Internet of Things (IoT) are employed in a variety of applications, leading to a significant demand for advanced antenna systems that can perform multiple distinct tasks from a single, compact hardware platform. In response to this demand, we propose a unified synthesis framework for reconfigurable sparse arrays based on a min-max beampattern matching metric. This framework integrates null/notch constraints, common excitation magnitudes, and explicit dynamic range ratio (DRR) bounds. Our approach distinguishes itself from existing research by addressing the impact of constrained DRR on excitation magnitudes, which is crucial for mitigating mutual coupling and simplifying feed networks. To solve the resultant nonconvex and nonlinear optimization problem, we introduce a Boolean selection vector, transforming the antenna position optimization problem into an antenna selection optimization problem. We then employ alternating minimization to decouple the antenna selection vector from the excitation vector. For each subproblem related to the weight vector and the antenna selection vector, we utilize successive convex approximation to derive a convex surrogate function for the nonconvex components of the subproblems. To ensure the feasibility of the transformed problem, we further introduce slack variables. Numerical experiments demonstrate that the developed approach facilitates precise control of multiple patterns with hardware-efficient sparse configurations for dynamic electromagnetic operations.

Direction-of-arrival (DOA) estimation for incoherently distributed (ID) sources is crucial for Industrial Internet of Things (IIoT) applications operating in complex multipath environments, yet it remains challenging due to the combined effects of angular spread and gain-phase uncertainties in cost-sensitive antenna arrays. This paper presents a two-stage sparse DOA estimation framework, transitioning from partial calibration to full potential, under the generalized array manifold (GAM) framework. In the first stage, coarse DOA estimates are obtained by exploiting the output from a subset of partly-calibrated arrays (PCAs). In the second stage, these estimates are utilized to determine and compensate for gain-phase uncertainties across all array elements. Then a sparse total least-squares optimization problem is formulated and solved via alternating descent to refine the DOA estimates. Simulation results demonstrate that the proposed method achieves superior estimation accuracy compared to existing approaches, while maintaining robustness against both noise and angular spread effects in practical industrial environments.

In sixth-generation and beyond, space-air-ground integrated networks (SAGINs) extend network connectivity to space, thereby enabling broader service coverage. This paper proposes a topology-aware SAGIN framework to address the integrated sensing, communication, and wireless power transfer (ISCPT) problem, leveraging the distinctive visibility of satellite-terrestrial and satellite-satellite users as well as their constructing in-between channel strengths. By modeling the topology of the SAGIN as a bipartite graph, we formulate the ISCPT problem as a multi-objective joint optimization problem with specified topological structures to reflect connection relationships of satellite-terrestrial and satellite-satellite users. The ISCPT problem is then reformulated and carefully decomposed as several mixed-integer linear programs (MILPs) by leveraging the network topology to individually optimize sensing, communication, and power transfer. To reduce the computational complexity of the proposed method, a greedy algorithm deal with generalized multi-assignment problem (GMAP) is developed. Simulation results demonstrate superior performance in communication and sensing, with a tolerable trade-off in wireless power transfer.

A common assumption in matrix completion (MC) and tensor completion (TC) is that the missing locations are sampled randomly. However, in real-world scenarios, the unobserved elements are often not arbitrarily located, and may concentrate within entire rows or columns. We refer to this missing mechanism as structural missingness, and traditional MC and TC schemes suffer from drastic degradation under these circumstances. This work addresses the challenge of restoring structural missingness by introducing a novel framework for simultaneously reconstructing multiple matrices, called multi-matrix completion (MMC). In MMC, tri-factorization across matrices captures the correlation between matrices, and Tikhonov regularization on each matrix exploits its correlation. This design enables MMC to efficiently handle both random and structural missingness. In addition, MMC is not affected by the smoothness along matrices which makes it suitable for a wider variety of data compared to Fourier transform based TC methods. The alternating direction method of multipliers is utilized to solve the resultant optimization problem. The global convergence of the algorithm is supported by comprehensive theoretical analyses. We demonstrate the versatility of MMC through extensive experiments in image and video restoration, and showcase its superior performance in comparison to traditional MC and TC methods.

This paper proposes a robust, energy-efficient multi-user OFDM chaotic vector cyclic shift keying (MU-OFDM-CVCSK) system for channels impaired by multi-user interference (MUI), Gaussian, and impulsive noise. The system’s co-designed transceiver uses cyclic shifts of a single reference signal for energy efficiency, while a novel receiver combines low-rank matrix factorization with a truncated-quadratic loss function to suppress both MUI and noise. In particular, the transmitted signal’s cyclical structure enables iterative reference refinement, further enhancing performance. We provide a comprehensive analysis of the algorithm’s convergence, complexity, energy efficiency, power spectral density, peak-to-average power ratio, and derive the bit error rate (BER) expressions. Simulations demonstrate superior BER performance compared to benchmark schemes in challenging interference and noise conditions.

Terahertz (THz) frequency band has been widely studied and is recognized as a promising candidate for centimeter-level localization. However, the limited coverage of THz networks may result in localization failures, while a heterogeneous deployment of millimeter-wave (mmWave) and THz radio units (RUs) offers a viable solution to mitigate this issue. This paper presents a theoretical framework for evaluating the performance limits of localization systems in mmWave and THz heterogeneous networks. In this architecture, the mmWave RUs serve as macro base stations (BSs), while the THz RUs function as micro BSs distributed around each mmWave RU. By leveraging the standard tools of stochastic geometry to model the spatial distributions of the RUs and ambient obstacles, the localizability of a target is computed to evaluate the probability of achieving sufficient signal-to-interference-plus-noise ratio for localization in both line-of-sight (LoS) and non-line-of-sight (NLoS) conditions. Furthermore, the Cram é r-Rao lower bounds in both LoS and NLoS scenarios are analytically derived to characterize the overall positioning performance. Numerical results demonstrate that the hybrid deployment strategy significantly improves both the network coverage and localization accuracy compared to mmWave-only and THz-only networks.

Fluid antenna (FA) technology has emerged as a promising approach in wireless communications due to its capability of providing increased degrees of freedom (DoFs) and exceptional design flexibility. This paper addresses the challenge of direction-of-arrival (DOA) estimation for aligned received signals (ARS) and non-aligned received signals (NARS) by designing two specialized uniform FA structures under time-constrained mobility. For ARS scenarios, we propose a fully movable antenna configuration that maximizes the virtual array aperture, whereas for NARS scenarios, we design a structure incorporating a fixed reference antenna to reliably extract phase information from the signal covariance. To overcome the limitations of large virtual arrays and limited sample data inherent in time-varying channels (TVC), we introduce two novel DOA estimation methods: TMRLS-MUSIC for ARS, combining Toeplitz matrix reconstruction (TMR) with linear shrinkage (LS) estimation, and TMR-MUSIC for NARS, utilizing sub-covariance matrices to construct virtual array responses. Both methods employ Nyström approximation to significantly reduce computational complexity while maintaining estimation accuracy. Theoretical analyses and extensive simulation results demonstrate that the proposed methods achieve underdetermined DOA estimation using minimal FA elements, outperform conventional methods in estimation accuracy, and substantially reduce computational complexity.

Extremely large-scale arrays (XL-arrays) have emerged as a key enabler in achieving the unprecedented performance requirements of future wireless networks, leading to a significant increase in the range of the near-field region. This transition necessitates the spherical wavefront model for characterizing the wireless propagation rather than the far-field planar counterpart, thereby introducing extra degrees-of-freedom (DoFs) to wireless system design. In this paper, we explore the beam focusing-based physical layer security (PLS) in the near field, where multiple legitimate users and one eavesdropper are situated in the near-field region of the XL-array base station (BS). First, we consider a special case with one legitimate user and one eavesdropper to shed useful insights into near-field PLS. In particular, it is shown that 1) Artificial noise (AN) is crucial to near-fieldsecurity provisioning, transforming an insecure system to a secure one; 2) AN can yield numeroussecurity gains, which considerably enhances PLS in the near field as compared to the case without AN taken into account. Next, for the general case with multiple legitimate users, we propose an efficient low-complexity approach to design the beamforming with AN to guarantee near-field secure transmission. Specifically, the low-complexity approach is conceived starting by introducing the concept ofinterference domainto capture the inter-user interference level, followed by athree-step identification frameworkfor designing the beamforming. Finally, numerical results reveal that 1) the PLS enhancement in the near field is pronounced thanks to the additional spatial DoFs; 2) the proposed approach can achieve close performance to that of the computationally-extensive conventional method yet with a significantly lower computational complexity.

Byzantine-robust federated learning aims to maintain resilient performance in the presence of malicious attacks that can impede the convergence of learning algorithms. Although numerous robust aggregators have been developed to merge the collected gradient information in the server, they either require data homogeneity and are suboptimal for heterogeneous data, or their breakdown points—the smallest proportion of outliers that can make the aggregators fail—are not theoretically analyzed or less than 0.5. In contrast to existing aggregators, this paper formulates the aggregation process as a low-rank plus sparse decomposition model, where the low-rank component, with a rank of one, facilitates accurate gradient computation, while the sparse component, penalized by the ℓ2,0-norm, mitigates the impact of outliers. We prove that the devised rule achieves the maximum breakdown point of 0.5. Besides, we apply our aggregation rule to Byzantine-robust federated learning and employ the Polyak’s momentum to reduce gradient variance among honest workers. It is analyzed that our aggregator achieves order-optimal Byzantine-resilient federated learning for heterogeneous data. Experimental results using MNIST, Fashion-MNIST and CIFAR-10 demonstrate that the developed approach yields higher classification accuracy than the competing aggregators under different attack types and heterogeneity levels.

Byzantine-robust distributed or federated learning (FL) refers to providing reliable performance under Byzantine attacks, which violate the prescribed protocols and transmit arbitrary information to the server to hamper the convergence of machine learning (ML) algorithms, via designing resilient aggregation rules to combat attacks. Although numerous robust rules have been suggested, their performance degrades for heterogeneous data. A few techniques have been exploited to handle this problem, but they either require preaggregation operations, hence increasing the computational load, or lack breakdown point analysis of their rules. This article proposes a new aggregation rule, which clips the gradients received from all workers according to the distance between the gradient and the aggregation center. That is, when the distance is larger than the radius $\gamma $ , the gradient will be clipped, and the longer the distance, the closer the clipped gradient is to the center. We theoretically analyze that the breakdown point of the developed rule is 0.5, the maximum value for robust aggregators. Moreover, our rule achieves order-optimal Byzantine-robust training error under data heterogeneity, while the median-based schemes, such as coordinate-wise median (CM) and geometric median (GM), are suboptimal. Experimental results demonstrate that the devised aggregation mechanism can handle different attacks well and outperforms the existing rules.

wireless communication environment may not experience direct line-of-sight propagation whereas the number of receivers (Rxs) is often limited. We propose the utilization of only non-line-of-sight (NLoS) received signal strength (RSS) measurements observed at a single Rx to locate a target, via a positioning algorithm accounting for data association ambiguity that may occur in a real-world scenario. Considering the stochastic nature of a network geometry, tractable expressions are derived for the probability of acquiring at leastLNLoS RSS measurements during localization. In light of the computational complexity of our solution, we investigate the minimum number of RSS samples required to meet the specified localization accuracy, thereby guiding system design. Furthermore, the probability distribution of the trace of the Cramér-Rao lower bound is obtained analytically, which offers a comprehensive understanding of the fundamental limits of the single-Rx localization scheme without resorting to intensive simulations.

Received signal strength (RSS) has been extensively studied for localization purposes, and the distributed nature of cell-free massive multiple-input multiple-output (CF-mMIMO) systems offers a new synergistic avenue for achieving high-precision localization. In this work, Open RAN and software-defined radio are used to realize the central and distributed units of a CF-mMIMO system to acquire the RSS measurements. By analyzing the experimental data, it is revealed that the RSS measured from the first-order reflection path can yield a sufficiently high signal-to-noise ratio for localization, enabling localization even without line-of-sight (LoS) paths. Inspired by this finding, a hybrid localization scheme, that can attain the best accuracy benchmarked by Cramér-Rao lower bound, is proposed to estimate the target position using both LoS and first-order non-line-of-sight RSS measurements. Furthermore, a theoretical framework is established to assess the fundamental limits of RSS-based localization in CF-mMIMO systems, offering a principled guideline for system designers to deploy and design localization systems in real-world scenarios.

Direct localization (DL) of high-order quadrature amplitude modulation (QAM) sources is a pivotal challenge in wireless communications, particularly in environments characterized by complex multipath propagation and the presence of multiple sensor array-based anchors. This paper introduces a novel solution based on dual atomic norm minimization (DANM) framework that capitalizes on the fourth-order cumulant property of QAM signals to suppress Gaussian noise and expand the effective array aperture. Unlike traditional DL frameworks based on discrete Fourier transform (DFT) and spatial smoothing pre-processing (SSP) techniques, the proposed framework enhances localization accuracy and improves robustness against multipath effects. By framing the localization problem as a semidefinite program that utilizes dual atomic norm properties, our solution eliminates the need for prior knowledge of the number of sources and achieves a favorable balance between computational complexity and localization performance. Simulation results reveal that the DANM-based DL algorithm outperforms existing DFT- and SSP-based DL methods in terms of localization accuracy, with its root mean square error (RMSE) closely approaching the Cramér-Rao bound (CRB) even under challenging conditions. These findings underscore the potential of DANM in advancing high-precision DL for high-order QAM sources, thereby paving the way for more reliable and precise wireless communication systems.

In this paper, we propose leveraging rotatable antennas (RAs) to enhance near-field communication and sensing performance by exploiting a new spatial degree-of-freedom (DoF) offered by array rotation. Specifically, we investigate an RA-aided near-field integrated sensing and communication (ISAC) system, where the transmit beamformers and the array rotation angle at the base station (BS) are jointly optimized to minimize the Cramér-Rao bounds (CRBs) for angle and range estimation, while ensuring a minimum signal-to-interference-plus-noise ratio (SINR) for communication users. To gain important insights into the impact of RAs on near-field ISAC, we analyze two special cases:communication-onlyandsensing-onlytransmission. For the communication-only case, we derive therotation-awarechannel path correlation using the Fresnel integrals and analytically demonstrate that RAs provide an additional rotation gain, thereby improving communication performance. For the sensing-only case, we derive closed-formrotation-awareCRBs for near-field angle and range estimation under bothisotropicanddirectionalbeamformers. It is theoretically unveiled that array rotation improves sensing performance by concurrently reducing both CRBs. Interestingly, the optimal rotation angles that minimize these CRBs are identical. Subsequently, to address the resultant non-convex optimization problem, we propose adouble-layeralgorithm to obtain a high-quality solution, where the inner layer optimizes the transmit beamformers using semidefinite relaxation (SDR), while the outer layer determines the array rotation through a one-dimensional exhaustive search. Finally, numerical results highlight the significant performance gains of the developed RA-aided near-field ISAC system over conventional fixed-antenna ISAC systems.

Movable antenna (MA) is envisioned as a promising technique in future wireless communication systems, offering flexible antenna movement to achieve enhanced communication performance. In this paper, we propose a new and efficient position optimization framework based on differential evolution (DE) to improve the communication performance of MA-enabled wireless systems. In particular, the proposed framework addresses two key issues of the widely used particle swarm optimization (PSO)-based methods, namely, the extremely high computational cost and the vanilla fitness function. First, instead of the conventionalall-in-oneindividual representation method, where all MA positions are encoded into a single individual, we introduce a newone-in-onerepresentation method, in which each MA’s position is treated as an individual. This design significantly reduces both the dimensionality of individuals and the total number of individuals, thereby significantly reducing computational complexity. Second, we propose anadaptive penalty mechanismthat imposes larger penalties/weights on constraints encountered stronger violations, in contrast to traditionally used uniform penalties. These two ideas are integrated into our proposed framework, referred to asDE with one-in-one representation (DEO). In addition, to further improve search capabilities, we extend our approach to a variant calledDE with both all-in-one and one-in-one representations (DEAO), which combines the strengths of both representations. This method balances exploration and exploitation by alternately identifying and refining promising solution regions. Then, we evaluate the effectiveness of DEO and DEAO in a typical MA-enabled multiuser downlink communication system, where a weighted sum-rate optimization problem is formulated and solved using atwo-layerapproach. Finally, numerical results demonstrate that our methods can achieve over 95% reduction in computational cost compared to PSO-based methods, while delivering superior performance.

Prior studies on mixed near-field and far-field communications have focused exclusively onsingle-cellscenarios, where both near-field and far-field users are served by the same base station (BS), leading tointra-cellmixed-field interference. In this paper, we consider a more general and practicalmulti-cell mixed-fieldscenario consisting of multiple cells, each serving multiple users, thus resulting in more complexinter-cellmixed-field interference. To address this new challenge, we propose leveragingrotatable antenna(RA) technology to enhance multi-cell mixed-field communication performance by exploiting the additional spatial degree-of-freedom (DoF) introduced by RA rotation to mitigate interference in an efficient way. Specifically, we study an RA-enabled multi-cell mixed-field communication system in which each BS is equipped with an RA array to serve its associated users. We formulate a network-wide sum-rate maximization problem that jointly optimizes the transmit beamforming and the rotation angles of the RA arrays, subject to per-BS power constraints and admissible array rotation limits. To gain useful insights into the role of RAs in multi-cell mixed-field communications, we first analyze a special case with a single user per cell. For this case, we obtain a closed-form expression for therotation-awareinter-cell mixed-field interference using the Fresnel integrals and analytically show that RA rotation can effectively mitigate such interference, thereby substantially improving system performance. For the general case with multiple users per cell, we develop an efficientdouble-layeralgorithm: the inner layer optimizes the transmit beamforming at each BS via semidefinite relaxation (SDR) and successive convex approximation (SCA); while the outer layer determines the rotation angles of the RA arrays using particle swarm optimization (PSO). Numerical results demonstrate that RA-enabled multi-cell systems achieve significant performance gains over conventional fixed-antenna systems, and the proposed joint design consistently outperforms various benchmark schemes.

As large language models continue to grow in size, parameter-efficient fine-tuning (PEFT) has become increasingly crucial.While lowrank adaptation (LoRA) offers a solution through low-rank updates, its static rank allocation may yield suboptimal results.Adaptive low-rank adaptation (AdaLoRA) improves this with dynamic allocation but remains sensitive to initial and target rank configurations.We introduce AROMA, a framework that automatically constructs layer-specific updates by iteratively building up rank-one components with very few trainable parameters that gradually diminish to zero.Unlike existing methods that employ rank reduction mechanisms, AROMA introduces a dual-loop architecture for rank growth.The inner loop extracts information from each rank-one subspace, while the outer loop determines the number of rankone subspaces, i.e., the optimal rank.We reset optimizer states to maintain subspace independence.AROMA significantly reduces parameters compared to LoRA and AdaLoRA while achieving superior performance on natural language understanding and generation, commonsense reasoning, offering new insights into adaptive PEFT.

This paper addresses reconfigurable intelligent surface (RIS)-assisted indoor localization and synchronization in the presence of multipaths. Considering the far field condition, direct range estimation becomes infeasible and there exists clock offset in the system, compounding the difficulty for a single RIS to accomplish user equipment (UE) positioning and synchronization. To tackle this challenge, a dual-RISs system is proposed. The extra degrees of freedom it offers can effectively resolve the problem It uses initial RIS phase design to separate components from dual RISs. Then, atomic norm minimization is employed to reconstruct the separated received signals, and 2D-MUSIC with single-snapshot estimates the angles-of-departure (AODs) of the UE and scatterers. After removing angle terms, root-MUSIC estimates the time-of-arrival (TOA). The UE’s position is derived via least squares using AODs from dual RISs. Combining the UE’s position with LOS path TOAs yields the clock offset. Scatterer positions are obtained using geometric relationships with the UE’s position, NLOS path TOAs, and clock offset. Channel parameters are refined via maximum likelihood estimation. Simulation results prove the method’s effectiveness.

This paper addresses target localization using a multistatic multiple-input multiple-output (MIMO) radar system with coprime L-shaped receive arrays (CLsA). A target localization method is proposed by modeling the observed signals as tensors that admit a coupled canonical polyadic decomposition (C-CPD) model without matched filtering. It consists of a novel joint eigenvalue decomposition (J-EVD) based (semi-)algebraic algorithm, and a post-processing approach to determine the target locations by fusing the direction-of-arrival estimates extracted from J-EVD-based C-CPD results. Particularly, by leveraging the rotational invariance of Vandermonde structure in CLsA, we convert the C-CPD problem into a J-EVD problem, significantly reducing its computational complexity. Experimental results show that our method outperforms existing tensor-based ones.

This letter presents an optimization approach for frequency increments tailored to Frequency Diverse Array (FDA)-Multiple-Input Multiple-Output (MIMO) radar for target localization. We start to formulate the problem as minimizing the Cramér-Rao Bounds (CRBs) for both range and angle estimation, subject to practical constraints on the frequency increments. To facilitate optimization, the objective function is mathematically transformed, which results in a maximization problem, leveraging its inherent non-negativity of both the numerator and denominator. To address the resultant non-convex and NP-hard optimization problem, a Minorization-Maximization (MM)-Maximum Block Improvement (MBI) algorithm is devised by partitioning the frequency increment vector into distinct blocks, allowing for alternating maximization. In particular, each frequency increment is refined with the MM algorithm, while holding the others fixed, and only the block yielding the maximum objective increment is updated within each iteration. Simulation results are provided to demonstrate the excellent target localization of our proposed approach.

In traditional multi-user orthogonal frequency division multiplexing differential chaos shift keying (MU-OFDM-DCSK) systems, the noisy correlation of reference signals with overlapped information-bearing signals from multiple users degrades the bit error rate (BER). This paper devises a MU-OFDM-DCSK receiver that enhances the BER performance for uplink transmission. In our design, the challenges of reducing multi-user interferences (MUIs) and noise in both reference and information-bearing chaotic signals are addressed via leveraging the low-rank structure of the received signal matrix. By exploiting low-rank matrix factorization, a novel objective function is constructed. Minimization of this function, which corresponds to a least squares optimization, can effectively decode the transmitted data bits, even in the presence of additive white Gaussian noise (AWGN) and MUIs. The BER of our scheme is analyzed and verified in both AWGN and multipath Rayleigh fading channels. Theoretical developments including uniqueness of matrix factorization and algorithm convergence as well as complexity, are also provided. Simulation results demonstrate that our designed receiver yields smaller BER than benchmark schemes.

Several existing works have revealed the effectiveness of arctangent-type penalties in exploiting sparsity for compressed sensing. However, addressing the subproblems associated with the arctangent penalty incurs considerable computational cost. Aiming to reduce complexity, we derive the closed-form proximity operator of an arctangent penalty, which is expressed as hyperbolic functions of sine and cosine in this paper. Accordingly, a computationally-efficient arctangent regularization iterative thresholding (ARIT) algorithm for sparse approximation is proposed. Furthermore, we theoretically prove that under certain conditions, the ARIT algorithm converges to a local minimizer of the arctangent regularization problem with an eventually linear convergence. Extensive experiments are conducted to compare our scheme with conventional iterative thresholding algorithms, demonstrating the former superiority in terms of the probability of successful recovery, rate of support recovery, phase transition, and robustness to noise.

Accurate prediction of mmWave time-varying channels is essential for mitigating the issue ofchannel agingin highly dynamic scenarios. Existing channel prediction methods have limitations: classical model-based methods often struggle to track highly nonlinear channel dynamics due to limited expert knowledge, while emerging data-driven methods typically require substantial labeled data for effective training and often lack interpretability. To address these issues, this paper proposes a novel hybrid method that integrates a data-driven neural network into a conventional model-based workflow based on a state-space model (SSM), implicitly tracking complex channel dynamics from data without requiring precise expert knowledge. Additionally, a novel unsupervised learning strategy is developed to train the embedded neural network solely with unlabeled data. Theoretical analyses and ablation studies are conducted to interpret the enhanced benefits gained from the hybrid integration. Numerical simulations based on the 3GPP mmWave channel model corroborate the superior prediction accuracy of the proposed method, compared to state-of-the-art methods that are either purely model-based or data-driven. Furthermore, extensive experiments validate its robustness against various challenging factors, including among others severe channel variations.

In robust matrix completion (MC), the Welsch function, also referred to as the maximum correntropy criterion with Gaussian kernel, has been widely employed. However, it suffers from the drawback of down-weighing normal data. This work is the first to uncover the explicit regularizer (ER) for the Welsch function based on the multiplicative form of half-quadratic (HQ) minimization. Leveraging this discovery, we develop a new function called t-Welsch, also with ER, which provides unity weight to normal data and exhibits stronger robustness against large-magnitude outliers compared to Huber's weight. We apply the t-Welsch to rank-one matching pursuit, enabling accurate and robust low-rank matrix recovery without the need of rank information and singular value decomposition (SVD). The resultant MC algorithm is realized via block coordinate descent (BCD), whose analyses of convergence and computational complexity are produced. Experiments are conducted using synthetic random data, as well as real-world images with salt-and-pepper noise and multiple-input multiple-output (MIMO) radar signals in the presence of Gaussian mixture disturbances. In all three scenarios, the proposed algorithm outperforms the state-of-the-art robust MC methods in terms of recovery accuracy. The code is available at https://github.com/ShuDun23/t-Welsch-and-RAR1MC.

In this work, we derive the proximity operator of an arctangent penalty, which is expressed using hyperbolic functions of sine and cosine. This penalty is then applied to sparse signal recovery, and an efficient arctangent regularization iterative thresholding (ARIT) algorithm is proposed, offering closed-form solutions for the subproblems associated with the arctangent penalty. Extensive experiments are conducted to compare the performance of ARIT with several existing iterative thresholding algorithms, and the results demonstrate that our algorithm achieves the best overall performance in terms of the probability of successful recovery, phase transition and running time.

This paper aims to suppress mainlobe deceptive jammers considering the multipath effect in a frequency diverse array-multiple-input multiple-output (FDA-MIMO) radar. At the problem formulation stage, the overall received signal including the true target, main-lobe deceptive jammers, and burst jamming signal in the presence of multipath propagation, is represented as a "low-rank + low-rank + sparse" decomposition model. Then, an improved Go Decomposition (GoDec) algorithm is developed to recover the components corresponding to the target signal and disturbance (including the mainlobe jammers and burst jamming signal). Furthermore, a data-dependent beamforming approach is implemented to eliminate the mainlobe deceptive jammers, where the covariance matrix is constructed using the recovered disturbance components, and the steering vector is obtained with a priori knowledge of the target position. Numerical results are provided to demonstrate the effectiveness of the devised technique and its superiority over competing methods in suppressing mainlobe deceptive jammers under multipath environments.

Although multi-beam multiplexing can be implemented merely by phase shifters with hybrid beamforming configured by the sub-connected subarray architecture since all the antennas share the same magnitude, they cannot be set to a predetermined value. To tackle this issue, a non-convex constraint to enforce the magnitudes to a fixed value is first introduced in this design and then an iterative method is employed to relax it into a convex one. In doing so, the weighting magnitudes of all antennas can be preset in advance according to given requirements and a more flexible solution with phase-only excitation is obtained for multi-beam multiplexing. Numerical results are presented to verify the effectiveness of the proposed approaches.

Subspace location estimators are a class of range-based source localization (SL) methods built upon the multidimensional similarity (MDS) theory. Since they are computationally lightweight while maintaining a reasonably good level of positioning accuracy, these techniques can be well-suited for the context of Internet of Things (IoT), where precise localization is necessary but the on-device computational resources turn out to be relatively limited. MDS analysis (MDSA), in signal processing terms, is the statistical process of disentangling the signal subspace components from their disturbance counterparts for an observed MDS matrix that measures the similarity among multiple source-sensor coordinate differences. A prominent drawback of traditional MDSA schemes devised under the assumption of Gaussian noise is their vulnerability to outliers in the available range-type data, which are frequently encountered in IoT SL applications due to adverse environmental factors like non line-of-sight signal propagation and interference. In this contribution, we use symmetric$\alpha $-stable$(S \alpha S)$distributions to systematically characterize the MDS matrix observation errors, thus accounting for the existence of outliers. To resist against$S \alpha S$disturbances, we cast MDSA as an$\ell _{p}$-norm-based robust low-rank approximation problem. We then develop a practical optimization solution by means of the alternating direction method of multipliers, for which we further conduct a theoretical analysis of convergence. Simulations and real-world experiments confirm the feasibility of our robust subspace positioning approach.

We introduce an efficient gradient based algorithm to minimize the peak sidelobe level (PSL) for binary sequence designs with or without low correlation zone requirements. The proposed algorithm calculates the effective step sizes by leveraging fast Fourier transform operations and employing low-complexity updates, and its local convergence is proved. Numerical examples are provided to demonstrate that our approach can outperform the state-of-the-art algorithms in generating binary sequences with lower PSL values.

We propose a novel mixed analog-to-digital converter (ADC) architecture for direction-of-arrival (DOA) estimation using a uniform linear array, where the in-phase and quadrature-phase channels can be independently sampled by different ADCs. We derive the Cramér-Rao bound (CRB) and utilize its lower bound to optimize the placement of different ADCs via a swap-based method. Numerical examples are provided to demonstrate the superiority of the optimized placement of different ADCs over existing schemes.

This paper considers the scenario of noisy inputs and compressive diffusion (for reducing communication load) with noisy links over sensor networks. We first study the implementation of diffusion bias-compensated Bayesian adaptation (DBCBA) for noisy inputs, which outperforms the existing solution. Next, an average-estimate step is applied to lessen the impact of link noise in the full diffusion case, yielding a diffusion average-estimate bias-compensated Bayesian adaptation (DABCBA) algorithm. A Bayes-based adaptation construction step is then presented to reconstruct the compressed diffusion information in the presence of link noise, resulting in a compressive DBCBA (CDBCBA) algorithm whose mean and mean-square behaviors are analyzed and the closed-form expression of the steady-state mean-square deviation is derived. In addition, estimators are devised for the input and output noise variances. The excellent performance of our algorithms is demonstrated via numerical examples while the theoretical calculation aligns closely with the simulation results.

Over the past two decades, sparse unmixing (SU) has gained significant attention in the realm of hyperspectral imaging. The aims of SU are to seek a subset of spectral signatures and estimate their fractional abundances to represent each mixed spectral pixel. Conventional SU methods often employ the Frobenius norm and thus cannot work satisfactorily in the presence of non-Gaussian noise. Second, the ideal$\ell _{0}$-norm is usually substituted with its convex or nonconvex approximation in most existing algorithms, which may degrade the recovery performance. To address these issues, this article proposes a novel approach, termed sparse unmixing using$\ell _{0}$-norm constraint and log-cosh loss (SUNNING). We exploit the$\log $-$\cosh $function to minimize the fitting errors subject to three constraints, namely, nonnegativity, sum-to-one, and upper bounded$\ell _{0}$-norm. Then, we adopt the projected gradient descent (PGD) framework to solve such an optimization problem. SUNNING includes two alternating steps, gradient descent and nonconvex projection, where an optimality of the solution is guaranteed. Also, we prove the convergence of SUNNING, including the objective value and variable sequence. In addition, to attain higher unmixing accuracy, we exploit the spectral library pruning (SLP) strategy to eliminate inactive endmembers, yielding an improved SUNNING. Experimental results on synthetic and real-world datasets exhibit improved robustness and effectiveness of the suggested methods over the state-of-the-art algorithms. MATLAB code is available at:https://github.com/freeLix-YY/IEEE_TGRS2024_SparseUnmixing_SUNNING_demo

We focus on visible light communication-based simultaneous position and orientation detection (SPAO) for user devices (UDs) using photodiodes, which is challenging due to scattering interference and small-scale fading. To address this challenge, a novel SPAO approach is proposed, which can jointly estimate UD location parameters and scattering channel states. As such, the disturbance of diffuse scattering and random fading on SPAO will be alleviated via scattering channel equalization. In addition, SPAO is non-convex in nature, and hence brute-force application of conventional optimization methods will lead to a poor SPAO solution. To address this issue, we devise a majorization minimization (MM)-based SPAO algorithm, where hidden convex structure of the non-convex SPAO problem is exploited, which renders an efficient closed-form iteration rule for joint SPAO and diffuse channel estimation. Due to the cross-layer cooperation between “VLC” and “ranging”, a robust SPAO solution against diffuse scattering and small-scale fading is achieved. It is corroborated by our simulations that the proposed MM-based SPAO algorithm achieves a large performance gain over state-of-the-art baseline methods.

Tensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery severely degrades in impulsive noise. Although the algorithms using the$\ell_{p}$-norm ($0<p<2$) or its variants can attain high restoration accuracy in the presence of gross errors, they are inferior to the Frobenius-norm-based methods when the noise is Gaussian-distributed. Therefore, an approach that is able to perform well in both Gaussian noise and impulsive noise is desired. In this work, we use a capped Frobenius norm to restrain outliers, which corresponds to a form of the truncated least-squares loss function. The upper bound of our capped Frobenius norm is automatically updated using normalized median absolute deviation during iterations. Therefore, it achieves better performance than the$\ell_{p}$-norm with outlier-contaminated observations and attains comparable accuracy to the Frobenius norm without tuning parameter in Gaussian noise. We then adopt the half-quadratic theory to convert the nonconvex problem into a tractable multivariable problem, that is, convex optimization with respect to (w.r.t.) each individual variable. To address the resultant task, we exploit the proximal block coordinate descent (PBCD) method and then establish the convergence of the suggested algorithm. Specifically, the objective function value is guaranteed to be convergent while the variable sequence has a subsequence converging to a critical point. Experimental results based on real-world images and videos exhibit the superiority of the devised approach over several state-of-the-art algorithms in terms of recovery performance. MATLAB code is available at https://github.com/Li-X-P/Code-of-Robust-Tensor-Completion.

Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality ($\ell _{0}$-norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.

With the emerging environment-aware applications, ubiquitous sensing is expected to play a key role in future networks. In this paper, we study a 3-dimensional (3D) multi-target localization system where multiple intelligent reflecting surfaces (IRSs) are applied to create virtual line-of-sight (LoS) links that bypass the base station (BS) and targets. To fully unveil the fundamental limit of IRS for sensing, we first study a single-target-single-IRS case and propose a novel two-stage localization protocol by controlling the on/off state of IRS. To be specific, in the IRS-off stage, we derive the Cramér-Rao bound (CRB) of the azimuth/elevation direction-of-arrival (DoA) of the BS-target link and design a DoA estimator based on the MUSIC algorithm. In the IRS-on stage, the CRB of the azimuth/elevation DoA of the IRS-target link is derived and a simple DoA estimator based on the on-grid IRS beam scanning method is proposed. Particularly, the impact of echo signals reflected by IRS from different paths on sensing performance is analyzed and we show that only the signal passing through the BS-IRS-target link is required while that of the BS-target link can be neglected provided that the number of BS antennas is sufficiently large and the dedicated sensing beam at the BS is aligned with the departure transmit array response from the BS to the IRS. Moreover, we prove that the single-beam of the IRS is not capable of sensing, but it can be achieved with multi-beam. Based on the two obtained DoAs, the 3D single-target location is constructed. We then extend to the multi-target-multi-IRS case and propose an IRS-adaptive sensing protocol by controlling the on/off state of multiple IRSs, and a multi-target localization algorithm is developed. Simulation results demonstrate the effectiveness of our scheme and show that sub-meter-level positioning accuracy can be achieved.

The inadvertent incorporation of deviating samples into the measured indirect and direct path delays is generally unavoidable in the practical implementation of passive elliptic localization. These outlying observations, however, can do great harm to the positioning performance if left untreated. Here, a robust statistics based method is put forward as the solution to such a problem. The non-outlier-resistant ℓ2cost function in the traditional least squares formulation is replaced by a certain differentiable error measure that possesses resistance to the presence of abnormally large fitting errors. A globally optimized hybrid quasi-Newton and particle swarm optimization algorithm is then developed for an efficient realization of the robust estimator. The strong capability of the presented approach to deal with outliers and its applicability to typical adverse localization environments are demonstrated via simulations.

Passive multistatic localization (PML) refers to locating a signal-reflecting/relaying target using the bistatic range and direct range measurements acquired by employing multiple spatially-separated transmitters and receivers, where the transmitter positions are unknown. In real-world applications, one of the major technical challenges faced in PML is the non-lineof-sight (NLOS) propagation of signals, and recent studies have turned to the concept of robust statistics to tackle such an issue. Continuing to delve into this research direction, here we address the discrepancy arising from the fact that the conventional robust statistical PML schemes inherently assume zero-centered error samples, which may not hold true when the positive NLOS biases are present. In contrast to the existing PML solutions, our proposal is based on the maximum correntropy criterion with variable center (MCC-VC), thereby taking into consideration the potential non-zero-centrality of error samples in the estimator derivation. Subsequently, we develop an alternating minimization algorithm to handle the nonconvex MCC-VC optimization problem in a way that can strike a fine balance between accuracy and computational efficiency. The superiority of our PML approach over its competitors is demonstrated via computer simulations

Graph signal processing refers to dealing with irregularly structured data. Compared with traditional signal processing, it can preserve the complex interactions within irregular data. In this work, we devise a robust algorithm to recover band-limited graph signals in the presence of impulsive noise. First, the observed data vector is recast, such that the noise component is divided into two vectors, representing the dense-noise component and sparse outliers, respectively. We then exploit ℓ0-norm to characterize the sparse vector as a regularization term. Alternating minimization is subsequently adopted as the solver for the resultant optimization problem. Besides, we suggest an approach to automatically update the penalty parameter of the ℓ0-norm term. In addition, we analyze the computational complexity and the steady-state convergence of our algorithm. Experimental results on synthetic and temperature data exhibit the superiority of the developed method over state-of-the-art algorithms in impulsive noise environments in terms of recovery accuracy and convergence speed.

In this paper, we devise a sparse-coded orthogonal frequency division multiplexing (OFDM) differential chaos shift keying (DCSK) communication system based on low-rank matrix recovery which can handle Gaussian background noise and outlier-contaminated symbols simultaneously. As the noise-free OFDM-DCSK symbol matrix has rank 1, we exploit the vector outer product for its modeling, while sparse coding is also applied to reduce the transmission energy. To demodulate information bits from the sparse-coded signal, we formulate an objective function which consists of a sum of Frobenius norm for rank-1 matrix recovery and$\ell _{0}$-norm for identifying the possibly outlier-contaminated symbols, with a self-adaptive weight parameter. The resultant optimization problem is solved iteratively via block coordinate descent, and the Laplacian kernel with the Silverman’s rule is adopted for outlier detection. Theoretical analysis including convergence of the objective function, bit error rate (BER), energy efficiency and computational complexity, are provided. Simulation results show that the proposed system has comparable mean square error and BER performance with the$\ell _{p}$-norm minimization based matrix recovery approach at$p=2$in additive white Gaussian noise, and is superior to that of$p=1$in Middleton class A noise, even when sparse coding is applied. Moreover, compared with other binary DCSK systems, our system achieves higher energy efficiency thanks to the sparse coding.

Robust matrix completion refers to recovering a low-rank matrix given a subset of the entries corrupted by gross errors, and has various applications since many real-world signals can be modeled as low-rank matrices. Most of the existing methods only perform well for noise-free data or those with zero-mean white Gaussian noise, and their performance will be degraded in the presence of outliers. In this paper, based on the factorization framework, we propose a novel robust matrix completion scheme via using the truncated-quadratic loss function, which is non-convex and non-smooth, and half-quadratic theory is adopted for its optimization. By introducing an auxiliary variable, half-quadratic optimization (HO) can transform the loss function into two tractable forms, that is, additive and multiplicative formulations. Block coordinate descent method is then exploited as their solver. Compared with the additive form, the multiplicative variant has lower computational cost since we attempt to take the observations contaminated by outliers as missing entries. Numerical simulations and experimental results based on image inpainting and hyperspectral image recovery demonstrate that our algorithms are superior to the state-of-the-art methods in terms of restoration accuracy and runtime. MATLAB code is available athttps://github.com/bestzywang.

Matrix completion refers to recovering a matrix from a small subset of its entries. It is an important topic because numerous real-world data can be modeled as low-rank matrices. One popular approach for matrix completion is based on low-rank matrix factorization, but it requires knowing the matrix rank, which is difficult to accurately determine in many practical scenarios. We propose a novel algorithm based on rank-one approximation that a matrix can be decomposed as a sum of outer products. The key idea is to find the basis vectors of the underlying matrix according to the observed entries, and gradually increase the vector number until an appropriate rank estimate is reached. In contrast to the conventional rank-one schemes that employ unchanging rank-one basis matrices, our algorithm performs completion from the vector viewpoint and is able to generate continuously updated rank-one basis matrices. Besides, we theoretically show that the developed method has a linear convergence rate and a smaller recovery error than existing rank-one based algorithms. Experimental results using both synthetic data and real-world images demonstrate that our solution has the best recovery performance among the competing algorithms when the observations are contaminated by Gaussian noise.

Matrix completion (MC) aims at recovering missing entries, given an incomplete matrix. Existing algorithms for MC are mainly designed for noiseless or Gaussian noise scenarios and, thus, they are not robust to impulsive noise. For outlier resistance, entry-wise$\ell _{p}$-norm with$0 < p < 2$and M-estimation are two popular approaches. Yet the optimum selection of$p$for the entrywise$\ell _{p}$-norm-based methods is still an open problem. Besides, M-estimation is limited by a breakdown point, that is, the largest proportion of outliers. In this article, we adopt entrywise$\ell _{0}$-norm, namely, the number of nonzero entries in a matrix, to separate anomalies from the observed matrix. Prior to separation, the Laplacian kernel is exploited for outlier detection, which provides a strategy to automatically update the entrywise$\ell _{0}$-norm penalty parameter. The resultant multivariable optimization problem is addressed by block coordinate descent (BCD), yielding$\ell _{0}$-BCD and$\ell _{0}$-BCD-F. The former detects and separates outliers, as well as its convergence is guaranteed. In contrast, the latter attempts to treat outlier-contaminated elements as missing entries, which leads to higher computational efficiency. Making use of majorization–minimization (MM), we further propose$\ell _{0}$-BCD-MM and$\ell _{0}$-BCD-MM-F for robust non-negative MC where the nonnegativity constraint is handled by a closed-form update. Experimental results of image inpainting and hyperspectral image recovery demonstrate that the suggested algorithms outperform several state-of-the-art methods in terms of recovery accuracy and computational efficiency.

As a frontier technology in radar imaging, hypersonic vehicle-borne (HSV) synthetic aperture radar (SAR) has several practical issues to be dealt with, namely, ground resolution capability, pulse repetition frequency (PRF) selection, and beam pointing description, especially for the near-vertical diving trajectory because of the extremely small angle between the velocity and slant range vectors. Moreover, its focusing approach design is greatly challenged by very large cross-couplings and spatial variations. Considering these practical problems, the constraints between system performance and parameter selection are analyzed firstly to obtain the parameter optimization procedure and avoid system design deviation. Then, a frequency radius/angle algorithm (FRAA) is devised, which is an extension of the radius/angle algorithm (RAA) performed in two-dimensional (2-D) frequency domain. In the FRAA, new range equation and 2-D frequency interpolation function are reconstructed with high accuracy by quadratic fitting and 3-D expansion. Compared with RAA, FRAA is more suitable for the HSV SAR with near-vertical diving trajectory. Simulation results verify the effectiveness of the proposed approach.

Elliptic target positioning from the bistatic ranges (BRs), as an emerging localization scheme, has recently gained considerable traction for its diverse applications in multistatic systems such as radar, sonar, and wireless sensor networks. This contribution extends the work of previous research on the low-rank property of the BR matrix (Xiong, “Denoising of bistatic ranges for elliptic positioning,” IEEE Geosci. Remote Sens. Lett., vol. 20, pp. 1–3, 2023, Art. no. 3500503) to the brand new use case of robust elliptic positioning in the presence of missing data. Due to the structures of the outlier-inducing errors when embodied in the BR matrix, many of the off-the-shelf low-rank matrix completion (LRMC) solutions cannot be applied. We address this challenge by formulating the problem of outlier-resistant BR matrix recovery as constrained minimization of an ℓ2,1-norm based loss function, and devising an algorithm based on alternating direction method of multipliers to efficiently solve the resultant LRMC. Simulations are conducted to demonstrate the efficacy of the developed robust elliptic positioning technique in various localization scenarios.

Sparse index tracking, as one of the passive investment strategies, is to track a benchmark financial index via constructing a portfolio with a few assets in a market index. It can be considered as parameter learning in an adaptive system, in which we periodically update the selected assets and their investment percentages based on the sliding window approach. However, many existing algorithms for sparse index tracking cannot explicitly and directly control the number of assets or the tracking error. This article formulates sparse index tracking as two constrained optimization problems and then proposes two algorithms, namely, nonnegative orthogonal matching pursuit with projected gradient descent (NNOMP-PGD) and alternating direction method of multipliers for$\ell _{0}$-norm (ADMM-$\ell _{0}$). The NNOMP-PGD aims at minimizing the tracking error subject to the number of selected assets less than or equal to a predefined number. With the NNOMP-PGD, investors can directly and explicitly control the number of selected assets. The ADMM-$\ell _{0}$aims at minimizing the number of selected assets subject to the tracking error that is upper bounded by a preset threshold. It can directly and explicitly control the tracking error. The convergence of the two proposed algorithms is also presented. With our algorithms, investors can explicitly and directly control the number of selected assets or the tracking error of the resultant portfolio. In addition, numerical experiments demonstrate that the proposed algorithms outperform the existing approaches.

Positioning based on received signal strength (RSS) is regarded as a promising candidate for localization purposes in wireless networks due to its feasibility and deployability. In general, multilateration and fingerprinting algorithms are the primary localization methods in RSS-based localization systems, which are assessed by the Cramér–Rao lower bound (CRLB), given fixed node locations, including the target and participating anchors. However, this methodology produces only definite values for the CRLB specific to the scenario of interest while does not provide insights into the fundamental limits of localization performance. Thus, we are motivated to analyze the RSS-based localization performance using stochastic geometry to allow for randomly distributed nodes and investigate how the nodes’ locations influence this performance. To characterize the localization performance of the multilateration method, a tractable expression of localizability is provided to indicate the probability that a target is localizable. Then, conditioned on the number of participating anchors$L$, we provide an accurate approximation of the CRLB using the$\lceil L/4 \rceil $th value of ordered distances to quantify the localization accuracy on a random network setting and examine how its performance is influenced under different propagation channels by utilizing$\kappa $–$\mu $shadowed fading. Next, the fingerprinting localization problem is regarded as a hypothesis testing problem, and thus, its performance can be evaluated based on the similarity analysis of the observed RSS fingerprints. A comprehensive analysis of these two methods is performed, and the derived calculations are compared with the experimental results to demonstrate that our unified framework can precisely reflect localization performance in real-world scenarios. Based on the analysis, we can develop an insight to optimally design an RSS-based localization system that achieves the specified localization requirements.

Elliptic positioning (EP) has been a topic of lively interest to localization practitioners owing to widespread adoption of the bistatic configuration in many location-enabling technologies nowadays. This letter addresses the problem of non-Gaussian error mitigation in EP, by formulating it as joint estimation of target position coordinates and a balancing parameter (BP) for the bias errors. An alternating minimization algorithm is put forward to break the original formulation down into a conventional weighted nonlinear least squares (WNLS) location estimator and a closed-form BP-update step. With its objective being properly decomposed, the WNLS subproblem is converted into the difference-of-convex programming framework, to which an efficient iterative solution based on the concave-convex procedure is applicable. Simulation results demonstrate that the proposed error-reduced EP approach can outperform a number of existing methods in terms of localization accuracy.

In this letter, we develop an effective algorithm for direction-of-arrival (DOA) estimation of coherent sources with coprime arrays. Firstly, we generate a virtual uniform linear array (ULA) through coprime array interpolation. Subsequently, we derive an augmented noise-free covariance matrix that is constructed using the entries of the covariance matrix of the virtual ULA outputs, and recover the Hermitian Toeplitz matrix by solving an atomic norm minimization problem with multiple measurement vectors. Finally, the DOAs of coherent sources are estimated via MUSIC spectral search. Unlike the state-of-the-art approach, our algorithm is insensitive to the phase differences among sources. Numerical results demonstrate the superiority of the proposed algorithm over several existing techniques.

The medium- and large- scale global sea surface temperature (SSTs), which is an important ocean parameter, are mainly measured by the space-borne microwave radiometry. However, the resolution and sensitivity are greatly limited by antenna size, orbit altitude, and flight speed. In this paper, an airborne C-band one-dimensional (1-D) microwave interferometric radiometer (ACMIR) is developed to obtain the SSTs with a high resolution and sensitivity. The spatial resolution of the ACMIR ranges from 40.7m to 612m, corresponding to the flight height of 500m to 8000m, while the sensitivity varies from 0.25K to 0.36K, associating with the boresight to the edge of the field of view. In order to evaluate the performance of the ACMIR, an ocean aviation experiment was conducted in the coastal area of the Yellow Sea in September 2020. The land observation results indicate that typical ground objects can be clearly distinguished. Furthermore, thesea surface brightness temperatures acquired by the ACMIR are compared with the estimates based on the radiative transfer model, with SST retrieval error of 0.77°C. The ACMIR can offer a high-resolution and accuracy of SST especially in coastal areas, and can meet several application requirements related to SSTs.

Motion errors are inevitable in real-world scenarios and introduce significant phase errors in airborne synthetic aperture radar (SAR) imaging. Generally, these errors consist of the cross-coupling and spatially variant components. Cross-coupling errors can usually be eliminated by motion compensation (MoCo), whereas the latter are seldom addressed, which deteriorate the imaging qualities, especially for the high-resolution cases. To solve the problem, a novel approach based on 2-D range-Doppler expansion is proposed. First, an accurate range equation of the aircraft is obtained based on the inertial navigation system (INS) data. Then, the range-Doppler expansion corresponding to the slant range and Doppler centroid are performed, by which the echo signal is decoupled into two spatially variant parts in range and azimuth directions. Finally, the chirp-z transforms (CZTs) are employed to remove the range and azimuth spatial variations introduced, respectively, by the cross-track and along-track errors. Different from the conventional methods, our approach can greatly decrease the cross-coupling and spatially variant effects brought by motion errors in high-resolution cases. Computer simulation and real data experiments demonstrate the effectiveness of the proposed approach.

Fault impulse extraction under strong background noise and/or multiple interferences is a challenging task for bearing fault diagnosis. Sparse representation has been widely applied to extract fault impulses and can achieve state-of-the-art performance. However, most of the current methods rely on carefully tuning several hyperparameters and suffer from possible algorithmic degradation due to the approximate regularization and/or heuristic sparsity model. To overcome these drawbacks, in this article, we present a sparse Bayesian learning (SBL) framework for bearing fault diagnosis, and then propose two group-sparsity learning algorithms to extract fault impulses, where the first one exploits the group-sparsity of fault impulses only, whereas the second one utilizes additional periodicity behavior of fault impulses. Due to the inherent learning capability of the SBL framework, the proposed algorithms can tune hyperparameters automatically and do not require any prior knowledge. Another advantage is that our solutions are maximuma$posteriori$estimators in the sense of Bayesian optimality, which can yield higher accuracy. Results on both simulated and real datasets demonstrate the superiority of the developed algorithms.

In this letter, we develop a coarray interpolation method for direction-of-arrival (DOA) estimation using the coprime electromagnetic vector-sensor (EMVS) array. Firstly, we derive the coarray signal model of the coprime EMVS array, which can be viewed as a combination of multiple polarization components. Subsequently, we fill in zero elements in each polarization component and recover the corresponding low-rank covariance matrix by solving a nuclear norm minimization (NNM) problem. By exploiting the recovered covariance matrices, we eventually construct a larger covariance matrix to carry out DOA estimation. Numerical experiment results demonstrate the superiority of the proposed algorithm over conventional methods.

We revisit herein the problem of time-difference-of-arrival (TDOA) based localization under the mixed line-of-sight/non-line-of-sight propagation conditions. Adopting the strategy of statistically robustifying the non-outlier-resistantl2loss, we formulate it as the minimization of a possibly non-differentiable generalized robust cost function, which is rooted in the analog locally competitive algorithm (LCA) for sparse approximation. We then present a Lagrange programming neural network to address the optimization formulation, with the non-differentiability issues being handled by grafting thereon the LCA concept of internal state dynamics. Compared with the existing algorithms, our approach is computationally less expensive, less reliant on the use of a priori error information, and observed to be capable of producing higher localization accuracy.

In this paper, we focus on wireless sensor network-based localization for user devices (UDs). Prior to UD localization, signal propagation model (SPM) is required to calibrate using training samples from a number of location grids. However, SPM usually suffers from measurement noise and inevitable error in calibration grid (CG) locations. This will significantly degrade UD localization performance. Nevertheless, the impact of CG location error, CG layout and the number of CGs on SPM calibration performance has not been characterized. Furthermore, the effect of SPM calibration error on UD localization performance has not been developed. In this paper, we aim to provide a unified framework for performance analysis of SPM calibration and UD localization. Firstly, we establish a closed-form Cramér-Rao lower bound on SPM calibration error and UD localization error, respectively. Secondly, the impact of measurement noise, CG location error and the number of CGs on SPM calibration performance is revealed. Thirdly, the influence of SPM calibration error, CG location error and measurement noise on UD localization performance is studied. The effect of modeling mismatch is also studied. The obtained analysis framework builds a theoretical basis for the design of efficient system optimization strategies, including resource allocation and CG deployment optimization, for UD localization performance enhancement.

An outlier-resistance phase retrieval algorithm based on alternating direction method of multipliers (ADMM) is devised in this paper. Instead of the widely used least squares criterion that is only optimal for Gaussian noise environment, we adopt the least absolute deviation criterion to enhance the robustness against outliers. Considering both intensity- and amplitude-based observation models, the framework of ADMM is developed to solve the resulting non-differentiable optimization problems. It is demonstrated that the core subproblem of ADMM is the proximity operator of the ℓ1-norm, which can be computed efficiently by soft-thresholding in each iteration. Simulation results are provided to validate the accuracy and efficiency of the proposed approach compared to the existing schemes.

The problem of row-sparse signal reconstruction for complex-valued data with outliers is investigated in this paper. First, we formulate the problem by taking advantage of a sparse weight matrix, which is used to down-weight the outliers. The formulated problem belongs to LASSO-type problems, and such problems can be efficiently solved via cyclic coordinate descent (CCD). We propose an extended CCD algorithm to solve the problem for complex-valued measurements, which requires careful characterization and derivation. Numerical simulation results show that the proposed algorithm is robust against outliers and has a higher empirical probability of exact recovery compared with other tested methods.

Beamspace processing is an efficient and commonly used approach in harmonic retrieval (HR). In the beamspace, measurements are obtained by linearly transforming the sensing data, thereby achieving a compromise between estimation accuracy and system complexity. Meanwhile, the widespread use of multi-sensor technology in HR has highlighted the necessity to move from a matrix (two-way) to tensor (multi-way) analysis. In this paper, we propose a beamspace tensor-ESPRIT for multidimensional HR. In our algorithm, parameter estimation and association are achieved simultaneously.

In the problem of image inpainting, one popular approach is based on low-rank matrix completion. Compared with other methods which need to convert the image into vectors or dividing the image into patches, matrix completion operates on the whole image directly. Therefore, it can preserve latent information of the two-dimensional image. An efficient method for low-rank matrix completion is to employ the matrix factorization technique. However, conventional low-rank matrix factorization-based methods often require a prespecified rank, which is challenging to determine in practice. The proposed method factorizes an image matrix as a sum of rank-one matrices so that it does not require rank information in advance as it can be automatically estimated by the algorithm itself when the algorithm has satisfactorily converged. In our study, matching pursuit is applied to search for the best rank-one matrix at each iteration. To be robust against impulsive noise, the residual error between the observed and estimated matrices is minimized by ℓp-norm with 0p-norm minimization is solved by the iteratively reweighted least squares method. The proposed model is beneficial for the robustness against outliers, and does not require rank information. Experimental results verify the effectiveness and higher accuracy of the proposed method with comparison to several state-of-the-art matrix completion-based image inpainting approaches.

In this letter, we propose a sparse array design method for adaptive beamforming in the presence of interferences. Our solution is based on finding the beamformer weight vector such that maximum output signal-to-interference-plus-noise ratio is attained. To control the sidelobes of the beampattern, quadratic fractional constraints are also introduced to optimize the beamformer weights. We formulate the array design problem as real-valued quadratically constrained quadratic program (QCQP) with reweighted l1-norm to promote sparsity. Moreover, we adopt semidefinite relaxation (SDR) and linear fractional SDR together to solve the QCQP problem. The resulting array yields excellent beamforming performance and a beampattern with low sidelobes. Numerical results demonstrate the effectiveness of the proposed sparse array design.

In this letter, we devise an efficient approach for estimating the directions-of-arrival (DOAs) of coherent signals using coprime arrays. Specifically, we firstly derive an augmented uniform linear array (ULA) via coprime array interpolation. Subsequently, we define a Toeplitz matrix that is formed using the correlation information of the interpolated ULA theoretical outputs, and recover the Toeplitz matrix by solving a nuclear norm minimization problem. After the low-rank Toeplitz matrix is recovered, the coherent signals are well resolved by the MUSIC algorithm. Simulation results demonstrate the advantages of the proposed approach over various existing methods when dealing with coherent signals.

In this letter, we focus on the problem of direction-of-arrival (DOA) estimation with a nested array in the presence of unknown mutual coupling. Firstly, the measurement model of the nested array with mutual coupling is established, and the properties of the corresponding array covariance matrix are derived. Based on the obtained properties, the coarray output signal is then reconstructed with reduced mutual coupling. Finally, joint sparse recovery technique is employed to extract the DOAs. Our algorithm can achieve underdetermined DOA estimation with satisfactory performance under unknown mutual coupling. Numerical results demonstrate the effectiveness of the proposed algorithm.

As a transition platform between aircraft and satellite, hypersonic vehicle-borne (HSV) synthetic aperture radar (SAR) could offer many advantages such as strong survival ability, fast response, and wide detection range. However, due to the complex aerodynamic configuration and flight characteristics of the hypersonic platform, the HSV SAR faces new challenges including serious cross-couplings and spatial variations. In order to deal with these issues, a radius/angle algorithm (RAA) is devised, which has a similar processing flow as that of the conventional polar format algorithm (PFA). In the RAA, a novel 2-D interpolation function, similar to that of the PFA which is performed in the Cartesian coordinates, is derived in the curvilinear coordinate system. Due to the high accuracy of the multi-decomposition by using the polar radius and polar angle, the RAA has a much larger depth-of-focus than that of the PFA. Moreover, the RAA approach is insensitive to the height variations for the HSV SAR with curved trajectory flight, whereas the PFA is not because of the out-of-plane projection effect. Simulation results verify the effectiveness of the proposed approach.

Smart grid has attracted increasing attention in the past decade, and one of its common problems is the variation of the nominal frequency (50 or 60 Hz) introduced by harmonics. In this paper, a batch-mode frequency estimator that can accurately obtain the deviation from the nominal frequency is proposed. The signal model, which includes not only the fundamental frequency but also the harmonics, is first defined, and its characteristic is then studied. Employing the linear prediction (LP) property of the model, the deviated frequency is iteratively updated according to the weighted LP errors, to achieve accurate fundamental frequency estimation. Computer simulations indicate that our proposed method is more accurate and reliable than the conventional estimators in the presence of harmonics and amplitude oscillation.

This paper proposes two methods for robust Capon beamforming. One is for the doubly constrained robust Capon beamforming problem, where the unit modular constraints on the elements of the steering vector of interest are enforced to circumvent the look direction error or phase perturbations of the signal-of-interest; and another addresses robust beamforming in impulsive noise environment, where we consider the lp-norm minimization (0 < p < 2) of the output while constraining the mainlobe response ripple term. We apply the splitting technique to simplify the resultant nonconvex optimization problem and solve it using alternating direction method of multipliers. The performance of the proposed methods is demonstrated via numerical examples.

This letter addresses the problem of signal detection in additive correlated noise whose covariance matrix is Toeplitz. Particularly, we design a novel detection approach in the framework of generalized likelihood ratio test, in which the maximum likelihood (ML) estimate of the Toeplitz covariance matrix is needed. Since there are no closed-form expressions for this ML estimate, we resort to the inverse iterative algorithm. The proposed detector surpasses existing methods in detection power and enjoys the constant false-alarm rate property. Besides, accurate asymptotic null and non-null distributions of the test statistic are derived. Numerical results are presented to validate our theoretical findings.

This letter focuses on time-of-arrival based localization using multidimensional similarity (MDS) analysis under non-line-of-sight (NLOS) propagation. To handle row-column structured outliers in the MDS matrix introduced by NLOS errors, we present a novel robust matrix approximation scheme with the use ofℓ2,1-norm and apply the alternating direction method of multipliers to solve the resultant nonlinear constrained optimization problem. The proposed method does not require any prior knowledge of NLOS information and can benefit from a comparatively low complexity. Simulation results show that our algorithm is superior to several existing approaches in mild and moderate NLOS environments.

In this letter, we devise a subspace updating algorithm for tracking directions-of-arrival (DOAs) using the difference coarray of a sparse array. Our solution is based on the projection approximation subspace tracking (PAST) framework, where we design new cost function and iterative process via spatial smoothing of the difference coarray output signal. Since the proposed spatial smoothing PAST (SS-PAST) algorithm exploits the aperture of the difference coarray, it attains higher DOA tracking accuracy than the conventional PAST method operating in a uniform linear array. Simulation results demonstrate the effectiveness of the SS-PAST algorithm.

Due to the freedom degree loss resulted from the unimodular constraints, it is not easy to specify proper and feasible stopband and passband levels for frequency grids of interest in spectrally constrained sequence design problems. In an attempt to avoid this difficulty, we devise a cost function that minimizes the ratio of the maximal stopband level to the minimal passband level. Next, we introduce auxiliary variables to simplify the optimization problem via decoupling the numerator and denominator. Then, the feasible solution is obtained by approximating the nondifferentiable objective function with a smooth function. We also apply an acceleration scheme to increase the algorithm convergence speed. The effectiveness of the proposed approach is demonstrated via numerical examples.

This letter addresses the problem of tensor completion. The properties of the tensor tubal rank (TTR) and tensor Kronecker rank are first discussed, and then a novel generalized tubal Kronecker decomposition together with a new tensor rank referred to as generalized tensor tubal rank (GTTR) are defined. It is shown that the GTTR is suitable for revealing both the Kronecker and tubal structures of a tensor. The general tensor completion idea is then presented following the procedure of alternate projection between tensor rank minimization and Frobenius-norm optimization. Furthermore, the GTTR minimization is relaxed to the problem of generalized tensor nuclear norm (TNN) minimization, and two solutions are derived. The first one is based on the idea of combining all generalized TNNs as a weighted sum, while the second one employs the alternate cancelation scheme. Experiments are also carried out using both simulated data and real datasets for comparison of the proposed and the state-of-the-art approaches.

Long integration time (LIT) indicates high resolution and/or large scene for spaceborne synthetic aperture radar (SAR) imaging and also means that the effects, brought by curved orbit, cannot be ignored. In this paper, considering the curved orbit caused by the relative motion between an SAR sensor in orbit and targets on a rotating planetary surface, the impacts of the LIT on the imaging results are discussed in detail. The analysis suggests that the cross-coupling phase is two-dimensional (2-D) with spatial variation. Employing the 2-D Taylor series expansion, the 2-D linear relationships between the spatially variant and invariant coefficients are derived, which are exploited to improve the echo formulation. Then, we apply the keystone transform (KT) to process the LIT spaceborne SAR data. Unlike the traditional application of the KT, our two proposed methods, which operate, respectively, in azimuth time and azimuth frequency domains, can greatly remove the spatially variant cross-coupling phase. Moreover, implementation considerations including the curved orbit of LIT spaceborne SAR, applicability of two methods, postprocessing for topography error compensation, and computational load are discussed. Simulation results verify the effectiveness of the developed focusing approaches.

Usually, it is very difficult to determine the exact distribution for a test statistic. In this paper, asymptotic distributions of locally most powerful invariant test for independence of complex Gaussian vectors are developed. In particular, its cumulative distribution function (CDF) under the null hypothesis is approximated by a function of chi-squared CDFs. Moreover, the CDF corresponding to the non-null distribution is expressed in terms of non-central chi-squared CDFs for close hypothesis, and Gaussian CDF as well as its derivatives for far hypothesis. The results turn out to be very accurate in terms of fitting their empirical counterparts. Closed-form expression for the detection threshold is also provided. Numerical results are presented to validate our theoretical findings.

A commonly used measurement model for locating a mobile source is time-difference-of-arrival (TDOA). As each TDOA measurement defines a hyperbola, it is not straightforward to compute the mobile source position due to the nonlinear relationship in the measurements. This brief exploits the Lagrange programming neural network (LPNN), which provides a general framework to solve nonlinear constrained optimization problems, for the TDOA-based localization. The local stability of the proposed LPNN solution is also analyzed. Simulation results are included to evaluate the localization accuracy of the LPNN scheme by comparing with the state-of-the-art methods and the optimality benchmark of Cramér-Rao lower bound.

One application for time-difference-of-arrival (TDOA) estimation is in emitter localization. A signal from an emitter reaching a group of sensors, each in a separate location, will have different arrival times. Finding the TDOAs between the output of pairs of sensors will provide the necessary measurements for the hyperbolic localization of the emitter. When the sensors acquire the signal by compressed sensing (CS), their outputs are reduced dimension linear transformation of the time samples of the signal. This shuffling of the time samples breaks up their time relation. Thus, a cross correlation of the CS output of two sensors cannot determine the TDOA. To apply cross correlation, it is necessary to reconstruct the time samples. This letter proposes an alternative that uses only the coefficients of the discrete Fourier transform (DFT) of the CS samples. It begins with the derivation of the maximum likelihood (ML) equation and the ML estimator. This estimator requires known values of signal and noise powers. Substituting these values by their estimates lead to the approximate ML estimator. The phase of the product of two DFT coefficients from each sensor is proportional to the unknown TDOA. Hence, these coefficients can provide an estimation of the TDOA. Simulation results show that although ML is the best, as expected, all these estimators have very close performance.

Matrix completion aims to find the missing entries from incomplete observations using the low-rank property. Conventional convex optimization based techniques for matrix completion minimize the nuclear norm subject to a constraint on the Frobenius norm of the residual. However, they are not robust to outliers and have a high computational complexity. Different from the existing schemes based on solving a minimization problem, we formulate matrix completion as a feasibility problem. An alternating projection algorithm (APA) is devised to find a feasible point in the intersection of the low-rank constraint set and fidelity constraint set. To achieve resistance to outliers, the fidelity constraint set is modeled as an ℓp-ball, where the ball center corresponds to the observed data. Furthermore, there is no stepsize within the framework of APA. Convergence of the APA is analyzed and the local linear convergence rate is established. Simulation results demonstrate the efficiency, accuracy, and outlier robustness of the APA.

Multiple sequence alignment (MSA) is the most common task in bioinformatics. Multiple alignment fast Fourier transform (MAFFT) is the fastest MSA program among those the accuracy of the resulting alignments can be comparable with the most accurate MSA programs. In this paper, we modify the correlation computation scheme of the MAFFT for further efficiency improvement in three aspects. First, novel complex number based amino acid and nucleotide expressions are utilized in the modified correlation. Second, linear convolution with a limitation is proposed for computing the correlation of amino acid and nucleotide sequences. Third, we devise a fast Fourier transform (FFT) algorithm for computing linear convolution. The FFT algorithm is based on conjugate pair split-radix FFT and does not require the permutation of order, and it is new as only real parts of the final outputs are required. Simulation results show that the speed of the modified scheme is 107.58 to 365.74 percent faster than that of the original MAFFT for one execution of the function Falign() of MAFFT, indicating its faster realization.

This paper considers the sparse recovery problem of multiple measurement vector (MMV) model corrupted in impulsive noise. To ensure outlier-robust sparse recovery, we formulate an MMV problem that includes the generalized ℓp-norm (12,0joint sparsity-promoting regularizer. The joint sparse penalty, however, is non-continuous and hence non-differentiable, which inevitably raises difficulty in optimization when using a gradient-based method. To address this, we build a smooth approximation for the ℓ2,0-based sparse metric via the log-sum based sparse-encouraging surrogate function. Then, we propose a block successive upper-bound minimization algorithm for the smooth MMV problem by solving a series of subproblems based on the block coordinate descent (BCD) method. Furthermore, local convergence of the proposed algorithm to a stationary point of the smooth problem is proved. Experiments demonstrate its efficiency and robust recovery performance for suppressing impulsive noise.

Phase retrieval has recently attracted renewed interest. It is revisited here through a new approach based on nonconvex quadratically constrained quadratic programming (QCQP). A least-squares (LS) formulation is adopted, and a recently developed non-convex QCQP approximation technique called feasible point pursuit (FPP) is tailored to obtain a new LS-FPP phase retrieval algorithm. The Cramér-Rao bound (CRB) is also derived for phase retrieval under additive white Gaussian noise. We demonstrate through simulations that the LS-FPP method outperforms the prior art and its mean square error approaches the CRB.

In this paper, parameter estimation for multi-dimensional sinusoids in additive impulsive noise is addressed. Our underlying idea is to minimize the ℓp-norm of the residual error tensor, where 12-norm minimization. In doing so, we can utilize the tensorial structure of the received data and then apply iteratively reweighted tensor singular value decomposition, referred to as IR-t-SVD, to recover the subspace or the signal tensor. After the recovery step, standard subspace techniques can be applied for parameter estimation. Based on the numerical results, IR-t-SVD outperforms several state-of-the-art methods in terms of mean square frequency error under α-stable noise.

John's test, which is also known as the locally most invariant test for sphericity of Gaussian variables, is one of the most frequently used methods in multichannel signal detection. The application of John's test requires closed-form and accurate formula to set threshold according to a prescribed false alarm rate. Asymptotic expansion is a powerful method in deriving the threshold expressions of detectors for large samples. However, the existing asymptotic analysis of John's test in the real-valued Gaussian case is not accurate, causing the obtained false alarm rate to deviate from the preset value. This work first corrects a miscalculation in the existing results. Then this accurate approach is extended to the complex-valued case. In this scenario our result is as accurate as the state-of-the-art scheme but enjoys higher computational efficiency.

Square-root least absolute shrinkage and selection operator (Lasso), a variant of Lasso, has recently been proposed with a key advantage that the optimal regularization parameter is independent of the noise level in the measurements. In this letter, we introduce a class of nonconvex sparsity-inducing penalties to the square-root Lasso to achieve better sparse recovery performance over the convex counterpart. The resultant formulation is converted to a nonconvex but multiconvex optimization problem, i.e., it is convex in each block of variables. Alternating direction method of multipliers is applied as the solver, according to which two efficient algorithms are devised for row-orthonormal sensing matrix and general sensing matrix, respectively. Numerical experiments are conducted to evaluate the performance of the proposed methods.

A high-pulse-repetition-frequency (PRF) radar can handle the high Doppler frequencies of clutter echoes received by a fast-moving airborne radar. However, high-PRF radar causes range ambiguity. In addition, the clutter is range dependent when the airborne radar works in a forward-looking geometry. The range ambiguity and range dependence will lead to severe performance degradation of the traditional space-time adaptive processing (STAP) methods. In this paper, a vertical frequency diverse array (FDA), which applies frequency diversity in the vertical of a planar array, is explored to circumvent the range ambiguity problem in STAP radar. A range-ambiguous clutter suppression approach is devised, which consists of vertical spatial frequency compensation and pre-STAP filtering. In the vertical-FDA radar, the vertical spatial frequency depends not only on the depression angle but also on the slant range. By using this characteristic, the range-ambiguous clutter can be separated in the vertical spatial frequency domain, and then, clutter suppression is achieved for each separated range region. As a result, both problems of range ambiguity and range dependence are solved. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Joint estimation of the directions-of-arrival (DOAs) and frequencies of multiple signals is addressed in this paper. By constructing a set of joint diagonalization matrices, two cost functions that do not require a priori information of the source number are devised for DOA and frequency estimation in a separate manner. This enables us to estimate DOAs and frequencies via two one-dimensional search steps in their corresponding spatial and frequency domains. Thus, the tremendous two-dimensional search required in the standard approaches can be avoided. Simulation results demonstrate the effectiveness of the proposed approach.

From the co-array perspective, sparse spatial sampling can significantly increase the degrees-of-freedom (DOFs), enabling us to perform underdetermined direction-of-arrival (DOA) estimation. By leveraging the increased DOFs from the sparse spatial sampling, we develop a new underdetermined DOA estimation method for wideband signals, named wideband sparse spectrum fitting (W-SpSF) estimator. In W-SpSF, we formulate a sparse reconstruction problem that includes a quadratic$({\ell_2})$weighted covariance fitting term added to a sparsity-promoting$({\ell _{2, 1}})$regularizer. Meanwhile, the optimal regularization parameter of W-SpSF is studied to ensure robust sparse recovery. Numerical results enabled nested arrays demonstrate that the W-SpSF estimator outperforms the spatial smoothing based MUSIC algorithm and works well in nonuniform noise environment.

Higher-order singular value decomposition (HOSVD) is usually required in$R$-dimensional ($R$-D) harmonic retrieval, where$R \geq 3$. In this letter, we devise an iteratively reweighted HOSVD technique, which is referred to as IR-HOSVD, for multi-dimensional frequency estimation in the presence of impulsive noise. The main idea is to minimize the${\ell _p}$-norm residual errors along all the$R$dimensions, where$1 < p < 2$. After decomposition, standard subspace techniques can be applied for parameter estimation. Based on the numerical results, IR-HOSVD outperforms several state-of-the-art techniques in terms of root mean square frequency error for different impulsive noise models.

Hadamard ratio test is a well-known approach to robust signal detection in multivariate analysis. Recently, it has been exploited for robust spectrum sensing in cognitive radio, but its detection performance is not yet completely analyzed. This work is devoted to accurate detection performance analysis of the Hadamard ratio method for robust spectrum sensing. By computing the first and second exact negative moments for the signal-presence hypothesis along with employing the Beta distribution approximation, we derive accurate analytic formulae for detection probability. This enables us to theoretically evaluate the detection behavior of the Hadamard ratio test. Numerical results are presented to validate our theoretical findings.

Spectrum sensing is a fundamental problem in cognitive radio. In this paper, we introduce two spectrum sensing methods based on Gerschgorin disk. The Gerschgorin radii contain the information of signal subspace, whereas the Gerschgorin centers capture the signal energy. The first proposal only relies on the Gerschgorin radii and thereby is robust against nonuniform noise. The second one, utilizing both the Ger-schgorin radii and centers, can significantly improve the detection performance. Simulation results are included to illustrate the superiority of the proposed methods.

A structured least squares based ESPRIT method is devised for joint direction-of-arrival and frequency estimation. By considering the errors in the estimated signal subspace and employing an iterative minimization procedure, the proposed approach is able to efficiently refine the estimated signal subspace, leading to significant enhancement in estimation performance. Simulation results demonstrate the effectiveness of the proposed approach.

Large time-bandwidth product waveform diversity design is a challenging topic in multiple-input multiple-output radar high-resolution imaging because existing methods usually can generate only two large time-bandwidth product waveforms. This paper proposes a new low peak-to-average ratio (PAR) orthogonal frequency division multiplexing chirp waveform diversity design through randomly subchirp modulation. This method can easily yield over two orthogonal large time-bandwidth product waveforms. More waveforms means that more degrees-of-freedom can be obtained for the system. The waveform performance is evaluated by the ambiguity function. It is shown that the designed waveform has the superiorities of a large time-bandwidth product which means high range resolution and low transmit power are allowed for the system, almost constant time-domain and frequency-domain modulus, low PAR and no range-Doppler coupling response in tracking moving targets.

Based on affine projection algorithm (APA) in adaptive filtering and the technique of parallel computing, we propose a novel algorithm called ℓ0-APA with its parallel implementation for sparse system identification and sparse signal recovery. For sparse system identification, parallel ℓ0-APA can serve as an effective approach for practical hardware implementation, since it lowers the requirement on the processors' clock speed. For sparse signal recovery, it can significantly reduce the convergence time. Prior algorithms such as ℓ0-LMS and ℓ0-ZAP can be seen as special cases of ℓ0-APA. Finally the performance of the proposed algorithm is analyzed and verified by numerical experiments.

Geostationary Doppler weather radar (GDWR), which is a novel and challenging instrument concept, can provide reflectivity profiles and Doppler dynamic information of meteorological targets over a circular disk coverage of approximately 5300km in diameter on the earth. In this paper, we estimate the mean Doppler radial velocity and Doppler spectrum width of GDWR, which have not been studied in the literature. We first calculate the relevant GDWR system parameters, and then investigate the accuracy of the mean Doppler radial velocity and Doppler spectrum width measurements using discrete Fourier transform and pulse pair methods. Simulation results show that the estimation performance is limited by the large normalized spectrum width of the echo when there is wind shear in the radar resolution volume. Proposals of improving the accuracy of the mean Doppler radial velocity and Doppler spectrum width estimates are also suggested.

A novel pseudo-noise resampling (PR) based unitary root-MUSIC algorithm for direction-of-arrival (DOA) estimation is derived in this letter. Our solution is able to eliminate the abnormal DOA estimator called outlier and obtain an approximate outlier-free performance in the unitary root-MUSIC algorithm. In particular, we utilize a hypothesis test to detect the outlier. Meanwhile, a PR process is applied to form a DOA estimator bank and a corresponding root estimator bank. We propose a distance detection strategy which exploits the information contained in the estimated root estimator to help determine the final DOA estimates when all the DOA estimators fail to pass the reliability test. Furthermore, the proposed method is realized in terms of real-valued computations, leading to an efficient implementation. Simulations show that the improved MUSIC scheme can significantly improve the DOA resolution at low signal-to-noise ratios and small samples.

Recently, the CORe CONsistency DIAgnostic (CORCONDIA) has attractedmore and more attention as an effective tool for determining the number of components in parallel factor analysis (PARAFAC) or Tucker 3 models. In CORCONDIA, a proper user-defined threshold is required to ensure reliable performance. The optimal threshold increases with the signal-to-noise ratio (SNR), which results in significant probability of over-enumeration of the number of components for high SNRs under fixed threshold settings. We propose to first use a threshold interval to obtain lower and upper bounds of the estimates. The estimate takes the upper bound as its initial value and is then refined based on a sequence of hypothesis tests by exploiting the reconstruction error of the PARAFAC decomposition. The proposed scheme provides accurate detection for both low and high SNRs at almost no extra computational cost.

In this work, the problem of joint direction-of-arrival and fundamental frequency estimation for multi-channel harmonic sinusoidal signals is addressed. Different from the conventional optimal filtering method, we estimate the covariance matrix with the 2-D iterative adaptive approach, which is based on a single snapshot. In addition, to improve the estimation accuracy for the off-grid sources, a relaxation technique is utilized. Then, joint estimation is conducted on this covariance matrix estimate with the optimal filtering method. As a result, the relaxed iterative adaptive approach - optimal filtering method is devised. Statistical evaluation with synthetic signals shows the accurate performance of the proposed method compared with the Cramér-Rao lower bound.

A novel R-dimensional (R ≥ 3) model order selection (MOS) criterion is proposed for estimating the number of sources embedded in noise. By extending the classical r-mode matrix unfolding of a Rth-order measurement tensor to multi-mode matrix unfolding, (2R−1− 1) unfolded matrices are obtained. To maximize the identifiability, the unfolded matrix whose number of rows is closest to that of the columns is chosen. Meanwhile, as the so-obtained unfolded matrix is of large size, a sequence of nested hypothesis tests on its associated eigenvalues is utilized for MOS in the framework of the random matrix theory. The maximum number of sources the proposed enumerator able to identify is on the order of the square root of the product of all dimension sizes, whereas the identifiability of existing criteria is limited to the maximum dimension size minus one. Numerical results are included to illustrate the performance of the proposed enumerator.

A new signal subspace approach for sinusoidal parameter estimation of multiple tones is proposed in this paper. Our main ideas are to arrange the observed data into a matrix without reuse of elements and exploit the principal singular vectors of this matrix for parameter estimation. Comparing with the conventional subspace methods which employ Hankel-style matrices with redundant entries, the proposed approach is more computationally efficient. Computer simulations are also included to compare the proposed methodology with the weighted least squares and ESPRIT approaches in terms of estimation accuracy and computational complexity.

A new phase-based approach for frequency estimation of a single cisoid in the presence of additive white noise is proposed in this paper. The main idea is to divide the observed data into a number of segments by downsampling and exploit this new structure for parameter estimation. The maximum likelihood estimator for frequency is then developed, which is shown to be superior to conventional phase-based methods in terms of uniform performance. Computer simulations also illustrate that the mean square frequency error of the proposed scheme can attain Cramér-Rao lower bound for sufficiently high signal-to-noise ratio conditions.

In this paper, the problem of fundamental frequency estimation for real harmonic sinusoids is addressed. By making use of the subspace technique and Markov-based eigenanalysis, an optimally weighted harmonic multiple signal classification (OW-HMUSIC) estimator is devised. The fundamental frequency estimates are computed in an iterative manner. The performance of the proposed method is derived. Computer simulations are performed to compare the proposed approach with nonlinear least squares and HMUSIC methods as well as Cramér-Rao lower bound.

In this work, we present a model-based approach to enhance noisy speech using an analysis-synthesis framework. Target speech is reconstructed with model parameters estimated from noisy observations. In particular, spectral envelope is estimated by tracking its temporal trajectories in order to improve the noise-distorted short-time spectral amplitude. Initially, we propose an analysis-synthesis framework for speech enhancement based on harmonic noise model (HNM). Acoustic parameters such as pitch, spectral envelope, and spectral gain are extracted from HNM analysis. Spectral envelope estimation is improved by tracking its line spectrum frequency trajectories through Kalman filtering. System identification of Kalman filter is achieved via a combined design of codebook mapping scheme and maximum-likelihood estimator with parallel training data. Complete system design and experimental validations are given in details. Through performance evaluation based on a study of spectrogram, objective measures and a subjective listening test, it is demonstrated that the proposed approach achieves significant improvement over conventional methods in various conditions. A distinct advantage of the proposed method is that it successfully tackles the “musical tones” problem.

An unknown-position sensor can be localized if there are three or more anchors making time-of-arrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are from non-line-of-sight (NLOS) paths. In this paper, a semi-definite programming (SDP) based node localization algorithm in NLOS environments is proposed for ultra-wideband (UWB) wireless sensor networks. The positions of sensors can be estimated using the distance estimates from location-aware anchors as well as other sensors. However, in the absence of line-of-sight (LOS) paths, e.g., in indoor networks, the NLOS range estimates can be significantly biased. As a result, the NLOS error can remarkably decrease the location accuracy, and it is not easy to accurately distinguish LOS from NLOS measurements. According to the information known about the prior probabilities and distributions of the NLOS errors, three different cases are introduced and the respective localization problems are addressed. Simulation results demonstrate that this algorithm achieves high location accuracy even for the case in which NLOS and LOS measurements are not identifiable.

In this paper, the problem of estimating the damping factor and frequency parameters from multiple cisoids in noise is addressed. We first propose a data matrix which generalizes the commonly used Hankel-style matrices so that the number of repeated entries can be reduced. A new computationally efficient ESPRIT estimator that makes use of the right singular vectors is then devised. Algorithm modification for un-damped sinusoids and complexity are also discussed. Computer simulations are included to compare the proposed approach with the conventional ESPRIT methods and Cramer-Rao lower bound.

In this paper, frequency estimation of a two-dimensional (2D) cisoid in the presence of additive white Gaussian noise is addressed. By utilizing the rank-one property of the 2D noise-free data matrix, the frequencies are estimated in a separable manner from the principal left and right singular vectors according to an iterative weighted least squares procedure. We have also derived the mean and variance expressions for the frequency estimates, which show that they are approximately unbiased and their accuracy achieves Cramér-Rao lower bound (CRLB) at sufficiently high signal-to-noise ratio conditions. Computer simulation results are included to corroborate the theoretical development as well as to contrast the performance of the proposed algorithm with the weighted phase averager and iterative quadratic maximum likelihood method as well as CRLB.

The problem of frequency estimation for noisy sinusoidal signals from multiple segments or channels, which are referred to as gapped data, is addressed. Based on linear prediction and weighted least squares techniques, an iterative relaxation-based frequency estimator is devised and analyzed. The proposed algorithm is also extended to harmonically related frequencies. Computer simulations are conducted to compare the estimation performance of the developed approach with an existing multichannel frequency estimator and Crame¿r-Rao lower bound.

Recent years have witnessed the deployments of wireless sensor networks in a class of mission-critical applications such as object detection and tracking. These applications often impose stringent Quality-of-Service requirements including high detection probability, low false alarm rate, and bounded detection delay. Although a dense all-static network may initially meet these Quality-of-Service requirements, it does not adapt to unpredictable dynamics in network conditions (e.g., coverage holes caused by death of nodes) or physical environments (e.g., changed spatial distribution of events). This paper exploits reactive mobility to improve the target detection performance of wireless sensor networks. In our approach, mobile sensors collaborate with static sensors and move reactively to achieve the required detection performance. Specifically, mobile sensors initially remain stationary and are directed to move toward a possible target only when a detection consensus is reached by a group of sensors. The accuracy of final detection result is then improved as the measurements of mobile sensors have higher Signal-to-Noise Ratios after the movement. We develop a sensor movement scheduling algorithm that achieves near-optimal system detection performance under a given detection delay bound. The effectiveness of our approach is validated by extensive simulations using the real data traces collected by 23 sensor nodes.

Wireless sensor networks (WSNs) deployed for mission-critical applications face the fundamental challenge of meeting stringent spatiotemporal performance requirements using nodes with limited sensing capacity. Although advance network planning and dense node deployment may initially achieve the required performance, they often fail to adapt to the unpredictability and variability of physical reality. This paper explores efficient use of mobile sensors to address limitations of static WSNs for target detection. We propose a data-fusion-based detection model that enables static and mobile sensors to effectively collaborate in target detection. An optimal sensor movement scheduling algorithm is developed to minimize the total moving distance of sensors while achieving a set of spatiotemporal performance requirements including high detection probability, low system false alarm rate, and bounded detection delay. The effectiveness of our approach is validated by extensive simulations based on real data traces collected by 23 sensor nodes.

This paper presents a speech enhancement method based on an analysis-synthesis framework using harmonic noise model (HNM) in car noise environment. The major advantages of this method are effective suppression of car noise even in very low signal-to-noise ratio environments and mitigation of ldquomusical tonesrdquo which are generally introduced by conventional methods. In this paper, we devise a complete analysis-synthesis based speech enhancement system, and give details in HNM modeling, parameter estimation, and car noise adaptation. Subjective evaluation results show that the proposed method exhibits better noise suppression ability over conventional approaches without obvious degradation of speech quality.

The problem of node localization in a wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an an important yet challenging research topic. Most WSN localization studies at present have assumed that the anchor positions are perfectly known which is not valid in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for finding the localizations of unknown-position nodes in the presence of anchor position uncertainty. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and Cramer-Rao lower bound.

In civilian communication systems, the signature sequence of the desired signal in training phase is known to the receiver. In this letter, using the mutual information, we bridge the probability density function and minimum mean-square error (MMSE) between the observed data and training sequence of the desired signal, and then employ the MMSE to construct a minimum description length (MDL) criterion for accurate source enumeration. Numerical results demonstrate that the proposed method is superior to existing MDL methods in terms of detection performance particularly for small number of snapshots and/or source angular separation.

In this letter, parameter estimation of a uniformly sampled signal that satisfies the lossy wave equation in Gaussian noise is investigated. By exploiting the linear prediction property of the noise-free signal, a maximum likelihood estimator for the parameters is first developed. Relaxation is then applied to yield a simple and accurate algorithm. It is shown that the estimation performance of the proposed method attains Cramer-Rao lower bound.

In this paper, we propose a range-free cooperative localization algorithm for mobile sensor networks by combining hop distance measurements and particle filtering. In the hop distance measurement step, a differential error correction scheme is devised to reduce the positioning error accumulated over multiple hops. A backoff-based broadcast mechanism is also introduced in our localization algorithm. It efficiently suppresses redundant broadcasts and reduces message overhead. The proposed localization method has fast converges with small location estimation error. We verify your algorithm in various scenarios and compare it with conventional localization methods. Simulation results show that our proposal is superior to the state-of-the-art localization algorithms for mobile sensor networks.

Wireless sensor networks (WSNs) deployed for mission-critical applications face the fundamental challenge of meeting stringent spatiotemporal performance requirements using nodes with limited sensing capacity. Although advance network planning and dense node deployment may initially achieve the required performance, they often fail to adapt to the unpredictability of physical reality. This paper explores efficient use of mobile sensors to address the limitations of static WSNs in target detection. We propose a data fusion model that enables static and mobile sensors to effectively collaborate in target detection. An optimal sensor movement scheduling algorithm is developed to minimize the total moving distance of sensors while achieving a set of spatiotemporal performance requirements including high detection probability, low system false alarm rate and bounded detection delay. The effectiveness of our approach is validated by extensive simulations based on real data traces collected by 23 sensor nodes.

Wireless sensor networks (WSNs) have been proposed for a multitude of location-dependent applications. To stamp the collected data and facilitate communication protocols, it is necessary to identify the location of each sensor. In this paper, we discuss the performance of a novel received signal strength indicator (RSSI) positioning scheme, which uses a generalized geometrical location algorithm to achieve an accurate estimation based on mean received signal strength measurements. In order to improve the network performance and address limitations of static WSNs position estimation, mobile sensors are utilized effectively and an attractive movement strategy with mobile elements is designed. The effectiveness of our approach is validated and compared with the traditional RSSI method by extensive simulations.

Recent years have witnessed the deployments of wireless sensor networks in a class of mission-critical applications such as object detection and tracking. These applications often impose stringent QoS requirements including high detection probability, low false alarm rate and bounded detection delay. Although a dense all-static network may initially meet these QoS requirements, it does not adapt to unpredictable dynamics in network conditions (e.g., coverage holes caused by death of nodes) or physical environments (e.g., changed spatial distribution of events). This paper exploits reactive mobility to improve the target detection performance of wireless sensor networks. In our approach, mobile sensors collaborate with static sensors and move reactively to achieve the required detection performance. Specifically, mobile sensors initially remain stationary and are directed to move toward a possible target only when a detection consensus is reached by a group of sensors. The accuracy of final detection result is then improved as the measurements of mobile sensors have higher signal-to-noise ratios after the movement. We develop a sensor movement scheduling algorithm that achieves near-optimal system detection performance within a given detection delay bound. The effectiveness of our approach is validated by extensive simulations using the real data traces collected by 23 sensor nodes.

In this paper, we present an online stochastic approach for landmine detection based on ground penetrating radar (GPR) signals using sequential Monte Carlo (SMC) methods. The processing applies to the two-dimensional B-scans or radargrams of 3-D GPR data measurements. The proposed state-space model is essentially derived from that of Zoubir, which relies on the Kalman filtering approach and a test statistic for landmine detection. In this paper, we propose the use of reversible jump Markov chain Monte Carlo in association with the SMC methods to enhance the efficiency and robustness of landmine detection. The proposed method, while exploring all possible model spaces, only expends expensive computations on those spaces that are more relevant. Computer simulations on real GPR measurements demonstrate the superior performance of the SMC method with our modified model. The proposed algorithm also considerably outperforms the Kalman filtering approach, and it is less sensitive to the common parameters used in both methods, as well as those specific to it.

The sum capacity of the one-sided parallel Gaussian interference channel is shown to be a concave function of user powers. Exploiting the inherent structure of the problem, we construct a numerical algorithm to compute it. Two suboptimal schemes are compared with the capacity-achieving scheme. One of the suboptimal schemes, namely iterative waterfilling, yields close-to-capacity performance when the cross link gain is small.

Estimating the positions of sensor nodes is a fundamental and crucial problem in wireless sensor networks. In this paper, a novel subspace approach for range-based measurements node localization is devised. Computer simulations are included to contrast the performance of the proposed algorithm with the conventional subspace positioning method, namely, classical multidimensional scaling, as well as the Cramer-Rao lower bound.

In this letter, we address the problem of adaptively estimating the time delay of a noisy sinusoid received at two spatially separated sensors. By choosing the sampling frequency equal to four times the signal frequency, a simple adaptive algorithm for direct delay estimation is derived. Algorithm convergence in mean and mean square error is proved. Computer simulations are also included to demonstrate the effectiveness of the proposed method.

In this letter, the problem of adaptive tracking the amplitude and phase of a noisy sinusoid with known frequency is addressed. Based on approximating the recursive Gauss-Newton approach, two computationally simple algorithms, which provide direct parameter estimates, are devised and analyzed. Simulation results show that the proposed methods can attain identical estimation performance as their original one.

Based on linear prediction and weighted least squares, an iterative procedure for frequency estimation of a complex sinusoid in white noise is devised. The proposed approach, which utilizes the first-order as well as higher-order linear prediction terms simultaneously but does not require phase unwrapping, can be considered as a generalized version of the weighted linear predictor frequency estimator. Computer simulations are included to contrast the performance of the proposed algorithms with Cramer-Rao lower bound in one-dimensional and two-dimensional frequency estimation

The techniques of using wireless cellular networks to locate mobile stations have recently received considerable interest. The paper addresses the problem of maximum likelihood (ML) location estimation using (uplink) time-of-arrival (TOA) measurements. Under the standard assumption of Gaussian TOA measurement errors, ML location estimation is a nonconvex optimization problem in which the presence of local minima makes the search of the globally optimal solution hard. To circumvent this difficulty, we propose to approximate the ML problem by relaxing it to a convex optimization problem, namely semidefinite programming. Simulation results indicate that this semidefinite relaxation location estimator provides mean square position error performance close to the Cramer-Rao lower bound for a wide range of TOA measurement error levels.

A linear prediction based method is proposed for real harmonic sinusoidal frequency estimation. The estimator basically involves two steps. An initial fundamental frequency estimate is first obtained by solving a standard least-squares equation with exploitation of the harmonic structure of the sinusoidal signal or by using the MUSIC approach. Based on the initial estimate, an optimally weighted least squares cost function is then constructed from which the final estimate is acquired. Computer simulations show that the performance of the estimator approaches Crame/spl acute/r-Rao lower bound for sufficiently high signal-to-noise ratios and/or data lengths.

Location estimation of mobile telephones has received considerable interest in the field of wireless communications. In this paper, a simple and efficient positioning algorithm using received signal strength measurements obtained from at least three base stations are developed. Our proposed method is based on solving a nonconvex constrained weighted least squares problem. Simulation results show that the performance of the proposed method achieves the Cramer-Rao lower bound.

By applying a two-dimensional parameter estimation method proposed by M. Viberg and P. Stoica (see Conf. Rec. 32nd Asilomar Conf. Signals, Systems, Computers, vol.2, p.735-9, 1998), we develop a subspace method for estimating the differential delay of a sinusoidal signal received at two separated sensors as well as the sinusoidal frequencies. Using state-space realization, the time delay and frequency estimates are obtained from the state transition and observation matrices. Performance evaluation via computer simulations is included to demonstrate the effectiveness of the proposed algorithm.

We devise a new subspace method for estimating the differential time delay of a signal received at two separated sensors as well as the frequencies of the source signal, assuming that it consists of multiple sinusoids. The time delay and frequency estimates are related to the eigenvalues and eigenvectors of a matrix obtained from the covariances of the received signals. The effectiveness of the proposed algorithm is demonstrated via computer simulations using sinusoidal signals as well as real speech data.

The problem of estimating the difference in arrival times of a noisy sinusoid received at two spatially separated sensors is considered. Given the sinusoidal frequency, a simple delay estimator using the phase difference of the discrete time Fourier transforms (DTFTs) of the received signals is devised. With the use of a periodogram, the algorithm is extended to estimate the delay when the frequency is unknown. The minimum achievable delay variances for the cases of known/unknown frequencies and constant/rectangular envelopes are also given. The effectiveness of the method is demonstrated by comparing with the performance bounds for different frequencies, envelopes and noise conditions.

An adaptive algorithm is proposed for time delay estimation between sinusoidal signals received at two spatially separated sensors. The idea is to model the differential delay by an FIR filter whose coefficients are samples of a sine function. The delay estimate is updated directly on a sample-by-sample basis using the least mean square method, and its convergence behavior and mean square delay error are analyzed. The delay estimation performance of the algorithm can be further improved when the signal and noise powers are available. Computer simulations are presented to validate the theoretical derivations of the proposed estimator for static and linearly varying delays.

The frequency estimate for a real sinusoid provided by the periodogram has a bias which is particularly severe for a short observation interval. In this paper, two improvements to the periodogram are proposed to reduce this bias. The first method transforms the real tone to an analytic signal while the second algorithm subtracts the negative spectral line from the received signal, prior to applying the periodogram. The performances of the two methods are illustrated by comparing with the periodogram and the Cramer-Rao lower bound.

Wavelet denoising is applied in time delay estimation between signals received at two spatially separated sensors in the presence of noise. Prior to cross correlation, each of the sensor outputs is denoised according to a novel thresholding rule in order to increase the input signal-to-noise ratio. Unlike conventional generalized cross correlators (GCCs), it does not require spectral estimation of the source signal and the corrupting noises which may introduce large delay variance. It is proved that the delay estimate provided by the proposed method is globally convergent to the true value with a high probability. Computer simulations illustrate that the technique outperforms other GCCs for different SNRs when the sampling rate is sufficiently high.

The explicit time delay estimator (ETDE) provides an efficient way to estimate the time difference of arrival between signals received at two separated sensors. However, the algorithm is biased for finite filter length and the delay bias increases when the signal-to-noise ratio (SNR) or the number of filter taps decreases. In this paper, we add an adaptive gain control to the ETDE to decouple the effect of changes in the SNR during adaptation. As a result, a smaller delay variance and an unbiased delay estimate for a wide range of filter lengths can be attained. Computer simulations are presented to validate the theoretical derivations of the proposed estimator for static and linearly time-varying delays under both stationary and nonstationary signal/noise power environments.