Tensor train (TT) representation has achieved tremendous success in visual data completion tasks, especially when it is combined with tensor folding. However, folding an image or video tensor breaks the original data structure, leading to local information loss as nearby pixels may be assigned into different dimensions and become far away from each other. In this paper, to fully preserve the local information of the original visual data, we explore not folding the data tensor, and at the same time adopt graph information to regularize local similarity between nearby entries. To overcome the high computational complexity introduced by the graph-based regularization in the TT completion problem, we propose to break the original problem into multiple sub-problems with respect to each TT core fiber, instead of each TT core as in traditional methods. Furthermore, to avoid heavy parameter tuning, a sparsity-promoting probabilistic model is built based on the generalized inverse Gaussian (GIG) prior, and an inference algorithm is derived under the mean-field approximation. Experiments on both synthetic data and real-world visual data show the superiority of the proposed methods.

Representing variable-length and continuous-indexed signals through a linear combination of basis functions poses a fundamental challenge in science and engineering. Current approaches resort to preprocessing steps, such as interpolation and extrapolation, to handle irregular and off-grid measurements, which compromise the physical nature of signals and degrade the representation performance. To address this challenge, rather than utilizing discrete vectors, we introduce a Bayesian functional representation model that capitalizes on the continuous nature and rich expressiveness of Gaussian processes to facilitate interpretable and effective basis function learning. Moreover, an analytical and efficient algorithm based on the variational inference framework is developed. Experimental results using real-life datasets demonstrate the superior performance of our proposed method.

Radio map estimation (RME) aims to construct a map of radio strength across multiple domains (e.g., space and frequency) from limited measurements. Data-driven deep neural model-based RME showed promising performance, yet requiring excessive training resources. This work puts forth an RME approach that can effectively incorporate learned information without training over radio map data. Our idea is to employ the plug-and-play (PnP) denoising scheme from computational imaging. The PnP framework allows incorporating denoisers trained over natural images to handle other types of data, e.g., ocean sound fields and medical images, due to the similarity of their denoising processes. Conventional PnP methods mostly use the learned denoisers in the data domain. Instead, the proposed approach applies PnP in the latent domain through a tailored algorithm design and spatial-spectral factorization of radio maps. This way, the proposed RME method exhibits enhanced scalability and noise robustness. Simulations are used to illustrate the effectiveness of the proposed approach.

Spatial-spectral radio map estimation (RME) from sparsely deployed sensors can be viewed as a tensor learning problem. Among tensor models, the block-term decomposition (BTD) model is especially effective for RME, enabling accurate recovery of the radio map as well as emitter-level spatial loss field (SLF) and power spectral density (PSD). However, selecting the appropriate tensor and block-term ranks in the BTD model is crucial yet challenging, as the ranks indicate the number and properties of emitters, which are typically unknown in practice. Inappropriate settings of these ranks leads to overfitting and underfitting of the model. Existing optimization-based BTD learning methods either unrealistically assume that these ranks are known or require parameter tuning. To address these issues, we propose a Bayesian BTD model that incorporates sparsitypromoting priors on the factor matrices for rank learning, eliminating the need for parameter tuning while learning all other parameters. Extensive numerical experiments showcase the effectiveness of the proposed method.

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they still struggle with general tensor data with continuous indexes not only in the temporal mode but also in other modes, such as spatial coordinates in climate data. Moreover, the challenge of self-adapting model complexity is largely unexplored in functional temporal tensor models, with existing methods being inapplicable in this setting. To address these limitations, we propose functional Complexity-Adaptive Temporal Tensor dEcomposition (Catte). Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors. To enable automatic adaptation of model complexity, we introduce a sparsity-inducing prior over the factor trajectories. We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that Catte not only reveals the underlying ranks of functional temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents sparse observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.

Spectrum cartography(SC) aims to estimate the radio power map of multiple emitters over space and frequency using limited sensor data. Recent advances leverage learneddeep generative models(DGMs) as structural priors, achieving state-of-the-art performance by capturing complex spatial-spectral patterns. However, DGMs require large training datasets and may suffer under distribution shifts. To address these limitations, we propose atraining-freeSC approach based onuntrained neural networks(UNNs), which encode structural priors through architectural design. Our custom UNN exploits a spatio-spectral factorization model rooted in the physical structure of radio maps, enabling low sample complexity. Experiments show that our method matches the performance of DGM-based SC without any training data.

Channel acquisition presents a major challenge in deploying intelligent reflecting surfaces (IRS) aided communication systems, due to massive reflective elements that create a complex multi-path channel and increase channel dimensions. For an IRS-aided communication system, complete channel includes three parts: From the users to IRS, from the IRS to BS, and from the BS back to the IRS. Thus, a generalized multi-IRS cascaded communication system with three cascaded IRSs is considered. Unfortunately, existing channel estimation methods focus on single or double IRS cascades, which is not applicable to the case of triple cascaded IRS channel estimation directly. In this paper, we study the uplink channel estimation for triple cascaded IRSs aided single-user single-input single-output (SISO) systems. Specifically, the triple IRS cascaded channel is typically sparse. It permits us to characterize the channel estimation as a problem of sparse matrix recovery. Then, the sparse learning is explored to achieve robust channel estimation with limited training overhead. Particularly, the sparse channel matrices of the cascaded triple IRS channels have a common row-column block sparsity structure. However, a unique challenge lies in characterizing and enhancing such a common row-column sparsity. To tackle this issue, we apply a random matrix prior to promote the common row-column-wise sparsity of the channel matrix, and then an efficient Bayesian tensor inference algorithm is proposed to estimate the IRS channel. Finally, simulation results confirm that the proposed scheme outperforms traditional counterparts in terms of accuracy.

Extremely large-scale multiple-input multiple-output (XL-MIMO) with orthogonal frequency division multiplexing (OFDM) transmission can provide unprecedented improvement in spectral efficiency and data rate. Dynamic metasurface antennas (DMAs) have been proposed as a cost-effective and power-efficient solution for realizing XL-MIMO systems. However, the extremely large number of antennas in XL-MIMO-OFDM with DMAs poses critical challenges in acquiring accurate channel state information. To address this issue, we propose in this paper a tensor-based channel estimation method for frequency-selective XL-MIMO-OFDM systems with DMAs. We first characterize the configurable property of DMAs and propose a microstrip-sequential channel training method with quasi-dynamically adjustable metamaterial elements, by representing the received frequency-domain training signals as a fourth-order tensor which admits the canonical polyadic decomposition. Then, by exploiting the sparsity of XL-MIMO channels, we propose a two-stage tensor decomposition-based channel estimation algorithm, where the four coupling factor matrices are obtained without the need of iterative refinement, and the channel multipath parameters can be extracted for reconstructing the entire high-dimensional channel matrix. In addition, we analyze the uniqueness condition for the proposed tensor-based channel estimation method, which reveals that the required channel training overhead is only proportional to the number of channel multipaths, instead of that of metamaterial elements and microstrips. Numerical results demonstrate the superior performance of our proposed design with significantly reduced training overhead as compared to various benchmark schemes.

Activity detection is an important task in the next generation Internet-of-things (IoT) networks. Existing algorithms mostly require precise information about the network, such as large-scale fading, noise variance, and small-scale fading statistics. Acquiring such information would take a significant overhead and their estimated values might not be accurate. This problem is even more severe in cell-free networks as more parameters are acquired. Therefore, this paper sets out to investigate this problem without the above mentioned information. In order to handle so many unknown parameters, this paper employs a Bayesian approach, where they are endowed with prior distributions as regularizations. Together with the likelihood function, a maximum a posteriori (MAP) estimator is derived. Simulations demonstrate that the proposed method outperforms state-of-the-art methods especially under imprecise information.

This letter introduces a structured high-rank tensor approach for estimating sub-6G uplink channels in multi-user multiple-input and multiple-output (MU-MIMO) systems. To tackle the difficulty of channel estimation in sub-6G bands with hundreds of sub-paths, our approach fully exploits the physical structure of channel and establishes the link between sub-6G channel model and a high-rank four-dimensional (4D) tensor Canonical Polyadic Decomposition (CPD) with three factor matrices being Vandermonde-constrained. Accordingly, a stronger uniqueness property is derived in this work. This model supports an efficient one-pass algorithm for estimating sub-path parameters, which ensures plug-in compatibility with the widely-used baseline. Our method performs much better than the state-of-the-art tensor-based techniques on the simulations adhering to the 3GPP-R18 5G protocols.

In the fifth-generation new radio (5G NR) frequency division duplex (FDD) massive multiple-input and multiple-output (MIMO) systems, downlink beamforming relies on the acquisition of downlink channel state information (CSI). Codebook based limited feedback schemes have been proposed and widely used in practice to recover the downlink CSI with low communication overhead. In such schemes, the performance of downlink beamforming is determined by the codebook design and the codebook indicator feedback. However, limited by the quantization quality of the codebook, directly utilizing the codeword indicated by the feedback as the beamforming vector cannot achieve high performance. Therefore, other feedback values, such as channel qualification indicator (CQI), should be considered to enhance beamforming. In this paper, we present the relation between CQI and the optimal beamforming vectors, based on which an empirical Bayes based intelligent tuning-free algorithm is devised to learn the optimal beamforming vector and the associated regularization parameter. The proposed algorithm can handle different communication scenarios of MIMO systems, including single stream and multiple streams data transmission scenarios. Numerical results have shown the excellent performance of the proposed algorithm in terms of both beamforming vector acquisition and regularization parameter learning.

Benefitting from the vast spatial degrees of freedom, the amalgamation of integrated sensing and communication (ISAC) and massive multiple-input multiple-output (MIMO) is expected to simultaneously improve spectral and energy efficiencies as well as the sensing capability. However, a large number of antennas deployed in massive MIMO-ISAC raises critical challenges in acquiring both accurate channel state information and target parameter information. To overcome these two challenges with a unified framework, we first analyze their underlying system models and then propose a novel tensor-based approach that addresses both the channel estimation and target sensing problems. Specifically, by parameterizing the high-dimensional communication channel exploiting a small number of physical parameters, we associate the channel state information with the sensing parameters of targets in terms of angular, delay, and Doppler dimensions. Then, we propose a shared training pattern adopting the same time-frequency resources such that both the channel estimation and target parameter estimation can be formulated as a canonical polyadic decomposition problem with a similar mathematical expression. On this basis, we first investigate the uniqueness condition of the tensor factorization and the maximum number of resolvable targets by utilizing the specific Vandermonde structure. Then, we develop a unified tensor-based algorithm to estimate the parameters including angles, time delays, Doppler shifts, and reflection/path coefficients of the targets/channels. In addition, we propose a segment-based shared training pattern to facilitate the channel and target parameter estimation for the case with significant beam squint effects. Simulation results verify our theoretical analysis and the superiority of the proposed unified algorithms in terms of estimation accuracy, sensing resolution, and training overhead reduction.

Variational autoencoders (VAE) are one of the most prominent deep generative models for learning the underlying statistical distribution of high-dimensional data. However, training VAEs suffers from a severe issue called posterior collapse; that is, the learned posterior distribution collapses to the assumed/pre-selected prior distribution. This issue limits the capacity of the learned posterior distribution to convey data information. Previous work has proposed a heuristic training scheme to mitigate this issue, in which the core idea is to train the encoder and the decoder in an alternating fashion. However, there is still no theoretical interpretation of this scheme, and this paper, for the first time, fills in this gap by inspecting the previous scheme under the lens of the expectation maximization (EM) framework. Under this framework, we propose a novel EM-type training algorithm that gives a controllable optimization process and it allows for further extensions, e.g., employing implicit distribution models. Experimental results have corroborated the superior performance of the proposed EM-type VAE training algorithm in terms of various metrics.

Gaussian process state-space model (GPSSM) is a fully probabilistic state-space model that has attracted much attention over the past decade. However, the outputs of the transition function in the existing GPSSMs are assumed to be independent, meaning that the GPSSMs cannot exploit the inductive biases between different outputs and lose certain model capacities. To address this issue, this paper proposes an output-dependent and more realistic GPSSM by utilizing the well-known, simple yet practical linear model of coregionalization (LMC) framework to represent the output dependency. To jointly learn the output-dependent GPSSM and infer the latent states, we propose a variational sparse GP-based learning method that only gently increases the computational complexity. Experiments on both synthetic and real datasets demonstrate the superiority of the output-dependent GPSSM in terms of learning and inference performance.

Multipath time-delay estimation is commonly encountered in radar and sonar signal processing. In some real-life environments, impulse noise is ubiquitous and significantly degrades estimation performance. Here, we propose a Bayesian approach to tailor the Bayesian Compressive Sensing (BCS) to mitigate impulsive noises. In particular, a heavy-tail Laplacian distribution is used as a statistical model for impulse noise, while Laplacian prior is used for sparse multipath modeling. The Bayesian learning problem contains hyperparameters learning and parameter estimation, solved under the BCS inference framework. The performance of our proposed method is compared with benchmark methods, including compressive sensing (CS), BCS, and Laplacian-prior BCS (L-BCS). The simulation results show that our proposed method can estimate the multipath parameters more accurately and have a lower root mean squared estimation error (RMSE) in intensely impulsive noise.

In this paper, the training time minimization problem is investigated in a quantized FEEL system, where the heterogeneous edge devices send quantized gradients to the edge server via orthogonal channels. In particular, a stochastic quantization scheme is adopted for compression of uploaded gradients, which can reduce the burden of per-round communication but may come at the cost of increasing number of communication rounds. The intrinsic trade-off between the number of communication rounds and per-round latency is characterized. Specifically, we analyze the convergence behavior of the quantized FEEL in terms of the optimality gap. Constrained by total bandwidth, the training time minimization problem is formulated as a joint quantization level and bandwidth allocation optimization problem. To this end, an algorithm based on alternating optimization is proposed, which alternatively solves the subproblem of quantization optimization via successive convex approximation and the subproblem of bandwidth allocation via bisection search. With different learning tasks and models, the validation of our analysis and the near-optimal performance of the proposed algorithm are demonstrated by the experimental results.

Neural networks often encounter various stringent resource constraints while deploying on edge devices. To tackle these problems with less human efforts, automated machine learning becomes popular in finding various neural architectures that fit diverse Artificial Intelligence of Things (AIoT) scenarios. Recently, to prevent the leakage of private information while enable automated machine intelligence, there is an emerging trend to integrate federated learning and neural architecture search (NAS). Although promising as it may seem, the coupling of difficulties from both tenets makes the algorithm development quite challenging. In particular, how to efficiently search the optimal neural architecture directly from massive nonindependent and identically distributed (non-IID) data among AIoT devices in a federated manner is a hard nut to crack. In this article, to tackle this challenge, by leveraging the advances in ProxylessNAS, we propose a federated direct neural architecture search (FDNAS) framework that allows for hardware-friendly NAS from non-IID data across devices. To further adapt to both various data distributions and different type of devices with heterogeneous embedded hardware platforms, inspired by meta-learning, a cluster federated direct neural architecture search (CFDNAS) framework is proposed to achieve device-aware NAS, in the sense that each device can learn a tailored deep learning model for its particular data distribution and hardware constraint. Extensive experiments on non-IID data sets have shown the state-of-the-art accuracy–efficiency tradeoffs achieved by the proposed solution in the presence of both data and device heterogeneity.

Training a machine learning model with federated edge learning (FEEL) is typically time consuming due to the constrained computation power of edge devices and the limited wireless resources in edge networks. In this study, the training time minimization problem is investigated in a quantized FEEL system, where heterogeneous edge devices send quantized gradients to the edge server via orthogonal channels. In particular, a stochastic quantization scheme is adopted for compression of uploaded gradients, which can reduce the burden of per-round communication but may come at the cost of increasing the number of communication rounds. The training time is modeled by taking into account the communication time, computation time, and the number of communication rounds. Based on the proposed training time model, the intrinsic trade-off between the number of communication rounds and per-round latency is characterized. Specifically, we analyze the convergence behavior of the quantized FEEL in terms of the optimality gap. Furthermore, a joint data-and-model-driven fitting method is proposed to obtain the exact optimality gap, based on which the closed-form expressions for the number of communication rounds and the total training time are obtained. Constrained by the total bandwidth, the training time minimization problem is formulated as a joint quantization level and bandwidth allocation optimization problem. To this end, an algorithm based on alternating optimization is proposed, which alternatively solves the subproblem of quantization optimization through successive convex approximation and the subproblem of bandwidth allocation by bisection search. With different learning tasks and models, the validation of our analysis and the near-optimal performance of the proposed optimization algorithm are demonstrated by the simulation results.

Massive multiple-input multiple-output (MIMO) integrated with millimeter-wave (mmWave) can provide unprecedented performance improvement for realizing future wireless communications. However, acquiring accurate channel state information in wideband mmWave massive MIMO systems with hybrid transceiver architectures is even challenging, especially in high-mobility scenarios with severe Doppler effects. In this paper, we propose a tensor decomposition-based method to estimate the time-varying and frequency-selective (TVFS) mmWave MIMO channels. Specifically, by exploiting the sparse scattering nature of TVFS channels, we model the frequency-domain received signal as a third-order tensor that admits a canonical polyadic (CP) decomposition format. Then, we analyze the uniqueness condition of the proposed CP decomposition-based channel estimation problem and propose a novel estimator to acquire TVFS channel parameters including angle of departure/arrival (AoD/AoA), time delay, path gain, and the Doppler shift. To address the sophisticated coupling among unknown parameters, we further propose a joint AoD and Doppler shift estimation (JADE) algorithm that provides reliable initial and iteratively refined estimates. The derived analysis and simulation results verify that the proposed JADE algorithm achieves higher estimation accuracy and guarantees the superiority of the proposed TVFS channel estimator over existing schemes.

This paper investigates a reconfigurable intelligent surface (RIS)-aided unsourced random access (URA) scheme for the sixth-generation (6G) wireless networks with massive sporadic traffic devices. First of all, this paper proposes a novel joint active device separation (the message recovery of active device) and channel estimation architecture for the RIS-aided URA. Specifically, the RIS passive reflection is optimized before the successful device separation. Then, by associating the data sequences to multiple rank-one tensors and exploiting the angular sparsity of the RIS-BS channel, the detection problem is cast as a high-order coupled tensor decomposition problem without the need of exploiting pilot sequences. However, the inherent coupling among multiple sparse device-RIS channels, together with the unknown number of active devices make the detection problem at hand deviate from the widely-used coupled tensor decomposition format. To overcome this challenge, this paper judiciously devises a probabilistic model that captures both the element-wise sparsity from the angular channel model and the low-rank property due to the sporadic nature of URA. Then, based on such a probabilistic model, a iterative detection algorithm is developed under the framework of sparse variational inference, where each update iteration is obtained in a closed-form and the number of active devices can be automatically estimated for effectively avoiding the overfitting of noise. Extensive simulation results confirm the excellence of the proposed URA algorithm, especially for the case of a large number of reflecting elements for accommodating a significantly large number of devices.

This paper investigates the problem of joint massive devices separation and channel estimation for a reconfigurable intelligent surface (RIS)-aided unsourced random access (URA) scheme in the sixth-generation (6G) wireless networks. In particular, by associating the data sequences to a rank-one tensor and exploiting the angular sparsity of the channel, the detection problem is cast as a high-order coupled tensor decomposition problem. However, the coupling among multiple devices to RIS (device-RIS) channels together with their sparse structure make the problem intractable. By devising novel priors to incorporate problem structures, we design a novel probabilistic model to capture both the element-wise sparsity from the angular channel model and the low rank property due to the sporadic nature of URA. Based on the this probabilistic model, we develop a coupled tensor-based automatic detection (CTAD) algorithm under the framework of variational inference with fast convergence and low computational complexity. Moreover, the proposed algorithm can automatically learn the number of active devices and thus effectively avoid noise overfitting. Extensive simulation results confirm the effectiveness and improvements of the proposed URA algorithm in large-scale RIS regime.

There is a fundamental trade-off between the channel representation resolution of codebooks and the overheads of feedback communications in the fifth generation new radio (5G NR) frequency division duplex (FDD) massive multiple-input and multiple-output (MIMO) systems. In particular, two types of codebooks (namely Type I and Type II codebooks) are introduced with different resolution and overhead. Although the Type I codebook based scheme requires lower feedback overhead, its channel state information (CSI) reconstruction and beamforming performance are not as good as those from the Type II codebook based scheme. However, since the Type I codebook based scheme has been widely used in 4G systems for many years, replacing it by the Type II codebook based scheme overnight is too costly to be an option. Therefore, in this paper, using Type I codebook, we leverage advances in cutting plane method to optimize the CSI reconstruction at the base station (BS), in order to close the gap between these two codebook based beamforming schemes. Numerical results based on channel samples from QUAsi Deterministic RadIo channel GenerAtor (QuaDRiGa) are presented to show the excellent performance of the proposed algorithm in terms of beamforming vector acquisition.

Tensor train (TT) decomposition, a powerful tool for analyzing multidimensional data, exhibits superior performance in many machine learning tasks. However, existing methods for TT decomposition either suffer from noise overfitting, or require extensive fine-tuning of the balance between model complexity and representation accuracy. In this paper, a fully Bayesian treatment of TT decomposition is employed to avoid noise overfitting without parameter tuning. In particular, theoretical evidence is established for adopting a Gaussian-product-Gamma prior to induce sparsity on the slices of the TT cores. Furthermore, based on the proposed probabilistic model, an efficient learning algorithm is derived under the variational inference framework. Experiments on real-world data demonstrate the proposed algorithm performs better in image completion and image classification, compared to other existing TT decomposition algorithms.

While deploying on edge devices, deep learning mod-els often encounter various strict resource constraints. Automated machine learning becomes popular in finding various neural architectures that fit diverse Internet of Things (IoT) scenarios to handle these problems with less human efforts. Recently, there is an emerging trend to integrate federated learning and Neural Architecture Search (NAS) to prevent private data leakage while enabling automated machine learning. The algorithm development is quite challenging because of the coupling of difficulties from both tenets, although promising as it may seem. Especially, it is a hard nut to efficiently search the optimal neural architecture directly from massive non-Independent and Identically Distributed (non-IID) data among IoT devices in a federated manner. In this paper, by leveraging the advances in ProxylessNAS, we propose a Federated Direct Neural Architecture Search (FDNAS) framework that allows hardware-friendly NAS from non-IID data across devices to tackle the challenge. Extensive experiments on non-IID datasets demonstrate the state-of-the-art accuracy-efficiency trade-offs achieved by proposed methods.

Due to the emergence of deep learning, signal recognition has made great strides in performance improvement. The success of most deep learning methods relies on the accessibility of abundant labelled training data. However, the annotation of signals is quite expensive, making it challenging to train deep learning models substantially. This calls for the development of semi-supervised learning (SSL) method to fully utilize the unlabelled data to assist the training of deep learning models. To achieve this goal, three types of loss function tailored to the task of signal recognition are carefully designed in this paper. Together with the novel design of neural network structure, the proposed SSL method can effectively extract the information from unlabelled training data and thus overcome the difficulty of insufficient training. Extensive numerical results using real-world signal datasets are presented to show the remarkable performance of the proposed SSL method.

Edge learning (EL), which uses edge computing as a platform to execute machine learning algorithms, is able to fully exploit the massive sensing data generated by Internet of Things (IoT). However, due to the limited transmit power at IoT devices, collecting the sensing data in EL systems is a challenging task. To address this challenge, this article proposes to integrate unmanned ground vehicle (UGV) with EL. With such a scheme, the UGV could improve the communication quality by approaching various IoT devices. However, different devices may transmit different data for different machine learning jobs and a fundamental question is how to jointly plan the UGV path, the devices' energy consumption, and the number of samples for different jobs? This article further proposes a graph-based path planning model, a network energy consumption model, and a sample size planning model that characterizes F-measure as a function of the minority class sample size. With these models, the joint path, energy and sample size planning (JPESP) problem is formulated as a large-scale mixed-integer nonlinear programming (MINLP) problem, which is nontrivial to solve due to the high-dimensional discontinuous variables related to UGV movement. To this end, it is proved that each IoT device should be served only once along the path, thus the problem dimension is significantly reduced. Furthermore, to handle the discontinuous variables, a tabu search (TS)-based algorithm is derived, which converges in expectation to the optimal solution to the JPESP problem. Simulation results under different task scenarios show that our optimization schemes outperform the fixed EL and the full path EL schemes.

One key feature of massive multiple-input multiple-output systems is the large number of antennas and users. As a result, reducing the computational complexity of beamforming design becomes imperative. To this end, the goal of this paper is to achieve a lower complexity order than that of existing beamforming methods, via the parallel accelerated random coordinate descent (ARCD). However, it is known that ARCD is only applicable when the problem is convex, smooth, and separable. In contrast, the beamforming design problem is nonconvex, nonsmooth, and nonseparable. Despite these challenges, this paper shows that it is possible to incorporate ARCD for multicast beamforming by leveraging majorization minimization and strong duality. Numerical results show that the proposed method reduces the execution time by one order of magnitude compared to state-of-the-art methods.

In this paper, direction-of-arrival (DOA) estimation problem for massive multiple-input multiple-output (MIMO) systems with a two dimensional (2D) array is investigated, assuming no knowledge of path number, noise power, path gain correlations and bad data statistics. A novel iterative algorithm operating on tensor represented data is proposed, with integrated features of effective bad data mitigation and automatic source enumeration. Simulation results are presented to illustrate the excellent performance of the proposed algorithm in term of accuracy and robustness.