A radiomap represents the spatial distribution of wireless signal strength, which is critical for applications like network optimization. However, constructing a radiomap relies on measuring radio signal power across the entire system, which is costly in outdoor environments due to large network scales. We present RadCloudSplat, a framework that extends 3D Gaussian Splatting (3DGS) to radio frequencies for efficient and accurate radiomap extrapolation from sparse measurements. RadCloudSplat models environmental scatterers and radio paths using 3D Gaussians, capturing key factors of radio wave propagation. It employs a relaxed-mean (RM) scheme to reparameterize the positions of 3D Gaussians from noisy and dense 3D point clouds. A camera-free 3DGS-based projection is proposed to map 3D Gaussians onto 2D radio beam patterns. Furthermore, a regularized loss function and recursive fine-tuning using highly structured sparse measurements in real-world settings are applied to ensure robust generalization. Experiments on synthetic and real-world data show state-of-the-art extrapolation accuracy and execution speed, solidifying the framework's credibility for real-world deployment.

Accurate localized wireless channel modeling is a cornerstone of cellular network optimization, enabling reliable prediction of network performance during parameter tuning. Localized statistical channel modeling (LSCM) is the state-of the-art channel modeling framework tailored for cellular network optimization. However, traditional LSCM methods, which infer the channel's angular power spectrum (APS) from reference signal received power (RSRP) measurements, suffer from critical limitations: they are typically confined to single-cell, single grid and single-carrier frequency analysis and fail to capture complex cross-domain interactions. To overcome these challenges, we propose RF-LSCM, a novel framework that models the channel APS by jointly representing large-scale signal attenuation and multipath components within a radiance field. RF-LSCM introduces a multi-domain LSCM formulation with a physics informed frequency-dependent attenuation model (FDAM) to facilitate the cross frequency generalization as well as a point cloud-aided environment enhanced method to enable multi-cell and multi-grid channel modeling. Furthermore, to address the computational inefficiency of typical neural radiance fields, RF LSCMleverages a low-rank tensor representation, complemented by a novel hierarchical tensor angular modeling (HiTAM) algo rithm. This efficient design significantly reduces GPU memory requirements and training time while preserving fine-grained accuracy. Extensive experiments on real-world multi-cell datasets demonstrate that RF-LSCM significantly outperforms state-of the-art methods, achieving up to a 30% reduction in mean absolute error (MAE) for coverage prediction and a 22% MAE improvement by effectively fusing multi-frequency data.

Localized statistical channel modeling (LSCM), a key enabler for digital twin networks, traditionally relies on costly and spatially limited drive test data to estimate the channel angular power spectrum (APS) from reference signal received power measurements. This paper proposes a measurement report (MR) data-driven LSCM framework (MR-LSCM) to leverage low-cost and ubiquitous MR data. However, integrating MR data presents critical challenges: the prevalent lack of location labels required for LSCM, and the mismatch between uniform geographic grids in LSCM and spatially non-uniform MR data in complex propagation environments. To address these issues, our MR-LSCM framework introduces two specialized modules. First, a semi-supervised hypergraph neural network is proposed for MR localization, which exploits multimodal information to achieve robust performance even with scarce labels. Second, we unify grid construction and APS estimation into a joint clustering and sparse recovery problem where the two tasks mutually reinforce each other. An improved sparse recovery algorithm tailored to the ill-conditioned measurement matrix and incomplete observation is developed by incorporating physical priors. Through comprehensive experiments on a real-world MR dataset, we demonstrate the superior performance and robustness of our framework in localization and channel modeling.

Accurate, site-specific channel information is crucial for optimizing next-generation wireless networks. Among various approaches, localized statistical channel modeling (LSCM), which models the channel multipath angular power spectrum (APS) from the reference signal received power (RSRP) measurement, has emerged as a state-of-the-art method tailored for efficient network optimization. However, despite its effectiveness, LSCM cannot predict APS at the vast majority of locations where no measurements are available, which significantly restricts its applicability in large-scale, real-world scenarios. To address this challenge, we present point-cloud-assisted tangent Gaussian splatting (PC-TGS), the first framework to extrapolate APS to unmeasured outdoor grids by integrating sparse radio measurements with dense LiDAR-based geometry. PC-TGS represents environmental scatterers as anisotropic 3D Gaussians, initialized and refined through a relaxed-mean reparaeterization of the raw point cloud. A tangent-plane projection accurately maps each Gaussian into the local angular domain, while a depth-aware electromagnetic splatting process aggregates their contributions. To ensure practical deployment, we derive a closed-form Gaussian-weighted average (GWA) for APS bin integration and provide a provable error bound. Evaluations on a LiDAR-scanned city-scale dataset (5M points, 6,310 RSRP samples) demonstrate that PC-TGS achieves better APS and RSRP prediction performance compared to state-of-the-art baselines and faster inference time for APS extrapolation task. These results highlight the potential of PC-TGS to enable geometry-aware and data-efficient channel prediction in large-scale wireless digital twins.

The Max-$k$-Cut problem is a fundamental combinatorial optimization challenge that generalizes the classic $\mathcal{NP}$-complete Max-Cut problem. While relaxation techniques are commonly employed to tackle Max-$k$-Cut, they often lack guarantees of equivalence between the solutions of the original problem and its relaxation. To address this issue, we introduce the Relax-Optimize-and-Sample (ROS) framework. In particular, we begin by relaxing the discrete constraints to the continuous probability simplex form. Next, we pre-train and fine-tune a graph neural network model to efficiently optimize the relaxed problem. Subsequently, we propose a sampling-based construction algorithm to map the continuous solution back to a high-quality Max-$k$-Cut solution. By integrating geometric landscape analysis with statistical theory, we establish the consistency of function values between the continuous solution and its mapped counterpart. Extensive experimental results on random regular graphs and the Gset benchmark demonstrate that the proposed ROS framework effectively scales to large instances with up to $20,000$ nodes in just a few seconds, outperforming state-of-the-art algorithms. Furthermore, ROS exhibits strong generalization capabilities across both in-distribution and out-of-distribution instances, underscoring its effectiveness for large-scale optimization tasks.

Localized statistical channel modeling (LSCM) is an efficient channel modeling framework recently proposed for wireless network optimization which learns the angular power spectrum (APS) of the downlink channel from the beam-wise reference signal receiving power (RSRP). However, the conventional LSCM is only based on RSRP measurements from one single geographical grid and ignores the inherent property of spatial consistency over wireless channels, resulting in suboptimal performance. To this end, we consider the LSCM in a manner of multiple geographical grids and further propose a novel graph-based approach for the multi-grid LSCM, called the accelerated Markovian variational Bayesian graph neural network (AMVB-GNN). The AMVB-GNN leverages a heterogeneous Markovian graph representation to capture the structured sparsity in the channel APSs and employs refined variational Bayesian inference (VBI) to learn the APSs of multiple grids. Notably, the design of AMVB-GNN eliminates the exact matrix inversion operations required in conventional VBI, thereby enhancing computational efficiency. Additionally, we demonstrate the partial permutation equivalence of AMVB-GNN, ensuring both interpretability and reliability. To address the issue of the demand for ground-truth APSs labels, we propose an unsupervised training loss function. Extensive simulation experiments validate the effectiveness and efficiency of the proposed AMVB-GNN model.

Wireless network optimization is essential for improving the network performance in mobile communications. However, due to the stochastic nature of wireless networks, existing schemes based on analytical models and deterministic optimization are less reliable. To this end, we design a framework for robust network optimization based on deep generative models and stochastic optimization. Inspired by the powerful diffusion process, we propose a deep generative simulator to capture the statistical distribution of the network performance. By sampling from the deep generative simulator, we can alleviate the inherent uncertainty related to the network performance and devise an innovative expectation-quantile-based stochastic objective function. The inner expectation is designed for the temporal statistics, while the outer quantile is developed for the spatial statistics. This designated two-tier objective function is capable of mitigating temporal fluctuations and ensuring satisfactory network performance across most geographical grids, thereby achieving robustness. To solve this stochastic optimization problem, a smooth zeroth-order approach is introduced by taking advantage of the unique structure of quantile functions. Through theoretical performance analysis and simulation experiments with real-world datasets, we demonstrate the superiority of our approach over other baseline schemes, highlighting its practical utility in robust network optimization.

In recent years, multimodal learning has attracted an increasing interest. A special scenario of multimodal learning, learning on temporal data, is common but has not been well studied. In multimodal temporal data, not all modalities of a sample arrive at the same time. Because of that, different types of samples may have different importance in many use cases, where an early sample with significant modalities may be more valuable than a later one as early predictions can be made to speed up decision-making processes. Besides, sample correlations are very common in multimodal temporal data, as samples accumulate in time and a late sample may contain the same data existing in an earlier sample. Training without the awareness of the importance and correlation yields less effective models. In this work, we define multimodal temporal data, discuss key challenges and propose two methods that improve traditional multimodal training on such data. We demonstrate the effectiveness of the proposed methods on several multimodal temporal datasets, where they show 1% to 3% improvements over the baseline.

This paper proposes an innovative graph neural network (GNN)-based approach to address the challenge of recovering ill-conditioned sparse signals within the task of multi-grid localized statistical channel modeling (LSCM). Our proposed GNN architecture captures the structural sparsity inherent in the channel angular power spectrum (APS) by leveraging reference signal receiving power (RSRP) measured from multiple grids. It can effectively mitigate the severe coherence in the measurement matrix. Furthermore, we present a novel online unsupervised training scheme that enables real-time adaptability for multi-grid LSCM applications. Through extensive simulations, we demonstrate the superior performance of our GNN-based method in the context of multi-grid LSCM, showcasing its advantages over existing sparse recovery techniques.

Vertical federated learning (VFL), where each participating client holds a subset of data features, has found numerous applications in finance, healthcare, and IoT systems. However, adversarial attacks, particularly through the injection of adversarial examples (AEs), pose serious challenges to the security of VFL models. In this paper, we investigate such vulnerabilities through developing a novel attack to disrupt the VFL inference process, under a practical scenario where the adversary is able to *adaptively corrupt a subset of clients*. We formulate the problem of finding optimal attack strategies as an online optimization problem, which is decomposed into an inner problem of adversarial example generation (AEG) and an outer problem of corruption pattern selection (CPS). Specifically, we establish the equivalence between the formulated CPS problem and a multi-armed bandit (MAB) problem, and propose the Thompson sampling with Empirical maximum reward (E-TS) algorithm for the adversary to efficiently identify the optimal subset of clients for corruption. The key idea of E-TS is to introduce an estimation of the expected maximum reward for each arm, which helps to specify a small set of *competitive arms*, on which the exploration for the optimal arm is performed. This significantly reduces the exploration space, which otherwise can quickly become prohibitively large as the number of clients increases. We analytically characterize the regret bound of E-TS, and empirically demonstrate its capability of efficiently revealing the optimal corruption pattern with the highest attack success rate, under various datasets of popular VFL tasks.

In massive machine-type communications, data transmission is usually considered sporadic, and thus inherently has a sparse structure. This paper focuses on the joint activity detection (AD) and channel estimation (CE) problems in massive-connected communication systems with low-resolution analog-to-digital converters. To further exploit the sparse structure in transmission, we propose a maximum posterior probability (MAP) estimation problem based on both sporadic activity and sparse channels for joint AD and CE. Moreover, a majorization-minimization-based method is proposed for solving the MAP problem. Finally, various numerical experiments verify that the proposed scheme outperforms state-of-the-art methods.

Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works on dictionary learning adopt an off-line approach, and there are two main off-line ways of conducting it. One is to alternately optimize both the dictionary and the sparse code, while the other is to optimize the dictionary by restricting it over the orthogonal group. The latter, called orthogonal dictionary learning (ODL), has a lower implementation complexity and, hence, is more favorable for low-cost devices. However, existing schemes for ODL only work with batch data and cannot be implemented online, making them inapplicable for real-time applications. This article, thus, proposes a novel online orthogonal dictionary scheme to dynamically learn the dictionary from streaming data, without storing the historical data. The proposed scheme includes a novel problem formulation and an efficient online algorithm design with convergence analysis. In the problem formulation, we relax the orthogonal constraint to enable an efficient online algorithm. We then propose the design of a new Frank–Wolfe-based online algorithm with a convergence rate of$\mathcal {O}(\ln t/t^{1/4})$. The convergence rate in terms of key system parameters is also derived. Experiments with synthetic data and real-world Internet of things (IoT) sensor readings demonstrate the effectiveness and efficiency of the proposed online ODL scheme.

Federated learning is a distributed machine learning paradigm where multiple data owners (clients) collaboratively train one machine learning model while keeping data on their own devices. The heterogeneity of client datasets is one of the most important challenges of federated learning algorithms. Studies have found performance reduction with standard federated algorithms, such as FedAvg, on non-IID data. Many existing works on handling non-IID data adopt the same aggregation framework as FedAvg and focus on improving model updates either on the server side or on clients. In this work, we tackle this challenge in a different view by introducing redistribution rounds that delay the aggregation. With delayed aggregations, local models are trained on data that are more representative to the global distribution. The proposed algorithm can also be used as a federated learning paradigm, as an alternative to FedAvg, where other methods can be plugged in. We perform experiments on multiple tasks and show that the proposed framework significantly improves the performance on non-IID data.

Federated learning (FL) is a machine learning framework, where multiple distributed edge Internet of Things (IoT) devices collaboratively train a model under the orchestration of a central server while keeping the training data distributed on the IoT devices. FL can mitigate the privacy risks and costs from data collection in traditional centralized machine learning. However, the deployment of standard FL is hindered by the expense of the communication of the gradients from the devices to the server. Hence, many gradient compression methods have been proposed to reduce the communication cost. However, the existing methods ignore the structural correlations of the gradients and, therefore, lead to a large compression loss which will decelerate the training convergence. Moreover, many of the existing compression schemes do not enable over-the-air aggregation and, hence, require huge communication resources. In this work, we propose a gradient compression scheme, named FedOComp, which leverages the correlations of the stochastic gradients in FL systems for efficient compression of the high-dimension gradients with over-the-air aggregation. The proposed design can achieve a smaller deceleration of the training convergence compared to other gradient compression methods since the compression kernel exploits the structural correlations of the gradients. It also directly enables over-the-air aggregation to save communication resources. The derived convergence analysis and simulation results further illustrate that under the same power cost, the proposed scheme has a much faster convergence rate and higher test accuracy compared to existing baselines.

Massive MIMO has been regarded as a key enabling technique for 5G and beyond networks. Nevertheless, its performance is limited by the large overhead needed to obtain the high-dimensional channel information. To reduce the huge training overhead associated with conventional pilot-aided designs, we propose a novel blind data detection method by leveraging the channel sparsity and data concentration properties. Specifically, we propose a novel$\ell _{3}$-norm-based formulation to recover the data without channel estimation. We prove that the global optimal solution to the proposed formulation can be made arbitrarily close to the transmitted data up to a phase-permutation ambiguity. We then propose an efficient parameter-free algorithm to solve the$\ell _{3}$-norm problem and resolve the phase-permutation ambiguity. We also derive the convergence rate in terms of key system parameters such as the number of transmitters and receivers, the channel noise power, and the channel sparsity level. Numerical experiments will show that the proposed scheme has superior performance with low computational complexity.

The problem of missing values in multivariable time series is a key challenge in many applications such as clinical data mining. Although many imputation methods show their effectiveness in many applications, few of them are designed to accommodate clinical multivariable time series. In this work, we propose a multiple imputation model that capture both cross-sectional information and temporal correlations. We integrate Gaussian processes with mixture models and introduce individualized mixing weights to handle the variance of predictive confidence of Gaussian process models. The proposed model is compared with several state-of-the-art imputation algorithms on both real-world and synthetic datasets. Experiments show that our best model can provide more accurate imputation than the benchmarks on all of our datasets.

In massive multiple-input multiple-output (MIMO) uplink, the minimum mean square error (MMSE) algorithm is near-optimal and linear, but still suffers from high-complexity of matrix inversion. Based on Gauss-Seidel (GS) method, an efficient architecture for massive MIMO soft-output detection is proposed in this paper. To further accelerate the convergence rate of the conventional GS method with acceptable overhead complexity, a truncated Neumann series of the first 2 terms, is employed for initialization. The architecture can meet various application requirements by flexibly adjusting the number of iterations. FPGA implementation for a 128 × 8 MIMO demonstrates its advantages in both hardware efficiency and flexibility.