Space-time Adaptive Processing Research Articles

A novel sparse recovery space‐time adaptive processing algorithm using the log‐sum penalty to approximate the ℓ0 − norm penalty

AbstractApplying the sparse recovery (SR) technique to airborne radar space‐time adaptive processing (STAP) can greatly reduce the number of required training samples, which is advantageous in detecting targets in non‐homogeneous and non‐stationary clutter environments. However, the poor performance, the slow convergence speed or the high computational complexity of the traditional SR STAP algorithms limit their practical application. To tackle this problem, a novel efficient SR STAP algorithm is proposed. The newly proposed SR STAP algorithm utilises the log‐sum penalty to approximate the penalty, which exhibits improved convergence performance and clutter suppression performance compared to the traditional SR STAP algorithms. Besides, the proposed algorithm can ensure the convergence in each iteration by offering a closed‐form analytic solution. Furthermore, the result of the mathematical derivation demonstrates the essential equivalence between our method and the iterative reweighted method. By utilising this equivalence, two additional methods are proposed that incorporate the knowledge of the clutter Capon spectrum and the clutter spectrum of the iterative adaptive approach (IAA) as the components of weighted values, resulting in further performance improvement of the proposed algorithm. Finally, simulation results with both simulated data and Mountain‐Top data demonstrate the high effectiveness and performance of the proposed methods.

A Fast IAA–Based SR–STAP Method for Airborne Radar

Space–time adaptive processing (STAP) is an effective technology in clutter suppression and moving target detection for airborne radar. When working in the heterogeneous environment, the number of training samples that satisfy independent and identically distributed (IID) conditions is insufficient, making it difficult to ensure the estimation accuracy of the clutter plus noise covariance matrix for traditional STAP methods. Sparse recovery–based STAP (SR–STAP) methods have received widespread attention in the past few years. The accurate estimation of the clutter plus noise covariance matrix can be achieved using only a few training samples. The iterative adaptive approach (IAA) can quickly and accurately estimate the power spectrum, but applying this method directly to the STAP method cannot produce good performance. In this paper, a fast IAA–based SR–STAP method is proposed. Based on the weighted l1 problem, the IAA spectrum is used as a weighted term to obtain a good approximation. In order to obtain an analytical solution, we use the weighted l2 norm to approximate the weighted l1 norm without loss of performance. Compared with the IAA–STAP method, the proposed method is more robust to errors. Moreover, the proposed method has a fast computational speed. The effectiveness of the proposed method is demonstrated by simulations.

Reweighted Extreme Learning Machine-Based Clutter Suppression and Range Compensation Algorithm for Non-Side-Looking Airborne Radar

Non-side-looking airborne radar provides important applications on account of its all-round multi-angle airspace coverage. However, it suffers clutter range dependence that makes the samples fail to satisfy the condition of being independent and identically distributed (IID), and it severely degrades traditional approaches to clutter suppression and target detection. In this paper, a novel reweighted extreme learning machine (ELM)-based clutter suppression and range compensation algorithm is proposed for non-side-looking airborne radar. The proposed method involves first designing the pre-processing stage, the special reweighted complex-valued activation function containing an unknown range compensation matrix, and two new objective outputs for constructing an initial reweighted ELM-based network with its training. Then, two other objective outputs, a new loss function, and a reverse feedback framework driven by the specifically designed objectives are proposed for the unknown range compensation matrix. Finally, aiming to estimate and reconstruct the unknown compensation matrix, special processes of the complex-valued structures and the theoretical derivations are designed and analyzed in detail. Consequently, with the updated and compensated samples, further processing including space–time adaptive processing (STAP) can be performed for clutter suppression and target detection. Compared with the classic relevant methods, the proposed algorithm achieves significantly superior performance with reasonable computation time. It provides an obviously higher detection probability and better improvement factor (IF). The simulation results verify that the proposed algorithm is effective and has many advantages.

Persymmetric detection based on asymptotically optimal convex linear combination

Persymmetric structure has been utilized in space-time adaptive processing for heterogeneous environment, which leads to some detection methods based on persymmetric structure, such as persymmetric adaptive matched filter (PS-AMF). However, when the sample support is extremely limited, these methods still suffer the serious degradation in detection performance due to the large error in estimating covariance matrix. In this paper, an asymptotically optimal convex linear combination between transformed sample covariance matrix and identity matrix is considered herein to improve PS-AMF. The asymptotically optimal convex linear combination is conducive to diminishing the estimate error in estimating the transformed covariance matrix by weighting the transformed sample covariance matrix and identity matrix. Furthermore, the asymptotically optimal convex linear combination is improved by the reutilization of the convex linear combination, and the corresponding coefficients are derived. Then, the detection performance of the proposed method is approximately analyzed. At last, numerical simulations show that the proposed method performs well, compared with its counterparts, when the sample support is extremely limited.

A novel non-convex penalty function-based STAP algorithm for airborne passive radar systems

In conventional sparse Space-Time Adaptive Processing (STAP) algorithms, the l0-norm is often used instead of the l1-norm to relax convexity constraints. The approach presented in this paper can be mathematically reformulated as a linear problem, which can be efficiently solved using various convex optimization techniques. While this method effectively circumvents the NP-Hard complexity associated with the l0-norm, it does come with certain potential challenges. For example, the observation matrix must meet the criteria of the Restricted Isometry Property (RIP) and other stringent conditions. In this research, a novel STAP algorithm is introduced, which is based on a non-convex penalty function. This innovative algorithm substitutes the traditional l0-norm with a custom-designed non-convex penalty function and is applied to the Direct Filter Processor (DFP), solved using the recursive least squares (RLS) algorithm. The resulting algorithm, known as gp-RLS, is demonstrated through Monte Carlo simulations to outperform other l1-based and reduced-rank STAP algorithms in terms of faster convergence, improved signal-to-clutter-plus-noise ratio (SCNR), and enhanced target detection performance.

A Reduced Sparse Dictionary Reconstruction Algorithm Based on Grid Selection

A sparse dictionary reconstruction algorithm based on grid selection is introduced to solve the grid mismatch when using the sparse recovery space time adaptive processing (SR-STAP) algorithm. First, the atom most closely related to clutter is selected from the traditional dictionary through the spectral value dimensionality reduction method. The local mesh is divided around the selected atoms to create mesh cells, and the mesh cells that are most likely to appear in the real clutter points are judged according to the local selection iteration criteria. In this way, the mesh spacing is refined, the local mesh selection is carried out step by step, and the optimal atoms in the local region are constantly adjusted and selected to narrow the search region until the iteration termination condition is met. Finally, the space-time plane is divided using a novel meshing technique that centers around the optimal atom. By removing atoms beyond the maximum range of spatial and Doppler frequencies, the simplified sparse dictionary can overcome the mesh mismatch problem. The simulation results demonstrate that the algorithm enhances the sparse recovery accuracy of clutter space-time spectrum, mitigates the mesh mismatch effect, and boosts STAP performance.

Low-cost solutions for mobile passive radar based on multichannel DPCA and NULA configurations

Abstract In this paper, we investigate low-cost solutions for enabling ground moving target indication applications with multichannel mobile passive radar systems. As known, in order to be competitive with their active counterparts, passive radars are typically characterized by severe constraints in terms of cost, complexity, and compactness, especially when installed on moving platforms. On the one hand, carrying out the computations onboard requires processing techniques as simple as possible. On the other hand, the need for lightweight and compact systems that can be installed on a moving platform requires using a limited number of receiving channels. To meet these requirements, we propose a series of nonadaptive detectors based on multichannel displaced phase center antennas, which allow suppressing the Doppler-spread clutter component without requiring computationally intensive space–time adaptive processing techniques. Moreover, we explore the use of nonuniformly spaced array configurations on receive, which represent a good alternative to conventional uniform linear arrays when a limited number of receiving channels can be implemented. The effectiveness of the proposed processing techniques and antenna design solutions is demonstrated via numerical analysis for the case of a DVB-T-based mobile passive radar system.

A Novel Non-Stationary Clutter Suppression Approach for Space-Based Early Warning Radar Using an Interpulse Multi-Frequency Mode

The non-stationary clutter of space-based early warning radar (SBEWR) is more serious than that of airborne early warning radar. This phenomenon is primarily attributed to the Earth’s rotation and range ambiguity. The increase in clutter degrees of freedom (DOFs) and the significant widening of the clutter suppression notch are not conducive to moving target detection near main lobe clutter. This paper proposes an effective approach to suppress non-stationary clutter based on an interpulse multi-frequency mode for SBEWR. Using the orthogonality of the uniform stepping frequency signal, partial range ambiguity can be effectively suppressed, and the clutter DOFs will be reduced. Subsequently, joint pitch-azimuth-Doppler three-dimensional spacetime adaptive processing and slant range preprocessing are used to perform clutter suppression. This combination not only curtails the estimation error associated with the clutter covariance matrix but also enhances the overall detection capabilities of the system. The simulation results verify the effectiveness of the proposed approach.

Beam-Space Post-Doppler Reduced-Dimension STAP Based on Sparse Bayesian Learning

The space–time adaptive processing (STAP) technique can effectively suppress the ground clutter faced by the airborne radar during its downward-looking operation and thus can significantly improve the detection performance of moving targets. However, the optimal STAP requires a large number of independent identically distributed (i.i.d) samples to accurately estimate the clutter plus noise covariance matrix (CNCM), which limits its application in practice. In this paper, we fully consider the heterogeneity of clutter in real-world environments and propose a sparse Bayesian learning-based reduced-dimension STAP method that achieves suboptimal clutter suppression performance using only a single sample. First, the sparse Bayesian learning (SBL) algorithm is used to estimate the CNCM using a single training sample. Second, a novel angular Doppler channel selection algorithm is proposed with the criterion of maximizing the output signal-to-clutter-noise ratio (SCNR). Finally, the reduced-dimension STAP filter is constructed using the selected channels. Simulation results show that the proposed algorithm can achieve suboptimal clutter suppression performance in extremely heterogeneous clutter environments where only one training sample can be used.

Memory-Augmented Autoencoder-Based Nonhomogeneous Detector for Airborne Radar Space-Time Adaptive Processing

Memory-Augmented Autoencoder-Based Nonhomogeneous Detector for Airborne Radar Space-Time Adaptive Processing

Space–Time Adaptive Processing Using Deep Neural Network-Based Shrinkage Algorithm Under Small Training Samples

This correspondence discusses a space-time adaptive processing (STAP) method using deep neural network (DNN) and shrinkage algorithm (SA) under small training samples. A DNN-based SA is developed to estimate the clutter-plus-noise covariance matrix (CNCM) from the sample covariance matrix. This technique establishes a learning-based nonlinear mapping between the sample eigenvalues and the optimal shrunk eigenvalues and thus provides an accurate CNCM estimation. Specifically, a DNN consisting of cascaded convolutional neural network (CNN) and fully connected network (FCN) is designed, where the CNN performs the feature extraction and the FCN derives the estimation of the shrunk eigenvalues. To improve the CNN performance, a deep residual learning strategy is introduced into CNN. Due to the lack of labeled data, an airborne radar system is simulated for the construction of dataset consisting of sample eigenvalues and optimal shrunk eigenvalues. Numerical results demonstrate that the proposed DNN-based SA STAP has superior performance in comparison with the state-of-the-art SA STAP methods.

Meshless Search SR-STAP for Airborne Radar Based on Meta-Heuristic Algorithms

The sparse recovery (SR) space-time adaptive processing (STAP) method has excellent clutter suppression performance under the condition of limited observation samples. However, when the cluttering is nonlinear in a spatial-Doppler profile, it will cause an off-grid effect and reduce the sparse recovery performance. A meshless search using a meta-heuristic algorithm (MH) can completely eliminate the off-grid effect in theory. Therefore, genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), and grey wolf optimization (GWO) methods are applied to SR-STAP for selecting exact clutter atoms in this paper. The simulation results show that MH-STAP can estimate the clutter subspace more accurately than the traditional algorithm; PSO-STAP and GWO-STAP showed better clutter suppression performance in four MH-STAP methods. To search for more accurate clutter atoms, PSO and GWO are combined to improve the method’s capacity for global optimization. Meanwhile, the fitness function is improved by using prior knowledge of the clutter distribution. The simulation results show that the improved PSO-GWO-STAP algorithm provides excellent clutter suppression performance, which solves the off-grid problem better than does single MH-STAP.

Estimation of clutter covariance matrix in stap based on knowledge-aided and geometric methods

The insufficient number of available samples can cause inaccurate estimation of the clutter covariance matrix (CCM) in space-time adaptive processing (STAP), resulting in degraded clutter suppression performance. To tackle this problem, a CCM estimation approach based on knowledge-aided (KA) and geometric methods is proposed in this paper. A combination of environmental as well as structural (Persymmetric or Symmetric structure) knowledge information is utilized to model the covariance matrix of each sample as a knowledge-aided Hermitian positive definite (KA-HPD) covariance matrix. The estimation problem is introduced into the Riemannian manifold composed of the KA-HPD covariance matrices, and the geometric method is used for nonlinear processing. Based on the Kullback-Leibler (KL) divergence and the KL mean, the final estimated CCM is designed as a weighted combination of each KA-HPD covariance matrix. Experiment results show that the two designed structural covariance matrix estimators possess superior clutter suppression performance.

Gridless sparse recovery STAP algorithm with array amplitude-phase errors for non-uniform linear array

In the continuous angle-Doppler profile, the gridless sparse recovery (SR) space-time adaptive processing (STAP) prevents the off-grid issue of conventional SR-STAP. However, the applicability of the technique is limited to uniform linear array (ULA), whose performance deteriorates significantly owing to the array amplitude-phase errors (AAPEs). To this end, this study proposes a novel gridless SR-STAP algorithm applicable to a non-ULA with AAPEs. First, considering the properties of clutter covariance matrix (CCM), the atomic norm minimization (ANM)-STAP model with AAPEs is established for non-ULA. Second, the ANM-STAP is derived as a joint optimization problem for the clutter subspace and AAPEs, which are iteratively updated using the alternating direction method of multipliers. Finally, CCM is reconstructed to design the STAP filter weight vector. Simulation results show that the proposed algorithm is advantageous for non-ULAs and improves the STAP performance in the presence of AAPEs.

Multi-scale moving target detection with FDA-MIMO radar

The recently developed frequency diverse array (FDA) radar applies a small frequency increment across the array elements, which provides advantages in clutter suppression, jamming suppression, and target detection for existing radar systems. In this paper, the frequency increment is enlarged to guarantee that the transmit waveforms are orthogonal in frequency domain for multiple-input multiple-output (MIMO) radar. A multi-scale moving target detection method of FDA-MIMO radar is proposed. The FDA radar with a large frequency increment suffers from the deteriorated decorrelation of scatterers within the same range bin and causes the inner-bin range dependence (IRD) property in transmit spatial domain. By taking additional space–time snapshots in transmit domain as training samples, the space–time adaptive processing (STAP) is applied in joint receive and Doppler domain for clutter suppression, which alleviates the requirement of insufficient training samples in non-stationary clutter environment. In the sequel, a set of beamformers within the whole angular domain of interest is utilized for target detection, which achieves target detection under the condition of random target locations and sizes. Numerical simulation results are provided to verify the effectiveness of the proposed method.

A novel vertical element-pulse coding scheme for range-ambiguous clutter elimination

The coexistence of clutter range ambiguity and range dependence in the airborne forward-looking radar may render the common space–time adaptive processing (STAP) ineffective. To cope with this challenge, a novel vertical element-pulse coding (EPC) radar is proposed in our paper. Note that both the elevation angles and coding factors determine the transmitted spatial frequency of the proposed vertical EPC radar. Therefore, the clutters corresponding to different ambiguous areas can be distinguished in the spatial frequency dimension based on this property. The element-pulse decoding and pre-STAP filtering are devised to separate and extract these clutters corresponding to different ambiguous areas. In the following, the clutter elimination is independently accomplished for each ambiguous area that has been separated. Consequently, the clutter range ambiguity as well as clutter range dependence are addressed simultaneously. The efficacy of the proposed approach is verified with simulation experiments.

A STAP Detection Scheme for Low Sample Support Maritime Environments

In airborne radar, reduced rank space-time adaptive processing techniques are employed when non-stationarity and non-homogeneity of the clutter causes insufficient sample support. There have been many approaches proposed to address this problem, including principal components, the cross-spectral metric and the multistage Wiener filter. This latter approach is superior to other reduced rank techniques in terms of computational efficiency, sample support and rank requirements. Regarding operation in heterogeneous environments, the single data set approach for clutter suppression has been proposed and operates solely on the cell under test to obtain a clutter covariance estimate. It is therefore highly effective in environments with limited training data that is homogeneous with the test data. In this paper, a single data set detection approach under the framework of the multistage Wiener filter is proposed and analysed to enhance clutter suppression capabilities. The target detection performance of the filter is evaluated using simulated maritime radar data.

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.

A novel gridless space-time adaptive processing method based cyclic minimization

Space-time adaptive processing (STAP) algorithm based on sparse recovery (SR) can effectively suppress clutter in limited sample scenarios. However, the clutter suppression performance will be reduced because of grid mismatch (off-grid), which happens when the clutter ridge fails to match the dictionary. To address this issue, a novel gridless STAP algorithm based on cyclic minimization is proposed in this paper. Compared with the STAP algorithm based on atomic norm minimization (ANM), the proposed algorithm avoids the approximate loss caused by relaxing the rank norm to the nuclear norm. In addition, in order to improve the computational efficiency, we derive a fast iterative structure based on the alternating direction method of multipliers (ADMM) framework. The proposed algorithm offers better clutter suppression performance and excellent computational efficiency, according to a vast collection of experiments based on simulation data and measured data.

Track-Before-Detect Using an Airborne Multichannel Radar in the Maritime Domain

This paper explores methods for detection and tracking of maritime targets using an airborne scanning multi-channel radar, operating at high altitudes. The main technical difficulties include: (a) the non-stationary and non-Gaussian nature of sea clutter when using a high-resolution airborne radar, and (b) low target signal-to-interference ratios due to higher grazing angles. It is proposed to carry out processing in two stages. First, space time adaptive processing (STAP) is applied to exploit the spatial and temporal degrees of freedom available in the multi-channel radar. Subsequently, target detection and tracking is performed using the track-before-detect method, applied to the STAP output. For the sake of comparison, a more traditional tracking method is also developed, where a detection threshold is applied to the STAP output, to obtain point measurements, subsequently processed via an extended target tracking methodology. The error performance of the proposed methodology is presented, using high-fidelity radar data generation.