Two-dimensional Direction Finding Research Articles

Compact Amplitude-Monopulse Antenna for Joint Two-Dimensional Direction Finding and Sectorized Communications in the 2.4 GHz ISM band

Compact Amplitude-Monopulse Antenna for Joint Two-Dimensional Direction Finding and Sectorized Communications in the 2.4 GHz ISM band

1-Bit Programmable Metasurface-Based 2-D Direction Finding

A novel two-dimensional (2-D) direction finding method is proposed, relying on a 1-bit programmable metasurface and the time modulation method. Both the azimuth and elevation angles of far-field signals are estimated simultaneously by analyzing the harmonic characteristic of received signals in the frequency domain. Low hardware cost and computational complexity can be achieved owing to the intrinsic nature of the single radio frequency (RF) chain in the proposed method. Extensive numerical results confirm that the direction finding attains a near-zero mean square error (MSE), when the signal-to-noise ratio (SNR) attains 10 dB. A Ka-band reflective programmable metasurface with 400 elements is fabricated and tested to verify its effectiveness partly.

A Computationally Efficient Estimator for the Target Angle, Delay, and Doppler Parameters in Passive Radar

The azimuth, elevation, time delay (TD), and Doppler shift (DS) of the target echo signal are important parameters for target localization in passive radar. In this paper, for the problem of joint estimation of target azimuth, elevation, TD, and DS parameters in passive radar, a computationally efficient estimator is proposed based on segmented coherent integration and uniform circular array (UCA) interferometer direction finding. First, according to the parameters of the target motion and illuminators of opportunity, the reference and surveillance signals are divided into segments, with fast time within a segment and slow time across the segments; then, matching filtering along the fast time and fast Fourier transform (FFT) along the slow time are performed to accumulate the target echo energy to the same delay-Doppler cell; finally, the UCA interferometer two-dimensional direction finding is performed at the delay-Doppler cell where the target echo is located, to achieve the target azimuth and elevation estimate. Simulation results demonstrate that the proposed algorithm has low computational complexity, high real-time processing capability, and can achieve efficient and real-time estimation of the azimuth, elevation, TD, and DS parameters of weak target echoes in passive radar.

Two-dimensional Direction Finding Based on Cylindrical Nested Conformal Array

Recently, nested conformal arrays have attracted considerable interest due to their ability of providing increased array aperture and enhanced degrees of freedom compared to uniform conformal arrays. In this paper, we address the problem of two-dimensional (2-D) direction finding using cylindrical nested conformal array (CNCA). First of all, we derive the coarray signal model of the CNCA, and utilize different coarray signal components to construct multiple Toeplitz matrices. Based on the constructed Toeplitz matrices, we further develop two direction finding algorithms to achieve the decoupled estimation of 2-D direction. Unlike the exiting approaches, the proposed two algorithms exploit more coarray output components, and hence they have better direction finding performance. Moreover, our algorithms can be applied to a larger number of nested subarrays in the CNCA. Numerical results demonstrate the superiority of the proposed algorithms in comparison to the exiting methods.

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.

A Unified Two-Dimensional Direction Finding Approach for Sensor Arrays Based on Deep Neural Networks With Inhomogeneous Angle and Frequency Partition

This paper develops a deep neural networks (DNNs) based direction finding approach for 2-D direction finding in multiple frequencies. The approach is frequency-unified and is capable of direction-of-arrival (DoA) prediction for multiple frequencies. A model output is proposed and proved for 2-D direction finding. In addition, different from the common mean squared error (MSE) loss, a label-dependent loss is proposed motivated by the different Cramer-Rao Lower Bound (CRLB) of direction finding accuracy for different DoAs, and an inhomogeneous angle and frequency partition strategy is suggested for efficient implementation. Following the model output and the partition strategy, the general DNN architecture consists of a series of classification networks for angle zoom partition and regression networks for DoA prediction. Several useful tips for model inputs and zoom partition are also suggested. Numerical investigations are included to evaluate the performance of the proposed approach and show desirable performance for both ideal and nonideal scenarios. The added value of treating samples of different frequencies in a unified manner is also shown.

A Two-Dimensional Direction Finding Method Based on Non-Uniform Array

In this paper, an aperture expanding direction finding algorithm using L-shaped non-uniform sparse array is proposed. Firstly, the virtual array is expanded by vectorizing, de-redundant and sorting of received data covariance matrix. Secondly, the full rank matrix is got by smoothing the virtual array data, and the signal subspace is obtained by matrix block processing. Finally, the elevation angle and azimuth angle are acquired by using the rotation invariant relation. The algorithm does not need to decompose the covariance matrix of the data, nor does it need to search the two-dimensional spectral peaks. It can greatly reduce the computational complexity when there are many array elements and large number of snapshots. The simulation results show that the sparse array arrangement can enlarge the array aperture, improve the parameter resolution and the accuracy of DOA estimation, and verify the effectiveness of the proposed algorithm.

2-D Direction FindingWith Pair-Matching Operation for L-Shaped Nested Array

In this letter, we devise a new approach for two-dimensional (2-D) direction finding using an L-shaped array structured by two nested arrays. By vectorizing the covariance matrices of the nested array outputs, the elevation and azimuth angles of the sources are firstly estimated separately. The pair-matching of the elevation and azimuth angle estimates is then achieved employing a permutation matrix which is obtained by solving an optimization problem with the array manifold matrices, cross-covariance matrix, and the source covariance matrix. Unlike the existing schemes, the proposed approach reconstructs the source covariance matrix in the coarray domain. Therefore, it can deal with more sources than the number of sensors in each nested array. Numerical results demonstrate the advantage of the proposed approach over the existing algorithms.

Two-Dimensional Direction Finding With Parallel Nested Arrays Using DOA Matrix Method

This article develops a new 2-D direction estimation algorithm using parallel arrays that consist of two parallel nested subarrays. The key idea behind the presented algorithm is to use the difference coarray properties embedded in the auto- and cross correlation matrices of the parallel nested arrays to form a direction-of-arrival (DOA) matrix with enhanced degree of freedoms for 2-D angle estimation. The presented algorithm does not require 2-D nonlinear searching or parameter paring processing. Simulation results demonstrate the superiority of the new algorithm.

Two-Dimensional Direction Finding Estimation for Uniform Rectangular Array with Unknown Mutual Coupling via Real-Valued PARAFAC Decomposition

Two-dimensional direction-of-arrival (2D-DOA) estimation for uniform rectangular array (URA) is a canonical problem with numerous applications, e.g., wireless communications, sonar and radar systems. The conventional 2D-DOA estimators usually are derived with the assumption of ideal arrays. However, in practice, the arrays may not be well calibrated and suffer from unknown mutual coupling. Using the conventional estimators may lead to low accuracy estimation and high computational complexity in the condition of large number of array elements. In this paper, a novel real-valued parallel factor (PARAFAC) decomposition algorithm is proposed to tackle this problem. The proposed algorithm has better angle estimation performance than the multiple signal classification (MUSIC) algorithm, estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm and conventional PARAFAC algorithm. But it has lower complexity than MUSIC algorithm. Moreover, the proposed algorithm can obtain automatically paired 2D-DOA estimation, and it is suitable to coherent or closely spaced signals and can eliminate the mutual coupling. Simulation results verify the effectiveness of the proposed algorithm.

Highly Accurate Two-Dimensional Direction Finding Using Cumulant

This paper proposes a new two-dimensional direction finding algorithm for estimating multiple non-Gaussian signals using cumulants. This new algorithm: 1) employs an array geometry consisting of a nine-element non-uniformly spaced cross-shaped sub-array plus another arbitrarily-spaced sub-array; 2) defines five cumulant matrices, from which the signal direction cosines can be estimated by using parallel factor fitting, and hence, requiring no open-form two-dimensional searching and parameter pairing; 3) can achieve array aperture extension by jointly extending array physical aperture and constructing virtual sensors, without adding more sensors; and 4) can resolve $2(L - 4)$ signals with an array of $L$ sensors in total. Simulation results are presented to verify the efficacy of the proposed algorithm.

ESPRIT-like two-dimensional direction finding for mixed circular and strictly noncircular sources based on joint diagonalization

In this paper, a two-dimensional (2-D) direction-of-arrival (DOA) estimation method for a mixture of circular and strictly noncircular signals is presented based on a uniform rectangular array (URA). We first formulate a new 2-D array model for such a mixture of signals, and then utilize the observed data coupled with its conjugate counterparts to construct a new data vector and its associated covariance matrix for DOA estimation. By exploiting the second-order non-circularity of incoming signals, a computationally effective ESPRIT-like method is adopted to estimate the 2-D DOAs of mixed sources which are automatically paired by joint diagonalization of two direction matrices. One particular advantage of the proposed method is that it can solve the angle ambiguity problem when multiple incoming signals have the same angle θ or β. Furthermore, the theoretical error performance of the proposed method is analyzed and a closed-form expression for the deterministic Cramer-Rao bound (CRB) for the considered signal scenario is derived. Simulation results are provided to verify the effectiveness of the proposed method.

Two-dimensional direction finding of coherent signals with a linear array of vector hydrophones

In this paper, we propose a parallel factor (PARAFAC) analysis based two dimensional direction finding algorithm for coherent signals using a uniformly linear array of vector hydrophones. By forming a PARAFAC model using spatial signature of vector hydrophone array, the new algorithm requires neither spatial smoothing nor vector-field smoothing to decorrelate the signal coherency. We also establish that the azimuth-elevation angles of K coherent signals can be uniquely determined by PARAFAC analysis, as long as the number of hydrophones $$L \ge 2K - 1$$Lź2K-1. In addition, because the vector hydrophone array manifold contains no phase information, this new algorithm can offer high azimuth-elevation estimation accuracy by setting vector hydrophones to space much farther apart than a half-wavelength. Simulation results are finally presented to verify the efficacy of the proposed algorithm.

Decoupled 2D direction-of-arrival estimation based on sparse signal reconstruction

A new two-dimensional direction-of-arrival estimation algorithm called 2D- l 1-singular value decomposition (SVD) and its improved version called enhanced-2D- l 1-SVD are proposed in this paper. They are designed for rectangular arrays and can also be extended to rectangular arrays with faulty or missing elements. The key idea is to represent direction-of-arrival with two decoupled angles and then successively estimate them. Therefore, two-dimensional direction finding can be achieved by applying several times of one-dimensional sparse reconstruction-based direction finding methods instead of directly extending them to two-dimensional situation. Performance analysis and simulation results reveal that the proposed method has a much lower computational complexity and a similar statistical performance compared with the well-known l 1-SVD algorithm, which has several advantages over conventional direction finding techniques due to the application of sparse signal reconstruction. Moreover, 2D- l 1-SVD has better robustness to the assumed number of sources over l 1-SVD.

Efficient Two-Dimensional Direction Finding via Auxiliary-Variable Manifold Separation Technique for Arbitrary Array Structure

A polynomial rooting direction of arrival (DOA) algorithm for multiple plane waves incident on an arbitrary array structure that combines the multipolynomial resultants and matrix computations is proposed in this paper. Firstly, a new auxiliary-variable manifold separation technique (AV-MST) is used to model the steering vector of arbitrary array structure as the product of a sampling matrix (dependent only on the array structure) and two Vandermonde-structured wavefield coefficient vectors (dependent on the wavefield). Then the propagator operator is calculated and used to form a system of bivariate polynomial equations. Finally, the automatically paired azimuth and elevation estimates are derived by polynomial rooting. The presented algorithm employs the concept of auxiliary-variable manifold separation technique which requires no sector by sector array interpolation and thus does not suffer from any mapping errors. In addition, the new algorithm does not need any eigenvalue decomposition of the covariance matrix and exhausted search over the two-dimensional parameter space. Moreover, the algorithm gives automatically paired estimates, thus avoiding the complex pairing procedure. Therefore, the proposed algorithm shows low computational complexity and high robustness performance. Simulation results are shown to validate the effectiveness of the proposed method.

Joint DOA and DOD Estimation in Bistatic MIMO Radar without Estimating the Number of Targets

Existing subspace-based direction finding methods for multiple-input multiple-output (MIMO) radar assume perfect knowledge about the dimension of the signal or noise subspace, which is hard to be established without prior knowledge of the signal environment. In this paper, an efficient method for joint DOA and DOD estimation in bistatic MIMO radar without estimating the number of targets is presented. The proposed method computes an estimate of the noise subspace using the power of R (POR) technique. Then the two-dimensional (2D) direction finding problem is decoupled into two successive one-dimensional (1D) angle estimation problems by employing the rank reduction (RARE) estimator.

Mutual Coupling in Antenna Arrays 2013

The invention of antenna arrays opened up the door for microwave sensing and communications. Most applications of antenna arrays are in the defense and wireless communications areas. The introduction of multiple-input-multiple-output (MIMO) concept in recent years has opened up further opportunities in that the system performance can be maintained with a smaller number of antennas. The existence of mutual coupling effect, that is, the electromagnetic interaction between antenna elements, appears as an undesirable effect in most of these cases. The transmitted and received signals can be significantly distorted such that the signals no longer depend solely on the antenna elements, but also on the array structure and the surrounding environment. Such distortions result in the reduction of channel capacities in communications applications, as well as poor accuracies in ranging and direction finding. In most applications, the mutual coupling effect is unknown. A major challenge is then to characterize this undesirable effect and to accurately estimate the unknown parameters (range, direction) without a priori knowledge of the signal environment. This special issue, which is the third one in its series, provides an international forum for researchers to disseminate their results and ideas to tackle some of these challenging research problems. Five dedicated papers have contributed to this special issue. These papers concern the mutual coupling and its impacts on MIMO communications, direction finding, and MIMO radar. To help interested readers with a quick reference to the main themes of these papers, we briefly introduce them as follows. The first paper entitled “Self-interference cancellation-based mutual-coupling model for full-duplex single-channel MIMO systems,” concerns the mutual coupling problem in MIMO communications. The paper addresses the self-interference and mutual-interference of a full-duplex single-channel MIMO communications system. In the presence of mutual coupling, the array manifold is perturbed, which results in poor accuracies in direction finding. The paper “Accurate DOA estimations using microstrip adaptive arrays in the presence of mutual coupling effect” proposes a method to calibrate the undesirable mutual coupling effect for arrays with non-omni-directional radiating elements. The third paper, entitled “2-D direction of arrival estimation for cross array in the presence of mutual coupling,” introduces a noniterative algorithm based on the Propagation Method for accurate two-dimensional direction finding problems using a cross array in the presence of mutual coupling. The paper “AR model-based direction-of-arrival estimation of coherent signals in the presence of unknown mutual coupling” provides a novel signal processing solution based on a spatial autoregression (AR) model for coherent direction finding of uniform linear arrays. The fifth paper of this special issue, entitled “Root-MUSIC based angle estimation for MIMO radar with unknown mutual coupling,” explores the direction finding solutions in MIMO radar. A Root-MUSIC based solution is proposed to estimate the incoming signal direction with unknown mutual coupling. All papers appearing in this special issue have been subject to a strict peer-reviewing process. They are of high quality and address the mutual coupling problem from different perspectives. Through this special issue, we have provided a medium of dissemination for valuable ideas and conclusions on mutual coupling research. At the same time, we hope that more research innovations can be stimulated for future advances on this subject.

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.

Direction and polarisation estimation using polarised cylindrical conformal arrays

In this study, the authors describe two-dimensional direction finding and signal polarisation estimation from a cylindrical conformal array consisting of directional and polarised antenna elements. Firstly, a simple and general transformation procedure, based on the mathematical framework of geometric algebra, is presented for arbitrary conformal arrays with polarised and directional antennas. Subsequently, the authors utilise the symmetry of cylindrical arrays to estimate signal parameters via rotational invariance techniques. The authors show how to iteratively estimate the azimuth and elevation angles of the incident signal, as well as its polarisation. To illustrate the versatility of this method, the results of simulations on a 3×4 cylindrical conformal array are shown and discussed.

Direction finding with automatic pairing for bistatic MIMO radar

Direction finding is an important issue for bistatic MIMO radar. A two-dimensional direction finding method with automatic pairing is developed. In the presented method, the property of the kronecker product is first utilized to reformulate the cost function in the quadratic form. Then, by constructing the orthogonality constraint of the target DOA to the quadratic form, all target DODs can be first estimated by solving the constrained quadratic form. Moreover, the pth target DOA can be directly estimated by the eigenvector which is related to the pth target DOD. Thus, the target DOD and DOA can be automatically paired. Finally, simulation results demonstrate that the effectiveness of the presented method.