One of the major early-career contributions to numerical optimization by Yurii Nesterov is the development of Nesterov's acceleration and the corresponding Fast Gradient Method (FGM). Accelerated first-order methods are very important in large-scale optimization and have applications in different fields of engineering and science. Such methods are devised in the context of the estimating sequences framework, which was also developed by Nesterov, but much later than FGM, and exhibit desirable properties such as fast convergence rate and low per-iteration complexity. In this paper, we devise new generalized estimating sequences with an objective of pushing acceleration to its limit and show how they can be used to construct accelerated first-order methods. We start our summary by considering the case of minimizing smooth convex objective functions. For this class of problems, we present a class of generalized estimating sequences, constructed by exploiting the history of the estimating functions that are obtained during the minimization process. Using these generalized estimating sequences, we devise an accelerated gradient method and prove that it converges to a tolerated neighborhood of the optimal solution faster than FGM and other first-order methods. We then consider a more general class of optimization problems, namely composite objectives. For this class of problems, we introduce the class of composite estimating sequences, which are obtained by making use of the gradient mapping framework and a tight lower bound on the function that should be minimized. Using these composite estimating sequences, we devise a composite objective accelerated multi-step estimating sequence technique and prove its accelerated convergence rate. Last, embedding the memory term coming from the previous iterates into the composite estimating sequences, we obtain the generalized composite estimating sequences. Using these estimating sequences, we construct another accelerated gradient method and prove its accelerated convergence rate.

The robust adaptive beamforming (RAB) problem for general rank signal models is addressed via the worst-case signal-to-interference-plus-noise ratio (SINR) maximization. The worst-case SINR maximization problem is reformulated into a maximin SINR problem. To tackle such nonconvex problem, the uncertainty sets for the parameters in the SINR; the matrix obtained by eigen-decomposition of the high rank desired signal covariance matrix and the interference-plus-noise covariance matrix; need to be convex and closed. Then the corresponding minimax SINR problem is shown to be convex and the maximin and minimax SINR problems are shown to be equivalent to each other in the sense that they enjoy the same set of optimal solutions and the equal optimal value. Further, the minimax SINR problem becomes a semidefinite program (SDP) if the two uncertainty sets are characterized by finite linear matrix inequality constraints. Therefore, a globally optimal RAB solution for the worst-case SINR maximization problem can be obtained by solving the SDP. When the RAB optimization problem for the general rank signal model reduces to the problem for the rank one signal model, the theoretical results established herein are the same as those state-of-the-art results developed earlier, but with a weaker condition. Our results are validated by numerical examples.

Frequency modulated continuous wave (FMCW) radar is widely used in autonomous driving and industrial inspection due to its high-resolution target location and velocity estimation capability. However, the plethora of connected devices in automotive applications introduces electromagnetic interference and brings challenges to location-aware services, primarily due to the issue of low signal-to-noise ratio (SNR) caused by mixed noise contamination. Conventional matrix-based signal processing methods exhibit performance deterioration when handling higher-order signals under low SNR conditions. To address this challenge, this paper proposes a tensor decomposition-based framework that jointly performs noise reduction and parameter estimation for four-dimensional signals in FMCW multiple-input multiple-output (MIMO) radar systems. Specifically, the framework exploits the inherent low-rank structure and multidimensional correlations of the received signals through tensor train decomposition to effectively separate noise subspace. A data smoothing processor then reconstructs an augmented signal tensor to resolve rank deficiency caused by coherent signals. Finally, an enhanced rotational subspace algorithm is employed to jointly decouple the distance, velocity, and angle parameters by exploiting the structural fitting to the restored signal. Both simulation and field experiments under real-world noise demonstrate that our proposed framework achieves significant noise reduction while improving target SNR and parameter estimation accuracy. These advancements make the proposed framework a robust solution for high-precision MIMO FMCW radar applications in dynamic, noise-polluted environments.

A novel multibeam time-division (TD) multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) approach is proposed to achieve a balanced tradeoff between sensing and communication functionalities and accurate sensing parameter estimation with a wide field-of-view. Firstly, the TD strategy is introduced to address the simultaneous high demands for sensing performance and communication rate. By allocating time resources between sensing and communications, this approach can reach a desired balance between them while avoiding spectrum and spatial interference, as well as competition in power allocation. Next, a new multibeam method is developed to achieve wide-area sensing for TD MIMO ISAC. Conventional multibeam methods typically rely on beam scanning for direction estimation, suffering from limited accuracy. Inspired by Doppler division multiple access (DDMA) approach, the proposed method divides the Doppler spectrum into more subbands, generating more beams than the number of transmit antenna elements using only phase modulation. Beyond enabling flexible control over the sensing coverage location through beam selection, the proposed method also improves parameter estimation accuracy by fully leveraging the inter-beam relationships, particularly for targets located at null directions. Specifically, for such targets, the proposed method achieves a significantly higher maximum unambiguous velocity, mitigating the velocity ambiguity inherent in conventional DDMA. Simulation results validate the effectiveness of the proposed approach in enhancing both the performance tradeoff between sensing and communication, and the accuracy of sensing parameter estimation.

A throughput-oriented optimization strategy using a residual neural network (ResNet) within convolutional neural network (CNN), enabled by a fully differentiable receiver chain, is proposed. Unlike conventional training with known channel conditions, the proposed method directly maximizes throughput. It is then evaluated under typical 5G channel models. Results show consistent improvements for block error rate (BLER) and uncoded bit error rate (BER) when compared against least squares estimation. Comparisons with conventionally trained neural networks are inconclusive. However, some scenarios demonstrate improvements in throughput optimized neural networks over those trained under ideal channel conditions. In addition to improved performance, the proposed approach also enables training applications in which ideal channel conditions are not available. The proposed training method can be used as long as transmitted bits are known. These findings highlight the practical value of a throughput-oriented optimization strategy in channel smoothing and indicate its feasibility as a direction for AI-enhanced receivers without relying on ideal channel conditions.

Robust hybrid beamforming for integrated sensing and communications (ISAC) system under bounded uncertainties is investigated using learning to optimize (L2O) techniques. Specifically, the robust hybrid beamforming design is initially formulated as an optimization problem aimed at jointly maximizes the worst-case communication sum-rate and the worstcase sensing mutual information, considering the uncertainties in communication channel and transmit/receive steering vectors. Projected gradient descent and ascent (PGDA) algorithm with momentum is then developed for solving the formulated optimization problem. To enhance the performance of the PGDA algorithm, we propose to use one of L2O techniques, i.e., algorithm unrolling, to transform the developed PGDA into a trainable neural network by learning its hyperparameters (i.e., step sizes and momentum coefficients) directly from data. To overcome the limitations of fixed-layer unrolled PGDA, we further devise a recurrent network-augmented unrolled PGDA architecture, providing the flexibility of training the unrolled PGDA network with finite layers and testing it with infinite layers. Furthermore, to enable adaptability to varying channel conditions, we design a neural network, called EpsNet, to learn the uncertainty bounds dynamically. Numerical results demonstrate that the unrolled PGDA networks outperform the standard PGDA benchmark both in performance and convergence, effectively addressing the newly introduced problem of robust hybrid beamforming design for ISAC system.

The growing demand for fast and reliable wireless connectivity, coupled with the limited availability of spectrum, has sparked significant interest in utilizing frequency bands near the operating bands of legacy wireless systems. Many legacy systems were designed when spectrum usage was sparse. Utilizing these new bands for commercial data communication might result in previously unforeseen interference issues with legacy wireless users. In many deployments, the operation of legacy wireless users is limited to specific geographic zones. We aim to mitigate interference caused to legacy wireless receivers by leveraging knowledge of these geographically-constrained regions. In a cell-free massive multiple-input multiple-output (CF-mMIMO) system, the interference at legacy wireless users may be caused by joint transmissions from multiple access points (APs). To limit this, we impose interference power constraints, referred to as region constraints, in CF-mMIMO downlink transmission. We consider per-AP transmit power constraints along with region constraints and provide a centralized minimum mean squared error (MMSE) precoder design method, as well as low-complexity solutions. To avoid the fronthaul network load, we also provide a distributed MMSE precoder design method with transmit power and region constraints. The proposed precoding methods protect the legacy wireless system from interference while enabling the use of new frequency bands.

Integrating sensing and communication (ISAC) can help overcome the challenges of limited spectrum and expensive hardware, leading to improved energy and cost efficiency. While full cooperation between sensing and communication can result in significant performance gains, achieving optimal performance requires efficient designs of unified waveforms and beamformers for joint sensing and communication. Sophisticated statistical signal processing and multi-objective optimization techniques are necessary to balance the competing design requirements of joint sensing and communication tasks. As model-based approaches can be suboptimal or too complex, deep learning offers a powerful data-driven alternative, especially when optimal algorithms are unknown or impractical for real-time use. Unified waveform and beamformer design problems for ISAC fall into this category, where fundamental design trade-offs exist between sensing and communication performance metrics, and the underlying models may be inadequate or incomplete. This tutorial paper explores the application of artificial intelligence (AI) to enhance efficiency or reduce complexity in ISAC designs. We emphasize the integration benefits through AI-driven ISAC designs, prioritizing the development of unified waveforms, constellations, and beamforming strategies for both sensing and communication. To illustrate the practical potential of AI-driven ISAC, we present three case studies on waveform, beamforming, and constellation design, demonstrating how unsupervised learning and neural network-based optimization can effectively balance performance, complexity, and implementation constraints.

Spanning 7-24 GHz, frequency range 3 (FR3), is a key enabler for next-generation wireless networks by bridging the coverage of sub-6 GHz and the capacity of millimeter-wave bands. Its unique propagation characteristics, such as extended near-field regions and spatially nonstationary fading, enable new transmission strategies. This article explores the potential of FR3 for integrated sensing and communication (ISAC), which unifies wireless communication and environmental sensing. We show that FR3's bandwidth and multiple-input multiple-output (MIMO) capabilities enable high-resolution sensing, multi-target tracking, and fast data transmission. We emphasize the importance of ultra-massive MIMO with extremely large aperture arrays (ELAAs) and the need for unified near-field and far-field channel models to support efficient ISAC. Finally, we outline challenges and future research directions for ELAA-based ISAC in 6G FR3.

First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce a new class of generalized composite estimating sequences, devised by exploiting the information embedded in the iterates generated during the minimization process. Building on these sequences, we propose a novel accelerated first-order method tailored for such objective structures. This method also features a backtracking line-search strategy and achieves an accelerated convergence rate, regardless of whether the true Lipschitz constant is known. Additionally, it exhibits robustness to hyperparameter initialization that depends on the strong convexity parameter, a property of practical importance. The method’s efficiency and robustness are substantiated by comprehensive numerical evaluations on both synthetic and real-world datasets, demonstrating its effectiveness in data processing applications.

This paper studies a near-field beamforming design problem for integrated sensing and communications (ISAC) systems. The design is formulated as an optimization problem that minimizes the Euclidean distance between the synthesized beamformers and the desired communication and sensing beamformers. An alternating minimization framework is developed to address the problem, where a critical subproblem is efficiently solved using the alternating direction method of multipliers. To improve convergence and performance, the resulting iterative procedure is unrolled into a neural network. Numerical results validate the effectiveness of the proposed wideband beamforming scheme for near-field ISAC systems.

A unified framework for distributionally robust adaptive beamforming is developed by combining convex optimization reformulations with learning-based enhancements. The starting point is a Wasserstein-based robust formulation, which is solved efficiently via fast iterative shrinkage-thresholding algorithm (FISTA) and subsequently unrolled into a trainable network, allowing layer-wise, data-driven adaptation of step sizes and robustness parameters. To further refine robustness, a knowledge-aided reconstruction network for the interference-plus-noise covariance matrix is incorporated. This module generates a data-driven prior solely from the sample data covariance matrix. Numerical experiments show that the proposed approach converges faster and attains a higher output signal-to-interference-plus-noise ratio (SINR) than classical methods, with the integrated network achieving performance close to the globally optimal benchmark.

Low-rank adapters are usually compared by sweeping a small set of ranks, but the rank also fixes the resolution of the parameter budget. For a 2048×2048 OPT attention projection, increasing LoRA by one rank stores 4096 trainable scalars, leaving large gaps between feasible low-budget adapter sizes. This paper asks whether a tensorized adapter with finer capacity increments changes the observed accuracy–budget trade-off. We instantiate this question with fixed-component canonical polyadic (CP) tensor adapters. Under a 32×64×32×64 tensorization, one normalized CP component stores 193 trainable scalars per projection, about 21 times smaller than one LoRA rank step. We compare CP adapters and LoRA on OPT-1.3B across SST-2, RTE, and BoolQ under matched target modules, training protocol, data caps, and seed schedules. CP trains stably and fills the gaps between LoRA ranks, but the effect is task-dependent: SST-2 reaches an early low-budget plateau, BoolQ benefits from additional CP components before saturating slightly below LoRA, and RTE remains LoRA-favored. Finer parameter steps are therefore useful for diagnosing PEFT budget sensitivity, but they do not by themselves guarantee a better accuracy–budget curve.

Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.We propose a parameter-parsimonious framework based on a low-rank Canonical Polyadic Decomposition (CPD) of the entire latent HSI 𝒳∈ℝ^P× Q × N.This approach recasts the problem from recovering a large-scale image with PQN variables to estimating the CPD factors with (P+Q+N)R variables.This model also enables a structure-aware, anisotropic Total Variation (TV) regularization applied only to the spatial factors, preserving the smooth spectral signatures.An efficient algorithm based on the Proximal Alternating Linearized Minimization (PALM) framework is developed to solve the resulting non-convex optimization problem.Experiments confirm the model's efficiency, showing a numerous parameter reduction of over two orders of magnitude and a compelling trade-off between model compactness and reconstruction accuracy.

The globally optimal robust adaptive beamforming (RAB) solution is studied for worst-case signal-to-interference-plus-noise ratio (SINR) maximization (the maximin SINR problem) under convex and closed uncertainty sets for the desired signal covariance and interference-plus-noise covariance (INC) matrices, considering a general-rank signal model. First, the corresponding minimax SINR problem is reformulated as a convex optimization problem. In particular, this problem becomes a semidefinite programming (SDP) problem when the uncertainty sets can be represented by finitely many linear matrix inequality constraints. It is then shown that, for a general-rank signal model, the maximin and minimax SINR problems are equivalent when the uncertainty sets are convex and closed, in the sense that they share the same optimal value and the same set of optimal solutions. The requirement of closedness is weaker than the compactness assumption previously used to establish the equivalence between minimax and maximin SINR problems for the rank-one signal model, a state-of-the-art result reported approximately two decades ago. Consequently, an optimal solution to the minimax SINR problem is also globally optimal for the maximin SINR problem, and this solution can be obtained by solving the equivalent SDP of the minimax problem in a single step. In contrast, existing iterative approximation algorithms for the maximin SINR problem yield only locally optimal solutions. Simulation results demonstrate that these approximation algorithms return suboptimal values that can be strictly smaller than the optimal value of the minimax problem, and that the beamformer output SINR obtained via the minimax formulation is higher than that achieved by beamformers derived from the maximin problem using approximation algorithms.

Optimization-based power control algorithms are predominantly iterative with high computational complexity, making them impractical for real-time applications in cell-free massive multiple-input multiple-output (CFmMIMO) systems. Learning-based methods have emerged as a promising alternative, and among them, graph neural networks (GNNs) have demonstrated their excellent performance in solving power control problems. However, all existing GNN-based approaches assume ideal orthogonality among pilot sequences for user equipments (UEs), which is unrealistic given that the number of UEs exceeds the available orthogonal pilot sequences in CFmMIMO schemes. Additionally, supervised training necessitates costly computational resources for computing the target power control solutions for a large volume of training samples. To address these issues, we propose a graph attention network for downlink power control in CFmMIMO systems that operates in a self-supervised manner while effectively handling pilot contamination and adapting to a dynamic number of UEs. Experimental results show its effectiveness, even in comparison to the optimal accelerated projected gradient method as a baseline.

We propose a novel multibeam time-division (TD) integrated sensing and communication approach. The TD strategy is introduced to address the simultaneous high requirements for sensing performance and communication rate, while the new multibeam design is proposed to achieve wide-area sensing with improved accuracy even for null-direction targets. Unlike most multibeam methods that typically rely on beam scanning and thus suffer from limited direction estimation accuracy, the proposed method exploits inter-beam relationships to enhance estimation accuracy. Moreover, the proposed multibeam method achieves a significantly higher maximum unambiguous velocity for null-direction targets, mitigating the velocity ambiguity inherent in the conventional Doppler division multiple access approach. Simulation results validate the effectiveness of the proposed approach.

This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity constraints. Our approach accommodates both linear and logistic regression formulations for diverse response variables while addressing the structural heterogeneity inherent in multidimensional tensor data. We integrate fused LASSO, total variation, and ridge regularizers, each tailored to specific tensor modes, and develop an efficient alternating direction method of multipliers (ADMM) based algorithm for parameter estimation. Comprehensive experiments on synthetic signals and real hyperspectral datasets demonstrate that NS-KTR consistently outperforms conventional tensor regression methods. The framework's ability to preserve distinct structural characteristics across tensor dimensions while ensuring physical interpretability makes it especially suitable for applications in signal processing and hyperspectral image analysis.

Integrated sensing, communication, and computation (ISCC) enables next-generation wireless networks to perform environmental perception while processing massive data under stringent quality-of-service (QoS) requirements. Energy consumption is a crucial indicator for the ISCC system design. However, accounting for energy heterogeneity in ISCC system design is an open problem. Specifically, battery-constrained user equipments (UEs) and energy-abundant access points (APs) require fundamentally different energy allocation strategies based on device computational capabilities, battery states, and QoS constraints. In this paper, we introduce a nonconvex energy cost minimization problem by considering a user-specific energy cost ratio coefficient that explicitly balances UE-AP energy consumption according to heterogeneous device energy states. To efficiently address this problem, a double-loop framework combining successive convex approximation and alternating direction method of multipliers is also developed. Numerical results demonstrate that the proposed scheme significantly outperforms the fixed offloading baselines (full offloading, full local and half offloading) in terms of the total energy cost. In particular, the proposed scheme achieves up to 25−47.6% energy cost reduction at moderate latency constraints over fixed offloading baselines, thereby supporting time-sensitive applications. Moreover, this work provides an effective solution for energy-efficient and QoS-aware 6G ISCC systems serving diverse devices with conflicting energy priorities.

Learning-based downlink power control in cell-free massive multiple-input multiple-output (CFmMIMO) systems offers a promising alternative to conventional iterative optimization algorithms, which are computationally intensive due to online iterative steps. Existing learning-based methods, however, often fail to exploit the intrinsic structure of channel data and neglect pilot allocation information, leading to suboptimal performance, especially in large-scale networks with many users. This paper introduces the pilot contamination-aware power control (PAPC) transformer neural network, a novel approach that integrates pilot allocation data into the network, effectively handling pilot contamination scenarios. PAPC employs the attention mechanism with a custom masking technique to utilize structural information and pilot data. The architecture includes tailored preprocessing and post-processing stages for efficient feature extraction and adherence to power constraints. Trained in an unsupervised learning framework, PAPC is evaluated against the accelerated proximal gradient (APG) algorithm, showing comparable spectral efficiency fairness performance, while significantly improving computational efficiency. Simulations demonstrate PAPC's superior performance over fully connected networks (FCNs) that lack pilot information, its scalability to large-scale CFmMIMO networks, and its computational efficiency improvement over APG. PAPC is further validated through ablation studies and evaluated across several representative CFmMIMO scenarios, demonstrating robustness to pilot contamination, scalability, and adaptability to varying user counts without retraining.