Electromagnetic Vector Sensor Research Articles

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

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.

Detection and localization of signals using an EMVS system in interference environments

In this paper, a new algorithm is devised to show how a complete electromagnetic vector sensor (EMVS) system enables handling the target detection and localization problem in interference-dominant scenarios. Specifically, our recently proposed sliding beamforming technique is first applied to EMVS systems to suppress the interference signal and reconstruct the EMVS steering vector (SV) of the target signal. Then, the strategy for the detection and localization of target signals is introduced in detail. Afterward, various numerical simulations are carried out to show the simplicity and efficacy of the proposed algorithm. Finally, an example of applying the proposed algorithm to radar detection and estimation is provided.

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.

Joint DOA, range and polarization estimation based on geometric algebra for near-field non-circular source with a symmetric MIMO array

Multiple-input multiple-output (MIMO) radar is a new type of radar with excellent performance in target detection and parameter estimations. The MIMO radar equipped with electromagnetic vector sensors (EMVSs) can record multi-dimensional information of the electromagnetic (EM) signal. Traditional methods based on long vector model cannot preserve orthogonality between the outputs of each component of the EMVS and have high computational complexity. In this paper, a novel geometric algebra (GA)-based localization method is proposed for direction of arrival (DOA), range, and polarization estimation of near-field (NF) non-circular (NC) sources for a symmetric MIMO array. First, the proposed method converts the output of an EMVS into a multi-vector through a GA matrix transformation. Then, the DOA and range parameters can be estimated by searching the one-dimensional (1-D) spectrum based on the GA-based NC rank reduction (GANC-RARE) algorithm. Finally, the polarization can be estimated by employing estimated DOAs and ranges based on the modified GA-based NC multiple signal classification (MGANC-MUSIC) algorithm. The computational complexity analysis demonstrates that our solution improves memory spaces of the covariance matrix and reduces computation efforts of the eigenvalue decomposition (EVD). The simulation results show the superiority and reliability of our proposed method in model error and coherent noise environment.

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.

Parameters Estimation of 3-D Near-Field Sources With Arbitrarily Spaced Electromagnetic Vector-Sensors

In this Letter, we consider the problem of parameters estimation for near-field sources (NFSs) in three-dimensional (3-D) space with arbitrarily spaced electromagnetic vector-sensors (EMVSs), by taking advantage of the high-order statistics (HOS) of the array observations. In particular, we devise several fourth-order cumulant (FOC) matrices and exploit them to capture the two-dimensional direction-of-arrival (2D-DOA) and polarization information at each EMVS with subspace techniques. On this basis, a linear equation is developed to determine the location parameters of NFSs. Unlike the existing methods, the proposed one is not necessary to use uniformly spaced linear or planar arrays and is applicable to arbitrary EMVS array geometries. Moreover, it is also able to achieve the 3-D localization of NFSs, as well as estimating the polarization parameters accurately. Simulation results are presented to validate the performance of the proposed algorithm.

DOA and polarization estimation for compressed EMVS array with arbitrary sensor geometry

Electromagnetic vector sensors (EMVS) are widely used in array signal processing because of their advantages in polarization diversity, which enables the estimation of the received polarization angle (RPA) in addition to the direction of arrival (DOA). However, these benefits are accompanied by a huge burden on hardware cost and computational complexity. Specifically, compared to scalar arrays, EMVS array signal processing requires more complex hardware devices, for instance, a larger number of front-end chains and higher computational complexity for multidimensional parameter estimation algorithms. We propose a novel compression framework to reduce the hardware cost while achieving high performance. Unlike the existing ones in the literature, the proposed compression network is a sparse network consisting of analog phase shifters; In addition, the proposed compression framework only works on spatial information except for polarization information; Further, for such a compressed EMVS array, we propose a two-step multi-parameter estimation algorithm. In detail, we firstly propose a compressed ESPRIT-like method to estimate the 2D-DOA coarsely. Then, we adopt a small-scale 2D search in the vicinity of the coarse estimate to obtain a high-accuracy estimate of 2D-DOA. After that, we obtain a high-accuracy estimate of 2D-RPA in a closed-form. Furthermore, to avoid any possible performance deterioration of the proposed estimators due to the randomly selected compression weights (a.k.a. compression matrix) from Gaussian distribution (as in literature) and thus cause loss of information, we propose an optimization algorithm to find the optimal solution for the compression matrix under the maximum signal-to-noise ratio (SNR) principle. In this way, we convert the intractable sparse complex matrix optimization problem into a quadratically constrained quadratic programming (QCQP); Then, we employ the semidefinite relaxation technique (SDR) to find the optimal compression matrix. Numerical simulations illustrate that the proposed algorithms could obtain high-accuracy multi-parameter estimates with reduced front-end chains and low computational complexity.

Coherent Targets Parameter Estimation for EVS-MIMO Radar

As an emerging technique for detection, electromagnetic vector sensor multiple-input multiple-output (EVS-MIMO) radar has attracted extensive interest recently. This paper focuses on the coherent targets issue in EVS-MIMO radar, and a spatial smoothing estimator is developed to estimate the multiple parameters. It first recovers the rank of the array data via forward spatial smoothing. Then, it estimates the elevation angles via the rotational invariance technique. Combined with the vector cross-product method, the azimuth angles are obtained. Thereafter, with the previously achieved direction angles, the polarized parameters are acquired by using the least squares technique. Unlike the existing polarization smoothing techniques, the proposed estimator is able to estimate the two-dimensional direction parameter. Furthermore, it can provide a polarized parameter of the target. In addition, the proposed estimator is computationally efficient, since it offers closed-form and automatically paired solutions to all the parameters. Numerical experiments are carried out to show its superiority and effectiveness.

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 estimation of coherent targets using EV sensors in MIMO radar

This letter presents an approach for estimating the joint two-dimensional (2D) direction of arrival (DOA) of coherent targets in monostatic multiple-input and multiple-output (MIMO) radar using the electromagnetic vector (EV) sensors. The approach resolves coherent targets without any preprocessing and locates two or more targets having identical azimuth/elevation angles, and also automatically pairs the 2D directional (i.e., azimuth and elevation) angles and the 2D polarization angles. Compared with the existing state-of-the art methods, the presented approach shows improved estimation performance verified by the simulation results.

Multi-Dimensional Parameter Estimation in Polarimetric ULA with Cross-Distribution Dipole Pairs

This paper investigates the estimation of parameters—including the elevation angle, azimuth angle, polarization auxiliary angle, polarization phase difference, frequency and range of near-field sources in a Polarimetric Uniform Linear Array (P-ULA) with defective electromagnetic vector sensors. The cross-distribution dipole pairs are alternately placed in the xoy plane and yoz plane, respectively, and the whole array is divided into two subarrays, where subarray 1 consists of all of the dipole pairs placed in the xoy plane, while the dipole pairs placed in yoz plane are gathered in subarray 2. Specifically, the polarization auxiliary angle and the polarization phase difference, as well as the elevation and azimuth angles of the sources, are firstly estimated based on the Fourth-Order Cumulant (FOC) matrix in each subarray. Moreover, a decoupling method is developed to obtain the elevation and azimuth. Subsequently, the frequency and range are estimated based on the FOC matrix. Then, the parameter pair matching method is performed in order to match the pairs. Finally, an analysis of the Cramér-Rao Bound (CRB) is provided, and comparisons of the root mean square error with respect to the different input signal-to-noise ratios and number of snapshots, among different estimation methods, are implemented in the environment of additive white gaussian noise. The simulation results are provided in order to verify the effectiveness and feasibility of the proposed method for multi-dimensional parameter estimation.

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.

A Propagator Method for Bistatic Coprime EMVS-MIMO Radar

In this paper, a novel two-dimensional (2D) direction-of-departure (DOD) and 2D direction-of-arrival (DOA) estimate algorithm is proposed for bistatic multiple-input multiple-output (MIMO) radar system equipped with coprime electromagnetic vector sensors (EMVS) arrays. Firstly, we construct the propagator to obtain the signal subspace. Then, the ambiguous angles are estimated by using rotation invariant technique. Based on the characteristic of coprime array, the unambiguous angles estimation is achieved. Finally, all azimuth angles estimation is followed via vector cross product. Compared to the existing uniform linear array, coprime MIMO radar is occupying large array aperture, and the proposed algorithm does not need to obtain signal subspace by eigendecomposition. In contrast to the state-of-the-art algorithms, the proposed algorithm shows better estimation performance and simpler computation performance. The proposed algorithm’s effectiveness is proved by simulation results.

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.

Polarised beampattern synthesis against array manifold mismatch

The problem of joint synthesis of spatial power pattern and mainlobe radiation polarisation using a vector antenna array is considered in the presence of array manifold errors. A general approach to the synthesis problem is to formulate the restriction on the power and radiation polarisation as a convex optimisation programing. However, for certain types of vector antennas like tripole and electromagnetic vector sensors, the optimal weights might be extremely large and the resultant beampattern could be very sensitive to the array manifold errors. An intuitive explanation on this phenomenon is given based on the subspace theory. A worst case performance optimisation technique- based scheme is presented to draw attention to the polarised beampattern synthesis against the large weights problem and array manifold errors. Numerical examples regarding different types of vector antennas used for one- and two-dimensional polarised beampattern synthesis are provided to validate the efficacy of the scheme.

Electromagnetic Vector Sparse Nested Array: Array Structure Design, Off-Grid Parameter Estimation Algorithm

In this paper, a new array structure of sparse nested array (SNA) for electromagnetic vector sensor is designed. An electromagnetic vector sensor is composed of six spatially colocated, orthogonally oriented, diversely polarized antennas, which can measure three-dimensional electric and magnetic field components. By introducing sparse factor (SF) between every adjacent sensor, the proposed SNA has flexibility of extending the array aperture and reducing the mutual coupling effect. Meanwhile, a low-complexity multiparameter estimation algorithm is proposed for SNA. First, the vectorization operation for array manifold ensures the large degrees of freedom for multiparameter estimation, where the initial coarse estimates decrease search range. In addition, the improved off-grid orthogonal matching pursuit method obtains joint direction of arrival (DOA) and polarization estimates with a relatively small overcomplete dictionary because this off-grid method achieves high performance even if the estimates do not fall on the grid of the dictionary. Theoretical analysis and simulation results verify the superiority of the proposed array structure and the algorithm.