Pub Date : 2025-12-15DOI: 10.1109/tsp.2025.3643595
Anton Björkman, David Sundström, Andreas Jakobsson, Filip Elvander
{"title":"Optimal Transport Regularization for Simulation-Informed Room Impulse Response Estimation","authors":"Anton Björkman, David Sundström, Andreas Jakobsson, Filip Elvander","doi":"10.1109/tsp.2025.3643595","DOIUrl":"https://doi.org/10.1109/tsp.2025.3643595","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"2 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145759597","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 : 2025-12-12DOI: 10.1109/tsp.2025.3643309
Zhidi Lin, Ying Li, Feng Yin, Juan Maroñas, Alexandre H. Thiéry
{"title":"Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems","authors":"Zhidi Lin, Ying Li, Feng Yin, Juan Maroñas, Alexandre H. Thiéry","doi":"10.1109/tsp.2025.3643309","DOIUrl":"https://doi.org/10.1109/tsp.2025.3643309","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"146 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731418","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 : 2025-12-11DOI: 10.1109/TSP.2025.3642042
Adarsh M. Subramaniam;Argyrios Gerogiannis;James Z. Hare;Venugopal V. Veeravalli
State of the art methods for target tracking with sensor management (or controlled sensing) are model-based and are obtained through solutions to Partially Observable Markov Decision Process (POMDP) formulations. In this paper a Reinforcement Learning (RL) approach to the problem is explored for the setting where the motion model for the object/target to be tracked is unknown to the observer. It is assumed that the target dynamics are stationary in time, the state space and the observation space are discrete, and there is complete observability of the location of the target under certain (a priori unknown) sensor control actions. Then, a novel Markov Decision Process (MDP) rather than POMDP formulation is proposed for the tracking problem with controlled sensing, which is termed as Track-MDP. In contrast to the POMDP formulation, the Track-MDP formulation is amenable to an RL based solution. It is shown that the optimal policy for the Track-MDP formulation, which is approximated through RL, is guaranteed to track all significant target paths with certainty. The Track-MDP method is then compared with the optimal POMDP policy, and it is shown that the infinite horizon tracking reward of the optimal Track-MDP policy is the same as that of the optimal POMDP policy. In simulations it is demonstrated that Track-MDP based RL can lead to a policy that can track the target with high accuracy and superior energy efficiency.
{"title":"Track-MDP: Reinforcement Learning for Target Tracking With Controlled Sensing","authors":"Adarsh M. Subramaniam;Argyrios Gerogiannis;James Z. Hare;Venugopal V. Veeravalli","doi":"10.1109/TSP.2025.3642042","DOIUrl":"10.1109/TSP.2025.3642042","url":null,"abstract":"State of the art methods for target tracking with sensor management (or controlled sensing) are model-based and are obtained through solutions to Partially Observable Markov Decision Process (POMDP) formulations. In this paper a Reinforcement Learning (RL) approach to the problem is explored for the setting where the motion model for the object/target to be tracked is unknown to the observer. It is assumed that the target dynamics are stationary in time, the state space and the observation space are discrete, and there is complete observability of the location of the target under certain (a priori unknown) sensor control actions. Then, a novel Markov Decision Process (MDP) rather than POMDP formulation is proposed for the tracking problem with controlled sensing, which is termed as Track-MDP. In contrast to the POMDP formulation, the Track-MDP formulation is amenable to an RL based solution. It is shown that the optimal policy for the Track-MDP formulation, which is approximated through RL, is guaranteed to track all significant target paths with certainty. The Track-MDP method is then compared with the optimal POMDP policy, and it is shown that the infinite horizon tracking reward of the optimal Track-MDP policy is the same as that of the optimal POMDP policy. In simulations it is demonstrated that Track-MDP based RL can lead to a policy that can track the target with high accuracy and superior energy efficiency.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5348-5361"},"PeriodicalIF":5.8,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145728939","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 : 2025-12-10DOI: 10.1109/TSP.2025.3642179
Ruiding Hou;Jiaheng Wang;Rui Zhou;Daniel P. Palomar;Xiqi Gao;Björn Ottersten
Precoding techniques, particularly linear precoding, are widely employed in multiple-input multiple-output (MIMO) systems. Although well-studied in the literature, linear precoding design still faces two fundamental challenges: high computational complexity and the lack of a general design approach. This paper presents an efficient and unified framework for linear precoding design in downlink multiuser systems that accommodates diverse criteria, such as weighted sum rate (WSR) maximization and weighted symbol error rate (WSER) minimization, while ensuring quality of service (QoS) requirements. The proposed framework achieves an order-of-magnitude reduction in per-iteration computational complexity compared to existing methods. In particular, by accurately characterizing the feasible signal-to-interference-plus-noise ratio (SINR) region, we transform the high-dimensional precoding design problem into a more manageable, low-dimensional SINR allocation problem. We propose an efficient SINR-based precoding (SBP) framework that employs a water-filling solution at each iteration, without the need for matrix inversion. The proposed framework can be extended to broadcast and interference channels with multi-antenna users under pre-fixed receivers. Simulation results demonstrate that our method achieves near-optimal performance while significantly reducing computational complexity compared to existing methods, such as the weighted minimum mean square error (WMMSE) method.
{"title":"An Efficient and Unified Framework for Downlink Linear Precoding with QoS Constraints","authors":"Ruiding Hou;Jiaheng Wang;Rui Zhou;Daniel P. Palomar;Xiqi Gao;Björn Ottersten","doi":"10.1109/TSP.2025.3642179","DOIUrl":"10.1109/TSP.2025.3642179","url":null,"abstract":"Precoding techniques, particularly linear precoding, are widely employed in multiple-input multiple-output (MIMO) systems. Although well-studied in the literature, linear precoding design still faces two fundamental challenges: high computational complexity and the lack of a general design approach. This paper presents an efficient and unified framework for linear precoding design in downlink multiuser systems that accommodates diverse criteria, such as weighted sum rate (WSR) maximization and weighted symbol error rate (WSER) minimization, while ensuring quality of service (QoS) requirements. The proposed framework achieves an order-of-magnitude reduction in per-iteration computational complexity compared to existing methods. In particular, by accurately characterizing the feasible signal-to-interference-plus-noise ratio (SINR) region, we transform the high-dimensional precoding design problem into a more manageable, low-dimensional SINR allocation problem. We propose an efficient SINR-based precoding (SBP) framework that employs a water-filling solution at each iteration, without the need for matrix inversion. The proposed framework can be extended to broadcast and interference channels with multi-antenna users under pre-fixed receivers. Simulation results demonstrate that our method achieves near-optimal performance while significantly reducing computational complexity compared to existing methods, such as the weighted minimum mean square error (WMMSE) method.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"276-292"},"PeriodicalIF":5.8,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11293380","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145717710","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 : 2025-12-09DOI: 10.1109/TSP.2025.3641941
Shenghua Hu;Guangyang Zeng;Wenchao Xue;Haitao Fang;Junfeng Wu;Biqiang Mu
We study the problem of signal source localization using received signal strength measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model’s asymptotic localizability. Then we establish the consistency and asymptotic efficiency of the maximum likelihood (ML) estimator. However, computing the ML estimator is challenging due to its reliance on solving a non-convex optimization problem. To overcome this, we propose a two-step estimator that retains the same asymptotic properties as the ML estimator while offering low computational complexity—linear in the number of measurements. The main challenge lies in obtaining a consistent estimator in the first step. To address this, we construct two linear least-squares estimation problems by applying algebraic transformations to the nonlinear measurement model, leading to closed-form solutions. In the second step, we perform a single Gauss-Newton iteration using the consistent estimator from the first step as the initialization, achieving the same asymptotic efficiency as the ML estimator. Finally, simulation results validate the theoretical property and practical effectiveness of the proposed two-step estimator.
{"title":"RSS-Based Localization: Ensuring Consistency and Asymptotic Efficiency","authors":"Shenghua Hu;Guangyang Zeng;Wenchao Xue;Haitao Fang;Junfeng Wu;Biqiang Mu","doi":"10.1109/TSP.2025.3641941","DOIUrl":"10.1109/TSP.2025.3641941","url":null,"abstract":"We study the problem of signal source localization using received signal strength measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model’s asymptotic localizability. Then we establish the consistency and asymptotic efficiency of the maximum likelihood (ML) estimator. However, computing the ML estimator is challenging due to its reliance on solving a non-convex optimization problem. To overcome this, we propose a two-step estimator that retains the same asymptotic properties as the ML estimator while offering low computational complexity—linear in the number of measurements. The main challenge lies in obtaining a consistent estimator in the first step. To address this, we construct two linear least-squares estimation problems by applying algebraic transformations to the nonlinear measurement model, leading to closed-form solutions. In the second step, we perform a single Gauss-Newton iteration using the consistent estimator from the first step as the initialization, achieving the same asymptotic efficiency as the ML estimator. Finally, simulation results validate the theoretical property and practical effectiveness of the proposed two-step estimator.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5257-5272"},"PeriodicalIF":5.8,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145717743","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}
Composite federated learning offers a general framework for solving machine learning problems with additional regularization terms. However, existing methods often face significant limitations: many require clients to perform computationally expensive proximal operations, and their performance is frequently vulnerable to data heterogeneity. To overcome these challenges, we propose a novel composite federated learning algorithm called FedCanon, designed to solve the optimization problems comprising a possibly non-convex loss function and a weakly convex, potentially non-smooth regularization term. By decoupling proximal mappings from local updates, FedCanon requires only a single proximal evaluation on the server per iteration, thereby reducing the overall proximal computation cost. Concurrently, it integrates control variables into local updates to mitigate the client drift arising from data heterogeneity. The entire architecture avoids the complex subproblems of primal-dual alternatives. The theoretical analysis provides the first rigorous convergence guarantees for this proximal-skipping framework in the general non-convex setting. It establishes that FedCanon achieves a sublinear convergence rate, and a linear rate under the Polyak-Łojasiewicz condition, without the restrictive bounded heterogeneity assumption. Extensive experiments demonstrate that FedCanon outperforms the state-of-the-art methods in terms of both accuracy and computational efficiency, particularly under heterogeneous data distributions.
{"title":"FedCanon: Non-Convex Composite Federated Learning With Efficient Proximal Operation on Heterogeneous Data","authors":"Yuan Zhou;Jiachen Zhong;Xinli Shi;Guanghui Wen;Xinghuo Yu","doi":"10.1109/TSP.2025.3642025","DOIUrl":"10.1109/TSP.2025.3642025","url":null,"abstract":"Composite federated learning offers a general framework for solving machine learning problems with additional regularization terms. However, existing methods often face significant limitations: many require clients to perform computationally expensive proximal operations, and their performance is frequently vulnerable to data heterogeneity. To overcome these challenges, we propose a novel composite federated learning algorithm called FedCanon, designed to solve the optimization problems comprising a possibly non-convex loss function and a weakly convex, potentially non-smooth regularization term. By decoupling proximal mappings from local updates, FedCanon requires only a single proximal evaluation on the server per iteration, thereby reducing the overall proximal computation cost. Concurrently, it integrates control variables into local updates to mitigate the client drift arising from data heterogeneity. The entire architecture avoids the complex subproblems of primal-dual alternatives. The theoretical analysis provides the first rigorous convergence guarantees for this proximal-skipping framework in the general non-convex setting. It establishes that FedCanon achieves a sublinear convergence rate, and a linear rate under the Polyak-Łojasiewicz condition, without the restrictive bounded heterogeneity assumption. Extensive experiments demonstrate that FedCanon outperforms the state-of-the-art methods in terms of both accuracy and computational efficiency, particularly under heterogeneous data distributions.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"215-229"},"PeriodicalIF":5.8,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145717742","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 : 2025-12-08DOI: 10.1109/TSP.2025.3641053
Matteo Nerini;Bruno Clerckx
Analog-domain operations offer a promising solution to accelerating signal processing and enabling future multiple-input multiple-output (MIMO) communications with thousands of antennas. In Part I of this paper, we have introduced a microwave linear analog computer (MiLAC) as an analog computer that processes microwave signals linearly, demonstrating its potential to reduce the computational complexity of specific signal processing tasks. In Part II of this paper, we extend these benefits to wireless communications, showcasing how MiLAC enables gigantic MIMO beamforming entirely in the analog domain. MiLAC -aided beamforming enables the maximum flexibility and performance of digital beamforming, while significantly reducing hardware costs by minimizing the number of radio-frequency (RF) chains and only relying on low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). In addition, it eliminates per-symbol operations by completely avoiding digital-domain processing and remarkably reduces the computational complexity of zero-forcing (ZF), which scales quadratically with the number of antennas instead of cubically. It also processes signals with fixed matrices, e.g., the discrete Fourier transform (DFT), directly in the analog domain. Numerical results show that it can perform ZF and DFT with a computational complexity reduction of up to $1.5times 10^{4}$ and $4.0times 10^{7}$ times, respectively, compared to digital beamforming.
{"title":"Analog Computing for Signal Processing and Communications – Part II: Toward Gigantic MIMO Beamforming","authors":"Matteo Nerini;Bruno Clerckx","doi":"10.1109/TSP.2025.3641053","DOIUrl":"10.1109/TSP.2025.3641053","url":null,"abstract":"Analog-domain operations offer a promising solution to accelerating signal processing and enabling future multiple-input multiple-output (MIMO) communications with thousands of antennas. In Part I of this paper, we have introduced a microwave linear analog computer (MiLAC) as an analog computer that processes microwave signals linearly, demonstrating its potential to reduce the computational complexity of specific signal processing tasks. In Part II of this paper, we extend these benefits to wireless communications, showcasing how MiLAC enables gigantic MIMO beamforming entirely in the analog domain. MiLAC -aided beamforming enables the maximum flexibility and performance of digital beamforming, while significantly reducing hardware costs by minimizing the number of radio-frequency (RF) chains and only relying on low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). In addition, it eliminates per-symbol operations by completely avoiding digital-domain processing and remarkably reduces the computational complexity of zero-forcing (ZF), which scales quadratically with the number of antennas instead of cubically. It also processes signals with fixed matrices, e.g., the discrete Fourier transform (DFT), directly in the analog domain. Numerical results show that it can perform ZF and DFT with a computational complexity reduction of up to <inline-formula><tex-math>$1.5times 10^{4}$</tex-math></inline-formula> and <inline-formula><tex-math>$4.0times 10^{7}$</tex-math></inline-formula> times, respectively, compared to digital beamforming.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5198-5212"},"PeriodicalIF":5.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145704091","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 : 2025-12-08DOI: 10.1109/TSP.2025.3640931
Matteo Nerini;Bruno Clerckx
Analog computing has been recently revived due to its potential for energy-efficient and highly parallel computations. In this two-part paper, we explore analog computers that linearly process microwave signals, named microwave linear analog computers (MiLACs), and their applications in signal processing and communications. In Part I of this paper, we model a MiLAC as a multiport microwave network with tunable impedance components, enabling the execution of mathematical operations by reconfiguring the microwave network and applying input signals at its ports. We demonstrate that a MiLAC can efficiently compute the linear minimum mean square error (LMMSE) estimator and matrix inversion, with remarkably low computational complexity. Specifically, a matrix can be inverted with complexity growing with the square of its size. We also show how a MiLAC can be used jointly with digital operations to implement sophisticated algorithms such as the Kalman filter. To enhance practicability, we propose a design of MiLAC based on lossless impedance components, reducing power consumption and eliminating the need for costly active components. In Part II of this paper, we investigate the applications of MiLACs in wireless communications, highlighting their potential to enable future wireless systems by executing computations and beamforming in the analog domain.
{"title":"Analog Computing for Signal Processing and Communications – Part I: Computing With Microwave Networks","authors":"Matteo Nerini;Bruno Clerckx","doi":"10.1109/TSP.2025.3640931","DOIUrl":"10.1109/TSP.2025.3640931","url":null,"abstract":"Analog computing has been recently revived due to its potential for energy-efficient and highly parallel computations. In this two-part paper, we explore analog computers that linearly process microwave signals, named microwave linear analog computers (MiLACs), and their applications in signal processing and communications. In Part I of this paper, we model a MiLAC as a multiport microwave network with tunable impedance components, enabling the execution of mathematical operations by reconfiguring the microwave network and applying input signals at its ports. We demonstrate that a MiLAC can efficiently compute the linear minimum mean square error (LMMSE) estimator and matrix inversion, with remarkably low computational complexity. Specifically, a matrix can be inverted with complexity growing with the square of its size. We also show how a MiLAC can be used jointly with digital operations to implement sophisticated algorithms such as the Kalman filter. To enhance practicability, we propose a design of MiLAC based on lossless impedance components, reducing power consumption and eliminating the need for costly active components. In Part II of this paper, we investigate the applications of MiLACs in wireless communications, highlighting their potential to enable future wireless systems by executing computations and beamforming in the analog domain.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5183-5197"},"PeriodicalIF":5.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145704015","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 : 2025-12-05DOI: 10.1109/TSP.2025.3640564
Guangpu Guo;Xiang-Gen Xia
Chinese remainder theorem (CRT) is widely applied in cryptography, coding theory, and signal processing. It has been extended to the multidimensional CRT (MD-CRT), which reconstructs an integer vector from its vector remainders modulo multiple integer matrices. This paper investigates a generalized MD-CRT for multiple integer vectors, where the goal is to determine multiple integer vectors from multiple vector residue sets modulo multiple integer matrices. Comparing to the existing generalized CRT for multiple scalar integers, the challenge is that the moduli in MD-CRT are matrices that do not commute and the corresponding uniquely determinable range is multidimensional and the inclusion relationship is much more complicated. In this paper, we address two fundamental questions regarding the generalized MD-CRT. The first question concerns the uniquely determinable range of multiple integer vectors when no prior information about them is available. The second question is about the conditions under which the maximal possible dynamic range can be achieved. To answer these two questions, we first derive a uniquely determinable range without prior information and accordingly propose an algorithm to achieve it. A special case involving only two integer vectors is investigated for the second question, leading to a new condition for achieving the maximal possible dynamic range. Interestingly, this newly obtained condition, when the dimension is reduced to 1, is even better than the existing ones for the conventional generalized CRT for scalar integers. These results may have applications for frequency detection in multidimensional signal processing.
{"title":"A Generalized Multidimensional Chinese Remainder Theorem (MD-CRT) for Multiple Integer Vectors","authors":"Guangpu Guo;Xiang-Gen Xia","doi":"10.1109/TSP.2025.3640564","DOIUrl":"10.1109/TSP.2025.3640564","url":null,"abstract":"Chinese remainder theorem (CRT) is widely applied in cryptography, coding theory, and signal processing. It has been extended to the multidimensional CRT (MD-CRT), which reconstructs an integer vector from its vector remainders modulo multiple integer matrices. This paper investigates a generalized MD-CRT for multiple integer vectors, where the goal is to determine multiple integer vectors from multiple vector residue sets modulo multiple integer matrices. Comparing to the existing generalized CRT for multiple scalar integers, the challenge is that the moduli in MD-CRT are matrices that do not commute and the corresponding uniquely determinable range is multidimensional and the inclusion relationship is much more complicated. In this paper, we address two fundamental questions regarding the generalized MD-CRT. The first question concerns the uniquely determinable range of multiple integer vectors when no prior information about them is available. The second question is about the conditions under which the maximal possible dynamic range can be achieved. To answer these two questions, we first derive a uniquely determinable range without prior information and accordingly propose an algorithm to achieve it. A special case involving only two integer vectors is investigated for the second question, leading to a new condition for achieving the maximal possible dynamic range. Interestingly, this newly obtained condition, when the dimension is reduced to 1, is even better than the existing ones for the conventional generalized CRT for scalar integers. These results may have applications for frequency detection in multidimensional signal processing.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5136-5151"},"PeriodicalIF":5.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680460","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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