{"title":"Observation Matrix Design for Densifying MIMO Channel Estimation via 2D Ice Filling","authors":"Zijian Zhang;Mingyao Cui","doi":"10.1109/TSP.2026.3657342","DOIUrl":"10.1109/TSP.2026.3657342","url":null,"abstract":"In recent years, densifying multiple-input multiple-output (MIMO) has attracted much attention from the communication community. Thanks to the subwavelength antenna spacing, the strong correlations among densifying antennas provide sufficient prior knowledge about channel state information (CSI). This inspires the careful design of observation matrices (e.g., transmit precoders and receive combiners), that exploits the CSI prior knowledge, to boost channel estimation performance. Aligned with this vision, this work proposes to jointly design the combiners and precoders by maximizing the mutual information between the received pilots and densifying MIMO channels. A two-dimensional ice-filling (2DIF) algorithm is proposed to efficiently accomplish this objective. The algorithm is motivated by the fact that the eigenspace of MIMO channel covariance can be decoupled into two sub-eigenspaces, which are associated with the correlations of transmitter antennas and receiver antennas, respectively. By properly setting the precoder and the combiner as the eigenvectors from these two sub-eigenspaces, the 2DIF promises to generate near-optimal observation matrices. Moreover, we further extend the 2DIF method to the popular hybrid combining systems, where a two-stage 2DIF (TS-2DIF) algorithm is developed to handle the analog combining circuits realized by phase shifters. Simulation results demonstrate that, compared to the state-of-the-art schemes, the proposed 2DIF and TS-2DIF methods can achieve superior channel estimation accuracy.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"798-814"},"PeriodicalIF":5.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tran Thien Dat Nguyen;Ba Tuong Vo;Ba-Ngu Vo;Hoa Van Nguyen;Changbeom Shim
{"title":"The Mean of Multi-Object Trajectories","authors":"Tran Thien Dat Nguyen;Ba Tuong Vo;Ba-Ngu Vo;Hoa Van Nguyen;Changbeom Shim","doi":"10.1109/TSP.2026.3657434","DOIUrl":"10.1109/TSP.2026.3657434","url":null,"abstract":"This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multi-sets of trajectories) along with algorithms for computing them. Specifically, we use the Fréchet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multi-object trajectories. Further, we develop efficient algorithms to compute these means using greedy search and Gibbs sampling. Using distributed multi-object tracking as an application, we demonstrate that the Fréchet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"531-544"},"PeriodicalIF":5.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhongtao Chen;Lei Cheng;Yik-Chung Wu;H. Vincent Poor
{"title":"Rank-Revealing Bayesian Block-Term Tensor Completion With Graph Information","authors":"Zhongtao Chen;Lei Cheng;Yik-Chung Wu;H. Vincent Poor","doi":"10.1109/TSP.2026.3656119","DOIUrl":"10.1109/TSP.2026.3656119","url":null,"abstract":"Block-term decomposition (BTD), particularly its rank-<inline-formula><tex-math>$left(L_{r},L_{r},1right)$</tex-math></inline-formula> special case, is widely used in signal processing. Traditional methods for computing BTD either unrealistically assume the number of blocks and block ranks are known or require exhaustive tuning of these parameters. While sparsity-promoting regularization has been introduced to estimate these parameters more efficiently, it still requires regularization parameter tuning. Bayesian learning addresses these issues by employing sparsity-promoting priors on the number of blocks and block ranks, but so far is limited to fully observed BTD tensors. To process incomplete BTD tensors, only a few optimization-based methods have been proposed, and they continue to suffer from heavy parameter tuning. To enable tuning-free BTD completion, a prior that simultaneously enforces block-wise sparsity and within-block column-wise sparsity while incorporating graph structure is introduced within the Bayesian framework. Besides theoretically establishing the legitimacy of the prior distribution, a mean-field design is developed to obtain a closed-form updating variational inference (VI) algorithm without loss of graph information. Extensive experiments on both synthetic datasets and real-world datasets demonstrate the superiority of the proposed method over existing optimization‐based algorithms and the Bayesian model without graph information, in terms of rank learning, tensor recovery, and factor recovery.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"654-669"},"PeriodicalIF":5.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thu Ha Phi;Alexandre Hippert-Ferrer;Florent Bouchard;Arnaud Breloy
{"title":"Leveraging Low-Rank Factorizations of Conditional Correlation Matrices in Graph Learning","authors":"Thu Ha Phi;Alexandre Hippert-Ferrer;Florent Bouchard;Arnaud Breloy","doi":"10.1109/TSP.2026.3656887","DOIUrl":"10.1109/TSP.2026.3656887","url":null,"abstract":"This paper addresses the problem of learning an undirected graph from data gathered at each node. Within Gaussian graphical models (GGM), the topology of such graph can be linked to the support of the conditional correlation matrix of the data. The corresponding graph learning problem then scales as the square of number of variables (nodes), which is usually problematic for large dimension. To tackle this issue, we propose a graph learning framework that leverages a low-rank factorization of the conditional correlation matrix. In order to solve the resulting optimization problem, we derive tools required to apply Riemannian optimization techniques for this particular structure. The proposal is then particularized to a low-rank constrained counterpart of the standard GGM estimation problem, i.e., the regularized maximum likelihood estimation of a precision matrix. Experiments on synthetic and real data demonstrate that a very efficient dimension-versus-performance trade-off can be achieved with this approach.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"750-764"},"PeriodicalIF":5.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Characteristics of the Conjugate Function Enabling Effective Dual Decomposition Methods","authors":"Hansi Abeynanda;Chathuranga Weeraddana;Carlo Fischione","doi":"10.1109/TSP.2026.3656332","DOIUrl":"10.1109/TSP.2026.3656332","url":null,"abstract":"We investigate a novel characteristic of the conjugate function associated to a generic convex optimization problem, which can subsequently be leveraged for efficient dual decomposition methods. In particular, under mild assumptions, we show that there is a specific region in the domain of the conjugate function such that for any point in the region, there is always a ray originating from that point along which the gradients of the conjugate remain constant. We refer to this characteristic as a <italic>fixed gradient over rays</i> (FGOR). We further show that this characteristic is inherited by the corresponding dual function. Then we provide a thorough exposition of the application of the FGOR characteristic to dual subgradient methods. More importantly, we leverage FGOR to devise a simple stepsize rule that can be prepended with state-of-the-art stepsize methods enabling them to be more efficient. Furthermore, we investigate how the FGOR characteristic is used when solving the global consensus problem, a prevalent formulation in diverse application domains. We show that FGOR can be exploited not only to expedite the convergence of the dual decomposition methods but also to reduce the communication overhead. FGOR is extended to nonconvex formulations, and its advantages in stochastic optimization are demonstrated. Numerical experiments using quadratic objectives and a regularized least squares regression with real datasets are conducted. The results show that FGOR can significantly improve the performance of existing stepsize methods and outperform the state-of-the-art splitting methods on average in terms of both convergence behavior and communication efficiency.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"572-588"},"PeriodicalIF":5.8,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11359597","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Biased Compression in Gradient Coding for Distributed Learning","authors":"Chengxi Li;Ming Xiao;Mikael Skoglund","doi":"10.1109/TSP.2026.3656662","DOIUrl":"10.1109/TSP.2026.3656662","url":null,"abstract":"Communication bottlenecks and the presence of stragglers pose significant challenges in distributed learning (DL). To deal with these challenges, recent advances leverage unbiased compression functions and gradient coding. However, the significant benefits of biased compression remain largely unexplored. To close this gap, we propose <bold>Co</b>mpressed Gradient <bold>Co</b>ding with <bold>E</b>rror <bold>F</b>eedback (COCO-EF), a novel DL method that combines gradient coding with biased compression to mitigate straggler effects and reduce communication costs. In each iteration, non-straggler devices encode local gradients from redundantly allocated training data, incorporate prior compression errors, and compress the results using biased compression functions before transmission. The server aggregates these compressed messages from the non-stragglers to approximate the global gradient for model updates. We provide rigorous theoretical convergence guarantees for COCO-EF and validate its superior learning performance over baseline methods through empirical evaluations. As far as we know, we are among the first to rigorously demonstrate that biased compression has substantial benefits in DL, when gradient coding is employed to cope with stragglers.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"514-530"},"PeriodicalIF":5.8,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiaohuan Wu;Jin Qiu;Ji Sun;Wei Liu;Haiyang Zhang;Yonina C. Eldar
{"title":"Source Localization for Extremely Large-Scale Antenna Arrays Under Spatial Non-Stationarity and Near-Field Effects","authors":"Xiaohuan Wu;Jin Qiu;Ji Sun;Wei Liu;Haiyang Zhang;Yonina C. Eldar","doi":"10.1109/TSP.2026.3654842","DOIUrl":"10.1109/TSP.2026.3654842","url":null,"abstract":"To achieve ultra-high precision positioning, the extremely large-scale antenna array (ELAA), consisting of hundreds or even thousands of antenna elements, has garnered significant attention. However, due to increased antenna aperture, it inevitably encounters both near-field effects and spatial non-stationarity effects. In the near-field region, the traditional assumption of far-field plane wavefront no longer holds, necessitating consideration of spherical wave characteristics. Spatial non-stationarity arises when signals fail to reach the entire array, but instead only impinge on a subset of antennas, which is referred to as the signal’s visible region (VR). Both effects cause model mismatch and therefore reduce positioning accuracy. In this paper, we introduce an exact near-field signal model in the context of ELAA. Based on this model, we prove that the steering vectors of source signals and the eigenvectors of the signal subspace become collinear as the number of antennas approaches infinity, which makes it easier to estimate the VR and source location parameters. Accordingly, we develop an estimation method to effectively extract the VR information of signals even when the VRs are discontinuous or overlapping. After obtaining the VR information, we propose three source localization methods that leverage the estimated VR and eigenvectors. Simulation results demonstrate that the proposed methods achieve high-precision localization while reducing computational complexity, thereby overcoming the model mismatch induced by near-field effects and spatial non-stationarity effects in ELAA.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"685-700"},"PeriodicalIF":5.8,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145993254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xi Wang;Yang Liu;Xiaotong Zhao;Qingjiang Shi;Ye Yang
{"title":"On Stochastic Beamforming for Ergodic Sum-Rate Maximization in Cooperative Transmission Systems","authors":"Xi Wang;Yang Liu;Xiaotong Zhao;Qingjiang Shi;Ye Yang","doi":"10.1109/TSP.2025.3648327","DOIUrl":"10.1109/TSP.2025.3648327","url":null,"abstract":"In this paper, we investigate stochastic beamforming approaches to maximize the ergodic sum-rate (ESR) for cooperative transmission systems. To this end, by utilizing the seminal weighted minimum mean square error (WMMSE) transform and adopting the stochastic successive upper-bound minimization framework, we first propose a stochastic WMMSE (SWMMSE) algorithm that maximizes the network’s ESR via analytically updating beamformers in an online manner. This algorithm can operate without any prior knowledge on the channel statistics and is applicable to very generic channel models with arbitrary probability distributions. Based on that, by substituting the SWMMSE update with the determinant equivalents (DEs) derived from large-dimensional random matrix theory, we further develop a DE-WMMSE algorithm. This method requires only the first- and second-order channel statistics and obviates the need for sampling channel. As will be proved, unlike the restrictions in the existing literature, the DE-WMMSE algorithm can be applied to rather generic channel models beyond Rayleigh. Numerical results verify the effectiveness and benefit of our proposed algorithms. Especially, the SWMMSE algorithm is highly computationally efficient for large-scale networks, while the DE-WMMSE algorithm is fast and convenient for modest-scale networks.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"781-797"},"PeriodicalIF":5.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145972096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Revised Maximum-Likelihood Detector With Quantization Design for One-Bit Massive MIMO Systems","authors":"Shumei Wei;Jin Xu;Xiaofeng Tao;Shixun Gong;Rui Meng","doi":"10.1109/TSP.2026.3653950","DOIUrl":"10.1109/TSP.2026.3653950","url":null,"abstract":"One-bit analog-to-digital converters (ADCs) offer a practical solution for reducing both cost and power consumption in massive multiple-input multiple-output (MIMO) systems. Nevertheless, the severe distortion induced by extremely coarse quantization significantly deteriorates the data detection performance. For 1-bit ADC, the conventional symmetric quantization may not necessarily be the optimal choice. This paper examines the impact of quantization thresholds on the performance of maximum likelihood (ML) data detection in one-bit massive MIMO systems, and proposes a revised ML (rML) detector with an iterative adaptive quantization design. Initially, the original ML detection problem, constrained by discrete constellations, is reformulated into the rML problem. By optimizing the quantization thresholds, the solution to the rML problem can be guided to converge to the true transmitted signal. Leveraging this characteristic, we propose the rML detector with iterative adaptive quantization design to progressively refine the quantization thresholds during data detection. We further present two implementation strategies for the rML detector: one iteration one quantization (1I1Q) and one iteration two quantization (1I2Q). Additionally, an rML-based joint channel estimation and data detection (JED) method is introduced, where the decoded data from 1I1Q is utilized to enhance the pilot data vectors, thereby refining the estimated channel and ultimately enhancing data detection performance. Finally, numerical results demonstrate that the proposed rML detector with iterative adaptive quantization design is both efficient and robust, significantly outperforming the state-of-the-art methods.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"409-422"},"PeriodicalIF":5.8,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145961946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mingjie Shao;Wei-Kun Chen;Cheng-Yang Yu;Ya-Feng Liu;Wing-Kin Ma
{"title":"One-Bit MIMO Detection: From Global Maximum-Likelihood Detector to Amplitude Retrieval Approach","authors":"Mingjie Shao;Wei-Kun Chen;Cheng-Yang Yu;Ya-Feng Liu;Wing-Kin Ma","doi":"10.1109/TSP.2026.3653849","DOIUrl":"10.1109/TSP.2026.3653849","url":null,"abstract":"As communication systems advance towards the future 6G era, the incorporation of large-scale antenna arrays in base stations (BSs) presents challenges such as increased hardware costs and energy consumption. To address these issues, the use of one-bit analog-to-digital converters (ADCs)/digital-to-analog converters (DACs) has gained significant attentions. This paper focuses on one-bit multiple-input multiple-output (MIMO) detection in an uplink multiuser transmission scenario where the BS employs one-bit ADCs. One-bit quantization retains only the sign information and loses the amplitude information, which poses a unique challenge in the corresponding detection problem. The maximum-likelihood (ML) formulation of one-bit MIMO detection has a challenging likelihood function that hinders the application of many high-performance detectors developed for classic MIMO detection (under high-resolution ADCs). While many approximate methods for the ML detection problem have been studied, it lacks an efficient <italic>global</i> algorithm. This paper fills this gap by proposing an efficient branch-and-bound algorithm, which is guaranteed to find the global solution of the one-bit ML MIMO detection problem. Additionally, a new amplitude retrieval (AR) detection approach is developed, incorporating explicit amplitude variables into the problem formulation. The AR approach yields simpler objective functions that enable the development of efficient algorithms offering both global and approximate solutions. The paper also contributes to the computational complexity analysis of both ML and AR detection problems. Extensive simulations are conducted to demonstrate the effectiveness and efficiency of the proposed formulations and algorithms.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"765-780"},"PeriodicalIF":5.8,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145961944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}