Electromagnetic Vector Sensor Research Articles

CS quadrilinear model-based angle estimation for MIMO radar with electromagnetic vector sensors

ABSTRACTIn order to estimate the angles for bistatic MIMO radar with electromagnetic vector sensors, we link the compressed sensing (CS) theory with quadrilinear model, and propose a novel angle estimation algorithm. In the proposed algorithm, the received data is firstly arranged into a quadrilinear model and then it is compressed according to the compressed sensing theory. We then perform quadrilinear decomposition on the compressed quadrilinear data model via the quadrilinear alternating least square (QALS) algorithm and finally obtain the automatically paired angle estimates with sparsity. Owing to compression, the proposed algorithm has smaller storage requirement and lower computational complexity than the conventional quadrilinear decomposition-based algorithm. Moreover, our algorithm has higher angle estimation accuracy than the estimation signal parameters via rotational invariance techniques (ESPRIT) algorithm and its estimation performance is close to that of the conventional quadrilinear decomposition-based algorithm. Our proposed algorithm needs neither additional pair matching, nor spectral peak searching, and it can be applied to both uniform and non-uniform arrays. Effectiveness of our proposed algorithm is assessed through various simulation results.

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.

Two-Dimensional DOA Estimation for Monostatic MIMO Radar with Electromagnetic Vector Received Sensors

We study two-dimensional direction of arrival (2D-DOA) estimation problem of monostatic MIMO radar with the receiving array which consists of electromagnetic vector sensors (EMVSs). The proposed angle estimation algorithm can be applied to the arbitrary and unknown array configuration, which can be summarized as follows. Firstly, EMVSs in the receiver of a monostatic MIMO radar are used to measure all six electromagnetic-field components of an incident wavefield. The vector sensor array with the six unknown electromagnetic-field components is divided into six spatially identical subarrays. Secondly, ESPRIT is utilized to estimate the rotational invariant factors (RIFs). Parts of the RIFs are picked up to restore the source’s electromagnetic-field vector. Last, a vector cross product operation is performed between electric field and magnetic field to obtain the Pointing vector, which can offer the 2D-DOA estimation. Prior knowledge of array elements’ positions and angle searching procedure are not necessary for the proposed 2D-DOA estimation method. Simulation results prove the validity of the proposed method.

应用分数低阶循环相关估计单电磁矢量传感器的波达方向和极化参数

应用分数低阶循环相关估计单电磁矢量传感器的波达方向和极化参数

Performance of a MIMO Y-Shaped Antenna Array with Electromagnetic Vector Sensors

This paper developed a uniform Y-shaped array (UYA) in a 3-dimensional (3-D) environment. While introducing electromagnetic vector sensor (EVS), the closed-form expression of spatial fading correlation (SFC) was derived. The SFC was expressed in terms of azimuth and elevation angles of arrival and the geometry of an antenna array. The developed SFC can be used to determine the covariance matrixes at both transmitter and receiver hence the capacity can be calculated in a specific channel state. This paper studied on the performance of azimuth and elevation angles of arrival, azimuth spread and elevation spread on the SFC and the capacity of a multiple input multiple output (MIMO) system. The performance comparison between antenna arrays while introducing EVS and the traditional scalar sensor array (SSA), as a uniform Y-shaped array and a uniform circular array (UCA), were made. Simulation results showed that comparing to SSA, the antenna array which introducing EVS had a significant advantage and, UCA and UYA both had its own superiorities. This investigation expanded the application of statistical channel model and optimized the study of terminal antenna array.

A novel spatially spread electromagnetic vector sensor for high-accuracy 2-D DOA estimation

In this paper, a new spatially spread electromagnetic vector sensor (SS-EMVS) is proposed by a two-step design. In addition, a novel DOA estimator with coarse-fine estimate combination is presented for the proposed array. The first step aims to make the configurations of SS-EMVS satisfy the "vector cross-product" estimator, leading to a coarse estimation of three direction-cosines. The second step focuses on extending the two dimensional (2-D) array apertures of SS-EMVS, resulting in two fine but ambiguous estimations on the direction-cosines by extracting inter-sensor phase-delay. Combination the coarse and fine estimations, the high-accuracy 2-D DOA estimation can be obtained by using the coarse estimation to disambiguate the fine estimation. The three- dipoles and loops of the proposed configuration are located separately, which are found to reduce mutual coupling as compared with collocated EMVS. Moreover, the new configuration is able to extend 2-D array aperture to improve the accuracy of 2-D direction-finding. Numerical Simulations are conducted to demonstrate the effectiveness of the proposed algorithm.

An Improved Adaptive Beamforming Method for Spatially Non-Collocated Vector Sensor Array

To reduce the mutual coupling effects among the collocated electromagnetic vector sensor and enhance the performance of the joint space-polarization filtering, an improved adaptive beamforming method is proposed for non-collocated vector sensor array in this paper. First, the distributed array geometry composed of the crossed dipole pair and the signal model are introduced. Second, theoretical derivation of the improved method is discussed. By projecting the weight vector of the joint space-polarization minimum variance distortionless response (SPMVDR) onto a signal subspace, the optimal weight vector of the improved method is obtained. The projection operation generates a lower power of the output noise and improves the signal to interference plus noise power ratio (SINR) compared with the conventional SPMVDR. Computer simulation results indicate that the improved algorithm can achieve a good joint filtering performance and enhance the robustness to array pointing error.

稀疏均匀非同心电磁矢量阵列的2D-DOA与极化联合估计

In this paper, a sparse uniform rectangular array of spatially non-collocating electromagnetic vector sensors is proposed. And a two-dimensional direction of arrival (2D-DOA) and polarization estimation algorithm for the array is proposed. First, the rotational invariance of the sparse uniform rectangular array is utilized to yield cyclically aliasing 2D-DOA estimation. Then we propose a simple non-aliasing 2D-DOA estimation algorithm with the spatially non-collocating electromagnetic vector sensor to solve the cyclically aliasing. And then the nonaliasing high accuracy 2D-DOA and polarization estimation is obtained by some triangular operations. Finally, the closed-form Cramer-Rao bound of the multiple parameters estimation is derived. The sparse configuration of the proposed array is capable of extending array aperture without increasing the number of sensors and the hardware complexity. The proposed array can also obtain the polarization diversity offered by electromagnetic vector sensor. The two factors can improve the 2D-DOA estimation accuracy greatly. In addition, the proposed algorithm provides the automatic pairing between the 2D-DOA and polarization parameters. And it is more important is that the proposed array consists of spatially non-collocating electromagnetic vector sensors, which can solve the problems of serious mutual coupling and difficult hardware design, yielded by spatially collocating electromagnetic vector sensor. Simulation results verify the effectiveness of the proposed multiple parameters estimation algorithm.

Nested Vector-Sensor Array Processing via Tensor Modeling

We propose a new class of nested vector-sensor arrays which is capable of significantly increasing the degrees of freedom (DOF). This is not a simple extension of the nested scalar-sensor array, but a novel signal model. The structure is obtained by systematically nesting two or more uniform linear arrays with vector sensors. By using one component's information of the interspectral tensor, which is equivalent to the higher-dimensional second-order statistics of the received data, the proposed nested vector-sensor array can provide O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) DOF with only N physical sensors. To utilize the increased DOF, a novel spatial smoothing approach is proposed, which needs multilinear algebra in order to preserve the data structure and avoid reorganization. Thus, the data is stored in a higher-order tensor. Both the signal model of the nested vector-sensor array and the signal processing strategies, which include spatial smoothing, source number detection, and direction of arrival (DOA) estimation, are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. The effectiveness of the proposed methods is verified through numerical examples.

Corrections to “Vector Cross-Product Direction-Finding’ With an Electromagnetic Vector-Sensor of Six Orthogonally Oriented But Spatially Noncollocating Dipoles/Loops” [Jan 11 160-171

In the above paper (ibid., vol. 59, no. 1, pp. 160-171, Jan. 2011), written by the second and the third authors of this correction, the Monte Carlo simulations are incorrectly conducted in Section V and in Figs. 4-5, for the case of arbitrarily oriented array-axes. This erratum presents a correct algorithm and the correct simulation results, for the case of arbitrarily oriented array-axes. Also presented here will be some other miscellaneous corrections. The second and the third authors apologize for these errors.

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.

The Generalized Sidelobe Canceller Based on Quaternion Widely Linear Processing

We investigate the problem of quaternion beamforming based on widely linear processing. First, a quaternion model of linear symmetric array with two-component electromagnetic (EM) vector sensors is presented. Based on array's quaternion model, we propose the general expression of a quaternion semiwidely linear (QSWL) beamformer. Unlike the complex widely linear beamformer, the QSWL beamformer is based on the simultaneous operation on the quaternion vector, which is composed of two jointly proper complex vectors, and its involution counterpart. Second, we propose a useful implementation of QSWL beamformer, that is, QSWL generalized sidelobe canceller (GSC), and derive the simple expressions of the weight vectors. The QSWL GSC consists of two-stage beamformers. By designing the weight vectors of two-stage beamformers, the interference is completely canceled in the output of QSWL GSC and the desired signal is not distorted. We derive the array's gain expression and analyze the performance of the QSWL GSC in the presence of one type of interference. The advantage of QSWL GSC is that the main beam can always point to the desired signal's direction and the robustness to DOA mismatch is improved. Finally, simulations are used to verify the performance of the proposed QSWL GSC.

Adaptive Beamforming Based on Complex Quaternion Processes

Motivated by the benefits of array signal processing in quaternion domain, we investigate the problem of adaptive beamforming based on complex quaternion processes in this paper. First, a complex quaternion least-mean squares (CQLMS) algorithm is proposed and its performance is analyzed. The CQLMS algorithm is suitable for adaptive beamforming of vector-sensor array. The weight vector update of CQLMS algorithm is derived based on the complex gradient, leading to lower computational complexity. Because the complex quaternion can exhibit the orthogonal structure of an electromagnetic vector-sensor in a natural way, a complex quaternion model in time domain is provided for a 3-component vector-sensor array. And the normalized adaptive beamformer using CQLMS is presented. Finally, simulation results are given to validate the performance of the proposed adaptive beamformer.

Electromagnetic Vector Sensor array parameter estimation method

Joint estimation method for DOA and polarization parameters of single electromagnetic vector sensor is mostly concerned in radar signal processing now. This paper presents a new algorithm which uses the cyclostationary property of signal. It gets the estimation of DOA and polarization parameters from the noise subspace with minimum norm method. This method can reduce the estimate error of noise subspace vector. At the same time, it is immune to the additional stationary noise of any distribution and interference signals with different cyclic frequencies. Method has been tested by computer simulation and the test result is show in the paper. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2562 Full Text: PDF

Using Single-Cycle-Related Electromagnetic Vector Sensors to Estimation DOA and Polarization Parameters

This paper proposes a new algorithm for joint estimation of Directions-Of-Arrival (DOA’s) and polarization parameters of the single electromagnetic vector sensor. Based on the cyclostationary properties of the signal,the algorithm uses minimum norm method to strike the signal steering vector solution, and then gets the estimation of DOA and polarization parameters. Besides limiting the distribution of additional stationary noise and interference signals on various frequencies, this algorithm also restraints the estimation error of the noise subspace singular vector with outstanding results. Computer simulation verified the effectiveness of the algorithm.

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.

MUTUAL COUPLING CALIBRATION FOR ELECTROMAGNETIC VECTOR SENSOR

A subspace self-calibration ESPRIT algorithm for mutual coupling across an electromagnetic vector sensor is proposed in this paper. By introducing an auxiliary array element, the mutual coupling is calibrated. The whole array's mutual coupling matrix can be obtained simultaneously. A mathematic model for mutual coupling across the six collocated antennas of an electromagnetic vector sensor is established. And the solution of mutual coupling matrix was transformed into the solution of several matrix elements. The Cramer- Rao Bound (CRB) is also derived in the end of this paper to verify the e-cacy of the proposed algorithm. The simulation results demonstrate that this approach is correct and efiective.

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.

Direction finding of coexisted independent and coherent signals using electromagnetic vector sensor

The existing direction of arrival (DOA) estimation algorithms based on the electromagnetic vector sensors array barely deal with the coexisting of independent and coherent signals. A two-dimensional direction finding method using an L-shape electromagnetic vector sensors array is proposed. According to this method, the DOAs of the independent signals and the coherent signals are estimated separately, so that the array aperture can be exploited sufficiently. Firstly, the DOAs of the independent signals are estimated by the estimation of signal parameters via rotational invariance techniques, and the influence of the coherent signals can be eliminated by utilizing the property of the coherent signals. Then the data covariance matrix containing the information of the coherent signals only is obtained by exploiting the Toeplitz property of the independent signals, and an improved polarimetric angular smoothing technique is proposed to de-correlate the coherent signals. This new method is more practical in actual signal environment than common DOA estimation algorithms and can expand the array aperture. Simulation results are presented to show the estimating performance of the proposed method.