The joint Doppler and Direction-of-Arrival (DOA) estimation of moving targets using an (Ultra-)Wideband (UWB) frequency modulated continuous-wave (FMCW) antenna array radar is investigated. Besides the well-known range migration problem, another concern for wideband signals is the DOA estimation problem. For the first time, both problems are considered in this paper simultaneously, where the wideband DOA is transformed into a second-order coupling system similar to the range migration problem by using the property of the FMCW signal. A novel embedded compensation approach to eliminate the coupling terms caused by range migration and wideband DOA is proposed and 2D multiple signal classification (2D MUSIC) algorithm is subsequently applied with dynamic noise subspace to joint estimation of Doppler and DOA. Further, to reduce the computational load caused by multiple eigendecompositions of large matrices, efficient implementation methods are proposed and their performance in speed, accuracy and robustness is compared. The performance of the proposed methods is validated by the numerical simulations and is compared with Keystone MUSIC. Finally, it is shown that for a small number of targets, the Rayleigh-Ritz is the most efficient approach among them.

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In this paper, the generalized multiple measurement vectors (GMMV) linear inversion method is applied to the reconstruction of the 3-D Fresnel data, provided by the Institue Fresnel (Marseille, France). The results show that the GMMV-based method can obtain good resolution along the x- and y- axes, while poor resolution along the z-axis, because there were only receiving antennas distributed on the x-o-y plane, indicating that the diversity of the measurement angle is critical for the GMMV method.

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In this paper, a linear model based on multiple measurement vectors' model is proposed to formulate the inverse scattering problem of highly conductive objects at one single frequency. Considering the induced currents that are mostly distributed on the boundaries of the scatterers, joint sparse structure is enforced by a sum-of-norm regularization. Since no a priori information is required and no approximation of the scattering model has been made, the proposed method is versatile. Imaging results with transverse magnetic and transverse electric polarized synthetic data and Fresnel data demonstrate its higher resolving ability than both linear sampling method and its improved version with higher, but acceptable, computational complexity.@en

Cross-correlated contrast source inversion (CC-CSI) is a nonlinear iterative inversion method that is proposed recently for solving the inverse scattering problems. In CC-CSI, a cross-correlated error is constructed and introduced to the cost functional, which improves the inversion ability when compared to the classical design of the cost functional by exploiting the mismatch between the data error and state error. In this paper, the multifrequency inversion for electromagnetic waves is considered and a multifrequency version of CC-CSI is proposed. Numerical and experimental inversion results of both transverse magnetic and transverse electric polarization demonstrate that when multifrequency data are available, CC-CSI still outperforms the multiplicative-regularized CSI method in the inversion of more complicated scatterers.

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The linear shape reconstruction method based on the generalized multiple measurement vectors model is a newly proposed approach which is able to effectively retrieve the morphological information of dielectric/metallic scatterers with competitive imaging resolution. In this letter, we have extended this approach to quantitative inversion, and the proposed approach turns out to be effective even for complicated scatterers and highly efficient in comparison to nonlinear iterative methods. The inverted results obtained by processing the transverse magnetic polarized Fresnel data-sets of the year 2005 demonstrate the validity of the proposed method in real applications.@en

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell’s equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations, such that the required estimation of the noise level is circumvented. The validity is demonstrated with an excitation of transverse magnetic (TM) experimental data, and it is observed that, in the aspect of focusing performance, the GMMV-based linear method outperforms the extensively used linear sampling method (LSM).

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One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse scattering problem is put into a discretized finite-difference frequency-domain scheme and linearized into a cascade of two linear functionals. To deal with the nonuniqueness effectively, the joint structure of the contrast sources is exploited using a sum-of- ℓ1 -norm optimization scheme. A cross-validation technique is used to check whether the optimization process is accurate enough. The total fields are, then, calculated and used to reconstruct the contrast by minimizing a cost functional defined as the sum of the data error and the state error. In this procedure, the total fields in the inversion domain are computed only once, while the quality and the accuracy of the obtained reconstructions are maintained. The novel method is applied to ground-penetrating radar imaging and through-the-wall imaging, in which the validity and the efficiency of the method are demonstrated.@en

In this paper, we improved the performance of the contrast source inversion (CSI) method by incorporating a so-called cross-correlated cost functional, which interrelates the state error and the data error in the measurement domain. The proposed method is referred to as the cross-correlated CSI. It enables better robustness and higher inversion accuracy than both the classical CSI and multiplicative regularized CSI (MR-CSI). In addition, we show how the gradient of the modified cost functional can be calculated without significantly increasing the computational burden. The advantages of the proposed algorithms are demonstrated using a 2-D benchmark problem excited by a transverse magnetic wave as well as a transverse electric wave, respectively, in comparison with classical CSI and MR-CSI.@en

This paper presents the application of the shape reconstruction method based on the generalized multiple measurement vectors (GMMV) model on the multi-frequency transverse magnetic (TM) and transverse electric (TE) polarized Fresnel data, measured by the Institue Fresnel (Marseille, France) from cylindrical objects. Finite difference frequency domain (FDFD) is applied to discretize the Maxwell's equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations and give the estimation of the noise level at the same time. The results show that the GMMV-based linear method successfully performs shape reconstruction of a large variety of scatterers.@en

In this paper, the nonlinear perfect electric conductor (PEC) inverse scattering problem was addressed with a linear model. First, finite difference frequency domain (FDFD) was used to discretize the problem. Then, the contrast and the total field were included into the contrast source to formulate a linear model. Due to the fact that the induced current only exists
on the surface of the PEC scatterers, reconstruction methods in compressive sensing (CS) can be used to recover the contrast source which is able to indicate the shape of the PEC objects. To further enhance the inversion performance, the multiple measurement vector (MMV) model was used to exploit the joint sparsity of the contrast sources corresponding to different incident angles. This method shares some common merits with other inversion methods: First, it does not require a priori information on the position and quantity of the scatterers. Second, nonconvex PEC objects can be successfully reconstructed. Third, it enables simple incorporation with complicated background media without increasing extra computational burden. In addition, it also shows its own advantages that cannot be achieved in other inversion methods: First, it solves the nonlinear inverse scattering problems based on the vectorial Maxwell equations with a linear model.
Second, the sensing matrix is much less compared to the inverse of the stiffness matrix in FDFD scheme, so it can be computed and stored beforehand to circumvent the matrix inverse computation and achieve fast inversion. Numerical simulation results with the transverse magnetic (TM) data in 2D configuration demonstrated the validity of the proposed method.@en