Bistatic Multiple-input Multiple-output Radar Research Articles

Joint DOD and DOA estimation using tensor reconstruction based sparse representation approach for bistatic MIMO radar with unknown noise effect

Achieving a fair balance between accuracy and computational complexity of limited measurement signals by algorithms for the bistatic multiple-input multiple-output (MIMO) radar under unknown noise effect has been a seemingly difficult task for most covariance methods. In this paper, the aim is to present an efficient method to achieve an improved estimation of the joint direction of departure (DOD) and direction of arrival (DOA) for the bistatic MIMO radar with an unknown ‘Toeplitz’ colored noise effect. First, by taking advantage of the static property of the noise effect, a tensor reconstruction-based imaginary Hermitian matrix is developed to eliminate the unknown noise effect. Then the 2D angle estimation problem is then reduced to a 1D sparse recovery problem where the target sparsity is exploited. Further, we formulate a reverse 1D pairwise Simultaneous Orthogonal Matching Pursuit and sparse Bayesian learning algorithms to reconstruct the sparse signal and estimate the joint DOD-DOA of the target. In contrast with the existing tensor-based methods, the proposed approach not only is robust to the influence of Toeplitz colored noise, resolves targets with limited measurement data but also ensures superior performance with lower computational complexity. Numerical simulation conducted under varying conditions verifies the effectiveness of the proposed approach.

Gridless DOD and DOA estimation in bistatic MIMO radar using 2D-ANM and its low complexity algorithms

Compared with the traditional subspace methods, the application of compressed sensing (CS) to the direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in bistatic multiple-input multiple-output (MIMO) radar can achieve robustness to coherent targets and high localization accuracy with a limited number of snapshots. However, the performance of grid-based CS reconstruction methods degrades since there is an unavoidable basis mismatch between the actual DOD/DOA and the assumed basis. As a gridless CS method, the atomic norm minimization (ANM) has attracted much attention. Specifically, the use of multiple snapshots in ANM has improved the parameter estimation accuracy in contrast with a single snapshot. In this paper, we address the problem of gridless DOD and DOA estimation in bistatic MIMO radar, and develop a multiple-snapshot 2D-ANM algorithm and its two low complexity versions. We start with a rigorous derivation on how to convert the multiple-snapshot 2D-ANM into a semi-definite programming problem, and then explore its dual problem. To overcome the heavy computational burden of the 2D-ANM when the numbers of snapshots and array elements increase, we further propose a 2D-ANM algorithm with snapshot reduction (2D-ANM-SR), as well as an improved 2D-ANM-SR algorithm based on alternating direction method of multipliers (2D-ANM-SR-ADMM). Numerical examples show that with similar accuracy in comparison to 2D-ANM, much lower computational complexity can be achieved via 2D-ANM-SR and 2D-ANM-SR-ADMM.

A modified spatial smoothing-based Nystrom approach for coherent target in bistatic MIMO radar

ABSTRACT The performance of most angle estimation system degrades when the signal attributes coherency coupled with the high computational burden of the preprocessing technique. This paper addresses the issue of the computational burden of the coherent angle estimation for the bistatic multiple-input multiple-output (MIMO) radar. A modified spatial smoothing technique is initially developed by ensuring the generation of a lower rank kernel matrix of the decorrelated signal via a Nyström approach. Then the formed data matrix is subjected to the shift-invariance technique where the automatic pairing of the angles is estimated without loss of the virtual aperture. Hence, in addition to significantly reducing the computational complexity, the proposed method presents an improved performance against existing techniques verifiable by simulation results.

Kalman filtering method for sparse off‐grid angle estimation for bistatic multiple‐input multiple‐output radar

In order to address the off-grid angular estimation of direction of departure and direction of arrival of a target for bistatic multiple-input multiple-output radar, a novel method involving the combined effect of compressive sensing theory and an optimal estimation algorithm is proposed. The proposed method, named as simultaneous orthogonal matching pursuit with Kalman filtering (SOMP-KF) first exploit the sparsity of the target in the spatial domain by discretising the area of detection to formulate a dictionary matrix. Sparse sampling created during the discretisation of the off-grid space leads to a remodelling of the problem where a linearisation technique that inculcates a grid-varying position vector is applied to the Kalman filtering method. The modified Kalman filtering method resolves the off-grid offset, which hence results in achieving the off-grid angle estimation objective. Additionally, the Cramer-Rao lower bounds are derived theoretically for all parameters to explain the estimation performance. Experimental analysis against existing methods indicates the proposed SOMP-KF effectiveness in improving the angle estimation of target whiles, maintaining a minimal computational cost than its competitors.

Fast Angle Estimation and Sensor Self-Calibration in Bistatic MIMO Radar With Gain-Phase Errors and Spatially Colored Noise

Multiple-input multiple-output (MIMO) radars are essential in many Internet-of-Things (IoT) applications. Gain-phase error calibration is an important branch in MIMO radar. Existing calibration algorithms are only suitable for white Gaussian noise scenario, however, spatially colored noise is more practical in engineering implementation. In this paper, we stress the problem of direction finding and sensor self-calibration in a bistatic MIMO radar in the co-exist of unknown gain-phase error and spatially colored noise, and a covariance tensor-based parallel factor analysis (PARAFAC) estimator is proposed. To suppress the spatially colored noise and exploit the multi-dimensional structure of the array measurement, a covariance tensor is firstly established and the temporal cross-correlation operation is followed. Then the PARAFAC decomposition is carried out to obtain the factor matrices. Thereafter, automatically paired direction estimation is achieved via least squares. Finally, the element-wise multiply/divide technique and the Lagrange multipliers are adopted to obtain the gain-phase error vectors. The algorithm is analyzed in terms of identifiability and Cramer-Rao bound (CRB). Numerical simulations results show the effectiveness and improvement of the proposed estimator.

Fast Logistics Vehicle Localizing Based on EMVS-MIMO Radar and Edge Computing

This article focus on logistics vehicle active localizing using multiple-input multiple output (MIMO) radar, and a fast localizing architecture that integrates edge computing and cloud platform is proposed. The core of the proposed methodology is to measure the angles of logistics vehicle using bistatic MIMO radars, which are configured with coprime electromagnetic vector sensors (EMVS). Unlike the existing localization systems, the proposed localizing architecture provides two-dimensional (2D) angle estimation, i.e., 2D direction-of-departure (DOD) estimation and 2D direction-of-arrival (DOA) estimation, and it offers additional polarization status of the logistics vehicle. A parallel factor (PARAFAC) estimator is developed. Firstly, it estimate the factor matrices via PARAFAC decomposition. Thereafter, the elevation angle estimation is accomplished via least squares (LS) technique, which are ambiguous due to the coprime property of the EMVS. The azimuth angle estimation are followed via vector cross-product. Besides, the polarization information of the targets can be obtained estimated via LS approach. The above process is accomplished at cloud platform. Finally, the localization of the logistics vehicle is achieved with the estimated 2D angles, which is computationally friendly and achieved via edge computing. Detailed analyses concerning degree-of-freedom, identifiability, complexity as well as Cramér-Rao bound (CRB) are provided. To show the effectiveness of the proposed architecture, numerical simulations have been designed.

Cramér-Rao Bounds on Angle Estimating in Bistatic MIMO Radar With Non-Orthogonal Waveforms

Angle estimation is a hot topic in multiple input multiple output (MIMO) radar. However, most of the existing algorithms are only focus on the scenario of ideal orthogonal transmission waveform. In engineering applications, however, non-orthogonal waveforms scenario is more practical. In this paper, we focus on the Cramer-rao bound (CRB) on angle estimation in MIMO radar with non-orthogonal waveforms. Firstly, the angle estimation model in bistatic MIMO radar with non-orthogonal transmit waveforms is given, and the general expression of CRB is deduced. Thereafter, the CRBs in some special cases are discussed, e.g., monostatic geometry, orthogonal transmit waveforms scenario. In addition, theoretical comparisons between the stochastic CRBs and the deterministic ones are presented. Finally, the computer simulations are carried out to verify the theoretically ones.

Direction Finding for Bistatic MIMO Radar with Unknown Spatially Colored Noise

In this paper, we investigate the problem of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation for bistatic multiple-input multiple-output radar with unknown spatially colored noise. By exploiting the sparse structure of the noise covariance matrix, a new de-noising scheme is designed. The signal covariance matrix is recast as a low-rank matrix with missing entries, which can be approximately tackled via solving an optimization problem. Thereafter, DODs and DOAs are obtained with the traditional subspace techniques. The proposed method does not bring any virtual aperture loss; thus, it achieves more accurate estimation performance than several state-of-the-art de-noising methods. Finally, the stochastic Cramer–Rao bound for joint direction finding is derived. Numerical computer simulations verify the effectiveness of the proposed algorithm.

Space‐time adaptive detection for bistatic MIMO system under covariance matrix persymmetry and symmetric spectrum

Space-time adaptive detection (STAD) is an important research aspect of the bistatic multiple-input multiple-output (MIMO) radar system. The signal and clutter space-time models of the bistatic MIMO radar are described in this study. The knowledge-aided (KA) transform, which utilises the structural properties of the target-free data and the sample covariance matrix, is applied to increase the independent secondary data fourfold in the STAD frame. The performance assessment of the KA–STAD detectors with generalised likelihood ratio test (GLRT), adaptive matched filter (AMF), and Rao rules is presented. The simulation experiments show that the detection and constant false alarm rate performances of the presented KA–GLRT, KA–AMF, and KA–Rao detectors outperform the GLRT, AMF, and Rao detectors for the bistatic MIMO radar system STAD frame in clutter background with limited secondary data.

Joint Sensor Failure Detection and Corrupted Covariance Matrix Recovery in Bistatic MIMO Radar With Impaired Arrays

A bistatic multiple-input multiple-output (MIMO) radar, which is usually constituted by a large number of antenna sensors, may encounter one or more failures in the transmit or receive array after long periods of continuous operation. In this paper, we present a novel technique that integrates the detection of faulty sensors and the recovery of the corrupted covariance matrix into a systematic process for a bistatic MIMO radar with impaired arrays. A simple scheme based on the cross-correlation method, which exploits different behaviors between the faulty and normal sensors, is developed for the detection of the faulty transmit and receive sensors without requiring external probes. To mitigate the negative effects brought by sensor failures, the matrix completion method is fully integrated with the structured processing of the four-fold Hankel matrix to more reliably recover the successive corrupted data in both the covariance matrix rows and columns that result from the failure of the sensors. The proposed technique can alleviate or even avoid the angle estimation performance loss of the array covariance matrix-based algorithms in the face of a wide range of faulty sensor numbers. Extensive numerical simulations verify the effectiveness of the proposed technique.

Unfolded coprime bistatic MIMO radar for joint DOD and DOA estimation: from viewpoint on aperture augment for sum coarray

ABSTRACTGenerally, the coprime linear array (CLA) consisting of two interleaved uniform linear subarrays can enlarge the array aperture to attain the better angle estimation performance compared with the uniform linear array (ULA). In this paper, we ulteriorly study the virtual sum coarray of the unfolded coprime (UC) bistatic multiple-input multiple-output (MIMO) radar whose transmitter and receiver array are both unfolded CLA from the viewpoint on the geometry and array aperture. The UC MIMO radar can be exploited to obtain the better joint direction of departure (DOD) and direction of arrival (DOA) estimation performance due to the larger array aperture. Furthermore, we propose an all sum coarray multiple signals classification (ASCA-MUSIC) algorithm for the UC MIMO radar. ASCA-MUSIC can fully exploit all the degrees of freedom (DOFs) in the sum coarray and can obtain the better estimation performance. We also prove that ASCA-MUSIC can avoid the phase ambiguity problem due to the coprime property. In addition, we devise a reduced complexity scheme for ASCA-MUSIC to reduce the high computational complexity and utilize Cramer–Rao Bound (CRB) as a benchmark for the lower bound on the root-mean-square error (RMSE) of unbiased angle estimation. Finally, the numerical simulations verify the effectiveness and superiority of the UC MIMO radar, ASCA-MUSIC and the reduced complexity scheme.

Array diagnosis and angle estimation in bistatic MIMO radar under array antenna failures

The presence of fault antennas in bistatic multiple-input–multiple-output (MIMO) radar causes a significant degradation of angle estimation performance. In this study, the authors present a signal-processing scheme for bistatic MIMO radar with impaired receive array including array diagnosis as well as angle estimation. The damaged antenna in the receiver, which is incapable of receiving the target signals and leaves only the thermal noise generated within the receiver itself, leads to a decrease in the entropy of its received data. The dissimilarity of the entropy values between the damaged and normal receive antennas is used for array diagnosis. Thereafter, the useless noise data of the detected fault antennas is removed in the receive signal matrix, so that the successive data missing occurs along the row directions of the signal subspace matrix. A low-rank block-Hankel structured matrix is constructed from the incomplete signal subspace matrix, which can facilitate the exploitation of the matrix completion technique to recover that successive missing data. On the basis of the restored rotational invariance structure of the complete signal subspace, the estimation of signal parameters via rotational invariance technique can then be applied for angle estimation. Simulation results confirm the validity of the proposed methods.

Low complexity 3D-OMP algorithms for DOD DOA and Doppler frequency estimation in bistatic MIMO radar

ABSTRACTThe biggest challenge of the traditional 3D orthogonal matching pursuit (OMP) method for direction-of-departure (DOD), direction-of-arrival (DOA) and Doppler frequency estimation in bistatic multiple-input multiple-output (MIMO) radar is the heavy computational burden due to a large number of atoms in the overcomplete dictionary. In this paper, low complexity 3D-OMP algorithms are investigated. First, the traditional 3D-OMP algorithm is given. Then, two-dimensionality reduced OMP-based algorithms are proposed exploiting the property of Khatri-Rao product and proper sparse representation. Also, the multiple measurement vectors (MMV) model is introduced to our OMP algorithms to guarantee the estimation performance. The simulation results show that the DOD, DOA and Doppler frequency can be effectively estimated with a small number of pulses and low computation cost. With similar accuracy compared with the traditional 3D-OMP method, much lower computational burden can be achieved by using the proposed methods.

Target Localization in Bistatic EMVS-MIMO Radar Using Tensor Subspace Method

Target localization is a fundamental task of multiple-input multiple-output (MIMO) radar systems with numerous applications. In this paper, we investigate into the localization problem in a bistatic MIMO radar with electromagnetic vector sensors (EMVS). Unlike the traditional scaler sensors, an EMVS is able to offer two dimensional (2D) direction finding, and it can provide additional polarization characteristics of the source. Therefore, target localization in bistatic EMVS-MIMO radar system involves 2D direction-of-departure (2D-DOD) and 2D direction-of-arrival (2D-DOA) estimation. Besides, we can obtain transmit polarization characteristics as well as polarization characteristics of the targets. To exploit the tensor nature of the array measurement after matched filters, a tensor subspace algorithm is developed, which estimates the target parameters via cross-product technique from tensor subspace. The proposed algorithm, which obtains closed-form solutions for parameters estimation, shows more accurate performance than the existing algorithm. Numerical simulations verify the effectiveness and improvement of the proposed algorithm.

Joint DOD and DOA Estimation for Coherently Distributed Sources in Bistatic MIMO Radar Based on Joint Diagonalization

In this paper, an efficient method via unitary joint diagonalization is proposed to deal with the coherently distributed sources in bistatic multiple-input multiple-output (MIMO) radar systems. In order to determine the direction of departure (DOD) and direction of arrival (DOA) of the coherently distributed source, a special array configuration is designed both for transmitter and receiver in bistatic MIMO radar system. Then, a new signal model can be obtained by utilizing the designed array characteristic and the rotational invariance relationship is constructed both for DOD and DOA. For the special rotational invariance relationship, the joint diagonalization technique is adopted to locate the coherently distributed sources and the angular parameters are automatically paired without multidimensional search process. The proposed joint diagonalization method can also determine the targets when multiple imping sources have the common DODs or DOAs. Finally, the approximate determined Cramer-Rao bound of the proposed estimator for the coherently distributed sources is also derived. And, additional numerical results are conducted to verify the effectiveness and superiority of the proposed method.

Fast PARAFAC Algorithm for Target Localization in Bistatic MIMO Radar in the Co-Existence of Unknown Mutual Coupling and Spatially Colored Noise

Target positioning using multiple-input multiple-output (MIMO) radar system has aroused extensive attention in the past decade. However, most of the existing positioning algorithms are only suitable for ideal scenarios (e.g., well-calibrated sensors, orthogonal waveforms, Gaussian white noise). In this paper, we focus on the target localization problem in a bistatic MIMO system in the co-existence of mutual coupling and spatially colored noise, i.e., to estimate the direction-of-arrival (DOA) and direction-of-departure (DOD) in such non-ideal scenario. To tackle this issue, a parallel factor (PARAFAC) analysis algorithm is proposed. Firstly, the de-noising operation is carried out to suppress the spatially colored noise. Then a PARAFAC analysis model is constructed to explore the tensor nature of measurement. After computing PARAFAC decomposition on the new tensor, the factor matrices associate with DOD and DOA are obtained. Thereafter, the de-coupling operation is followed to eliminate the mutual coupling. Finally, the idea of least squares is utilized to recovery DOD and DOA from the factor matrices. The proposed algorithm can achieve closed-form solution for DOD and DOA estimation without pairing calculation. Moreover, it provides better estimation performance than the state-of-the-art approaches. Detailed analyses are illustrated and simulation results verify the effectiveness of the proposed algorithm.

Joint DOD and DOA Estimation for Bistatic MIMO Radar: A Covariance Trilinear Decomposition Perspective

The covariance methods exert an effect on spatially colored (correlated) noise elimination during direction finding in multiple-input multiple-output (MIMO) radar. However, most of the existing methods seem difficulty to achieve a good balance between accuracy and efficiency. This paper aims at formulating a covariance trilinear decomposition perspective for direction-of-departure (DOD) and direction-of-arrival (DOA) estimation for bistatic MIMO radar. First, the array covariance matrix model is presented for de-noising. Furthermore, the noiseless covariance matrix is rearranged into a trilinear decomposition model. Finally, joint DOD and DOA estimation are linked to trilinear decomposition, which can be easily accomplished by exploiting the existing COMFAC technique. The proposed scheme can exploit the tensor structure of the covariance matrix, and it is attractive from the perspective of computational complexity. Moreover, it can be easily extended to the spatially colored noise scenario. The proposed algorithm is analyzed in terms of identifiability, flexibility, and complexity, and the stochastic Cramer-Rao bound on joint DOD and DOA estimation is derived. The computer simulations verify the effectiveness and improvement of the proposed method.

Transmit beamspace-based DOD and DOA estimation method for bistatic MIMO radar

Abstract In this paper, we propose a novel angle estimation method in bistatic multiple-input multiple-output (MIMO) radar, which combines the transmit beamspace (TB) technique with the unitary ESPRIT (U-ESPRIT) model. The TB matrix is designed to focus the transmitted energy within the desired spatial sector, thus achieving the transmit coherent gain. Due to the special data structure of the TB-based bistatic MIMO radar, a corresponding method is proposed to construct the real-valued model. Unfortunately, the existed interpolation error inevitably degrades the direction-of-departure (DOD) estimation performance. To compensate the DOD estimation error, a look-up table is created, which establishes a one-to-one mapping relationship for DOD. The Cramer-Rao bound (CRB) on angle estimation in TB-based bistatic MIMO radar is also derived for performance analysis. Compared with existing methods, the proposed algorithm has better estimation performance due to the improved signal-to-noise ratio (SNR) gain and requires less computational complexity. Numerical simulations are presented to demonstrate the estimation performance of the proposed algorithm.

Tensor based angle estimation scheme for strictly noncircular sources in bistatic MIMO radar

In this paper, joint direction of departure (DOD) and direction of arrival (DOA) estimation for strictly noncircular sources in multiple-input multiple-output (MIMO) radar is dealt with by a novel tensor based subspace method. The proposed method firstly formulates a novel augmented tensor for capturing both the noncircularity and inherent multidimensional structure of strictly noncircular signals, and then a tensor based signal subspace is constructed by utilizing the high-order singular value decomposition (HOSVD). Finally, the DODs and DOAs are achieved by calculating the rotational invariance factors corresponding to the augmented steering matrix. The proposed method provides better angle estimation performance than the existing subspace based algorithms, especially in the case of low SNR and a small number of snapshots. In addition, the DODs and DOAs are paired automatically. The effectiveness and advantages of the proposed method are demonstrated via simulation results.

Tensor-Based Angle Estimation Approach for Strictly Noncircular Sources with Unknown Mutual Coupling in Bistatic MIMO Radar

In the paper, the estimation of joint direction-of-departure (DOD) and direction-of-arrival (DOA) for strictly noncircular targets in multiple-input multiple-output (MIMO) radar with unknown mutual coupling is considered, and a tensor-based angle estimation method is proposed. In the proposed method, making use of the banded symmetric Toeplitz structure of the mutual coupling matrix, the influence of the unknown mutual coupling is removed in the tensor domain. Then, a special enhancement tensor is formulated to capture both the noncircularity and inherent multidimensional structure of strictly noncircular signals. After that, the higher-order singular value decomposition (HOSVD) technology is applied for estimating the tensor-based signal subspace. Finally, the direction-of-departure (DOD) and direction-of-arrival (DOA) estimation is obtained by utilizing the rotational invariance technique. Due to the use of both noncircularity and multidimensional structure of the detected signal, the algorithm in this paper has better angle estimation performance than other subspace-based algorithms. The experiment results verify that the method proposed has better angle estimation performance.