Electromagnetic Vector-sensor Array Research Articles

Coarray Interpolation for Direction Finding and Polarization Estimation Using Coprime EMVS Array via Atomic Norm Minimization

In this paper, we develop an efficient algorithm for direction finding and polarization estimation using coprime electromagnetic vector sensor (EMVS) array. First of all, we represent the coarray outputs of coprime EMVS array as the multiple-component form and perform interpolation on each coarray output component. Using the interpolated measurement matrix, we subsequently formulate an atomic norm minimization problem to reconstruct the noise-free covariance matrix and measurement matrix of the interpolated ULA measurements. Finally, we estimate the directions-of-arrival (DOAs) of sources by applying MUSIC on the reconstructed covariance matrix, and utilize the reconstructed measurement matrix and the estimated DOAs to derive the closed-form estimates of polarization parameters. Compared with various existing methods, the proposed algorithm can provide higher estimation accuracy. Furthermore, our algorithm is able to handle more sources and has lower computational complexity. Numerical results illustrate the superiority of the proposed algorithm over the state-of-the-art methods.

2D-DOA Estimation in Multipath Using EMVS Rectangle Array

Electromagnetic vector sensor (EMVS) arrays bring an epochal opportunity for direction finding, as they enable the estimation of two-dimensional direction of arrival (2D-DOA) and polarization characteristics. In this paper, we revisit the 2D-DOA estimation problem in an EMVS rectangle array under multipath propagation. An improved subspace estimator is proposed, which addresses the rank-deficit problem through matrix arrangement, and the 2D-DOA and polarization parameters are estimated via combining the normalized vector cross-product with the least squares method. Our proposed method is suitable for a single snapshot scenario and offers superior accuracy compared to existing methods. To validate its effectiveness, several numerical simulations have been designed and conducted.

Coarray Polarization Smoothing for DOA Estimation with Coprime Vector Sensor Arrays

In this paper, the problem of direction-of-arrival (DOA) estimation of multiple sources using a coprime electromagnetic vector sensor (EMVS) array is addressed. Each EMVS consists of three mutually orthogonal electric dipoles and three mutually orthogonal magnetic loops, all collocated at a single point in space. By exploiting the polarization diversities embedded in the vector sensors, the coarray polarization smoothing (COPS) is presented to increase the degrees of freedom (DOFs) from the polarization coarray domain. In contrast to the widely used spatial smoothing technique, the COPS offers the following insights: (1) it is source polarization-dependent and is proved to offer 20 DOFs at most, (2) it does not reduce the efficient spatial coarray aperture of the coprime array so that it enables the use of all virtual coarray sensors without resorting to the nontrivial sparse recovery or array interpolation operations, and (3) it can be synthesized with the spatial smoothing to get the DOFs multiplied. Finally, the efficacy of the COPS scheme is verified by numerical examples.

A coarray processing technique for nested vector-sensor arrays with improved resolution capabilities

In this paper, we propose a new coarray processing technique for nested electromagnetic vector-sensor (EMVS) arrays. Vector-sensors by providing multi-component measurements of the incident waves offer additional information over the common single-output scalar sensors. The current paper takes the advantage of the multi-component measurements of vector-sensors combined with the elegant nested array strategy to design a new coarray processing technique. In this way, we utilize the auto/cross-correlation matrices of the underlying subarrays of the nested EMVS array to serve as snapshots in the coarray domain. Then, we apply two levels of spatial and temporal smoothing procedure to recover the rank of the model and also improve the covariance matrix estimation in the difference coarray domain. The proposed method can provide O(N2) degrees of freedom (DOFs) with only N physical EMVSs. The effectiveness of the proposed coarray processing technique is demonstrated through several simulation examples. Simulation results show that the proposed technique provides superior resolution capabilities and more accurate DOA estimates in the asymptotic region compared to the other counterparts. Moreover, the proposed method requires relatively less computational efforts among the other methods.

Joint 2D‐DOA and polarization estimation for Electromagnetic vector sensors array with compressive measurements

Electromagnetic vector sensors (EMVS) arrays have been employed extensively in the field of array signal processing for their advantage in terms of polarization diversity. However, with the introduction of EMVS, the cost of the hardware equipment and the complexity of the corresponding parameter estimation algorithms increase considerably, as the number of received signal channels and the dimension of the received signal are much larger than the traditional scalar array. In order to effectively reduce hardware cost and algorithm complexity, we propose a scheme that combines an electromagnetic vector sensor array with a compression network. We construct the corresponding signal model and based on this we derive a Compressed Reduced Dimensional MUltiple SIgnal Classification (Compressed To avoid the multi-dimensional search, Reduced Dimension MUSIC) algorithm which can effectively reduce the computational complexity. While selecting the coefficient matrix of the compressed network, random selection can cause information loss, which leads to the performance degradation of the estimation algorithm. To address this problem, we propose an optimization method for coefficient matrix selection based on the maximum signal-to-noise ratio (SNR) criterion. Numerical simulations are conducted in different scenarios to verify the effectiveness of the parameter estimation algorithm and the optimization algorithm.

PARAFAC Estimators for Coherent Targets in EMVS-MIMO Radar with Arbitrary Geometry

In the past few years, multiple-input multiple-output (MIMO) radar with electromagnetic vector sensor (EMVS) array, or called EMVS-MIMO radar, has attracted extensive attention in target detection. Unlike the traditional scalar sensor-based MIMO radar, an EMVS-MIMO radar can not only provides a two-dimensional (2D) direction finding of the targets but also offers 2D polarization parameter estimation, which may be important for detecting weak targets. In this paper, we investigate into multiple parameter estimations for a bistatic EMVS-MIMO radar in the presence of coherent targets, whose transmitting EMVS and receiving EMVS are placed in an arbitrary topology. Three tensor-aware spatial smoothing estimators are introduced. The core of the proposed estimators is to de-correlate the coherent targets via the spatial smoothing technique and then formulate the covariance matrix into a third-order parallel factor (PARAFAC) tensor. After the PARAFAC decomposition of the tensor, the factor matrices can be obtained. Thereafter, the 2D direction finding can be accomplished via the normalized vector cross-product technique. Finally, the 2D polarization parameter can be estimated via the least squares method. Unlike the state-of-the-art PARAFAC estimator, the proposed estimators are suitable for arbitrary sensor geometries, and they are robust to coherent targets as well as sensor position errors. In addition, they have better estimation performance than the current matrix-based estimators. Moreover, they are computationally efficient than the current subspace methods, especially in the presence of a large-scale sensor array. In addition, the proposed estimators are analyzed in detail. Numerical experiments coincide with our theoretical findings.

Geometric Algebra-Based ESPRIT Algorithm for DOA Estimation

Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding in an electromagnetic vector-sensor (EMVS) array; however, existing ESPRIT algorithms treat the output of the EMVS array either as a “long vector”, which will inevitably lead to loss of the orthogonality of the signal components, or a quaternion matrix, which may result in some missing information. In this paper, we propose a novel ESPRIT algorithm based on Geometric Algebra (GA-ESPRIT) to estimate 2D-DOA with double parallel uniform linear arrays. The algorithm combines GA with the principle of ESPRIT, which models the multi-dimensional signals in a holistic way, and then the direction angles can be calculated by different GA matrix operations to keep the correlations among multiple components of the EMVS. Experimental results demonstrate that the proposed GA-ESPRIT algorithm is robust to model errors and achieves less time complexity and smaller memory requirements.

2D-DOA Estimation for EMVS Array with Nonuniform Noise

Electromagnetic vector sensor (EMVS) array is one of the most potential arrays for future wireless communications and radars because it is capable of providing two-dimensional (2D) direction-of-arrival (DOA) estimation as well as polarization angles of the source signal. It is well known that existing subspace algorithm cannot directly be applied to a nonuniform noise scenario. In this paper, we consider the 2D-DOA estimation issue for EMVS array in the presence of nonuniform noise and propose an improved subspace-based algorithm. Firstly, it recasts the nonuniform noise issue as a matrix completion problem. The noiseless array covariance matrix is then recovered via solving a convex optimization problem. Thereafter, the shift invariant principle of the EMVS array is adopted to construct a normalized polarization steering vector, after which 2D-DOA is easily estimated as well as polarization angles by incorporating the vector cross-product technique and the pseudoinverse method. The proposed algorithm is effective to EMVS array with arbitrary sensor geometry. Furthermore, the proposed algorithm is free from the nonuniform noise. Several simulations verify the improvement of the proposed method.

Source Localization Using Distributed Electromagnetic Vector Sensors

Electromagnetic vector sensor (EVS) array has drawn extensive attention in the past decades, since it offers two‐dimensional direction‐of‐arrival (2D‐DOA) estimation and additional polarization information of the incoming source. Most of the existing works concerning EVS array are focused on parameter estimation with special array architecture, e.g., uniform manifold and sparse arrays. In this paper, we consider a more general scenario that EVS array is distributed in an arbitrary geometry, and a novel estimator is proposed. Firstly, the covariance tensor model is established, which can make full use of the multidimensional structure of the array measurement. Then, the higher‐order singular value decomposition (HOSVD) is adopted to obtain a more accurate signal subspace. Thereafter, a novel rotation invariant relation is exploited to construct a normalized Poynting vector, and the vector cross‐product technique is utilized to estimate the 2D‐DOA. Based on the previous obtained 2D‐DOA, the polarization parameter can be easily achieved via the least squares method. The proposed method is suitable for EVS array with arbitrary geometry, and it is insensitive to the spatially colored noise. Therefore, it is more flexible than the state‐of‐the‐art algorithms. Finally, numerical simulations are carried out to verify the effectiveness of the proposed estimator.

Coarray Interpolation for DOA Estimation Using Coprime EMVS Array

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.

Elevation, azimuth, and polarization estimation with nested electromagnetic vector-sensor arrays via tensor modeling

In this paper, we address the joint estimation problem of elevation, azimuth, and polarization with nested array consists of complete six-component electromagnetic vector-sensors (EMVS). Taking advantage of the tensor permutation, we convert the sample covariance matrix of the receive data into a tensorial form which provides enhanced degree-of-freedom. Moreover, the parameter estimation issue with the proposed model boils down to a Vandermonde constraint Canonical Polyadic Decomposition problem. The structured least squares estimation of signal parameters via rotational invariance techniques is tailored for joint auto-pairing elevation, azimuth, and polarization estimation, ending up with a computational efficient method that avoids exhaustive searching over spatial and polarization region. Furthermore, the sufficient uniqueness analysis of our proposed approach is addressed, and the stochastic Cramér-Rao bound for underdetermined parameter estimation is derived. Simulation results are given to verify the effectiveness of the proposed method.

Joint DOA and Polarization Estimation With Crossed-Dipole and Tripole Sensor Arrays

Electromagnetic vector sensor arrays can track both the polarization and direction of arrival (DOA) of the impinging signals. For linear crossed-dipole arrays, as shown by our analysis, due to inherent limitation of the structure, it can only track one DOA parameter and two polarization parameters. For full 4-D (two DOA, and two polarization parameters) estimation, we could extend the linear crossed-dipole array to the planar case. In this article, instead of extending the array geometry, we replace the crossed-dipoles by tripoles and construct a linear tripole array. Detailed proof shows that such a structure can estimate the 2-D DOA and 2-D polarization information effectively in general. A brief comparison between the planar crossed-dipole array and the linear tripole array is performed at last, showing that although the planar structure has a better performance, it is achieved at the cost of increased physical size.

Rectangular array of electromagnetic vector sensors: tensor modelling/decomposition and DOA‐polarisation estimation

In this study, the authors propose a fast quadrilinear decomposition algorithm for estimation of the directions-of-arrival and polarisations of the incident sources via a uniform rectangular array of electromagnetic vector sensors (EMVSs). Conventional quadrilinear alternating least squares (QALS), involves computationally intensive Khatri-Rao products in each iteration, to update the parameter matrices (factors). Moreover, QALS is more likely to fall in a local minimum and tends to take more steps before an acceptable solution, which further slows down the convergence and often mis-converges, thereby yielding meaningless results. To preserve the quadrilinearity, they arrange the measurements as a four-dimensional (4D) data (fourth-order tensor), from which a third-order sub-tensor (3D slice) can be obtained by fixing one index along any dimension. These slices are used to create new cost functions that are alternately minimised while updating the factors until convergence. They show that the rows of parameter matrices form the diagonal elements of a tensor, which capture the internal quadrilinearity of data and significantly reduce the cost function in few iterations only. Simulation results verify that the authors’ algorithm holds faster convergence, does not mis-converge, provides parameter estimation accuracy similarly to the QALS and superior of the Estimation of Signal Parameters via Rotational Invariance Technique and propagator method.

DOA estimation for coprime EMVS arrays via minimum distance criterion based on PARAFAC analysis

This study presents a minimum distance-based direction-of-arrival (DOA) estimation algorithm for coprime electromagnetic vector sensor (EMVS) arrays. The idea is to split-up the coprime array into two uniform linear arrays (ULAs) of vector sensors and arrange the received ULA data in the form of a three-way array suitable for parallel factor (PARAFAC) analysis, which fits least-square models to the received source signal mixtures of ULAs and thus enables to retrieve the model matrices corresponding to each ULA. Nevertheless, because of the array splitting the estimated DOAs from these matrices are not unique. To uniquely determine the DOA, the authors state and prove a theorem which is fundamental to the proposed algorithm and provides a means to find an estimate based on the minimum distance criterion. Efficacy of the proposed algorithm is demonstrated through performance comparison with other existing algorithms such as Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), long vector MUltiple SIgnal Classification (MUSIC), conventional PARAFAC and the propagator method being simulated for an equivalent element ULA of EMVS and spaced half a wavelength apart. Numerical simulations reveal that the proposed algorithm outperforms the others.

Joint DOA and Polarization Estimation via Canonical Polyadic Decomposition With Constant Modulus Constraints

We consider the joint estimation of direction-of-arrival (DOA) and polarization of constant modulus (CM) signals based on an electromagnetic vector-sensor (EMVS) array. Two algebraic algorithms for canonical polyadic decomposition (CPD) with CM constraint are proposed in two scenarios, in which the source signals are fully and partially CM, respectively. The proposed algorithms use the analytic CM algorithm in the first step to calculate the source matrix, and then exploit the CPD structure of the data tensor to compute the remaining factor matrices, from which the DOA and polarization parameters can finally be obtained. Due to the algebraic nature, the proposed algorithms are faster and more stable than the optimization based algorithms, and can be used to effectively initialize the latter. We have shown that the proposed algorithms have more relaxed uniqueness conditions than unconstrained CPD, and thus can be applied in highly underdetermined cases where the number of source signals greatly exceeds that of the EMVSs. Simulation results are provided to illustrate the performance of the proposed algorithms.

Vector-Sensor-Based Signal Parameter Estimation by Exploiting CPD of Tensors

An approach for parameter estimation of signals impinging on an array of electromagnetic vector sensors is presented by exploiting canonical polyadic decomposition of tensors. The uniqueness of the approach is that it can distinguish the signals with the same direction of arrival (DOA) and copolarized state: one function that has not been fulfilled by the up-to-date approaches such as the derivative approaches of multiple signal classification and estimation of signal parameters via rotational invariance techniques, which are the traditional tensor-based approaches. Regarding the reason of our superiority in this function, it lies in that the traditional approaches usually require that the matrices involved in the operations are full column rank. However, in this article, the parameters can be estimated by virtue of the factor matrices, as long as the matrices satisfy the requirement that at least one is full column rank. In other words, as long as the signals comply with any one of the spatial, temporal, and polarized diversities, the proposed approach can effectively estimate the parameters of these signals.

Successive Method for Angle-Polarization Estimation With Vector-Sensor Array

A successive method for joint angle and polarization estimation of multiple narrowband incoherent sources using linear electromagnetic vector-sensor (EMVS) arrays is proposed in this article. First, the polarization field smoothing root-multiple signal classification (MUSIC) algorithm is presented to estimate the elevation angles. Second, the estimated elevation angles are applied to extract the EMVS manifolds and then to estimate the azimuth angles. Finally, the estimated angles are used to provide the polarization parameter estimates. Compared with most of the previous algorithms, the proposed algorithm first uses the polarization field vector smoothing, which enables the offering of more accurate elevation angle estimates for correlated sources, with no loss of array aperture, and, second, requires no spectral searching and parameter pairing procedures. Simulations results are provided to show the efficacy of the proposed algorithm.

DOA estimation for conformal vector-sensor array using geometric algebra

In this paper, the problem of direction of arrival (DOA) estimation is considered in the case of multiple polarized signals impinging on the conformal electromagnetic vector-sensor array (CVA). We focus on modeling the manifold holistically by a new mathematical tool called geometric algebra. Compared with existing methods, the presented one has two main advantages. Firstly, it acquires higher resolution by preserving the orthogonality of the signal components. Secondly, it avoids the cumbersome matrix operations while performing the coordinate transformations, and therefore, has a much lower computational complexity. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array.

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank- BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method.

Quaternion based joint DOA and polarization parameters estimation with stretched three-component electromagnetic vector sensor array

The three-component electromagnetic vector sensor (EMVS) consisting of co-centered orthogonally oriented x-dipole, z-dipole and z-loop is considered. In order to make full use of the spatial aperture of each component, the original uniform linear three-component EMVS array (ULTEA) is stretched into one half-wavelength spaced uniform linear loop subarray (ULLSA) along the z axis, and one sparse uniform linear co-centered orthogonally oriented dual-dipole (CODD) subarray (SULCSA) along the x axis. Then, a generalized rotation invariance based quaternion multiple signal classification (GRIQ-MUSIC) algorithm is presented for direction of arrival (DOA) and polarization parameters estimation. According to the proposed algorithm, the elevation angles are firstly estimated based on the half-wavelength spaced ULLSA. Then the polarization phase differences and azimuth angles are obtained based on the coupling relationship between the angle domain and polarization domain, but the azimuth angles are in coarse-resolution since the array aperture is not utilized. Next, the SULCSA is used to re-estimate the azimuth angles in fine resolution, and the ambiguity problem can be resolved by the least square method. Finally, based on the estimated elevation angles, azimuth angles and polarization phase differences, the corresponding auxiliary polarization angles can be estimated by N times one-dimensional parameter search, where N is the sources number, and the parameters high dimensional parameters search problemare matched automatically. Based on the GRIQ-MUSIC algorithm, the high dimensional parameters search problem of the conventional Q-MUSIC algorithm is simplified to a one-dimensional parameter search problem, thus the proposed algorithm not only reduces the computation complexity considerably, but also avoids the performance degradation caused by the failure in parameters pairing. The simulation examples demonstrate the effectiveness and feasibility of the proposed algorithm.