Coprime array enables derivation of an extended array with the number of virtual elements beyond the number of physical sensors, resolving the underdetermined direction of-arrival (DOA) estimation problem while mitigating mutual coupling effects. However, the virtual array is discontinuous and contains some holes. To fully exploit the information of the virtual array, conventional methods typically employ complex matrix completion (MC) to iteratively recover the data of the covariance matrix, resulting in high complexity, particularly with large-scale coprime arrays. In this letter, a real-valued DOA estimation via the construction of Toeplitz covariance matrix and spline interpolation is proposed. The algorithm complexity is reduced by real-valued Toeplitz matrix, and then the holes are filled by spline interpolation. The recovered matrix can be used for DOA estimation by conventional subspace approaches. The superior computational performance of our approach is validated through comparative simulations with established methods.

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.

This letter investigates the multi-target direction of arrival (DOA) tracking problem under wireless sensor networks (WSNs), where each node is equipped with a uniform linear array (ULA). A WSN probability hypothesis density (WSN-PHD) tracking algorithm is proposed with two key innovations: 1) an exponential accumulation (EA) fusion strategy that aggregates multi-node measurements to resolve occlusions in WSNs, thereby improving tracking continuity under time-varying targets, and 2) a non-circular phase-assisted likelihood function to enhance target tracking accuracy. Numerical results show that the proposed algorithm achieves average optimal sub-pattern assignment (OSPA) distance and location errors reduction of 78.18% and 76.82% compared to the algorithm without EA fusion.

The traditional subspace-based algorithms in the process of coherent direction of arrival (DOA) estimation get in trouble because of the rank loss of the signal covariance matrix. To this end, this paper introduces a forward/backward convolution kernel (FBCK) method, which not only reconstructs the signal covariance matrix and its diagonal elements, but also efficiently solves the signal coherence problem by utilizing the moving array technique. More precisely, the FBCK operation is applied to the signal space matrix at a given instant and utilizes the forward/backward convolution kernel to recover the rank corresponding to the number of signals without loss of the arrays' aperture. In a comparison evaluation with state-of-the-art spatial smoothing methods (including MSSP, SSP, ESS, ESS-SS, SSS and ASS), the proposed FBCK algorithm demonstrates excellent estimation capabilities in terms of snapshot number and signal-to-noise ratio (SNR), thus providing a robust and effective solution for DOA estimation in coherent signal environments.

Recently, direction-of-arrival (DOA) estimation in impulsive noise scenarios has been extensively investigated in the field of co-prime array signal processing. This paper proposes a combined enhanced bounded nonlinear covariance and phased fractional low-order moment (EBNC-PFLOM) method, which incorporates the advantages of both EBNC and PFLOM and mitigates the impulsive noise by constructing the equivalent data covariance matrix of the received signals. Furthermore, when dealing with a limited number of input signals, the proposed method is capable of directly estimating the signals’ DOA without spatial smoothing. Simulation results show that the proposed method outperforms the recently reported methods.

In this paper, we propose a nested sampling based off-grid block sparse representation method (Nested-OGBSR) for time-delay estimation (TDE) of coherent ground penetrating radar (GPR) backscattered echoes. Nested sampling strategy is taken to reduce the sampling rate and computational burden. The off-grid data model is adopted to eliminate the effect of basis mismatch caused by the predefined grids in sparse representation (SR) and thus improve the estimation accuracy. The non-circularity of GPR signals is also utilized to enhance the temporal resolution of sparse block representation (BSR). Numerical and experimental results are provided to show the superiority of the proposed method in terms of estimation accuracy, temporal resolution and computational complexity.

For the target tracking problem where the number of targets fluctuates with time and the measurement is a point measurement, the random finite set (RFS) class filtering is an available solution. However, in direction of arrival (DOA) tracking, the array observation is a super-positional value, and the tracking performance can be severely impaired if the RFS-based filter approach is applied. As a result, a novel measurement association mapping (NMAP) approach has been presented to cope with the mapping problem between the array observations and sources. Nevertheless, the tracking performance is poor when the number of particles is small. In this paper, a modified delta-Generalized Labeled Multi-Bernoulli ($\delta $-GLMB) DOA tracking particle filter is proposed in combination with the NMAP strategy, which can achieve the same tracking performance with a smaller number of particles by modifying the particles in the$\delta $-GLMB prediction step. Furthermore, the approach is extended to a coprime array and can achieve better DOA tracking performance than a uniform linear array. Simulation experiments validate the effectiveness of the proposed algorithm.

Time-delay estimation (TDE) for thin top layers of asphalt pavement is a challenging task due to the limited resolution of ground penetrating radar (GPR) as well as small permittivity difference between top layers. Echoes backscattered from the interfaces of top layers with similar permittivity have usually much smaller amplitudes compared with other echoes, which can be called weak signals. The weak backscattered echoes are usually too sensitive to the noise and other strong echoes that current signal processing approaches (subspace-based methods and compressed sensing based methods) might have false estimation results even failures without proper processing of them. Therefore, in this paper, an enhanced orthogonal matching pursuit (OMP) method is proposed to deal with weak signals resulting from similar permittivity of adjacent asphalt layers. Based on the orthogonality between signal and noise subspaces, we firstly apply the truncated singular value decomposition (SVD) on the received signals, in order to reduce the noise impact. Secondly, we build an orthogonal matrix to the mode matrix of the pre-estimated strong backscattered echoes, and map it to the overcomplete dictionary matrix, such that the influence of the residual of the strong backscattered echoes can be reduced. Finally, the time-delays of backscattered echoes and layer thicknesses are estimated. Compared with conventional approaches, the proposed method is more suitable for TDE in thin asphalt pavement detection. The accuracy of the proposed method is validated by both numerical and experimental data.

Pavement survey is one of the most important applications for ground penetrating radar (GPR) in civil engineering. In the case of centimeter scale of GPR waves, the influence of interface roughness cannot be neglected and should be taken into account in the radar data model. The objective of this article is to estimate the time-delay in the presence of interface roughness by GPR. Using the property of noncircular signals, we propose a modified orthogonal matching pursuit method to estimate the pavement parameters for both overlapped and nonoverlapped echoes. Compared with subspace-based methods in coherent scenarios, the proposed method can estimate the time delays of backscattered echoes without applying the cumbersome interpolation and spatial smoothing procedures, which are more practical in real applications. The performance of the proposed method is tested on both simulated and experimental data. The estimation results show the good performance of the proposed method.

Ground Penetrating Radar (GPR) is a widely used tool in the management and monitoring of pavement structures. In this paper, we focus on the detection of thin inter-layer debondings between the hot mix asphalt layers of pavement structures. A Stepped-Frequency Radar (SFR) associated with a Support Vector Regression based Linear Prediction (LP-SVR) method is used to detect thin debondings. The performance of SFR with the LP-SVR method is analyzed according to various used frequency bandwidths on the experimental data.

In civil engineering, roadway structure evaluation is an important application which can be carried out by ground penetrating radar. This paper focuses on the estimation of the time delay and interface roughness of civil engineering structure, like pavements. The influence of interface roughness is taken into account in the signal model. Therefore, we propose a new method which allows to efficiently estimate the time delay and interface roughness. Like in [1], the modified MUSIC is used for time delay estimation. In interface roughness estimation, we propose a modified orthogonal propagator method (OPM) to estimate the interface roughness with estimated time delay. While in [1], maximum likelihood method is applied, which needs multiple dimensional search. The proposed method is tested on the experimental data. The experimental results show the performance of the proposed method.

In the field of civil engineering, ground penetrating radar (GPR) is a highly efficient nondestructive testing tool for sustainable management of pavement infrastructures. GPR allows to evaluate the structure of the roadway over large distances (with contactless configurations) and to detect significant subsurface defects. This letter presents a new method to detect thin debondings within pavement structures with the step-frequency GPR. The proposed method enables us to carry out the detection with only a small number of frequency samples and A-scans. It is based on the linear prediction and support vector regression theories. Two experimental results show its effectiveness.

The development of methods and tools for the road infrastructure sustainable management is a research challenge, especially for nondestructive testing methods. This letter focuses on the estimation of the thickness of civil engineering structures, like pavements, and more precisely, the time delay and interface roughness. We propose a modified Min-Norm algorithm which allows efficiently estimating the time delay and interface roughness without the eigenvalue decomposition. Therefore, it has a smaller computational load compared with subspace-based methods. The experimental results show the efficiency of the proposed algorithm.

Ground-penetrating radars (GPR) are widely used in media parameters' estimation and targets' localization. This paper focuses on time-delay estimation (TDE) using the GPR signal, which contains important information about the probed media structure. However, TDE tends to be a challenging task in GPR applications, in the scenarios of overlapping, coherent signals and limited snapshots. Forward-backward linear prediction (FBLP) is a high time-resolution method, which is able to directly deal with coherent signals. Support vector regression (SVR) is robust with small samples. Therefore, we propose to combine the theory of FBLP and SVR together to enhance the robustness of TDE in the case of coherent, overlapping signals as well as limited snapshots. The proposed method is tested with both numerical and experimental data. Both the results demonstrate the effectiveness of the proposed method.

In civil engineering, ground penetrating radar is a common technique for evaluating the structure and quality of road pavement. This paper focuses on the estimation of the time delay and interface roughness of civil engineering structure, like pavements. The influence of interface roughness is taken into account in the signal model. A modified estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm combined with an interpolated spatial smoothing technique is proposed. It allows us to jointly and efficiently estimate the time delay and interface roughness by ultrawideband radar (the upper frequency up to 8-10 GHz) with low computational complexity. The proposed algorithm is tested on both numerical and experimental data. Simulation and experimental results show the good performance of the proposed algorithm.

In this letter, a new method is proposed to enhance the ground-penetrating radar (GPR) signal for time-delay estimation in a low signal-to-noise ratio. It is based on a subspace method and a clustering technique. The proposed method makes it possible to improve the estimation accuracy in a noisy context. It is used with a compressive sensing method to estimate the time delay of layered media backscattered echoes coming from the GPR signal. Several simulations and an experiment are presented to show the effectiveness of signal enhancement.

In the electromagnetic field, radar is widely used to measure or estimate the media parameters or to detect targets through obstructions. For horizontally stratified media, the layer thickness can be deduced from the time delays of backscattered echoes and the dielectric constants. The high-resolution method estimation of signal parameters via rotation invariance techniques (ESPRIT) has been proposed for time-delay estimation. In practice with a radar, backscattered echoes are correlated. In order to apply the ESPRIT method, in this letter, we propose to use two adaptive improved spatial smoothing techniques with the propagator method for fighting against the correlation between the echoes. The proposed solution does not use any approximation. Numerical examples are provided to show the performance of the algorithm.

In civil engineering, ground penetrating radar is widely used for road pavement surveys. In this paper, the influence of interface roughness is taken into account. We propose a Modified ESPRIT algorithm for the data processing of radar signal, in order to jointly estimate the time delay and the interface roughness. The algorithm is tested on simulated data from the propagation inside layer expansion (PILE) method. Numerical examples are provided to demonstrate the performance of the algorithm.