Pub Date : 2026-01-08DOI: 10.1016/j.sigpro.2026.110497
Bingyi Ren , Tianyi Jia , Hongwei Liu , Chang Gao , Hongtao Su , Chunlei Zhao
The spatial bias of sensor in the process of target tracking and the temporal bias between the time axis of each sensor and the absolute time axis, if not accounted for, can seriously affect the positioning accuracy. Meanwhile, the sensor position reported by Global Positioning System (GPS) is not accurate. In this paper, the problem of angles-only target motion analysis (TMA) by asynchronous sensors is studied in the presence of spatiotemporal bias and sensor position error. A new target tracking method is proposed by taking the target state, spatiotemporal bias and sensor position as the augmented state vector. Using the filter concept and the minimum mean square error (MMSE) criterion for real-time processing, the augmented state vector can be estimated simultaneously. Simulation results show the superiority of the proposed algorithm for target position estimation, and verify the effectiveness of the proposed in achieving the Posterior Cramér-Rao lower bound (PCRLB) performance under the distance-dependent measurement noise.
{"title":"3D angles-only target tracking in the presence of spatiotemporal bias and sensor position error","authors":"Bingyi Ren , Tianyi Jia , Hongwei Liu , Chang Gao , Hongtao Su , Chunlei Zhao","doi":"10.1016/j.sigpro.2026.110497","DOIUrl":"10.1016/j.sigpro.2026.110497","url":null,"abstract":"<div><div>The spatial bias of sensor in the process of target tracking and the temporal bias between the time axis of each sensor and the absolute time axis, if not accounted for, can seriously affect the positioning accuracy. Meanwhile, the sensor position reported by Global Positioning System (GPS) is not accurate. In this paper, the problem of angles-only target motion analysis (TMA) by asynchronous sensors is studied in the presence of spatiotemporal bias and sensor position error. A new target tracking method is proposed by taking the target state, spatiotemporal bias and sensor position as the augmented state vector. Using the filter concept and the minimum mean square error (MMSE) criterion for real-time processing, the augmented state vector can be estimated simultaneously. Simulation results show the superiority of the proposed algorithm for target position estimation, and verify the effectiveness of the proposed in achieving the Posterior Cramér-Rao lower bound (PCRLB) performance under the distance-dependent measurement noise.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110497"},"PeriodicalIF":3.6,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037939","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 : 2026-01-08DOI: 10.1016/j.sigpro.2026.110492
Jinli Chen , Yang Song , Hua Shao , Jiaqiang Li
Conventional angle estimation methods are highly sensitive to outliers, causing severe performance degradation under impulsive noise. Although existing tensor-based Bayesian approaches can alleviate the impact of outliers, strongly impulsive noise in multiple-input multiple-output (MIMO) radar often leads to outlier model mismatch, reducing robustness against outliers. To address this, we propose a fast Bayesian method for angle estimation under impulsive noise, which exploits the tensor intra-dimension correlations and incorporates the Vandermonde structure of factor matrices within a Bayesian tensor decomposition framework. Strong outliers in the array measurements are first removed via thresholding to mitigate model mismatch. A hierarchical probabilistic model based on canonical polyadic (CP) decomposition is then developed to capture the correlation structure and the Vandermonde structural prior. Model parameters are efficiently inferred via an expectation–maximization (EM) algorithm, which recovers missing entries caused by thresholding and suppresses residual outliers. Furthermore, a complexity-reduction method is developed to accelerate computation by employing a snapshot-wise stackable strategy and leveraging the sparsity of thresholded entries, enabling efficient estimation of factor matrices across multiple snapshots. Finally, DOAs and DODs are jointly estimated from the decomposed factor matrices. Simulations verify the outlier-robust performance of the proposed method in providing high-accuracy angle estimation under impulsive noise.
{"title":"Robust angle estimation in MIMO radar under impulsive noise via fast bayesian tensor decomposition with intra-dimension correlation","authors":"Jinli Chen , Yang Song , Hua Shao , Jiaqiang Li","doi":"10.1016/j.sigpro.2026.110492","DOIUrl":"10.1016/j.sigpro.2026.110492","url":null,"abstract":"<div><div>Conventional angle estimation methods are highly sensitive to outliers, causing severe performance degradation under impulsive noise. Although existing tensor-based Bayesian approaches can alleviate the impact of outliers, strongly impulsive noise in multiple-input multiple-output (MIMO) radar often leads to outlier model mismatch, reducing robustness against outliers. To address this, we propose a fast Bayesian method for angle estimation under impulsive noise, which exploits the tensor intra-dimension correlations and incorporates the Vandermonde structure of factor matrices within a Bayesian tensor decomposition framework. Strong outliers in the array measurements are first removed via thresholding to mitigate model mismatch. A hierarchical probabilistic model based on canonical polyadic (CP) decomposition is then developed to capture the correlation structure and the Vandermonde structural prior. Model parameters are efficiently inferred via an expectation–maximization (EM) algorithm, which recovers missing entries caused by thresholding and suppresses residual outliers. Furthermore, a complexity-reduction method is developed to accelerate computation by employing a snapshot-wise stackable strategy and leveraging the sparsity of thresholded entries, enabling efficient estimation of factor matrices across multiple snapshots. Finally, DOAs and DODs are jointly estimated from the decomposed factor matrices. Simulations verify the outlier-robust performance of the proposed method in providing high-accuracy angle estimation under impulsive noise.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110492"},"PeriodicalIF":3.6,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978345","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}
Although existing diffusion-based methods produce visually rich textures at extremely low bitrates, they often sacrifice structural fidelity, resulting in significant deviations from the original image. To address this fundamental trade-off, we propose Fidelity-Perception Diffusion-based Image Compression (FPD-IC), a two-stage conditional diffusion framework that explicitly separates structure reconstruction and detail restoration. In Stage I, we use a VAE-based compressor to recover structurally faithful conditional images from highly compact bitstreams. In Stage II, a diffusion model, guided by the output from Stage I, generates visually rich details. This conditional approach allows the diffusion model to focus exclusively on perceptual enhancement while preserving the overall structure established in Stage I. Additionally, we introduce a lightweight Fidelity-Perception Tuner Module (FPTM) to combine the outputs of both stages, enabling controllable trade-offs between fidelity and perceptual quality. Extensive experiments on the Kodak and Tecnick datasets demonstrate the effectiveness and robustness of FPD-IC. On the Tecnick dataset, FPD-IC outperforms state-of-the-art diffusion-based methods by 2.24–3.57 dB in PSNR at bitrates below 0.06 bpp, while also achieving superior perceptual quality. Furthermore, FPD-IC shows strong robustness to input noise, consistently maintaining high fidelity and perceptual quality under Gaussian perturbations. The code will be released at https://github.com/mlkk518/FPD-IC.
{"title":"From structure to detail: A conditional diffusion framework for extremely low-bitrate image compression","authors":"Junhui Li, Yiyang Zou, Xingsong Hou, Yutao Zhang, Zhixuan Guo","doi":"10.1016/j.sigpro.2025.110480","DOIUrl":"10.1016/j.sigpro.2025.110480","url":null,"abstract":"<div><div>Although existing diffusion-based methods produce visually rich textures at extremely low bitrates, they often sacrifice structural fidelity, resulting in significant deviations from the original image. To address this fundamental trade-off, we propose Fidelity-Perception Diffusion-based Image Compression (FPD-IC), a two-stage conditional diffusion framework that explicitly separates structure reconstruction and detail restoration. In Stage I, we use a VAE-based compressor to recover structurally faithful conditional images from highly compact bitstreams. In Stage II, a diffusion model, guided by the output from Stage I, generates visually rich details. This conditional approach allows the diffusion model to focus exclusively on perceptual enhancement while preserving the overall structure established in Stage I. Additionally, we introduce a lightweight Fidelity-Perception Tuner Module (FPTM) to combine the outputs of both stages, enabling controllable trade-offs between fidelity and perceptual quality. Extensive experiments on the Kodak and Tecnick datasets demonstrate the effectiveness and robustness of FPD-IC. On the Tecnick dataset, FPD-IC outperforms state-of-the-art diffusion-based methods by 2.24–3.57 dB in PSNR at bitrates below 0.06 bpp, while also achieving superior perceptual quality. Furthermore, FPD-IC shows strong robustness to input noise, consistently maintaining high fidelity and perceptual quality under Gaussian perturbations. The code will be released at <span><span>https://github.com/mlkk518/FPD-IC</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110480"},"PeriodicalIF":3.6,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978344","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 : 2026-01-07DOI: 10.1016/j.sigpro.2026.110493
Haixin Jia , Han Wang , Yu Zhang , Guoying Zhang , Zhengfan Li , Hengchen Xu
Atmospheric haze degrades image quality, impairing downstream vision tasks like object detection and segmentation. While wavelet-based deep learning methods are effective by leveraging lossless downsampling and spectral discrepancies, they often suffer from limited multi-scale feature extraction, inadequate frequency-domain enhancement, and a lack of structural priors. To overcome these issues, we propose MWNet, a novel framework integrating structural constraints into a U-Net with wavelet transforms. Our approach introduces dense multi-scale blocks for robust feature extraction, a hierarchical attention mechanism for high-frequency detail enhancement, and a cross-enhancement module for frequency feature interaction. Extensive experiments conducted on four benchmark datasets (SOTS-Indoor, Haze4K, Dense-Haze, NH-Haze) have demonstrated consistent superiority, with MWNet achieving SOTA in quantitative results compared to existing advanced methods (Surpassing the second-best method with average improvements of 0.16 dB in PSNR and 0.0026 in SSIM.), while qualitative results demonstrate enhanced detail preservation and noise suppression. In addition, we conducted generalization tests on three other datasets (RTTS, REAL-NH, CM-Haze), fully verifying the good generalization performance of MWNet.
{"title":"MWNet: Image dehazing network based on multi-scale feature extraction and wavelet feature enhancement","authors":"Haixin Jia , Han Wang , Yu Zhang , Guoying Zhang , Zhengfan Li , Hengchen Xu","doi":"10.1016/j.sigpro.2026.110493","DOIUrl":"10.1016/j.sigpro.2026.110493","url":null,"abstract":"<div><div>Atmospheric haze degrades image quality, impairing downstream vision tasks like object detection and segmentation. While wavelet-based deep learning methods are effective by leveraging lossless downsampling and spectral discrepancies, they often suffer from limited multi-scale feature extraction, inadequate frequency-domain enhancement, and a lack of structural priors. To overcome these issues, we propose MWNet, a novel framework integrating structural constraints into a U-Net with wavelet transforms. Our approach introduces dense multi-scale blocks for robust feature extraction, a hierarchical attention mechanism for high-frequency detail enhancement, and a cross-enhancement module for frequency feature interaction. Extensive experiments conducted on four benchmark datasets (SOTS-Indoor, Haze4K, Dense-Haze, NH-Haze) have demonstrated consistent superiority, with MWNet achieving SOTA in quantitative results compared to existing advanced methods (Surpassing the second-best method with average improvements of 0.16 dB in PSNR and 0.0026 in SSIM.), while qualitative results demonstrate enhanced detail preservation and noise suppression. In addition, we conducted generalization tests on three other datasets (RTTS, REAL-NH, CM-Haze), fully verifying the good generalization performance of MWNet.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110493"},"PeriodicalIF":3.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978340","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 : 2026-01-07DOI: 10.1016/j.sigpro.2026.110495
Boyang Jia , Jianwei Zhao , Yaxing Yue , Xuepan Zhang , Jiayi Zhao , Sining Liu , Guisheng Liao
We propose a Weighted Coherent Integration (WCI) algorithm for weak target detection. This method aims to achieve maximum signal-to-noise ratio (SNR) gain by coherently accumulating echoes from active and passive radars. Two key challenges about range-Doppler misalignment and inter-channel differences are addressed by a two-stage framework. First, spatial alignment is achieved by partitioning the surveillance area, and Doppler resolutions are unified via adaptive integration time. Target fluctuations and phase errors between channels are then mitigated via inter-channel coherent integration with phase compensation. Simulation results validate that WCI outperforms conventional monostatic and multistatic non-coherent fusion methods, achieving superior detection capability in both low-SNR and multi-target scenarios.
{"title":"A weighted coherent integration method for weak target detection based on active-passive radar","authors":"Boyang Jia , Jianwei Zhao , Yaxing Yue , Xuepan Zhang , Jiayi Zhao , Sining Liu , Guisheng Liao","doi":"10.1016/j.sigpro.2026.110495","DOIUrl":"10.1016/j.sigpro.2026.110495","url":null,"abstract":"<div><div>We propose a Weighted Coherent Integration (WCI) algorithm for weak target detection. This method aims to achieve maximum signal-to-noise ratio (SNR) gain by coherently accumulating echoes from active and passive radars. Two key challenges about range-Doppler misalignment and inter-channel differences are addressed by a two-stage framework. First, spatial alignment is achieved by partitioning the surveillance area, and Doppler resolutions are unified via adaptive integration time. Target fluctuations and phase errors between channels are then mitigated via inter-channel coherent integration with phase compensation. Simulation results validate that WCI outperforms conventional monostatic and multistatic non-coherent fusion methods, achieving superior detection capability in both low-SNR and multi-target scenarios.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110495"},"PeriodicalIF":3.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927620","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 : 2026-01-05DOI: 10.1016/j.sigpro.2025.110481
Yanbin Zou , Xiaofei Li , Shiru Chen , Yihan Wang , Yimao Sun
This paper addresses the problem of hybrid angle-of-arrival (AOA) and time-difference-of-arrival (TDOA) localization in the presence of sensor position errors. Existing weighted least-squares (WLS) estimators for this scenario often exhibit suboptimal performance because the linearization of TDOA measurements introduces a detrimental cross-coupling between AOA and TDOA noise. To overcome this limitation, a novel WLS estimator is proposed that fundamentally decouples these heterogeneous noise sources through a new linearization procedure for the TDOA equations that is independent of AOA measurements. The proposed estimator is formulated as a WLS problem with a single quadratic constraint, which admits an efficient algebraic solution. Simulation results demonstrate that the proposed algorithm significantly outperforms existing WLS methods, with its estimation accuracy closely approaching the Cramér-Rao Lower Bound (CRLB).
{"title":"A noise-decoupled WLS solution for hybrid AOA-TDOA localization in the presence of sensor position errors","authors":"Yanbin Zou , Xiaofei Li , Shiru Chen , Yihan Wang , Yimao Sun","doi":"10.1016/j.sigpro.2025.110481","DOIUrl":"10.1016/j.sigpro.2025.110481","url":null,"abstract":"<div><div>This paper addresses the problem of hybrid angle-of-arrival (AOA) and time-difference-of-arrival (TDOA) localization in the presence of sensor position errors. Existing weighted least-squares (WLS) estimators for this scenario often exhibit suboptimal performance because the linearization of TDOA measurements introduces a detrimental cross-coupling between AOA and TDOA noise. To overcome this limitation, a novel WLS estimator is proposed that fundamentally decouples these heterogeneous noise sources through a new linearization procedure for the TDOA equations that is independent of AOA measurements. The proposed estimator is formulated as a WLS problem with a single quadratic constraint, which admits an efficient algebraic solution. Simulation results demonstrate that the proposed algorithm significantly outperforms existing WLS methods, with its estimation accuracy closely approaching the Cramér-Rao Lower Bound (CRLB).</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110481"},"PeriodicalIF":3.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927502","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 : 2026-01-05DOI: 10.1016/j.sigpro.2026.110491
Chengxin Yang , Benoit Champagne , Wei Yi
This paper addresses the optimization problem of transmit beamforming design for area surveillance and multi-target tracking (MTT) in a colocated multiple-input multiple-output (C-MIMO) radar system. We first establish the relationship between the detection probability and the predictive Cramér-Rao lower bound (PCRLB) as performance metrics, and the transmit signal correlation matrix as the design variable. The surveillance area, defined as a circular sector bounded by a polar angle and the intersecting arc, is divided into independent smaller sectors, each corresponding to a different illumination direction of the C-MIMO radar. To maximize the efficient utilization of power resources, we then aim to maximize the number of simultaneously illuminated sectors while achieving desired detection probability and target tracking accuracy. Given that the formulated optimization problem is an intractable non-convex mixed-integer nonlinear problem, we propose a beamforming algorithm based on Quality of Service (QoS) to solve it efficiently. Simulation results indicate that the proposed algorithm is capable of effectively maximizing the illuminated area while consistently meeting the specified detection probability and MTT accuracy requirements.
{"title":"Transmit beamforming design for area surveillance and multi-target tracking in colocated MIMO radar","authors":"Chengxin Yang , Benoit Champagne , Wei Yi","doi":"10.1016/j.sigpro.2026.110491","DOIUrl":"10.1016/j.sigpro.2026.110491","url":null,"abstract":"<div><div>This paper addresses the optimization problem of transmit beamforming design for area surveillance and multi-target tracking (MTT) in a colocated multiple-input multiple-output (C-MIMO) radar system. We first establish the relationship between the detection probability and the predictive Cramér-Rao lower bound (PCRLB) as performance metrics, and the transmit signal correlation matrix as the design variable. The surveillance area, defined as a circular sector bounded by a polar angle and the intersecting arc, is divided into independent smaller sectors, each corresponding to a different illumination direction of the C-MIMO radar. To maximize the efficient utilization of power resources, we then aim to maximize the number of simultaneously illuminated sectors while achieving desired detection probability and target tracking accuracy. Given that the formulated optimization problem is an intractable non-convex mixed-integer nonlinear problem, we propose a beamforming algorithm based on Quality of Service (QoS) to solve it efficiently. Simulation results indicate that the proposed algorithm is capable of effectively maximizing the illuminated area while consistently meeting the specified detection probability and MTT accuracy requirements.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110491"},"PeriodicalIF":3.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978342","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 : 2026-01-03DOI: 10.1016/j.sigpro.2026.110487
Kunlong Zhao , Jilu Jin , Xueqin Luo , Gongping Huang , Jingdong Chen , Jacob Benesty
Differential microphone arrays (DMAs) are recognized for their highly directive broadband beampatterns and have attracted significant interest in the design of compact microphone arrays. It has been shown that increasing the number of microphones in a DMA can improve array performance. However, when applying DMAs to embedded systems, this creates challenges due to the increased number of parameters, higher computational complexity, and the need to maintain the array’s robustness. To address these challenges, this paper presents a method for designing robust low-rank (LR) differential beamformers. Initially, we extend traditional differential beamforming by introducing an LR differential beamforming framework, which represents a long filter as the Kronecker product of two sets of shorter filters, significantly reducing both the number of parameters and computational complexity. Next, we derive robust designs for the two sets of shorter filters by maximizing the directivity factor (DF) subject to a white noise gain (WNG) constraint, or by maximizing the WNG subject to a DF constraint. This results in two types of LR differential beamformers that achieve the desired DF or WNG levels. The optimization problems are formulated and transformed into quadratic eigenvalue problems (QEPs), leading to closed-form solutions for both the WNG-constrained and DF-constrained LR differential beamformers. Simulation results demonstrate the effectiveness of the proposed method, confirming its robustness and enhanced computational efficiency.
{"title":"Design of Low-Rank differential beamformers with constrained directivity or robustness","authors":"Kunlong Zhao , Jilu Jin , Xueqin Luo , Gongping Huang , Jingdong Chen , Jacob Benesty","doi":"10.1016/j.sigpro.2026.110487","DOIUrl":"10.1016/j.sigpro.2026.110487","url":null,"abstract":"<div><div>Differential microphone arrays (DMAs) are recognized for their highly directive broadband beampatterns and have attracted significant interest in the design of compact microphone arrays. It has been shown that increasing the number of microphones in a DMA can improve array performance. However, when applying DMAs to embedded systems, this creates challenges due to the increased number of parameters, higher computational complexity, and the need to maintain the array’s robustness. To address these challenges, this paper presents a method for designing robust low-rank (LR) differential beamformers. Initially, we extend traditional differential beamforming by introducing an LR differential beamforming framework, which represents a long filter as the Kronecker product of two sets of shorter filters, significantly reducing both the number of parameters and computational complexity. Next, we derive robust designs for the two sets of shorter filters by maximizing the directivity factor (DF) subject to a white noise gain (WNG) constraint, or by maximizing the WNG subject to a DF constraint. This results in two types of LR differential beamformers that achieve the desired DF or WNG levels. The optimization problems are formulated and transformed into quadratic eigenvalue problems (QEPs), leading to closed-form solutions for both the WNG-constrained and DF-constrained LR differential beamformers. Simulation results demonstrate the effectiveness of the proposed method, confirming its robustness and enhanced computational efficiency.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110487"},"PeriodicalIF":3.6,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927621","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 : 2026-01-03DOI: 10.1016/j.sigpro.2025.110479
Srihari P V, Anik Kumar Paul, Bharath Bhikkaji
This paper considers the Federated learning (FL) in a stochastic approximation (SA) framework. Here, each client i trains a local model using its dataset and periodically transmits the model parameters to a central server, where they are aggregated into a global model parameter and sent back. The clients continue their training by re-initializing their local models with the global model parameters.
Prior works typically assumed constant (and often identical) step sizes (learning rates) across clients for model training. As a consequence the aggregated model converges only in expectation. In this work, client-specific tapering step sizes are used. The global model is shown to track an ODE with a forcing function equal to the weighted sum of the negative gradients of the individual clients. The weights being the limiting ratios of the step sizes, where . Unlike the constant step sizes, the convergence here is with probability one.
In this framework, the clients with the larger p(i) exert a greater influence on the global model than those with smaller p(i), which can be used to favor clients that have rare and uncommon data. Numerical experiments were conducted to validate the convergence and demonstrate the choice of step-sizes for regulating the influence of the clients.
{"title":"Federated learning: A stochastic approximation approach","authors":"Srihari P V, Anik Kumar Paul, Bharath Bhikkaji","doi":"10.1016/j.sigpro.2025.110479","DOIUrl":"10.1016/j.sigpro.2025.110479","url":null,"abstract":"<div><div>This paper considers the Federated learning (FL) in a stochastic approximation (SA) framework. Here, each client <em>i</em> trains a local model using its dataset <span><math><msup><mi>D</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msup></math></span> and periodically transmits the model parameters <span><math><msubsup><mi>w</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup></math></span> to a central server, where they are aggregated into a global model parameter <span><math><msub><mover><mi>w</mi><mo>¯</mo></mover><mi>n</mi></msub></math></span> and sent back. The clients continue their training by re-initializing their local models with the global model parameters.</div><div>Prior works typically assumed constant (and often identical) step sizes (learning rates) across clients for model training. As a consequence the aggregated model converges only in expectation. In this work, client-specific tapering step sizes <span><math><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup></math></span> are used. The global model is shown to track an ODE with a forcing function equal to the weighted sum of the negative gradients of the individual clients. The weights being the limiting ratios <span><math><mrow><msup><mi>p</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msup><mo>=</mo><msub><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><mfrac><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></mfrac></mrow></math></span> of the step sizes, where <span><math><mrow><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mo>≥</mo><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup><mo>,</mo><mo>∀</mo><mi>n</mi></mrow></math></span>. Unlike the constant step sizes, the convergence here is with probability one.</div><div>In this framework, the clients with the larger <em>p</em><sup>(<em>i</em>)</sup> exert a greater influence on the global model than those with smaller <em>p</em><sup>(<em>i</em>)</sup>, which can be used to favor clients that have rare and uncommon data. Numerical experiments were conducted to validate the convergence and demonstrate the choice of step-sizes for regulating the influence of the clients.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110479"},"PeriodicalIF":3.6,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927505","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 : 2026-01-03DOI: 10.1016/j.sigpro.2026.110490
Khadija Omar Mohammed, Liping Du, Yueyun Chen
Effective spectrum sensing in fading environments faces challenges due to correlated noise, strong multipath effects, and complex non-linear dependencies among received signals. Traditional eigenvalue-based detectors often assume independence or capture only limited forms of dependence, which reduces reliability in realistic conditions. This study proposes an Adaptive Joint Metric Detection Algorithm (AJMDA) that integrates both independent and dependency eigenvalue statistics into a unified framework. The independent metric represents the signal energy through the sum of eigenvalues, while the dependency metric captures the statistical structure using copula modeling with the Cramér–von Mises (CVM) goodness-of-fit test. An adaptive weighting factor balances these two metrics, and a generalized extreme value (GEV) model provides analytical threshold estimation. Simulation results under Rayleigh fading show that AJMDA significantly improves detection performance over classical energy detectors, eigenvalue-based GOF tests, and copula-only methods. At –15 dB SNR, the proposed detectors achieve a 45–50% higher detection probability, and at –10 dB SNR, they maintain a 20–60% gain, depending on the baseline. In ROC analysis, AJMDA achieves 10–25% higher performance at low-to-moderate false-alarm levels, approaching the ideal vertical ROC curve.
衰落环境下的有效频谱感知面临着相关噪声、强多径效应和接收信号之间复杂的非线性依赖关系的挑战。传统的基于特征值的检测器通常假设独立性或只捕获有限形式的依赖性,这降低了现实条件下的可靠性。本文提出了一种自适应联合度量检测算法(AJMDA),该算法将独立和依赖特征值统计集成到一个统一的框架中。独立度量通过特征值的和表示信号能量,而依赖度量使用与cram - von Mises (CVM)拟合优度检验的copula建模来捕获统计结构。自适应加权因子平衡这两个度量,广义极值(GEV)模型提供分析阈值估计。Rayleigh衰落下的仿真结果表明,与经典能量检测器、基于特征值的GOF测试和纯copula方法相比,AJMDA检测性能有显著提高。在-15 dB信噪比下,所提出的检测器实现了45-50%的高检测概率,在-10 dB信噪比下,它们保持了20-60%的增益,具体取决于基线。在ROC分析中,AJMDA在中低虚警水平下的性能提高了10-25%,接近理想的垂直ROC曲线。
{"title":"Adaptive joint-metric detection algorithm for efficient spectrum sensing: A deep-water case study","authors":"Khadija Omar Mohammed, Liping Du, Yueyun Chen","doi":"10.1016/j.sigpro.2026.110490","DOIUrl":"10.1016/j.sigpro.2026.110490","url":null,"abstract":"<div><div>Effective spectrum sensing in fading environments faces challenges due to correlated noise, strong multipath effects, and complex non-linear dependencies among received signals. Traditional eigenvalue-based detectors often assume independence or capture only limited forms of dependence, which reduces reliability in realistic conditions. This study proposes an Adaptive Joint Metric Detection Algorithm (AJMDA) that integrates both independent and dependency eigenvalue statistics into a unified framework. The independent metric represents the signal energy through the sum of eigenvalues, while the dependency metric captures the statistical structure using copula modeling with the Cramér–von Mises (CVM) goodness-of-fit test. An adaptive weighting factor balances these two metrics, and a generalized extreme value (GEV) model provides analytical threshold estimation. Simulation results under Rayleigh fading show that AJMDA significantly improves detection performance over classical energy detectors, eigenvalue-based GOF tests, and copula-only methods. At –15 dB SNR, the proposed detectors achieve a 45–50% higher detection probability, and at –10 dB SNR, they maintain a 20–60% gain, depending on the baseline. In ROC analysis, AJMDA achieves 10–25% higher performance <span><math><mrow><msub><mi>P</mi><mi>d</mi></msub><mspace></mspace></mrow></math></span>at low-to-moderate false-alarm levels, approaching the ideal vertical ROC curve.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110490"},"PeriodicalIF":3.6,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927509","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}