Search arXiv⌕ Search

SEARCH · Search arXiv

Results for “math.SP”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

1,005 records · Page 2Linked to original sources
arXiv2026

Grassmannian-Coded Beamforming for mmWave Channel Sensing with Unknown Complex Path Gain

This paper introduces a subspace-coding perspective to millimeter-wave channel sensing with a single RF chain when the complex channel gain is unknown. We show that in this case, candidate directions-of-arrival (DoAs) map naturally to subspaces through their beamspace responses, revealing an intrinsic Grassmannian geometry. This motivates beamspace Grassmannian codes (BGCs), designed to reduce DoA error by maximizing the minimum subspace distance of the joint beamformer-array response. We identify two regimes: one in which existing Grassmannian packings are exactly realizable as BGCs when the angular grid matches the array size, and another in which realizability for finer grids is constrained by the array geometry. Our analysis establishes the joint roles of subspace distance and beamforming gain in sensing performance and motivates two complementary beamformer designs. Without prior DoA information, we develop spatially isotropic beamformers based on algebraic Grassmannian packings and modulation-based channel codes. With a known DoA region of interest, we design convolutional beamspaces that combine directional gain with favorable subspace distance. Numerical results demonstrate robust BGC performance for both on-grid and off-grid DoAs, supporting the effectiveness of the proposed Grassmannian framework for mmWave channel sensing.

eess.SP↗
arXiv2026

Operational Regimes in Non-Convex Optimization: A Multiplier-Based Taxonomy

This paper introduces a structural taxonomy for constrained non-convex optimization based on the signature of Lagrange multipliers at KKT stationary points. Leveraging a unified game-theoretic interpretation of eight classical algorithm families--including block coordinate descent, ADMM, generalized Benders decomposition, successive convex approximation, interior-point methods, mirror descent, Frank-Wolfe, and Riemannian gradient descent--we show that the normalized multiplier vector carries an algorithm-independent structural fingerprint. Four scale-free shape features of this vector partition the dual space into five operational regimes: Unconstrained, Resource-Limited, Saturation, Strongly-Coupled, and Hybrid. We establish four structural theorems characterizing the partition: invariance under natural KKT symmetries, local stability under data perturbation with explicit Lipschitz margins from Robinson's strong regularity, codimension-one regime transitions, and the topological identification of the Hybrid regime as the Lebesgue-null boundary of the core regimes. A linear-time classifier is proposed with provable guarantees on correctness, iteration stabilization, sample complexity, and online tracking under data drift. Numerical experiments on 104 mixed-integer nonlinear programs and a downlink beamforming instance validate the theoretical predictions. The framework provides a foundational tool for regime-aware algorithm design and robustness analysis in non-convex optimization.

math.OC↗
arXiv2026

Differential Space-Time Block Coding for Phase-Unsynchronized Cell-Free MIMO Downlink

In the downlink of CF-mMIMO systems, spectral efficiency gains critically rely on joint coherent transmission, as all APs must align their transmitted signals in phase at the UE. Achieving such phase alignment is challenging, as it requires tight synchronization among geographically distributed APs. In this paper, we address this issue by introducing a DSTBC approach that bypasses the need for AP phase synchronization. We first provide analytic bounds to the achievable spectral efficiency of CF-mMIMO with phase-unsynchronized APs. Then, we propose a DSTBC-based transmission scheme tailored to CF-mMIMO, which operates without CSI and phase synchronization among the APs. We derive a closed-form expression for the resulting SINR, enabling quantitative comparisons among different DSTBC schemes. Numerical simulations confirm that phase misalignments can significantly impair system performance. In contrast, the proposed DSTBC scheme can mitigate these effects, achieving performance comparable to that of fully synchronized systems. However, when more than two APs jointly serve a UE, the code rate of DSTBC schemes can limit their SE gains. Hence, we also investigate DQO-STBC schemes that achieve full code rate by relaxing the orthogonality constraints.

cs.IT↗
arXiv2026

Learning the Channel Gain from Anywhere to Anywhere via Cross-environment Transformer Estimators

Channel-gain maps provide the channel gain between any two locations in a geographical region. They find numerous applications, from resource allocation and interference control to path planning for autonomous vehicles. Channel-gain map estimation (CGME) is considerably more challenging than conventional radio map estimation (RME) because channel-gain maps are functions over a 6-dimensional input space. This calls for specialized methods, which currently rely on the (inaccurate) radio tomographic model or require a prohibitively large number of measurements since they do not exploit any spatial structure. This paper overcomes this issue by leveraging spatial patterns that channel-gain maps exhibit across environments, as dictated by the laws of physics and typical environmental characteristics (e.g. building materials and layouts). Adopting a metalearning perspective, a transformer-based estimator is proposed to implicitly learn this common structure from measurements collected in multiple environments. This enables CGME in new environments from significantly fewer measurements (five times less in our experiments). To maximize learning efficiency, the transformer is composed with a feature map that enforces the invariances of CGME, such as those following from reciprocity. Numerical experiments corroborate the merits of the proposed estimator relative to existing methods.

eess.SP↗
arXiv2026

Semantic Freshness Optimal Sampling and Transmission for Gossiping Receivers

We study the optimal joint sampling and transmission policy for a transmitter communicating with two gossiping receivers that share information with each other, with the objective of tracking a source under the Version Age of Information (VAoI) metric. The transmitter can observe source-version changes, but it has to pay a sampling cost to get the current source information content. Similarly, it can communicate with a receiver by paying a transmission cost. Gossiping enables local information exchange and is able to reduce costly direct transmissions. With imperfect communication links, we formulate an infinite-horizon average-cost Markov Decision Process (MDP) to jointly minimize receiver VAoI, sampling cost, and transmission cost. Using Relative Value Iteration (RVI), we evaluate the optimal policy and establish several properties of its structure. We prove that sampling has a threshold structure in the transmitter VAoI. Among direct transmissions, it is optimal to serve the older receiver. We further characterize the transmit or idle decision through the receiver VAoI difference. Our analysis shows that link reliability and receiver VAoI imbalance have a significant effect on the optimal policy structure. Numerical results verify the structural properties and demonstrate the performance gains of the optimal policy over multiple baselines.

cs.IT↗
arXiv2026

On the Impact of Site-Specific Training for a Real-World 5G NR System

Site-specific training can improve wireless receiver performance without increasing computational complexity. However, real-world results have so far focused on fully trainable neural receivers and single-layer transmissions. We study site-specific finetuning of three receiver architectures: fully trainable neural, model-driven neural, and model-based. We train and evaluate these receivers using new measurements from a standard-compliant 5G NR testbed at ETH Zurich with dual-layer uplink transmission, including measurement campaigns conducted more than six months apart. Our results show that site-specific finetuning (i) substantially improves fully trainable and model-driven neural receivers, while resulting in only marginal gains for the less tunable model-based receiver; (ii) enables a single neural receiver jointly finetuned for single- and dual-layer transmission to closely match receivers finetuned separately for each configuration; and (iii) remains effective across measurement campaigns separated by more than six months. We also investigate site-specific linear minimum mean-square error channel estimation using covariance matrices estimated from either synthetic channels or site-specific measurements. When combined with iterative detection and decoding, site-specific channel estimation achieves the lowest error rate observed in our datasets. Our finetuning code and measurement datasets are publicly available at https://github.com/IIP-Group/site_specific_training

cs.IT↗
arXiv2026

Direct Satellite-to-Device Communications: From Cooperative Task Offloading to Non-Cooperative Access Monitoring

Direct satellite-to-device (DS2D) communication is emerging as a transformative paradigm for extending ubiquitous connectivity and edge computing capabilities to remote and underserved regions within 6G non-terrestrial networks. However, practical deployment faces dual critical challenges: i) dynamic satellite channel conditions (e.g., severe Doppler shifts, fast fading) and constrained satellite computing resources in cooperative scenarios; and ii) unauthorized satellite access introduces significant spectrum security threats in non-cooperative scenarios. To address these challenges, we propose a versatile DS2D system that supports cooperative task offloading and non-cooperative access monitoring. For cooperative DS2D communications, we integrate a channel estimation module with a dueling double deep Q-network (D3QN) to dynamically optimize task offloading strategy. For non-cooperative DS2D communications, we propose Transformer-based models to enable blind signal detection and automatic modulation classification (AMC). Simulation results show that: 1) The D3QN algorithm reduces average latency by up to 225\% compared to static association policies. 2) Our signal detection model achieves an average presence detection probability of 90.5\% for DS2D signals. 3) The proposed AMC algorithm achieves superior performance across different signal-to-noise ratios (SNRs), with a 9.4\% accuracy gain in low-SNR regimes compared to existing methods.

cs.IT↗
arXiv2026

A Unified Pulse-Shaped OFDM Framework for Chirp-Domain Waveforms: Continuous-Time Modeling and Practical I/O Analysis

A unified framework for chirp-domain waveforms, including orthogonal chirp division multiplexing (OCDM) and affine frequency division multiplexing (AFDM), is developed. Their continuous-time representations are shown to fall within the conventional Weyl-Heisenberg (WH) framework for multicarrier waveforms, with the root chirp as the prototype pulse. Since the root chirp has constant envelope and is transparent to subcarrier orthogonality, these waveforms can be further interpreted as pulse-shaped (PS) orthogonal frequency division multiplexing (OFDM) signals, whose power spectral density is derived analytically. The derived spectrum reveals that implementations based on the discrete affine Fourier transform rely on sub-Nyquist samples and exhibit frequency aliasing. We prove that the corresponding aliased chirps are only conditionally orthogonal, whereas sample-wise root-Nyquist pulse shaping of the discrete-time AFDM (DT-AFDM) sequence produces mutually orthogonal pulse-shaped chirps, resulting in the pulse-shaped AFDM (PS-AFDM) waveform. We then derive an exact waveform-level input-output (I/O) relation for PS-AFDM over delay-Doppler (DD) channels, showing that the effective channel at a practical receiver is generally not a superposition of pure path-wise DD components. Waveform simulations verify the derived relation to machine precision, while the conventional sequence-level I/O relation for DT-AFDM exhibits a substantial mismatch with waveform behavior for practical channels with continuous-valued delays.

cs.IT↗
arXiv2026

A Token/KV-Cache Communication Media Selection and Resource Allocation Strategy for Multi-Agent Collaboration

The convergence of large language models (LLMs) with 6G networks is fostering a paradigm of autonomous multi-agent cooperation, which in turn is expected to substantially increase east-west traffic. Although latent-space interaction mechanisms can enable more efficient collaboration than symbolic natural-language (NL) exchanges, prior work often abstracts away the associated communication overhead under practical wireless constraints. In embodied multi-agent settings, heterogeneous interaction media incur disparate inference and transmission costs, thereby inducing an inherent end-to-end (E2E) latency trade-off. To address this, we propose a joint design that integrates communication-media selection with wireless resource allocation. Through analytical characterization and simulation-based evaluation, we show that neither token-based transmission nor key-value (KV) cache-based transmission is uniformly optimal across operating regimes, as performance depends critically on system parameters such as available computational resources and channel conditions. Accordingly, we formulate a joint optimization problem aimed at minimizing the E2E latency of multi-agent collaboration and develop a low-complexity joint media selection and resource allocation (JMSRA) algorithm. Numerical results further confirm that, by adaptively coordinating the interaction media and bandwidth allocation over heterogeneous links, the proposed scheme achieves markedly reduced E2E latency relative to conventional NL-only and KV-cache-only baselines, enabling efficient and robust multi-agent collaboration in future wireless networks.

eess.SP↗
arXiv2026

AirFM-DDA: Air-Interface Foundation Model in the Delay-Doppler-Angle Domain for AI-Native 6G

The success of large foundation models is catalyzing a new paradigm for AI-native 6G network design: wireless foundation models for physical-layer design. However, existing models often operate on channel state information (CSI) in the spatial-temporal-frequency (STF) domain, where multipath components are superimposed and structurally entangled. This hinders the learning of a universal channel representation. Their reliance on global attention also incurs prohibitive overhead. In this paper, we propose AirFM-DDA, an Air-interface Foundation Model in the Delay-Doppler-Angle (DDA) domain. AirFM-DDA reparameterizes CSI into the DDA domain to resolve multipath components along physically meaningful axes and employs window-based attention with frame-structure-aware positional encoding. Extensive experiments demonstrate transferability across scenarios, tasks, datasets, and antenna configurations. For channel prediction and estimation, AirFM-DDA generalizes zero-shot to unseen cities, achieving average normalized mean-square error (NMSE) gains of 4.9-8.5 dB over the strongest baselines. With only 10% labeled data, it achieves average gains of 12.0 percentage points in Top-1 accuracy for beam prediction and 3.4 percentage points in F1 score for line-of-sight (LoS) identification. It further transfers across simulated datasets and adapts to measured data and different antenna arrays. Compared with global attention, window-based attention reduces training and inference costs by nearly an order of magnitude.

cs.LG↗
arXiv2026

Statistical Characterization and Block-EM Estimation of Frequency-Domain NSI for OFDM Systems in Bursty Impulsive Noise

Impulsive noise (IN), characterized by its high power and non-Gaussian distribution, poses a critical challenge in modern orthogonal frequency-division multiplexing (OFDM) systems, driven by the proliferation of electronic devices. Current IN mitigation techniques rely heavily on time-domain processing. These methods are applied before the discrete Fourier transform (DFT), introducing additional complexity, failing to align with OFDM's inherent frequency-domain processing flow, and risking the destruction of subcarrier orthogonality due to imperfect IN subtraction. To address these limitations, we propose a frequency-domain, block-based framework for mitigating IN. The statistical representation of IN in the frequency domain is first derived using a transformed Gaussian mixture model. Based on this model, we develop an optimal receiver that leverages perfect noise state information (NSI), thereby identifying scenarios in which NSI is critical. We then propose an unsupervised block-based expectation-maximization (EM) framework for NSI estimation and develop three variants for evaluation. These include a simple symbol-by-symbol variance-updated EM, a sequence-based transition-updated EM, and a MAP-based EM that exploits a sparsity-promoting prior to automatically prune the number of states. Our frequency-domain design operates after the DFT, seamlessly integrates with the OFDM processing chain, preserves subcarrier orthogonality, and leverages the known IN block structure to achieve substantial performance gains without the immense complexity of time-domain impulse reconstruction.

eess.SP↗
arXiv2026

MaskCode: Mask Transformer for Feedback-Assisted Coding With Linear Block Codes

Feedback-based coding schemes have demonstrated substantial performance gains over today's open-loop coding schemes. Unfortunately, these gains are usually achieved in idealized settings with perfect feedback. Over the last few years, machine learning-based schemes have been shown to be promising solutions for implementing feedback-based codes, particularly when combined with short-block-length open-loop error correcting codes (ECCs) in a concatenated coding structure. However, existing ML-based feedback schemes remain agnostic to the outer code's structure, potentially misallocating feedback resources on error patterns already correctable by the outer ECC. To address this, we propose MaskCode, a Transformer-based inner feedback code for concatenated coding systems, which explicitly incorporates structural knowledge of the outer linear block code into the inner feedback encoder design via two synergistic mechanisms: 1) a soft syndrome-based input that informs the encoder about potential parity constraint violations, and 2) a code-aware attention mask derived from the Tanner graph. We further show that end-to-end training with a differentiable belief propagation (BP) decoder offers no additional gain, as MaskCode's structure-aware design already internalizes the structural knowledge of the outer code; in fact, backpropagation through the iterative BP decoder introduces gradient explosion, which degrades rather than improves performance. Extensive evaluations on BCH and LDPC outer codes demonstrate that MaskCode consistently outperforms all baselines, achieving up to 1.5 dB SNR gain.

cs.IT↗
arXiv2026

Generalized Hankel/Toeplitz matrix for array signal processing

In this paper, we introduce generalized Hankel/Toeplitz matrices (GHM/GTM) and the associated generalized Vandermonde decomposition for nonuniform array signal processing and multi-dimensional super-resolution. The proposed framework was discovered from the study of resolution limit theory and extends the classical Hankel/Toeplitz structure by allowing substantially more flexible sampling geometries while preserving the underlying low-rank Vandermonde factorization. Through devising an optimal algorithm based on this GHM framework, we derive the state-of-the-art upper bound estimate for the computational resolution limit (CRL) of source-number detection in general $d$-dimensional super-resolution problems. For segmented sampling sets, whose geometry is closely related to sparse and distributed arrays, we establish deterministic lower bounds for the minimum singular values of the associated generalized Vandermonde matrices and derive corresponding stability and number-detection guarantees for multi-clump source configurations. To address the computational bottleneck of conventional multi-level Hankel constructions in high dimensions, we further introduce randomized GHM constructions whose matrix dimensions scale with the effective degrees of freedom rather than with the full tensor-product grid, together with deterministic recovery guarantees conditional on the realized Vandermonde factors. We also extend the framework to source localization by developing GHM-based MUSIC algorithms for nonuniform measurements, with stability characterized through the conditioning of the generalized Vandermonde factors. Numerical experiments on synthetic data demonstrate that the proposed GHM-based methods achieve competitive resolution and recovery accuracy while substantially reducing matrix size and computational cost, especially in high-dimensional settings.

eess.SP↗
arXiv2026

Adaptive Beam Hopping and Power Control for Dual-Layer Over-the-Air Online Federated Learning in LEO Satellite Networks

This paper investigates over-the-air (OTA) computation enabled online federated learning (FL) in low-Earth orbit (LEO) satellite networks. Specifically, we consider a dual-layer OTA aggregation architecture, where ground devices upload analog model updates to serving satellites via uplink OTA aggregation, and satellites forward the aggregated signals to a data processing center through the second round OTA aggregation. Then, we formulate a long-term data-utilization maximization problem in which devices continuously collect new data and untrained samples gradually lose freshness. The problem is subject to the satellite beam budget, transmit-power limit, and global mean squared error (MSE) constraint that governs end-to-end aggregation distortion. This yields a coupled mixed-integer nonlinear programming (MINLP) problem, involving tightly coupled discrete beam-hopping decisions and continuous power control. Due to the combinatorial action space and nonconvex constraints, the problem is NP-hard and computationally intractable. Furthermore, the time-varying satellite topology and dynamic data generation render it a sequential decision-making problem, necessitating adaptive online scheduling. To address these issues, we cast the problem as a Markov decision process and develop a proximal policy optimization (PPO)-based deep reinforcement learning framework that jointly optimizes adaptive beam hopping and power control, using an MSE-aware reward to balance data utilization and aggregation accuracy. Numerical simulation results verify that the proposed algorithm consistently outperforms other benchmark schemes, achieving superior long-term data utilization and faster FL convergence while satisfying the MSE requirement.

cs.IT↗
arXiv2024

3D Extended Target Sensing in ISAC: Cramér-Rao Bound Analysis and Beamforming Design

This paper investigates an integrated sensing and communication (ISAC) system where the sensing target is a three-dimensional (3D) extended target, for which multiple scatterers from the target surface can be resolved. We first introduce a second-order truncated Fourier series surface model for an arbitrarily-shaped 3D ET. Utilizing this model, we derive tractable Cramer-Rao bounds (CRBs) for estimating the ET kinematic parameters, including the center range, azimuth, elevation, and orientation. These CRBs depend explicitly on the transmit covariance matrix and ET shape. Then we formulate two transmit beamforming optimization problems for the base station (BS) to simultaneously support communication with multiple users and sensing of the 3D ET. The first minimizes the sensing CRB while ensuring a minimum signal-to-interference-plus-noise ratio (SINR) for each user, and it is solved using semidefinite relaxation. The second balances minimizing the CRB and maximizing communication rates through a weight factor, and is solved via successive convex approximation. To reduce the computational complexity, we further propose ISACBeam-GNN, a novel graph neural network-based beamforming method that employs a separate-then-integrate structure, learning communication and sensing (C&S) objectives independently before integrating them to balance C&S trade-offs. Simulation results show that the proposed beamforming designs that account for ET shapes significantly outperform existing baselines, offering better communication-sensing performance trade-offs as well as an improved beampattern for sensing. Results also demonstrate that ISACBeam-GNN is an efficient alternative to the optimization-based methods, with remarkable adaptability and scalability.

cs.IT↗
arXiv2026

Reinforcement Learning for Heterogeneous Sensor Selection in Maritime Surveillance

This paper presents an information-gain-guided reinforcement-learning sensor-selection framework for single-vessel tracking in heterogeneous maritime sensor networks. The proposed approach is motivated by information-theoretic sensor management: instead of activating all sensors or repeatedly performing computationally expensive online expected-information-gain evaluation, a learned policy selects one tracking-relevant sensor at each decision epoch. A Bayesian sequential Monte Carlo tracker estimates the vessel state from noisy measurements and provides a belief representation for scheduling under nonlinear and non-Gaussian conditions. A Proximal Policy Optimization agent selects one of five sensors in a georeferenced simulation of the CMMI Smart Marina testbed at Ayia Napa Marina, Cyprus. The policy is trained on the testbed's actual five-sensor configuration. The agent observes belief-state, detection-history, coverage, sensor-geometry, and realized-information-gain features. The reward is defined as a realized-information-gain term gated by an observability mask. Final-test simulations compare the proposed framework with random single-sensor selection, always-on sensing using all sensors simultaneously, and the expected-information-gain sensor-selection baseline proposed in our previous work. Results show that the learned policy achieves tracking performance close to always-on sensing while activating only one sensor per decision time step and avoiding the computationally expensive online entropy search required by expected-information-gain selection. Additional zero-shot evaluation without retraining on ten moderately perturbed versions of actual layout configuration showed broadly stable tracking, with any increase in positional tracking error remaining below 1 meter across all perturbations.

cs.AI↗
arXiv2026

ODMA-based MIMO Massive Unsourced Random Access with Soft-Output Polar Codes

This paper investigates the design of the on-off division multiple access (ODMA) transmission scheme for multiple-input multiple-output (MIMO) massive unsourced random access (URA) systems with soft-output (SO) polar codes. First, a three-segment pilot-uncoupled coding scheme is introduced under the ODMA framework, which reduces the coding rate of the data segment without increasing the transmission overhead, improving the overall system performance. Building upon this architecture, a hierarchical pattern detection framework is developed. Specifically, a coarse-grained candidate set of transmission patterns is first identified through correlation operations. Based on this, a message-passing (MP)-based pattern detection algorithm is developed to iteratively estimate the posterior probabilities of transmission patterns, followed by the \textit{maximum a posteriori} (MAP) estimation to obtain the precise pattern detection result. Furthermore, a joint pattern detection and data decoding algorithm based on the bit-wise SO information of polar decoder is investigated, where the posterior probability information provided by the polar decoder is exploited to refine the pattern detection and contribute to an improved accuracy. In addition, by leveraging bit-wise SO information of the successive cancellation list polar decoder, an MP-based iterative decoding algorithm is developed to significantly enhance the decoding performance. The proposed scheme simultaneously exploits the transmission gain of uncoupled-ODMA framework, the coding gain of polar codes in the short-blocklength regime, and the iterative decoding gain enabled by SO information, while the computational complexity is significantly reduced through the hierarchical detection framework. Simulation results demonstrate that the proposed scheme achieves strong robustness ...

cs.IT↗
arXiv2026

Local Private Information Retrieval for Graph-Based Replicated Systems

We rethink the definition of privacy in multi-server, graph-replicated private information retrieval (PIR) systems, by introducing a novel setting where the user's privacy is governed by the servers' storage structure. In classical graph-replicated PIR, the user retrieves a single message stored at the servers, while hiding the message index from each server. In our proposed privacy setting, the user is concerned with hiding the message index from a particular server, only if that server stores the message being retrieved, and privacy is not imposed otherwise. We coin this relaxed privacy requirement as local user privacy and the resulting PIR problem as local PIR on the graph. Our focus is on two-replicated PIR systems, where every message is replicated twice and stored on two distinct servers. Specifically, we study local PIR systems where the storage is represented by simple graphs, i.e., every pair of vertices is associated with at most one edge, and by their multigraph extension, i.e., $r$ parallel edges replace every edge. For these settings, we establish bounds on the local PIR capacity, defined as the maximum number of message symbols retrieved, per downloaded symbol. The local privacy requirement yields significant capacity gain over the classical PIR capacity under the same storage structure. For instance, in settings where the graph is a disjoint union of multiple identical sub-graphs, the gain in the local PIR capacity over classical PIR capacity is multiplicative in the number of sub-graphs. Further, for connected graphs, we derive capacity lower bounds for edge-transitive and bipartite graphs, which are greater than the best-known PIR capacity bounds. From these and by establishing matching upper bounds, we exactly characterize the capacity for star graphs, cyclic graphs, and path graphs with odd number of vertices. We introduce two local PIR schemes for general graphs.

cs.IT↗