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Sub-Nyquist USF Spectral Estimation: K Frequencies With 6K+4 Modulo Samples

IEEE TRANSACTIONS ON signal processing 2024年 72卷 5065-5076页

作者： Guo, Ruiming Zhu, Yuliang Bhandari, Ayush Imperial Coll London Dept Elect & Elect Engn London SW7 2AZ England

Digital acquisition of high bandwidth signxals is particularly challenging when Nyquist rate sampling is impractical. This has led to extensive research in sub-Nyquist sampling methods, primarily for spectral and sinusoidal frequency estimation. However, these methods struggle with high-dynamic-range (HDR) signals that can saturate analog-to-digital converters (ADCs). Addressing this, we introduce a novel sub-Nyquist spectral estimation method, driven by the Unlimited Sensing Framework (USF), utilizing a multi-channel system. The sub-Nyquist USF method aliases samples in both amplitude and frequency domains, rendering the inverse problem particularly challenging. Towards this goal, our exact recovery theorem establishes that K sinusoids of arbitrary amplitudes and frequencies can be recovered from 6K+4 modulo samples, remarkably, independent of the sampling rate or folding threshold. In the true spirit of sub-Nyquist sampling, via modulo ADC hardware experiments, we demonstrate successful spectrum estimation of HDR signals in the kHz range using Hz range sampling rates (0.078% Nyquist rate). Our experiments also reveal up to a 33-fold improvement in frequency estimation accuracy using one less bit compared to conventional ADCs. These findings open new avenues in spectral estimation applications, e.g., radars, direction-of-arrival (DoA) estimation, and cognitive radio, showcasing the potential of USF.

关键词： Hardware Frequency estimation Sensors Estimation Quantization (signal) Noise Vectors Time-domain analysis signal processing algorithms Radar imaging Unlimited sampling sub-Nyquist sampling robust recovery multi-channel architecture spectral estimation

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Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 4286-4301页

作者： Lin, Zhidi Sun, Yiyong Yin, Feng Thiery, Alexandre Hoang Chinese Univ Hong Kong Sch Sci & Engn Future Network Intelligence Inst Shenzhen 518172 Peoples R China Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China Natl Univ Singapore Dept Stat & Data Sci Singapore 117546 Singapore Chinese Univ Hong Kong Sch Sci & Engn Shenzhen Peoples R China

The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational inference approaches, particularly under the more realistic non-mean-field (NMF) assumption, including extensive training effort, compromised inference accuracy, and infeasibility for online applications, among others. In this paper, we tackle these challenges by incorporating the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, into the NMF variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO). Moreover, owing to the streamlined parameterization via the EnKF, the new GPSSM model can be easily accommodated in online learning applications. We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting. We also provide detailed analysis and fresh insights for the proposed algorithms. Comprehensive evaluation across diverse real and synthetic datasets corroborates the superior learning and inference performance of our EnKF-aided variational inference algorithms compared to existing methods.

关键词： Heuristic algorithms signal processing algorithms Inference algorithms Gaussian processes Computational modeling Kalman filters Approximation algorithms Gaussian process state-space model ensemble Kalman filter online learning variational inference

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Efficient Singular Spectrum Mode Ensemble for Extracting Wide-Band Components in Overlapping Spectral Environments

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 4666-4681页

作者： Zhang, Hongcheng Lu, Wenhuan Wei, Jianguo Huang, Xiangdong Yang, Xiaokang Lu, Xugang Tianjin Univ Coll Intelligence & Comp Tianjin 300354 Peoples R China Tianjin Univ Sch Elect & Informat Engn Tianjin 300072 Peoples R China Natl Inst Informat & Commun Technol Adv Speech Translat Res & Dev Promot Ctr Kyoto 6190289 Japan

Mode decomposition methods decompose a complex signal into several principal components, which are prone to be demodulated out of non-stationary features. The efficacy of current approaches deteriorates when the components spectrally overlap, owing to their limited frequency resolution and inadequate decomposition levels. To overcome these limitations, we propose a Singular Spectrum Mode Ensemble (SME) method as an extension of the Singular Spectrum Analysis (SSA), which was traditionally considered a linear approach. The SME method employs the high-rank Hankel matrix and Singular Value Decomposition (SVD), complemented by our proposed Fast Singular Spectrum Decomposition (FSSD) and a grouping method based on Singular Value-Frequency Band correlations. Theoretical research in this paper reveals that our method achieves exceptionally high resolution in the frequency domain, facilitating the separation of the components intermixed in the spectrum. Verification experiments demonstrate our method's ability to separate non-stationary components overlapping with others in the time-frequency domain, unveiling some components in mechanical and speech signals that were previously difficult to separate and discern.

关键词： Matrix decomposition Time series analysis Spectral analysis signal processing algorithms Matrix converters Time-frequency analysis Bandwidth Model decomposition non-stationary analysis amplitude modulation-frequency modulation (AM-FM) analysis singular spectrum analysis speech signal processing mechanical fault diagnosis

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Joint Beamforming for RIS-Assisted Integrated Sensing and Communication Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2024年第4期72卷 2232-2246页

作者： Xu, Yongqing Li, Yong Zhang, J. Andrew Renzo, Marco Di Quek, Tony Q. S. Beijing Univ Posts & Telecommun Key Lab Universal Wireless Commun Beijing 100876 Peoples R China Univ Technol Sydney UTS Global Big Data Technol Ctr GBDTC Sydney NSW 2007 Australia Univ Technol Sydney UTS Sch Elect & Data Engn Sydney NSW 2007 Australia Univ Paris Saclay CNRS Lab Signaux & Syst Cent Supelec F-91192 Gif Sur Yvette France Singapore Univ Technol & Design Singapore 487372 Singapore Yonsei Univ Yonsei Frontier Lab Seoul 03722 South Korea

Integrated sensing and communications (ISAC) is an emerging technique for the next generation of communication systems. However, due to multiple performance metrics used for communication and sensing, the limited number of degrees-of-freedom (DoF) in optimizing ISAC systems poses a challenge. Reconfigurable intelligent surfaces (RISs) can introduce new DoF for beamforming in ISAC systems, thereby enhancing the performance of communication and sensing simultaneously. In this paper, we propose two optimization techniques for beamforming in RIS-assisted ISAC systems. The first technique is an alternating optimization (AO) algorithm based on the semidefinite relaxation (SDR) method and a one-dimension iterative (ODI) algorithm, which can maximize the radar mutual information (MI) while imposing constraints on the communication rates. The second technique is an AO algorithm based on the Riemannian gradient (RG) method, which can maximize the weighted ISAC performance metrics. Simulation results verify the effectiveness of the proposed schemes. The AO-SDR-ODI method is shown to achieve better communication and sensing performance, than the AO-RG method, at a higher complexity. It is also shown that the mean-squared-error (MSE) of the estimates of the sensing parameters decreases as the radar MI increases.

关键词： Radar Sensors Array signal processing Optimization Measurement Estimation signal processing algorithms Integrated sensing and communication reconfigurable intelligent surface radar mutual information beamforming manifold optimization

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On Partial Smoothness, Activity Identification and Faster algorithms of L1 Over L2 Minimization

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 2874-2889页

作者： Tao, Min Zhang, Xiao-Ping Xia, Zi-Hao Nanjing Univ Dept Math Natl Key Lab Novel Software Technol Nanjing 210093 Peoples R China Tsinghua Univ Shenzhen Int Grad Sch Shenzhen Key Lab Ubiquitous Data Enabling Shenzhen 518055 Peoples R China Nanjing Univ Dept Math Nanjing 210093 Peoples R China

The L-1 /L-2 norm ratio arose as a sparseness measure and attracted a considerable amount of attention due tothree merits: (i) sharper approximations ofL0compared to theL(1);(ii) parameter-free and scale-invariant;(iii) more attractive than L-1 under highly-coherent matrices. In this paper, we firstestablish the partly smooth property of L-1 ove rL(2) minimizationrelative to an active manifold M and also demonstrate itsprox-regularity property. Second, we reveal that AD M Mp(orADMM+p) can identify the active manifold within a finite itera-tions. This discovery contributes to a deeper understanding of the optimization landscape associated with L-1 over L-2 minimization. Third, we propose a novel heuristic algorithm framework that combines ADMMp(or ADMM+p) with a globalized semismooth Newton method tailored for the active manifold M. This hybrid approach leverages the strengths of both methods to enhance convergence. Finally, through extensive numerical simulations, we show case the superiority of our heuristic algorithm over existing state-of-the-art methods for sparse recovery.

关键词： Manifolds Minimization signal processing algorithms Convergence Newton method Vectors Linear programming Sparse recovery partly smooth prox-regularity active set nonsmooth analysis identifiable surface

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Recursive State Estimation for Discrete-Time Nonlinear Systems With Binary Sensors: A Locally Minimized Variance Approach

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第9期69卷 6317-6324页

作者： Huang, Yi-Bo Wang, Zidong He, Yong Wu, Min Zhejiang Univ Coll Control Sci & Engn Hangzhou 310027 Peoples R China Brunel Univ London Dept Comp Sci Uxbridge UB8 3PH England China Univ Geosci Sch Automat Wuhan 430074 Peoples R China Hubei Key Lab Adv Control & Intelligent Automat Co Wuhan 430074 Peoples R China Minist Educ Engn Res Ctr Intelligent Technol Geoexplorat Wuhan 430074 Peoples R China

In this article, the locally minimized-variance state estimation problem is investigated for a class of discrete-time nonlinear systems with Lipschitz nonlinearities and binary sensors. The output of each binary sensor takes two possible values (e.g., 0 and 1) in accordance with whether the sensed variable surpasses a prescribed threshold or not. The purpose of this article is to design a state estimation algorithm such that an upper bound of the estimation error covariance is firstly guaranteed and then minimized at each sampling instant by properly designing the estimator gain. The valid information of sensed variables is extracted from binary measurements, and a novel state estimator is constructed in a recursive form, which is suitable for online computations. Moreover, a sufficient condition is established to ensure the exponential boundedness of the prediction error in the mean square sense. Finally, two examples are presented to verify the effectiveness of the proposed method.

关键词： Sensors Sensor systems State estimation Upper bound Nonlinear systems signal processing algorithms Measurement uncertainty Binary sensors difference equations nonlinear systems recursive state estimation variance constraints

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CRB Analysis for Mixed-ADC Based DOA Estimation

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 3043-3058页

作者： Zhang, Xinnan Cheng, Yuanbo Shang, Xiaolei Liu, Jun Univ Sci & Technol China Dept Elect Engn & Informat Sci Hefei 230027 Peoples R China

We consider a mixed analog-to-digital converter (ADC) based architecture consisting of high-precision and one-bit ADCs with the antenna-varying threshold for direction of arrival (DOA) estimation using a uniform linear array (ULA), which utilizes fixed but different thresholds for one-bit ADCs across different receive antennas. The Cramer-Rao bound (CRB) with the antenna-varying threshold is obtained. Then based on the lower bound of the CRB, we derive the asymptotic CRB of the DOA, which depends on the placement of mixed-ADC. Our analysis shows that distributing high-precision ADCs evenly around the two edges of the ULA yields improved performance. This result can be extended to a more general case where the ULA is equipped with two types of ADCs with different quantization precisions. To efficiently obtain the maximum likelihood DOA estimates, we propose a two-step algorithm. Firstly, we formulate the model as a sparse signal representation problem, and modify the sparse learning via iterative minimization (SLIM) approach to the mixed-ADC based DOA estimation. In the second step, we use the relaxation-based approach to cyclically refine the estimates of SLIM, further enhancing the DOA estimation performance. Numerical examples are presented to demonstrate the validity of the CRB analysis and the effectiveness of our methods.

关键词： Direction-of-arrival estimation Vectors Noise signal processing algorithms Data models Antennas Receiving antennas Cramer-Rao bound (CRB) direction of arrival (DOA) placement of mixed-ADC maximum likelihood (ML) estimation mixed-ADC architecture uniform linear array (ULA)

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Constant Wideband Compressive Spectrum Sensing With Cascade Forward-Backward Propagating and Prior Knowledge Refining

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2024年第3期23卷 1855-1870页

作者： Liu, Jianfeng Huang, Xin-Lin Yu, Shui Tongji Univ Dept Informat & Commun Engn Shanghai 201804 Peoples R China Univ Technol Sydney Sch Comp Sci Sydney NSW 2007 Australia

Compressive spectrum sensing (CSS) is regarded as one of the promising techniques to detect wideband spectrum holes. How to formulate an accurate prior knowledge in CSS is still an important and open topic. In this paper, we propose a novel CSS algorithm with cascade forward-backward propagation and prior knowledge refining. Firstly, the wideband signal reconstruction model is formulated as a & ell;(p) -norm ( 0 < p < 1 ) nonconvex optimization problem where the temporal correlation between continuous observed spectrum signals is exploited to improve the reconstruction accuracy of the current spectrum signal, and such nonconvex optimization problem is solved by iteratively reweighted least squares algorithm. Then, the multiple reconstructed versions of the current spectrum signal obtained by forward-backward propagation are fused into a prior. Finally, such fused prior is modified adaptively in each iteration, and thus significantly improves the accuracy of spectrum decision and speeds up the convergence. The simulation results show that compared with other CSS schemes based on weighted & ell;(1) minimization, & ell;(1) - & ell;(1) minimization, & ell;(1) - & ell;(2) minimization, and maximizing correlation, the proposed scheme has more than 7% and 10% detection performance improvement when the probability of false alarm is 10%, under received signal-to-noise ratio as -10 dB and -5 dB, respectively.

关键词： Minimization Wideband Wireless communication Sensors signal reconstruction signal processing algorithms Optimization Compressive spectrum sensing l(p)-norm minimization iterative reweighted least squares forward-backward propagation

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Towards Inversion-Free Sparse Bayesian Learning: A Universal Approach

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 4992-5006页

作者： Song, Yuhui Gong, Zijun Chen, Yuanzhu Li, Cheng Mem Univ Dept Comp Sci St John NF A1B 3X5 Canada Hong Kong Univ Sci & Technol HKUST Guangzhou IoT Thrust Guangzhou 511453 Peoples R China HKUST Dept ECE Hong Kong 999077 Peoples R China Queens Univ Sch Comp Kingston ON K7L 2N8 Canada Simon Fraser Univ Sch Engn Sci Vancouver BC V5A 1S6 Canada Mem Univ Elect & Comp Engn St John NF A1B 3X5 Canada

Sparse Bayesian Learning (SBL) has emerged as a powerful tool for sparse signal recovery, due to its superior performance. However, the practical implementation of SBL faces a significant computational complexity associated with matrix inversion. Despite numerous efforts to alleviate this issue, existing methods are often limited to specifically structured sparse signals. This paper aims to provide a universal inversion-free approach to accelerate existing SBL algorithms. We unify the optimization of SBL variants with different priors within the expectation-maximization (EM) framework, where a lower bound of the likelihood function is maximized. Due to the linear Gaussian model foundation of SBL, updating this lower bound requires maximizing a quadratic function, which involves matrix inversion. Thus, we employ the minorization-maximization (MM) framework to derive two novel lower bounds that diagonalize the quadratic coefficient matrix, thereby eliminating the need for any matrix inversions. We further investigate their properties, including convergence guarantees under the MM framework and the slow convergence rate due to reduced curvature. The proposed approach is applicable to various types of structured sparse signals, such as row-sparse, block-sparse, and burst-sparse signals. Our simulations on synthetic and real data demonstrate remarkably shorter running time compared to state-of-the-art methods while achieving comparable recovery performance.

关键词： signal processing algorithms Inference algorithms Sparse matrices Vectors Computational modeling Complexity theory Convergence Brain modeling Dictionaries Bayes methods Compressed sensing sparse Bayesian learning inversion-free expectation-maximization (EM) algorithm minorization-maximization (MM) algorithm

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Fast Recursive Greedy Methods for Sparse signal Recovery

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 4381-4394页

作者： Xiang, Min Zhang, Zhenyue Zhejiang Univ Sch Math Sci Hangzhou 310008 Peoples R China Shenzhen MSU BIT Univ MSU BIT SMBU Joint Res Ctr Appl Math Shenzhen 518172 Guangdong Peoples R China

Theory and algorithms of greedy methods for sparse signal recovery using l(0)-minimization are developed. The theoretical analysis shows that l(0)-minimization is more suitable for sparse signal recovery and that the greedy method based on active set updating can solve l(0)-minimization problems under weak conditions. A fast recursive algorithm RASU is given to greedily update the active set with a given sparsity level, and an adaptive strategy is proposed to escape from the local minima achieved by RASU. RASU is further applied to minimize the residual. The algorithm FRASM repeats this procedure, using multiple starting points to enhance the efficiency. A fast algorithm SHTP is proposed to provide the multiple choices for FRASM, and itself is also an efficient algorithm solving the sparse problem. By combining an adaptive updating rule to estimate the sparsity of the sparsest signal, the FRASM is adopted to minimize the sparsity level subject to a residual constraint, yielding the algorithm SASSP. Numerical experiments demonstrate the superior performance of FRASM and SASSP compared to other sparse algorithms.

关键词： Indexes Matching pursuit algorithms Thresholding (Imaging) signal processing algorithms Iterative methods Vectors Convergence Sparse signal recovery fast recursion active set updating adaptive pursuing

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