Energy-Efficient Velocity Profile Optimization for Movable Antenna-Enabled Sensing Systems

Movable antennas (MAs) enable the reconfiguration of array geometry within a bounded region to exploit sub-wavelength spatial degrees of freedom in wireless communication and sensing systems. However, most prior research has predominantly focused on the communication and sensing performance, overlooking the mechanical power consumption inherent in antenna movement. To bridge this gap, this paper investigates a velocity profile optimization framework for MA-assisted direction-of-arrival (DoA) estimation, explicitly balancing sensing accuracy with mechanical energy consumption of MAs. We first establish a Newtonian-based mechanical energy model, and formulate a functional optimization problem for sensing energy efficiency (EE) maximization. By applying the calculus of variations, this formulation is transformed into an infinite-dimensional problem defined by the Euler-Lagrange equation. To solve it, we propose a spectral discretization framework based on the Galerkin method, which expands the velocity profile over a sinusoidal basis. In the regime where energy consumption is dominated by linear damping, we prove that the optimal velocity profile follows a closed-form sinusoidal shape. For more general scenarios involving strong nonlinear aerodynamic drag, we leverage the Markov-Lukács theorem to transform the kinematic constraints into strictly convex sum-of-squares (SOS) conditions. Consequently, the infinite-dimensional problem is reformulated as a tractable finite-dimensional nonlinear algebraic system, which is solved by a two-layer algorithm combining Dinkelbach's method with successive convex approximation (SCA). Numerical results demonstrate that our optimized velocity profile significantly outperforms baselines in terms of EE across various system configurations. Insights into the optimized velocity profiles and practical design guidelines are also provided.

A Unified Codebook Design for Curvature-Reconfigurable Apertures: Seamless Near to Far Field Coverage

Beam training for extremely large-scale arrays with curvature-reconfigurable apertures (CuRAs) faces the critical challenge of severe, geometry-dependent angle-range coupling. While most existing designs compartmentalize near field and far field scenarios, we propose a unified, distance-adaptive hierarchical codebook framework for 1-D and 2-D CuRAs that seamlessly bridges both propagation regimes. Under a spherical-wave model, we first characterize the beamforming-gain correlation in a polar angular domain, deriving an angle-dependent angular sampling rule to capture the varying curvature. To achieve full-range coverage, we introduce a direction-dependent effective Rayleigh distance (ERD) as a soft boundary to gate the range sampling. Crucially, by sampling uniformly in the reciprocal-range domain, the proposed codebook provides precise, dense focusing within the ERD and automatically degenerates into sparse, angle-only steering beyond it. This mechanism eliminates the need for hard mode-switching between near- and far-field operations. Simulation results demonstrate that our unified design consistently outperforms representative baselines in spectral efficiency and alignment accuracy, offering a comprehensive solution for full-range CuRA communications.

Robust and Secure Near-Field Communication via Curved Caustic Beams

Near-field beamfocusing with extremely large aperture arrays can effectively enhance physical layer security. Nevertheless, even small estimation errors of the eavesdropper's location may cause a pronounced focal shift, resulting in a severe degradation of the secrecy rate. In this letter, we propose a physics-informed robust beamforming strategy that leverages the electromagnetic (EM) caustic effect for near-field physical layer security provisioning, which can be implemented via phase shifts only. Specifically, we partition the transmit array into caustic and focusing subarrays to simultaneously bypass the potential eavesdropping region and illuminate the legitimate user, thereby significantly improving the robustness against the localization error of eavesdroppers. Moreover, by leveraging the connection between the phase gradient and the EM wave departing angle, we derive the corresponding piece-wise closed-form array phase profile for the subarrays. Simulation results demonstrate that the proposed scheme achieves up to an 80% reduction of the worst-case eavesdropping rate for a localization error of 0.25 m, highlighting its superiority for providing robust and secure communication.

Optimal Movable Antenna Placement for Near-Field Wireless Sensing

Movable antennas (MAs) have emerged as a promising technology for wireless sensing by reconfiguring antenna positions to exploit additional spatial degrees of freedom (DoFs). This paper investigates a robust movable antenna placement strategy for near-field wireless sensing to minimize the worst-case squared position error bound (SPEB). By temporarily relaxing the minimum inter-element spacing constraint, we first establish the optimality of centro-symmetric antenna position distribution, which simplifies the identification of the worst-case source, locating it at the array broadside on the Rayleigh boundary. Moreover, by leveraging moment-based analysis with the Richter-Tchakaloff theorem, we derive a closed-form optimal solution with three points supported on the center and two edges of the array. Guided by this structural insight, we finally develop an efficient three-point discrete deployment strategy to ensure the minimum inter-element spacing. Simulations demonstrate that the proposed design consistently outperforms conventional fixed antenna arrays and matches the exhaustive search benchmark at negligible computational complexity.

MIMO Beam Map Reconstruction via Toeplitz-Structured Matrix-Vector Tensor Decomposition

As wireless networks progress toward sixthgeneration (6G), understanding the spatial distribution of directional beam coverage becomes increasingly important for beam management and link optimization. Multiple-input multipleoutput (MIMO) beam map provides such spatial awareness, yet accurate construction under sparse measurements remains difficult due to incomplete spatial coverage and strong angular variations. This paper presents a tensor decomposition approach for reconstructing MIMO beam map from limited measurements. By transforming measurements from a Cartesian coordinate system into a polar coordinate system, we uncover a matrix-vector outer-product structure associated with different propagation conditions. Specifically, we mathematically demonstrate that the matrix factor, representing beam-space gain, exhibits an intrinsic Toeplitz structure due to the shift-invariant nature of array responses, and the vector factor captures distance-dependent attenuation. Leveraging these structural priors, we formulate a regularized tensor decomposition problem to jointly reconstruct line-of-sight (LOS), reflection, and obstruction propagation conditions. Simulation results confirm that the proposed method significantly enhances data efficiency, achieving a normalized mean square error (NMSE) reduction of over 20% compared to state-of-the-art baselines, even under sparse sampling regimes.

Near-Field Communication with Massive Movable Antennas: An Electrostatic Equilibrium Perspective

Recent advancements in large-scale position-reconfigurable antennas have opened up new dimensions to effectively utilize the spatial degrees of freedom (DoFs) of wireless channels. However, the deployment of existing antenna placement schemes is primarily hindered by their limited scalability and frequently overlooked near-field effects in large-scale antenna systems. In this paper, we propose a novel antenna placement approach tailored for near-field massive multiple-input multiple-output systems, which effectively exploits the spatial DoFs to enhance spectral efficiency. For that purpose, we first reformulate the antenna placement problem in the angular domain, resulting in a weighted Fekete problem. We then derive the optimality condition and reveal that the {optimal} antenna placement is in principle an electrostatic equilibrium problem. To further reduce the computational complexity of numerical optimization, we propose an ordinary differential equation (ODE)-based framework to efficiently solve the equilibrium problem. In particular, the optimal antenna positions are characterized by the roots of the polynomial solutions to specific ODEs in the normalized angular domain. By simply adopting a two-step eigenvalue decomposition (EVD) approach, the optimal antenna positions can be efficiently obtained. Furthermore, we perform an asymptotic analysis when the antenna size tends to infinity, which yields a closed-form solution. Simulation results demonstrate that the proposed scheme efficiently harnesses the spatial DoFs of near-field channels with prominent gains in spectral efficiency and maintains robustness against system parameter mismatches. In addition, the derived asymptotic closed-form {solution} closely approaches the theoretical optimum across a wide range of practical scenarios.

Detection in Bistatic ISAC with Deterministic Sensing and Gaussian Information Signals

Integrated sensing and communications (ISAC) is a disruptive technology enabling future sixth-generation (6G) networks. This paper investigates target detection in a bistatic ISAC system, in which the base station (BS) transmits superimposed ISAC signals comprising both Gaussian information-bearing and deterministic sensing components to simultaneously provide communication and sensing functionalities. First, we develop a Neyman-Pearson (NP)-based detector that effectively utilizes both the deterministic sensing and random communication signals. Closed-form analysis reveals that both signal components contribute to improving the overall detection performance. Subsequently, we optimize the BS transmit beamforming to maximize the detection probability, subject to a minimum signal-to-interference-plus-noise ratio (SINR) constraint for the communication user (CU) and a total transmit power budget at the BS. The resulting non-convex beamforming optimization problem is addressed via semi-definite relaxation (SDR) and successive convex approximation (SCA) techniques. Simulation results demonstrate the superiority of the proposed NP-based detector, which leverages both types of signals, over benchmark schemes that treat information signals as interference. They also reveal that a higher communication-rate threshold directs more transmit power to Gaussian information-bearing signals, thereby diminishing deterministic-signal power and weakening detection performance.

Structure-Aware Near-Field Radio Map Recovery via RBF-Assisted Matrix Completion

This paper proposes a novel structure-aware matrix completion framework assisted by radial basis function (RBF) interpolation for near-field radio map construction in extremely large multiple-input multiple-output (XL-MIMO) systems. Unlike the far-field scenario, near-field wavefronts exhibit strong dependencies on both angle and distance due to spherical wave propagation, leading to complicated variations in received signal strength (RSS). To effectively capture the intricate spatial variations structure inherent in near-field environments, a regularized RBF interpolation method is developed to enhance radio map reconstruction accuracy. Leveraging theoretical insights from interpolation error analysis of RBF, an inverse μ-law-inspired nonuniform sampling strategy is introduced to allocate measurements adaptively, emphasizing regions with rapid RSS variations near the transmitter. To further exploit the global low-rank structure in the near-field radio map, we integrate RBF interpolation with nuclear norm minimization (NNM)-based matrix completion. A robust Huberized leave-one-out cross-validation (LOOCV) scheme is then proposed for adaptive selection of the tolerance parameter, facilitating optimal fusion between RBF interpolation and matrix completion. The integration of local variation structure modeling via RBF interpolation and global low-rank structure exploitation via matrix completion yields a structure-aware framework that substantially improves the accuracy of near-field radio map reconstruction. Extensive simulations demonstrate that the proposed approach achieves over 10% improvement in normalized mean squared error (NMSE) compared to standard interpolation and matrix completion methods under varying sampling densities and shadowing conditions.

Flow Matching-Based Active Learning for Radio Map Construction with Low-Altitude UAVs

The employment of unmanned aerial vehicles (UAVs) in the lowaltitude economy necessitates precise and real-time radio maps for reliable communication and safe navigation. However, constructing such maps is hindered by the infeasibility of exhaustive measurements due to UAVs' limited flight endurance. To address this, we propose a novel active learning framework for low-altitude radio map construction based on limited measurements. First, a Plug-and-Play (PnP)-refined flow matching algorithm is introduced, which leverages flow matching as a powerful generative prior within a PnP scheme to reconstruct high-fidelity radio maps. Second, the generative nature of flow matching is exploited to quantify uncertainty by generating an ensemble of radio maps and computing the location-wise variance. The resulting uncertainty map guides a multi-objective candidate selection and then a trajectory is planned via utility-aware path search (UAPS), directing the UAV to the most informative locations while taking travel costs into account. Simulation results demonstrate that our method significantly outperforms the baselines, achieving more than a 70% reduction in normalized mean squared error (NMSE).

CRB-Rate Tradeoff for Bistatic ISAC with Gaussian Information and Deterministic Sensing Signals

In this paper, we investigate a bistatic integrated sensing and communications (ISAC) system, consisting of a multi-antenna base station (BS), a multi-antenna sensing receiver, a single-antenna communication user (CU), and a point target to be sensed. Specifically, the BS transmits a superposition of Gaussian information and deterministic sensing signals. The BS aims to deliver information symbols to the CU, while the sensing receiver aims to estimate the target's direction-of-arrival (DoA) with respect to the sensing receiver by processing the echo signals. For the sensing receiver, we assume that only the sequences of the deterministic sensing signals and the covariance matrix of the information signals are perfectly known, whereas the specific realizations of the information signals remain unavailable. Under this setup, we first derive the corresponding Cram\'er-Rao bounds (CRBs) for DoA estimation and propose practical estimators to accurately estimate the target's DoA. Subsequently, we formulate the transmit beamforming design as an optimization problem aiming to minimize the CRB, subject to a minimum signal-to-interference-plus-noise ratio (SINR) requirement at the CU and a maximum transmit power constraint at the BS. When the BS employs only Gaussian information signals, the resulting beamforming optimization problem is convex, enabling the derivation of an optimal solution. In contrast, when both Gaussian information and deterministic sensing signals are transmitted, the resulting problem is non-convex and a locally optimal solution is acquired by exploiting successive convex approximation (SCA). Finally, numerical results demonstrate that employing Gaussian information signals leads to a notable performance degradation for target sensing and the proposed transmit beamforming design achieves a superior ISAC performance boundary compared with various benchmark schemes.