Space-time Steering Vector Research Articles

Joint velocity and angle estimation for single-cycle TDM MIMO automotive radar

Time-division multiplexing (TDM) multiple-input multiple-output (MIMO) radar systems have gained popularity in automotive applications, thanks to their high-resolution and cost-effective properties. However, when the relative motion between the target and the radar is significant and possibly fast time-varying, TDM MIMO systems suffer for reduced maximum unambiguous velocity and angle-Doppler coupling. In this work, a novel off-grid estimation method for TDM MIMO systems is developed that operates on a single cycle and is able to accurately estimate unambiguously the instantaneous velocity and the target direction of arrival (DOA). We model the angle-Doppler coupling through a space-time steering vector. Then, an iterative adaptive approach (IAA)-based method is exploited to reconstruct the 2D velocity-angle spectrum. Additionally, we account for off-grid errors when the targets do not lie on the search grids. A coarse-to-fine strategy is proposed to alleviate the computational burden, where a maximum likelihood (ML) estimator iteratively corrects the off-grid velocity and DOA estimates of each target. Simulated and experimental data are processed to demonstrate the effectiveness of the proposed method.

Robust Space-Time Adaptive Processing Method for GNSS Receivers in Coherent Signal Environments

In the coherent signal environments caused by multipath propagation, the interference suppression performance of the global navigation satellite systems (GNSS) receivers decreases sharply. In this paper, a robust space-time adaptive processing (STAP) method for GNSS receivers is proposed to suppress interferences in coherent signal environments, by using the modified space-time two-dimensional iterative adaptive approach (ST2D-IAA) spectrum estimation. This method applies the IAA algorithm to the ST2D signal model of GNSS receivers, and further modifies the ST2D-IAA algorithm to accurately estimate the power spectrum and noise power simultaneously. The space-time interference-plus-noise covariance matrix (STINCM) is reconstructed by using the estimated power spectrum and noise power in the interference angle region. Based on the reconstructed STINCM, we construct the STAP beamforming optimization problem for the space-time steering vector (STSV) error vector, and further correct the STSV of GNSS signal. Finally, the weight vector of STAP beamforming is calculated by using the reconstructed STINCM and the corrected STSV of GNSS signal. Simulation results show that the proposed method can suppress interferences in coherent signal environments and outperforms the current methods.

Low-Altitude Windshear Wind Speed Estimation Method Based on KASPICE-STAP

Aiming at the problem of low-altitude windshear wind speed estimation for airborne weather radar without independent identically distributed (IID) training samples, this paper proposes a low-altitude windshear wind speed estimation method based on knowledge-aided sparse iterative covariance-based estimation STAP (KASPICE-STAP). Firstly, a clutter dictionary composed of clutter space-time steering vectors is constructed using prior knowledge of the distribution position of ground clutter echo signals in the space-time spectrum. Secondly, the SPICE algorithm is used to obtain the clutter covariance matrix iteratively. Finally, the STAP processor is designed to eliminate the ground clutter echo signal, and the wind speed is estimated after eliminating the ground clutter echo signal. The simulation results show that the proposed method can accurately realize a low-altitude windshear wind speed estimation without IID training samples.

Main lobe interference suppression method of Skywave OTHR based on fast-time STAP

For the sky-wave over-the-horizon radar (OTHR), how to effectively suppress the radio frequency interference (RFI)from the main-lobe direction is a problem. To solve this problem, this paper proposes a new space-fast time adaptive processing (fast-time STAP) which merges the matched filter coefficients used for pulse compression and the time steering vector of fast-time STAP. To compare with conventional methods, the method improves the match between the space-time steering vector of fast-time STAP and the real target signal, while the RFI and the noise from RFI are effectively suppressed by the interference-plus-noise covariance matrix which is composed of raw data. At the same time, the signal-to-noise ratio is improved. Compared with the traditional method, this method can be better applied to practical engineering. The results of computer simulation and experiments with real radar data verify the effectiveness of the proposed method.

Space-Time Adaptive Processing Based on Modified Sparse Learning via Iterative Minimization for Conformal Array Radar.

Space-time adaptive processing (STAP) is a well-known technique for slow-moving target detection in the clutter spreading environment. For an airborne conformal array radar, conventional STAP methods are unable to provide good performance in suppressing clutter because of the geometry-induced range-dependent clutter, non-uniform spatial steering vector, and polarization sensitivity. In this paper, a knowledge aided STAP method based on sparse learning via iterative minimization (SLIM) combined with Laplace distribution is proposed to improve the STAP performance for a conformal array. The proposed method can avoid selecting the user parameter. the proposed method constructs a dictionary matrix that is composed of the space-time steering vector by using the prior knowledge of the range cell under test (CUT) distributed in clutter ridge. Then, the estimated sparse parameters and noise power can be used to calculate a relatively accurate clutter plus noise covariance matrix (CNCM). This method could achieve superior performance of clutter suppression for a conformal array. Simulation results demonstrate the effectiveness of this method.

Search-Free Angle, Range, and Velocity Estimation for Monostatic FDA-MIMO

The monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) has attracted much attention recently. However, much research is concentrated on the estimation of angle-range parameters based on the FDA-MIMO radar, and the velocity has not been considered. In this study, we propose a search-free method to estimate these parameters. To overcome the problem of the high computational complexity associated with the searching estimation algorithms, the parallel factor (PARAFAC) decomposition is introduced to estimate the space-time steering vector. Next, we can utilize the least square method to solve the angle, range, and velocity of each target. In addition, the Cramér–Rao bounds (CRBs) of angle, range, and velocity are derived. Besides, the other performance analysis consists of the root mean square error, and complexity is derived. We compare the PARAFAC decomposition algorithm with the estimation of signal parameters via the rotational invariance techniques (ESPRIT) algorithm, and our method owns a superior performance. Finally, the proposed method is verified by simulations and has the ability to achieve greater estimation accuracy than existing algorithms.

Gridless Sparse Clutter Nulling STAP Based on Particle Swarm Optimization

Sparse clutter nulling space–time adaptive processing (STAP) methods achieve superior performance in the case of limited samples, so they are suitable for nonhomogeneous clutter environments. Traditional sparse clutter nulling STAP algorithms try to estimate the clutter subspace by selecting a suitable set of space–time steering vectors (atoms) in spatial-Doppler profile grids. However, the off-grid effect is inevitable for the nonside-looking case due to the nonlinear distribution of clutter and, thus, leads to significant performance degradation. To solve this problem, a gridless sparse clutter nulling STAP algorithm based on the particle swarm optimization (PSO) named PSO-STAP is proposed in this letter. A criterion function to evaluate the suitability of atoms is first devised. By regarding the criterion as a fitness function, PSO-STAP can select atoms in gridless spatial-Doppler profile, which is more suitable to construct the accurate clutter subspace. Numerical results verified the feasibility and superiority of the proposed algorithm.

A Grid-Less Total Variation Minimization-Based Space-Time Adaptive Processing for Airborne Radar

Sparse recovery (SR) based space-time adaptive processing (STAP) has attracted much attention due to its small requirement of snapshots in the estimation of the clutter plus noise covariance matrix (CNCM). However, most of the existing SR STAP methods suffer from the grid mismatch effect of the dictionary matrix. In this paper, a novel grid-less total variation minimization (TVM) based STAP approach is proposed, which avoids the discretization of the spatial-temporal profile and possible mismatch of the spatial-temporal gird. The optimization problem is firstly introduced to estimate the clutter subspace steering vector by minimizing the defined atomic norm based on the TVM. Then the optimization problem is reformulated via utilizing the property of the radar space-time steering vector and approximation of the Bessel function. Finally, with a solution obtained by the optimization problem, a projection method is presented to obtain an accurate estimation of the CNCM. The proposed STAP method can be applied for both the side-looking and non-side-looking case. Numerical results validate its effectiveness compared with the other SR STAP methods.

Robust knowledge‐aided sparse recovery STAP method for non‐homogeneity clutter suppression

Conventional space–time adaptive processing (STAP) methods would suffer severely performance loss in the complex clutter environment of an airborne-phased array radar, especially when the estimated clutter covariance matrix (CCM) is corrupted by the interference targets (outliers). In order to improve the clutter suppression in a practical complex clutter, a robust knowledge-aided sparse recovery STAP method for non-homogeneity clutter suppression is proposed. In the proposed method, the spectral profiles of the clutter and outliers are firstly estimated by sparse recovery processing. Then based on the system prior parameters, the clutter mask is constructed to select the space–time steering vectors corresponding to the clutter components. Afterwards the clutter suppression is achieved based on the clutter subspace obtained from the selected space–time steering vectors. Since the clutter and outlier profiles are effectively estimated and distinguished by the knowledge-aided sparse recovery processing, robust clutter subspace estimation can be achieved for clutter suppression. Through the simulated and actual airborne-phased array radar data, it is verified that the proposed method can effectively improve the STAP performance in a non-homogeneous environment.

Robust STAP Against Unknown Mutual Coupling Based on Middle Subarray Clutter Covariance Matrix Reconstruction

The presence of mutual coupling usually causes space-time steering vector distortion for space-time adaptive processing (STAP) in airborne radar, thereby causing significant performance degradation. In this paper, a robust STAP approach was proposed against mutual coupling based on middle subarray clutter covariance matrix reconstruction. To address the space-time steering vector distortion caused by the mutual coupling, the training snapshots of middle subarray were obtained using the spatial-temporal selection matrix, and they were collected to compute the sample covariance matrix (SCM). Thus, the clutter-plus-noise covariance matrix (CNCM) of middle subarray was reconstructed by utilizing the clutter Capon spectrum of middle subarray to integrate over the possible clutter spatial-temporal domain. Moreover, the target covariance matrix of middle subarray was calculated by employing the target Capon spectrum of middle subarray to integrate over the possible target region, and the space-time steering vector of the target was estimated with the eigenvector corresponding to its maximum eigenvalue. Finally, the proposed robust STAP weight vector of middle subarray was built. The proposed method is capable of simultaneously mitigating the mutual coupling, target components in the SCM, and target space-time steering vector mismatch. The simulation results verified the effectiveness of the proposed approach.

A Robust STAP Method Based on Alternating Projection and Clutter Cancellation

Space-time steering vector mismatch of targets usually happens in the space-time adaptive processing (STAP) technique, causing space-time beam distortion. Due to the effects of clutter spectrum broadening and jamming, performance of the conventional STAP method deteriorates dramatically. This paper proposes a novel robust STAP method to improve the performance of clutter suppression and moving target detection. The proposed method employs the alternating projection and clutter cancellation method, to reconstruct the clutter plus jamming plus noise covariance matrix (CJNCM) and re-estimate the target steering vector. Firstly, reconstruction of CJNCM consists of summing the eigenvectors of the projection operator, combining the sample covariance matrix and the integral covariance matrix (ICM) of specific region. Secondly, the re-estimated target steering vector is obtained by estimating the dominant eigenvector of the ICM of the Region of Interest (ROI), which contains the target signal purely because CJNCM is cancelled before estimation. Finally, the robust space-time adaptive filtering weight vector is calculated through the MVDR method with the reconstructed CJNCM and the re-estimated target steering vector. Simulation results indicate that the proposed algorithm shows robust performance against space-time steering vector mismatch, better output signal-to-noise ratio performance and better moving target detection performance than the traditional robust STAP method.

Robust STAP With Reduced Mutual Coupling and Enhanced DOF Based on Super Nested Sampling Structure

In practical airborne radar, mutual coupling between array elements usually leads to space-time steering vector distortion for space-time adaptive processing (STAP), which seriously degrades radar performance. In this paper, a robust STAP algorithm coupling the second order super nested arrays with pulses (2OSNAP) sampling structure is developed. The proposed method applies difference operation to construct virtual space-time snapshots in the virtual domain. To solve the clutter plus noise covariance matrix (CNCM) corresponding to the virtual space-time snapshots, the space-time smoothing method is used in this paper. Furthermore, the proposed method can directly give a set of virtual and robust STAP weight vector, which is convenient for the subsequent signal processing. Extensive numerical experiments were performed to verify the effectiveness and superiority of the proposed method. The test results also show that our proposed method provides more degrees of freedom (DOF), and eliminates the mutual coupling effect between array elements compared to most existing methods.

Low-Complexity Off-Grid STAP Algorithm Based on Local Search Clutter Subspace Estimation

Space–time adaptive processing (STAP) based on sparse recovery (SR-STAP) techniques exhibits significantly better performance than conventional STAP algorithms within a very small number of snapshots. However, when the clutter patches do not locate exactly on the discrete space–time grid points, the performances of SR-STAP algorithms degrade severely. In this letter, a low-complexity off-grid STAP algorithm based on local search clutter subspace estimation is proposed to overcome this issue. In the proposed algorithm, the global atoms are first selected from the reduced-dimension global STAP dictionary using the design selection criterion. Then, the optimal atoms are searched from the local STAP dictionary. Finally, these space–time steering vectors corresponding to the optimal atoms are used to construct the clutter subspace iteratively, and the STAP weight is obtained by projecting the snapshot on the subspace orthogonal to the clutter subspace. Numerical experiments with both simulated and Mountain-Top data are carried out to demonstrate the effectiveness of the proposed algorithm.

A knowledge aided SPICE space time adaptive processing method for airborne radar with conformal array

Abstract For airborne conformal array radar, it is difficult to suppress clutter using conventional space-time adaptive processing (STAP) methods because the geometry results in range-dependent clutter and nonuniform spatial steering vector. In order to improve the performance of conformal array clutter suppression, a knowledge aided method based on semiparametric/sparse iterative covariance-based estimation STAP, named with KASPICE-STAP, is proposed here. The KASPICE-STAP method requires the knowledge of the clutter ridge spread of the testing range cell. Based on this knowledge, we can construct a dictionary matrix which consists of the clutter space-time steering vectors. Subsequently, by using the dictionary matrix, a relatively accurate covariance matrix of clutter plus noise can be calculated with the KASPICE-STAP method. The proposed approach can work efficiently in complex environments only with the data of cell under test. Compared with other existing sparse recovery STAP methods, the proposed method has global convergence properties and it does not require making any difficult selection of hyperparameters. The improvement factor (IF) curves and range-Doppler images demonstrate the effectiveness of the proposed method.

Direct Localization of Multiple Stationary Narrowband Sources Based on Angle and Doppler

Direct position determination (DPD) is a single-step method that directly localizes transmitters from sensor outputs without estimating intermediate parameters. With a moving array, DPDs are usually performed by implicitly using only angle information. This letter proposes a DPD algorithm for multiple stationary transmitters by exploiting location information embedded in angles and Doppler shifts. We fit all signal subspaces with the space-time steering vectors at all positions of the moving array using the weighted subspace fitting method, and then perform an alternating projection procedure to directly localize transmitters. The simulation results corroborate the good localization performance of the proposed algorithm.

Robust STAP algorithm based on knowledge‐aided SR for airborne radar

Space–time adaptive processing (STAP) for airborne radar employs training snapshots to estimate a clutter covariance matrix (CCM). However, the resulting estimated covariance matrix can be corrupted by a target-like signal (outlier), which leads to a further target self-nulling phenomenon. When these outliers are dense, STAP performance degradation is most severe. To cope with this problem, a novel robust STAP algorithm based on knowledge-aided sparse recovery (SR) is proposed, which can eliminate the influence of dense outliers on target detection. This algorithm exploits the property that the clutter components of side-looking airborne radar are distributed along the clutter ridge, which is used to distinguish clutter components and outliers. Each snapshot is decomposed by the SR method, and then the similar degree function is defined to recognise and select clutter components via a threshold. Subsequently, the CCM is estimated by the select clutter components. Therefore, this algorithm can select appropriate coefficients and space–time steering vectors to assess clutter accurately. Monte Carlo experiments affirm that the proposed algorithm has advantages in robustness and target detection over other conventional STAP algorithms [e.g. samples matrix inverse-STAP, prolate spheroidal wave function-generalised inner product, and SR-STAP algorithms] in heterogeneous clutter environments.

Clutter nulling space‐time adaptive processing algorithm based on sparse representation for airborne radar

Traditional clutter subspace estimation algorithms try to solve the problem by estimating the clutter subspace eigenvectors from training samples, which are inevitably contaminated by noise. Actually, this can never be the best estimate, especially when the size of the training set is small. Furthermore, the omnipresent noise precludes the seeking of a pure clutter subspace. To cope with above drawbacks, the authors appeal to the sparse representation/recovery technique. From a mathematical viewpoint, the pure clutter subspace is spanned by the space-time steering vectors corresponding to the clutter component, and it can be constructed by a suitable set of space-time steering vectors selected from an overcomplete space-time steering dictionary. A criterion for selecting these space-time steering vectors is devised. Moreover, a clutter nulling type space-time adaptive processing algorithm is derived based on the proposed criterion. The resulting algorithm only needs the knowledge of the noise power rather than the clutter rank, which is quite troublesome to estimate in practice. Numerical results with both simulated and the Mountain-Top data demonstrate that the proposed algorithm has superior clutter suppression performance even with limited training samples.

Enhanced knowledge-aided space–time adaptive processing exploiting inaccurate prior knowledge of the array manifold

The accuracy of the prior knowledge of the clutter environments is critical to the clutter suppression performance of knowledge-aided space–time adaptive processing (KA-STAP) algorithms in airborne radar applications. In this paper, we propose an enhanced KA-STAP algorithm to estimate the clutter covariance matrix considering inaccurate prior knowledge of the array manifold for airborne radar systems. The core idea of this algorithm is to incorporate prior knowledge about the range of the measured platform velocity and the crab angle, and other radar parameters into the assumed clutter model to obtain increased robustness against inaccuracies of the data. It first over-samples the space–time subspace using prior knowledge about the range values of parameters and the inaccurate array manifold. By selecting the important clutter space–time steering vectors from the over-sampled candidates and computing the corresponding eigenvectors and eigenvalues of the assumed clutter model, we can obtain a more accurate clutter covariance matrix estimate than directly using the prior knowledge of the array manifold. Some extensions of the proposed algorithm with existing techniques are presented and a complexity analysis is conducted. Simulation results illustrate that the proposed algorithms can obtain good clutter suppression performance, even using just one snapshot, and outperform existing KA-STAP algorithms in presence of the errors in the prior knowledge of the array manifold.

Subspace-Augmented Clutter Suppression Technique for STAP Radar

Subspace space–time adaptive processing (STAP) algorithms are able to eliminate clutter completely. However, when the number of training samples is smaller than the clutter rank, the performances of subspace STAP algorithms degrade severely due to the inaccurate estimate of clutter subspace. To remedy this problem, a novel subspace STAP algorithm is proposed. In the proposed algorithm, the entire clutter subspace is constructed by two portions. The direct portion is estimated by a conventional method from limited training samples, while the supplemented portion is constructed by some space–time steering vectors selected from an overcomplete space–time steering dictionary. Clutter suppression is achieved by projecting the data into the subspace orthogonal to the clutter subspace. Numerical results with both simulated and mountain-top data demonstrate that the proposed algorithm has superior performance in a finite-training-sample situation.

Knowledge-Aided STAP Using Low Rank and Geometry Properties

This paper presents knowledge-aided space-time adaptive processing (KA-STAP) algorithms that exploit the low-rank dominant clutter and the array geometry properties (LRGP) for airborne radar applications. The core idea is to exploit the clutter subspace that is only determined by the space-time steering vectors, by employing the Gram-Schmidt orthogonalization approach to compute the clutter subspace. Simulation results illustrate the effectiveness of our proposed algorithms.