Pub Date : 2025-11-17DOI: 10.1109/TSP.2025.3632064
Xiaomeng Chen;Huiwen Yang;Subhrakanti Dey;Ling Shi
Distributed non-cooperative games are prevalent in emerging applications such as traffic control, vehicle charging, and smart grid management. In distributed systems without central coordinators, agents must share and retrieve information locally to seek a Nash equilibrium (NE). However, this extensive data exchange can lead to significant communication bottlenecks. To address this challenge, over-the-air computing provides a promising solution by exploiting the superposition property of wireless multiple access channels (MAC), allowing for substantial bandwidth savings. In this paper, we propose an over-the-air framework for general distributed non-cooperative games. Specifically, we introduce an algorithm based on non-coherent over-the-air computing, AirNES, to find an NE in distributed non-cooperative games. Our algorithm accounts for noisy channels and non-coherent transmission, eliminating the need for channel state information. We demonstrate that, with properly tuned decreasing consensus and gradient stepsizes, AirNES guarantees almost sure convergence to the exact NE, even in the presence of channel fading and additive noise. Additionally, we extend our analysis to scenarios with fixed stepsizes, where linear convergence can be achieved at the expense of reduced accuracy. Finally, we provide numerical simulations to demonstrate the effectiveness of the proposed protocol.
{"title":"Non-Coherent Over-the-Air Decentralized Method for Non-Cooperative Games in Multi-Agent Systems","authors":"Xiaomeng Chen;Huiwen Yang;Subhrakanti Dey;Ling Shi","doi":"10.1109/TSP.2025.3632064","DOIUrl":"10.1109/TSP.2025.3632064","url":null,"abstract":"Distributed non-cooperative games are prevalent in emerging applications such as traffic control, vehicle charging, and smart grid management. In distributed systems without central coordinators, agents must share and retrieve information locally to seek a Nash equilibrium (NE). However, this extensive data exchange can lead to significant communication bottlenecks. To address this challenge, over-the-air computing provides a promising solution by exploiting the superposition property of wireless multiple access channels (MAC), allowing for substantial bandwidth savings. In this paper, we propose an over-the-air framework for general distributed non-cooperative games. Specifically, we introduce an algorithm based on non-coherent over-the-air computing, AirNES, to find an NE in distributed non-cooperative games. Our algorithm accounts for noisy channels and non-coherent transmission, eliminating the need for channel state information. We demonstrate that, with properly tuned decreasing consensus and gradient stepsizes, AirNES guarantees almost sure convergence to the exact NE, even in the presence of channel fading and additive noise. Additionally, we extend our analysis to scenarios with fixed stepsizes, where linear convergence can be achieved at the expense of reduced accuracy. Finally, we provide numerical simulations to demonstrate the effectiveness of the proposed protocol.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4684-4699"},"PeriodicalIF":5.8,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535611","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}
Machine learning (ML) models are often sensitive to carefully crafted yet seemingly unnoticeable perturbations. Such adversarial examples are considered to be a property of machine learning (ML) models, often associated with their black-box operation and sensitivity to features learned from data. This work examines the adversarial sensitivity of non-learned decision rules, and particularly of iterative optimizers. Our analysis is inspired by the recent developments in deep unfolding, which cast such optimizers as ML models. We show that non-learned iterative optimizers share the sensitivity to adversarial examples of ML models, and that attacking iterative optimizers effectively alters the optimization objective surface in a manner that modifies the minima sought. We then leverage the ability to cast iteration-limited optimizers as ML models to enhance robustness via adversarial training. For a class of proximal gradient optimizers, we rigorously prove how their learning affects adversarial sensitivity. We numerically back our findings, showing the vulnerability of various optimizers, as well as the robustness induced by unfolding and adversarial training.
{"title":"Unveiling and Mitigating Adversarial Vulnerabilities in Iterative Optimizers","authors":"Elad Sofer;Tomer Shaked;Caroline Chaux;Nir Shlezinger","doi":"10.1109/TSP.2025.3633304","DOIUrl":"10.1109/TSP.2025.3633304","url":null,"abstract":"Machine learning (ML) models are often sensitive to carefully crafted yet seemingly unnoticeable perturbations. Such adversarial examples are considered to be a property of machine learning (ML) models, often associated with their black-box operation and sensitivity to features learned from data. This work examines the adversarial sensitivity of non-learned decision rules, and particularly of iterative optimizers. Our analysis is inspired by the recent developments in deep unfolding, which cast such optimizers as ML models. We show that non-learned iterative optimizers share the sensitivity to adversarial examples of ML models, and that attacking iterative optimizers effectively alters the optimization objective surface in a manner that modifies the minima sought. We then leverage the ability to cast iteration-limited optimizers as ML models to enhance robustness via adversarial training. For a class of proximal gradient optimizers, we rigorously prove how their learning affects adversarial sensitivity. We numerically back our findings, showing the vulnerability of various optimizers, as well as the robustness induced by unfolding and adversarial training.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4669-4683"},"PeriodicalIF":5.8,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535610","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}
Pub Date : 2025-11-17DOI: 10.1109/TSP.2025.3633496
Tiancheng Li;Jingyuan Wang;Guchong Li;Dengwei Gao
To solve the target tracking problem with little a-priori information about the target dynamics, our series of studies, including this paper as the third part, propose a continuous-time trajectory estimation approach (dubbed targeting track) based on the stochastic process (SP) theory and a deterministic-stochastic decomposition framework. Specifically, we decompose the learning of the trajectory SP into two sequential stages: the first fits the deterministic trend of the trajectory using a curve function of time, while the second estimates the residual stochastic component through learning either a Gaussian process (GP) or Student’s-$t$ process (StP). The former has been addressed in the companion paper and the latter is the focus of this paper. This leads to a data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. Notably, our approach models the temporal correlations of the state sequence and of measurement noise using separate GP or StP. It does not only take advantage of the smooth trend of the target but also makes use of the long-term temporal correlation of both the data and the model fitting error. Although the GP admits an exact closed-form expression for the linear system, approximations have to be adopted for StP modeling. Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches.
{"title":"From Target Tracking to Targeting Track — Part III: Stochastic Process Modeling and Online Learning","authors":"Tiancheng Li;Jingyuan Wang;Guchong Li;Dengwei Gao","doi":"10.1109/TSP.2025.3633496","DOIUrl":"10.1109/TSP.2025.3633496","url":null,"abstract":"To solve the target tracking problem with little a-priori information about the target dynamics, our series of studies, including this paper as the third part, propose a continuous-time trajectory estimation approach (dubbed targeting track) based on the stochastic process (SP) theory and a deterministic-stochastic decomposition framework. Specifically, we decompose the learning of the trajectory SP into two sequential stages: the first fits the deterministic trend of the trajectory using a curve function of time, while the second estimates the residual stochastic component through learning either a Gaussian process (GP) or Student’s-<inline-formula><tex-math>$t$</tex-math></inline-formula> process (StP). The former has been addressed in the companion paper and the latter is the focus of this paper. This leads to a data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. Notably, our approach models the temporal correlations of the state sequence and of measurement noise using separate GP or StP. It does not only take advantage of the smooth trend of the target but also makes use of the long-term temporal correlation of both the data and the model fitting error. Although the GP admits an exact closed-form expression for the linear system, approximations have to be adopted for StP modeling. Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5336-5347"},"PeriodicalIF":5.8,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535609","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}
Pub Date : 2025-11-13DOI: 10.1109/TSP.2025.3632146
Chengyu Yang;Jinling Liang;Zhongyi Zhao
This paper investigates the distributed fusion filtering problem for a class of two-dimensional nonlinear systems subject to unknown-but-bounded noises over sensor networks using the zonotopic set-membership approach. Distinct from the existing studies, a novel channel-based bit rate constraint model associated with a binary encoding scheme is introduced to characterize the limited bandwidth of sensor networks, where the length of the binary code sequences in communication channels among sensors is directly influenced by the limited bit rate. The objective is to design a distributed fusion filter which can effectively estimate the system states and construct a zonotope which encloses the overall filtering error. To this end, multiple local filters are developed, and the corresponding zonotopes that respectively bound the local filtering errors and the encoding errors are derived using set operation techniques. By minimizing the $F$-radius of these zonotopes, the locally optimal filter gains and the optimal channel bit rate allocation strategy are obtained. Subsequently, the fused estimation is generated by integrating these local estimations with appropriately determined fusion weights. Finally, the effectiveness of the proposed filtering algorithm is validated through a numerical example.
{"title":"Zonotopic Distributed Fusion Filtering for 2-D Nonlinear Systems Over Sensor Networks: A Channel-Based Bit Rate Constraint","authors":"Chengyu Yang;Jinling Liang;Zhongyi Zhao","doi":"10.1109/TSP.2025.3632146","DOIUrl":"10.1109/TSP.2025.3632146","url":null,"abstract":"This paper investigates the distributed fusion filtering problem for a class of two-dimensional nonlinear systems subject to unknown-but-bounded noises over sensor networks using the zonotopic set-membership approach. Distinct from the existing studies, a novel channel-based bit rate constraint model associated with a binary encoding scheme is introduced to characterize the limited bandwidth of sensor networks, where the length of the binary code sequences in communication channels among sensors is directly influenced by the limited bit rate. The objective is to design a distributed fusion filter which can effectively estimate the system states and construct a zonotope which encloses the overall filtering error. To this end, multiple local filters are developed, and the corresponding zonotopes that respectively bound the local filtering errors and the encoding errors are derived using set operation techniques. By minimizing the <inline-formula><tex-math>$F$</tex-math></inline-formula>-radius of these zonotopes, the locally optimal filter gains and the optimal channel bit rate allocation strategy are obtained. Subsequently, the fused estimation is generated by integrating these local estimations with appropriately determined fusion weights. Finally, the effectiveness of the proposed filtering algorithm is validated through a numerical example.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4654-4668"},"PeriodicalIF":5.8,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145509292","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}
Pub Date : 2025-11-10DOI: 10.1109/tsp.2025.3629292
Jiayi Huang, Sangwoo Park, Osvaldo Simeone
{"title":"Calibrating Bayesian Learning via Regularization, Confidence Minimization, and Selective Inference","authors":"Jiayi Huang, Sangwoo Park, Osvaldo Simeone","doi":"10.1109/tsp.2025.3629292","DOIUrl":"https://doi.org/10.1109/tsp.2025.3629292","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"47 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145484819","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}
Pub Date : 2025-11-10DOI: 10.1109/tsp.2025.3629732
Yunlian Tian, Wei Yi, Wujun Li, Hongbin Li
{"title":"Joint Coherent Integration and Detection of Radar Spread Targets with Range Migration","authors":"Yunlian Tian, Wei Yi, Wujun Li, Hongbin Li","doi":"10.1109/tsp.2025.3629732","DOIUrl":"https://doi.org/10.1109/tsp.2025.3629732","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"99 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145484820","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}
Pub Date : 2025-11-07DOI: 10.1109/tsp.2025.3630236
Guangle Jia, Yulong Huang, Henry Leung
{"title":"A Novel Robust Kalman Filter Based on Normal-Bernoulli Distribution for Non-stationary Heavy-tailed Measurement Noise","authors":"Guangle Jia, Yulong Huang, Henry Leung","doi":"10.1109/tsp.2025.3630236","DOIUrl":"https://doi.org/10.1109/tsp.2025.3630236","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"167 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145461395","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}
Satellite-integrated Internet is regarded as one of the promising frameworks for supporting massive machine type communications-satellite (mMTC-s) via code domain grant-free random access (GFRA). However, the sporadic activation and short-packet transmissions of mMTC-s user equipments (UEs) lead to pilot collisions and decoding failures, which compromise the reliability of massive access and present significant challenges in existing GFRA schemes. By combining the zero-correlation-zone shift-and-superposition pilot (ZSP) with the $ T $-order codebook, this paper proposes a $ZT$-collision resolution GFRA ($ZT$-GFRA) scheme to address these limitations. In the $ZT$-GFRA scheme, each activated UE splits its $ k $-bit message into $r + 1$ parts. The first $ r $ parts are each $ b $ bits long and are assigned to different zero-correlation-zone periodic sequences. These $ r $ sequences are then superimposed to generate a ZSP, thereby expanding the available pilot set. The remaining $k-rb$ bits are encoded using a $ T $-order codebook and concatenated with the ZSP to form a complete frame for access. Moreover, we design a successive iteration then joint ordered likelihood decoder to decode up to $ T $ UEs transmitting the same ZSP, supporting access for up to $binom{Z}{r}cdot T$ UEs. We derive the theoretical expressions for the access failure probability (AFP) of the $ZT$-GFRA scheme under a shadowed-Rician fading channel. Simulation results demonstrate that, compared to the state-of-the-art schemes, our $ZT$-GFRA scheme achieves a significantly lower pilot collision probability and AFP under the same sequence length and SNR conditions.
卫星集成互联网被认为是通过码域无授权随机接入（GFRA）支持大规模机器型卫星通信（mMTC-s）的有前途的框架之一。然而，mMTC-s用户设备（ue）的零星激活和短包传输导致导频碰撞和解码失败，影响了大规模接入的可靠性，给现有的GFRA方案带来了重大挑战。通过将零相关区偏移叠加导频（ZSP）与$ T$阶码本相结合，提出了$ZT$碰撞分辨率GFRA （$ZT$ -GFRA）方案来解决这些限制。在$ZT$ -GFRA方案中，每个激活的UE将其$ k $位消息分成$r + 1$部分。前$ r $部分各$ b $位长，并分配给不同的零相关区周期序列。然后将这些$ r $序列叠加以生成ZSP，从而扩展可用的导频集。剩余的$k-rb$位使用$ T $顺序码本进行编码，并与ZSP连接以形成一个完整的帧供访问。此外，我们设计了一个连续迭代然后联合有序似然解码器来解码多达$ T$ ue传输相同的ZSP，支持访问多达$binom{Z}{r}cdot $ T$ ue。导出了在阴影-梯度衰落信道下ZT -GFRA方案的接入失败概率（AFP）的理论表达式。仿真结果表明，与现有方案相比，在相同序列长度和信噪比条件下，我们的ZT -GFRA方案具有较低的先导碰撞概率和AFP。
{"title":"ZT-Collision Resolution Grant-Free Random Access for Satellite-Integrated Internet","authors":"Liang Xu;Xue Zhao;Yaosheng Zhang;Ye Wang;Jian Jiao;Qinyu Zhang","doi":"10.1109/TSP.2025.3628609","DOIUrl":"10.1109/TSP.2025.3628609","url":null,"abstract":"Satellite-integrated Internet is regarded as one of the promising frameworks for supporting massive machine type communications-satellite (mMTC-s) via code domain grant-free random access (GFRA). However, the sporadic activation and short-packet transmissions of mMTC-s user equipments (UEs) lead to pilot collisions and decoding failures, which compromise the reliability of massive access and present significant challenges in existing GFRA schemes. By combining the zero-correlation-zone shift-and-superposition pilot (ZSP) with the <inline-formula> <tex-math>$ T $</tex-math> </inline-formula>-order codebook, this paper proposes a <inline-formula> <tex-math>$ZT$</tex-math> </inline-formula>-collision resolution GFRA (<inline-formula> <tex-math>$ZT$</tex-math> </inline-formula>-GFRA) scheme to address these limitations. In the <inline-formula> <tex-math>$ZT$</tex-math> </inline-formula>-GFRA scheme, each activated UE splits its <inline-formula> <tex-math>$ k $</tex-math> </inline-formula>-bit message into <inline-formula> <tex-math>$r + 1$</tex-math> </inline-formula> parts. The first <inline-formula> <tex-math>$ r $</tex-math> </inline-formula> parts are each <inline-formula> <tex-math>$ b $</tex-math> </inline-formula> bits long and are assigned to different zero-correlation-zone periodic sequences. These <inline-formula> <tex-math>$ r $</tex-math> </inline-formula> sequences are then superimposed to generate a ZSP, thereby expanding the available pilot set. The remaining <inline-formula> <tex-math>$k-rb$</tex-math> </inline-formula> bits are encoded using a <inline-formula> <tex-math>$ T $</tex-math> </inline-formula>-order codebook and concatenated with the ZSP to form a complete frame for access. Moreover, we design a successive iteration then joint ordered likelihood decoder to decode up to <inline-formula> <tex-math>$ T $</tex-math> </inline-formula> UEs transmitting the same ZSP, supporting access for up to <inline-formula> <tex-math>$binom{Z}{r}cdot T$</tex-math> </inline-formula> UEs. We derive the theoretical expressions for the access failure probability (AFP) of the <inline-formula> <tex-math>$ZT$</tex-math> </inline-formula>-GFRA scheme under a shadowed-Rician fading channel. Simulation results demonstrate that, compared to the state-of-the-art schemes, our <inline-formula> <tex-math>$ZT$</tex-math> </inline-formula>-GFRA scheme achieves a significantly lower pilot collision probability and AFP under the same sequence length and SNR conditions.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4573-4588"},"PeriodicalIF":5.8,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11229876","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145447584","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}
Pub Date : 2025-11-05DOI: 10.1109/tsp.2025.3628349
Christof Baeriswyl, Frédéric Waldmann, Alexander Bertrand, Reto A. Wildhaber
{"title":"Multi-Resolution Autonomous Linear State Space Filters for N-Dimensional Signals","authors":"Christof Baeriswyl, Frédéric Waldmann, Alexander Bertrand, Reto A. Wildhaber","doi":"10.1109/tsp.2025.3628349","DOIUrl":"https://doi.org/10.1109/tsp.2025.3628349","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"1 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145447586","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}
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