Electromagnetic Vector-sensor Array Research Articles

Biquaternion beamspace with its application to vector-sensor array direction findings and polarization estimations

In this paper, a biquaternion beamspace, constructed by projecting the original data of an electromagnetic vector-sensor array into a subspace of a lower dimension via a quaternion transformation matrix, is first proposed.To estimate the direction and polarization angles of sources, biquaternion beamspace multiple signal classification (BB-MUSIC) estimators are then formulated. The analytical results show that the biquaternion beamspaces offer us some additional degrees of freedom to simultaneously achieve three goals. One is to save the memory spaces for storing the data covariance matrix and reduce the computation efforts of the eigen-decomposition. Another is to decouple the estimations of the sources’ polarization parameters from those of their direction angles. The other is to blindly whiten the coherent noise of the six constituent antennas in each vector-sensor. It is also shown that the existing biquaternion multiple signal classification (BQ-MUSIC) estimator is a specific case of our BB-MUSIC ones.The simulation results verify the correctness and effectiveness of the analytical ones.

DOA and Polarization Estimation Using an Electromagnetic Vector Sensor Uniform Circular Array Based on the ESPRIT Algorithm.

In array signal processing systems, the direction of arrival (DOA) and polarization of signals based on uniform linear or rectangular sensor arrays are generally obtained by rotational invariance techniques (ESPRIT). However, since the ESPRIT algorithm relies on the rotational invariant structure of the received data, it cannot be applied to electromagnetic vector sensor arrays (EVSAs) featuring uniform circular patterns. To overcome this limitation, a fourth-order cumulant-based ESPRIT algorithm is proposed in this paper, for joint estimation of DOA and polarization based on a uniform circular EVSA. The proposed algorithm utilizes the fourth-order cumulant to obtain a virtual extended array of a uniform circular EVSA, from which the pairs of rotation invariant sub-arrays are obtained. The ESPRIT algorithm and parameter pair matching are then utilized to estimate the DOA and polarization of the incident signals. The closed-form parameter estimation algorithm can effectively reduce the computational complexity of the joint estimation, which has been demonstrated by numerical simulations.

Polarisation smoothing for coherent source direction finding with multiple‐input and multiple‐output electromagnetic vector sensor array

This study proposes a new polarisation smoothing algorithm with multiple-input and multiple-output (MIMO) electromagnetic vector sensor array to address the problem of coherent source angle estimation in MIMO radar. This algorithm can be summarised as follows: (i) matched filtering for echoes is performed to get virtual MIMO array; (ii) the virtual array is divided into six spatially identical subarrays according to polarisation information offered by electromagnetic vector sensor; and (iii) the six subarrays covariance matrices are processed with weighted smoothing to obtain polarisation smoothing covariance matrix, which can restore the rank loss of the covariance matrix of coherent sources. When compared with spatial smoothing, the proposed algorithm is suitable for spatially arbitrary array configuration, without the price of reducing effective array aperture. Simulation results show that the proposed algorithm substantially outperforms the spatial smoothing algorithm.

Joint estimation of DOA and polarization based on phase difference analysis of electromagnetic vector sensor array

The spatially separated electromagnetic vector sensor array (SS-EVSA) has been widely used in passive radar direction-finding systems. However, when the directional angles of array elements are different, this changes law of the phase difference between the array elements. In this paper, an explicit theoretical analysis of the characteristics of the phase difference between any two array elements in SS-EVSA is conducted. Theoretical formulas describing the phase difference between array elements are derived from the phase descriptor and the geometric descriptor. Based on the characteristics of the phase difference, a new half-interval search MUSIC(HIS-MUSIC) algorithm is proposed. By searching half of the four-dimensional space, a joint estimation of the direction of arrival and polarization of the incident signal is obtained, which can effectively reduce the computational complexity of the joint estimation of the four-dimensional space. Finally, the efficiency of the algorithm is demonstrated by simulation experiments.

Quaternion-valued robust adaptive beamformer for electromagnetic vector-sensor arrays with worst-case constraint

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternion domain. After defining the uncertainty set of the desired signal׳s quaternionic steering vector, two quaternion-valued constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the so-called second-order cone (SOC) programming method. It is also demonstrated that the proposed algorithms can be classified as a specific type of the diagonal loading scheme, in which the optimal loading factor is a function of the known level of uncertainty of the desired steering vector. Numerical simulations show that our new method can cope with the steering vector mismatch problem well, and alleviate the finite sample size effect to some extent. Besides, the proposed beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) and the quaternion Capon (Q-Capon) beamformers in all the scenarios studied, and achieves a better performance than the traditional diagonal loading scheme, in the case of smaller sample sizes and higher SNRs.

Adaptive tensorial beamformer based on electromagnetic vector-sensor arrays with coherent interferences

An adaptive beamforming scheme based on vector-sensor arrays is implemented using two different matrix contractions of the 4th order covariance tensor. This tensorial beamformer has a two-stage str...

Direction Finding and Positioning Algorithm with COLD-ULA Based on Quaternion Theory

Electromagnetic vector sensor arrays have been widely applied in the communication, radio, navigation, and so on. The application of electromagnetic vector sensor antenna array will greatly improve the overall performance of the communication system. In this paper, a novel quaternion- ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm for direction finding and positioning based on COLD (cocentered orthogonal loop and dipole) uniform linear array (COLD-ULA) is proposed. First, quaternion data model of COLD-ULA is deduced and constructed. Second, the array steering vector and the angle of arrival (DOA) are estimated using a quaternion eigenvalue decomposition of the data covariance matrix. Finally, the estimation of polarization parameters are required using the relationships between the dipoles and the loops. The proposed technique not only decouples the DOA estimation information from the polarization estimation information, but also improves the ability of signal detection. Moreover, the proposed technique has the advantage of small amount of calculation and parameter automatic matching. Simulation results show that the performance of quaternion method is obviously better than that of the long-vector method.

Source localization using a non-cocentered orthogonal loop and dipole (NCOLD) array

A uniform array of scalar-sensors with intersensor spacings over a large aperture size generally offers enhanced resolution and source localization accuracy, but it may also lead to cyclic ambiguity. By exploiting the polarization information of impinging waves, an electromagnetic vector-sensor array outperforms the unpolarized scalar-sensor array in resolving this cyclic ambiguity. However, the electromagnetic vector-sensor array usually consists of cocentered orthogonal loops and dipoles (COLD), which is easily subjected to mutual coupling across these cocentered dipoles/loops. As a result, the source localization performance of the COLD array may substantially degrade rather than being improved. This paper proposes a new source localization method with a non-cocentered orthogonal loop and dipole (NCOLD) array. The NCOLD array contains only one dipole or loop on each array grid, and the intersensor spacings are larger than a half-wavelength. Therefore, unlike the COLD array, these well separated dipoles/loops minimize the mutual coupling effects and extend the spatial aperture as well. With the NCOLD array, the proposed method can efficiently exploit the polarization information to offer high localization precision.

A Novel Combined Beamformer Based on Hypercomplex Processes

The problem of beamforming based on hypercomplex processes is considered for an airborne electromagnetic (EM) vector-sensor array. The quaternion domain facilitates modeling and processing of four-dimensional real signals (or two-dimensional complex signals). Based on the quaternion model of an airborne EM vector-sensor, a quaternion spatial matched filter (QSMF) is presented and its characteristics are analyzed. The quaternion-valued output y(n) of the QSMF consists of two complex components y1(n) and y2(n). The analysis in theory highlights the fact that y2(n) includes only the interference component and noise, but doesn't include the desired signal. By employing y2(n) to cancel the interference component in y1(n), we propose an interference cancellation algorithm (ICA) of the QSMF. In the presence of a strong interference, the ICA can improve the output signal-to-noise ratio (SNR). Based on the interference cancellation structure, we propose two schemes of combined QSMF and complex minimum variance distortionless response (CMVDR) beamformer (one is referred to QSMF-CMVDR and the other is referred to QSMF-DCMVDR) for an airborne EM vector-sensors array. The advantages of the proposed beamformers are that the interference can be canceled by ICA of the QSMF and the additive noise can be reduced by CMVDR beamformer. The output SNR expressions of two combined beamformers that we derive reveal that the output SNR of the QSMF-DCMVDR beamformer is superior to that of a conventional linearly constrained minimum variance (LCMV) beamformer. And in the presence of the coherent (or correlated) interferences, two combined beamformers are not subject to performance degradation. Simulation results are in agreement with our analysis.

Performance analysis for interference and noise canceller based on hypercomplex and spatio‐temporal‐polarisation processes

In this study, the problem of spatio-temporal-polarisation filtering based on hypercomplex processes is considered for an electromagnetic (EM) vector-sensor array. The quaternion domain facilitates modelling and processing of four-dimensional real signals (or two-dimensional complex signals). Based on the quaternion model of linear symmetric array with two-components EM vector-sensors, an interference and noise canceller (INC) is presented for polarised signals. Then, the output signal to interference-plus-noise ratio (SINR) expression of INC is derived and its performance is analysed. The performance analysis reveal explicitly the fact that even though no separation between the direction of arrival (DOAs) of the desired signal and interference, the maximum value of output SINR can be obtained employing the orthogonality between the polarisations of the desired signal and interference. Simulation results show that if sample size N is large enough, the INC has larger output SINR and better robustness against the DOA mismatch.

OPTIMAL POLARIZATION DESIGN FOR DIRECTION FINDING USING MIMO ELECTROMAGNETIC VECTOR-SENSOR ARRAY

In this paper, transmitter polarization optimization is flrstly proposed to improve the accuracy of azimuth-elevation arrival angles estimation within MIMO electromagnetic vector-sensor array (EMVA). Minimizing of Cramer-Rao bound is used as cost function for the optimal design of transmitting signal polarization. Computer simulation results verify that the optimal polarization design provides increased estimation accuracy of direction flnding in MIMO-EMVA, compared with that of using flxed polarization of transmitting signal. Moreover, the optimal polarization design retains all advantages of using flxed polarization of transmitting signal for MIMO-EMVA direction flnding.

An Enumerative NonLinear Programming approach to direction finding with a general spatially spread electromagnetic vector sensor array

In this paper, the geometry of a general spatially spread electromagnetic vector sensor (SSEMVS) array is firstly presented. This array has a special cross product structure of the array manifold vector. The g parameters are then defined to uniquely characterize the cross product. With g parameters, the identifiability analysis of the cross product vector based direction finding algorithms of the general SSEMVS array is carried out. The analysis shows that the array has to be carefully designed to avoid ambiguity directions. Finally, a cross-product based Enumerative NonLinear Programming (ENLP) algorithm for the direction of arrival (DOA) estimation with the general SSEMVS array is proposed. The algorithm finds the optimum estimation of DOA in least square sense. Extensive simulations show that the proposed algorithm outperforms existing algorithms, and can approach the CRB effectively.

Coherent Source Localization: Bicomplex Polarimetric Smoothing with Electromagnetic Vector-Sensors

The work presented here considers coherent source localization with bicomplex. A new polarimetric smoothing variant is proposed by using bicomplex modeled subarrays obtained from complete electromagnetic vector-sensor array, and a MUSIC-like algorithm is further developed. The identifiability, computational complexity, and the choice of selection vectors for the proposed method are also addressed. Simulations show that the proposed method can provide better direction-of-arrival estimates than the complex methods in perturbations caused by noise, short data, and model errors.

Computationally Efficient DOA and Polarization Estimation of Coherent Sources with Linear Electromagnetic Vector-Sensor Array

This paper studies the problem of direction finding and polarization estimation of coherent sources using a uniform linear electromagnetic vector-sensor (EmVS) array. A novel preprocessing algorithm based on EmVS subarray averaging (EVSA) is firstly proposed to decorrelate sources' coherency. Then, the proposed EVSA algorithm is combined with the propagator method (PM) to estimate the EmVS steering vector, and thus estimate the direction-of-arrival (DOA) and the polarization parameters by a vector cross-product operation. Compared with the existing estimate methods, the proposed EVSA-PM enables decorrelation of more coherent signals, joint estimation of the DOA and polarization of coherent sources with a lower computational complexity, and requires no limitation of the intervector sensor spacing within a half-wavelength to guarantee unique and unambiguous angle estimates. Also, the EVSA-PM can estimate these parameters by parameter-space searching techniques. Monte-Carlo simulations are presented to verify the efficacy of the proposed algorithm.

Geometric Algebra of Euclidean 3-Space for Electromagnetic Vector-Sensor Array Processing, Part I: Modeling

A new mathematical tool, the geometric algebra of Euclidean 3-space (G3), is introduced for electromagnetic vector-sensor array processing herein. This paper focuses on modeling the six-component outputs of a vector-sensor holistically by an entry called as a multivector in G3. A compact polarized model for the array, termed as a geometric algebra model (G-MODEL), is then presented. Using the G-MODEL, a novel data covariance matrix model is defined by the geometric products in G3 and then analyzed. The analytical results show that the six-component measurement noise of a vector-sensor can naturally be whitened if the noise cross-correlations between the different axial electric and magnetic components are equal to one another. Compared with the known best quad-quaternion model, the new covariance matrix model results in a reduction of half memory requirements while the amount of divisions is reduced to 1/2, multiplications and additions reduced to almost 1/7.

Direction finding via biquaternion matrix diagonalization with vector-sensors

Direction-of-arrival (DOA) estimation based on the array of three-component electromagnetic vector-sensors is considered within a biquaternion framework. A relationship is established between the biquaternion covariance and the combination of both complex covariance and cross-product. By exploiting this relationship, the DOA estimates can finally be obtained by diagonalizing the biquaternion covariance matrix of the array outputs in a trilinear PARAFAC manner. This method does not require any a priori knowledge on the position of each sensor, and is shown to offer high robustness to colored noise for direction finding of non-linearly polarized signals. Simulations are provided to illustrate the performance of the proposed method.

Efficient 2D DOA estimation of coherent signals in spatially correlated noise using electromagnetic vector sensors

This paper considers a new azimuth-elevation DOA estimation algorithm for multiple signals using electromagnetic vector sensor array. We firstly exploit the planar-plus-an-isolated sensor array geometry (Li et al. in IEE Proc Radar Sonar Navig 143(5):295---299, 1996) to define a full rank cross-covariance matrix. Then we develop an efficient ESPRIT-like algorithm using the so-called propagator to estimate the steering vectors of electromagnetic vector sensor, without performing eigen-decomposition into signal subspaces. Finally, we compute the vector cross product to obtain the closed-form azimuth-elevation angle estimates. The new algorithm does not require 2D iterative searching, and is applicable to coherent (fully correlated) signals and spatially correlated noise. In addition, the proposed algorithm offers enhanced estimation precision by sparse array aperture extension, but suffers no DOA cyclical ambiguity. Monte-Carlo simulations are presented to verify the effectiveness of the proposed algorithm.

Polarization Difference Smoothing for Direction Finding of Coherent Signals

The subspace-based two-dimensional direction finding with an array of electromagnetic vector sensors for multiple coherent signals amid unknown noise fields is investigated. The noise can be spatially nonuniform and/or correlated. A novel preprocessing method, called polarization difference smoothing (PDS), is proposed. With PDS the unknown noise is removed by using the difference of pairs of electromagnetic component's data correlation matrices, and the coherent signals are decorrelated by summing these difference correlation matrices. Unlike most other existing preprocessing techniques, such as spatial smoothing and forward-backward averaging, PDS processing does not decrease the array aperture and is applicable to arbitrary array geometry. As an example a uniform rectangular array is considered, and a computationally-efficient propagator-based algorithm (PDS-propagator) is derived. Monte Carlo simulations demonstrate that, with an appropriately chosen PDS matrix, the PDS-based eigenstructure algorithms can offer better performance than the polarization smoothing-based (PS) counterparts. Incidently in the presence of external interference noise, the PDS-based algorithms can underperform the PS-based algorithms.

Quad-Quaternion MUSIC for DOA Estimation Using Electromagnetic Vector Sensors

A new quad-quaternion model is herein established for an electromagnetic vector-sensor array, under which a multidimensional algebra-based direction-of-arrival (DOA) estimation algorithm, termed as quad-quaternion MUSIC (QQ-MUSIC), is proposed. This method provides DOA estimation (decoupled from polarization) by exploiting the orthogonality of the newly defined signal and noise subspaces. Due to the stronger constraints that quad-quaternion orthogonality imposes on quadquaternion vectors, QQ-MUSIC is shown to offer high robustness to model errors, and thus is very competent in practice. Simulation results have validated the proposed method.

Virtual-manifold ambiguity in HOS-based direction-finding with electromagnetic vector-sensors

Herein derived are the lower and upper bounds for the number of linearly independent ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2Q</i> )th-order virtual steering vectors of an array of electromagnetic vector-sensors, with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> being any positive integer over one. These bounds help determine the number of non-Gaussian signals whose directions-of-arrival (DOAs) can be uniquely identified from ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2Q</i> )th-order statistics data. The derived lower bounds increase with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> , whereas the derived upper bounds often fall below the maximum number of virtual sensors achievable from ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2Q</i> )th-order statistics manipulation. These bounds are independent of the permutation of the ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2Q</i> )th-order statistics entries in the higher order cumulant matrix that has a similar algebraic structure of the classical covariance matrix used in the second-order subspace-based direction-finding algorithms.