least-squares problem and solved using a novel sphere decoding (SD) algorithm. Additionally, a low-complexity expectation propagation (EP)-based method is introduced to enable the practical implementation of quantized precoding in MU-massive MIMO (MU-mMIMO) systems. Furthermore, numerical evaluations demonstrate that the proposed precoding schemes outperform conventional approaches that optimize infinite-resolution precoding followed by element-wise quantization. We also propose a heuristic quantization-aware precoding method with comparable complexity to the baseline but superior performance. In particular, the EP-based approach offers near-optimal performance with substantial complexity reduction, making it well-suited for real-time MU-mMIMO applications.

Analyzing URA Geometry for Enhanced Near-Field Beamfocusing and Spatial Degrees of Freedom

With the deployment of large antenna arrays at high-frequency bands, future wireless communication systems are likely to operate in the radiative near-field. Unlike far-field beam steering, near-field beams can be focused on a spatial region with a finite depth, enabling spatial multiplexing in the range dimension. Moreover, in the line-of-sight MIMO near-field, multiple spatial degrees of freedom (DoF) are accessible, akin to a scattering- rich environment. In this paper, we derive the beamdepth for a generalized uniform rectangular array (URA) and investigate how the array geometry influences near-field beamdepth and its limits. We define the effective beamfocusing Rayleigh distance (EBRD), to present a near-field boundary with respect to beamfocusing and spatial multiplexing gains for the generalized URA. Our results demonstrate that under a fixed element count constraint, the array geometry has a strong impact on beamdepth, whereas this effect diminishes under a fixed aperture length constraint. Moreover, compared to uniform square arrays, elongated configurations such as uniform linear arrays (ULAs) yield narrower beamdepth and extend the effective near-field region defined by the EBRD. Building on these insights, we design a polar codebook for compressed-sensing-based channel estimation that leverages our findings. Simulation results show that the proposed polar codebook achieves a 2 dB NMSE improvement over state-of-the-art methods. Additionally, we present an analytical expression to quantify the effective spatial DoF in the near-field, revealing that they are also constrained by the EBRD. Notably, the maximum spatial DoF is achieved with a ULA configuration, outperforming a square URA in this regard.

Sparse Array Design for Near-Field MU-MIMO: Reconfigurable Array Thinning Approach

Future wireless networks, deploying thousands of antenna elements, may operate in the radiative near-field (NF), enabling spatial multiplexing across both angle and range domains. Sparse arrays have the potential to achieve comparable performance with fewer antenna elements. However, fixed sparse array designs are generally suboptimal under dynamic user distributions, while movable antenna architectures rely on mechanically reconfigurable elements, introducing latency and increased hardware complexity. To address these limitations, we propose a reconfigurable array thinning approach that selectively activates a subset of antennas to form a flexible sparse array design without physical repositioning. We first analyze grating lobes for uniform sparse arrays in the angle and range domains, showing their absence along the range dimension. Based on the analysis, we develop two particle swarm optimization-based strategies: a grating-lobe-based thinned array (GTA) for grating- lobe suppression and a sum-rate-based thinned array (STA) for multiuser sum-rate maximization. Simulation results demonstrate that GTA outperforms conventional uniform sparse arrays, while STA achieves performance comparable to movable antennas, thereby offering a practical and efficient array deployment strategy without the associated mechanical complexity.

Statistics Approximation-Enabled Distributed Beamforming for Cell-Free Massive MIMO

We study a distributed beamforming approach for cell-free massive multiple-input multiple-output networks, referred to as Global Statistics \& Local Instantaneous information-based minimum mean-square error (GSLI-MMSE). The scenario with multi-antenna access points (APs) is considered over three different channel models: correlated Rician fading with fixed or random line-of-sight (LoS) phase-shifts, and correlated Rayleigh fading. With the aid of matrix inversion derivations, we can construct the conventional MMSE combining from the perspective of each AP, where global instantaneous information is involved. Then, for an arbitrary AP, we apply the statistics approximation methodology to approximate instantaneous terms related to other APs by channel statistics to construct the distributed combining scheme at each AP with local instantaneous information and global statistics. With the aid of uplink-downlink duality, we derive the respective GSLI-MMSE precoding schemes. Numerical results showcase that the proposed GSLI-MMSE scheme demonstrates performance comparable to the optimal centralized MMSE scheme, under the stable LoS conditions, e.g., with static users having Rician fading with a fixed LoS path.

Cell-Free MIMO in Space: Cooperative Satellite Transmission with Multi-Antenna Ground Users

This paper develops a multi-user downlink communication framework for distributed low Earth orbit satellite networks serving ground users equipped with multiple antennas. Building upon the concept of cell-free multiple-input multiple-output in terrestrial networks, we propose a coordinated transmission scheme where multiple satellites jointly transmit spatially multiplexed data streams to each user. Using a new approximate achievable rate expression, we formulate a sum rate maximization problem under per-satellite and per-antenna power constraints and use the classical equivalence between sum rate maximization and mean square error minimization to optimize the satellites' precoding matrices using statistical channel state information. We numerically examine the performance of the proposed scheme in different settings and validate its effectiveness by comparing it against traditional precoding designs.