Space-time Adaptive Processing Algorithm 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 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 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.

Unsupervised Affinity Propagation Clustering Based Clutter Suppression and Target Detection Algorithm for Non-Side-Looking Airborne Radar

Aimingat non-side-looking airborne radar, we propose a novel unsupervised affinity propagation (AP) clustering radar detection algorithm to suppress clutter and detect targets. The proposed method first uses selected power points as well as space-time adaptive processing (STAP) weight vector, and designs matrix-transformation-based weighted input data, with which the first unsupervised weighted AP clustering is proposed by means of their similarity matrix, responsibility values and availability values. Then, new reconstructed weighted power inputs are designed, and the second weighted AP clustering is proposed. Finally, with their cluster results, a detection-discriminant criterion is designed for the judgment of target detection, and simultaneously, the clutter is suppressed. Compared with the conventional and important STAP, ADC and JDL algorithms, and several SO-based, GO-based and OS-based CFAR algorithms, the proposed unsupervised algorithm achieves much higher probability of detection and provides distinctly superior target-detection performance. With reasonable computation time, it can better conquer the range dependence in characteristic of clutter and better process non-independent identically distributed (non-IID) samples of non-side-looking radar. Sufficient simulations are performed, and they demonstrate that the proposed unsupervised algorithm is preferable and advantageous.

Mitigation of Wind Turbine Clutter With Digital Phased Array Radar

Wind turbine clutter (WTC) contamination affects polarimetric meteorological observations and automatic high-impact weather detection algorithms in several ways, such as, misidentification of precipitation echoes, false mesocyclone detections, and incorrect storm cell identification. With the dramatic growth of the wind power industry, this would only aggravate in the future. Since fully digital Phased Array Radar (PAR) is a promising candidate technology for the next generation of weather radars, evolutionary signal processing algorithms that make use of their capabilities should be investigated to mitigate WTC contamination. This article investigates the use of Space-Time Adaptive Processing (STAP) to mitigate WTC contamination with ground-based polarimetric PAR. First, a flexible wind turbine time-series signal simulator is developed to characterize the contamination signatures in the space-time domain. Then, a STAP algorithm that removes the contamination is presented and demonstrated on simulated data. Two digital radar back-end architectures are considered to evaluate the performance of the proposed algorithm. One with digital sub-array outputs the other one with fully digital outputs (i.e., element-level digital). Results indicate the the WTC spectrum has a characteristic structure in the space-time domain, and that biases induced in polarimetric weather variables can be more effectively mitigated using an fully digital PAR.

Space‐time adaptive processing algorithm based on hyper beamforming for ionospheric clutter suppression in small‐array high‐frequency surface wave radar

AbstractSmall‐array high‐frequency surface wave radar (HFSWR) is widely used to monitor maritime targets as it can be used to save on‐land resources. In small‐array HFSWR systems, the main lobe of the receiving angle spectrum is significantly broadened. In complex clutter backgrounds, an extremely wide beam severely influences clutter suppression performance; consequently, targets with a low signal‐to‐clutter ratio (SCR) may be eliminated, or the angle may be barely estimated. This study proposes a space‐time adaptive processing (STAP) algorithm based on hyper beamforming (HBF) to improve the clutter suppression performance of small‐array HFSWR. In addition, HBF can obtain more independent identical distributed training samples than the conventional beamforming; thus, the STAP algorithm can extract the clutter information with high accuracy in the covariance matrix estimation. Moreover, this study combines an efficient STAP algorithm with a joint domain localised (JDL) algorithm to improve clutter suppression. Based on the experimental results, the proposed HBF‐JDL algorithm performs satisfactorily and significantly improves the SCR. Moreover, HBF‐JDL is still applicable at lower SCRs of the target compared with JDL.

Autoencoder Neural Network-Based STAP Algorithm for Airborne Radar with Inadequate Training Samples

Clutter suppression is a key problem for airborne radar, and space-time adaptive processing (STAP) is a core technology for clutter suppression and moving target detection. However, in practical applications, the non-uniform time-varying environments including clutter range dependence for non-side-looking radar lead to the training samples being unable to satisfy the sample requirements of STAP that they should be independent identical distributed (IID) and that their number should be greater than twice the system’s degree of freedom (DOF). The lack of sufficient IID training samples causes difficulty in the convergence of STAP and further results in a serious degeneration of performance. To overcome this problem, this paper proposes a novel autoencoder neural network for clutter suppression with a unique matrix designed to be decoded and encoded. The main challenges are improving the accuracy of the estimation of the clutter-plus-noise covariance matrix (CNCM) for STAP convergence, designing the form of the data input to the network, and making the network successfully explored to the improvement of CNCM. For these challenges, the main proposed solutions include designing a unique matrix with a certain dimension and a series of covariance data selections and matrix transformations. Consequently, the proposed method compresses and retains the characteristics of the covariances, and abandons the deviations caused by the non-uniformity and the deficiency of training samples. Specifically, the proposed method firstly develops a unique matrix whose dimension is less than half of the DOF, meanwhile, it is based on a processing of the selected clutter-plus-noise covariances. Then, an autoencoder neural network with l2 regularization and the sparsity regularization is proposed for the unique matrix to be decoded and encoded. The training of the proposed autoencoder can be achieved by reducing the total loss function with the gradient descent iterations. Finally, an inverted processing for the autoencoder output is designed for the reconstruct ion of the clutter-plus-noise covariances. Simulation results are used to verify the effectiveness and advantages of the proposed method. It performs obviously superior clutter suppression for both side-looking and non-side-looking radars with strong clutter, and can deal with the insufficient and the non-uniform training samples. For these conditions, the proposed method provides the relatively narrowest and deepest IF notch. Furthermore, on average it improves the improvement factor (IF) by 10 dB more than the ADC, DW, JDL, and original STAP methods.

End-to-End Moving Target Indication for Airborne Radar Using Deep Learning

Moving target indication (MTI) based on space–time adaptive processing (STAP) has been widely used in airborne radar due to its ability for clutter suppression performance. However, the existing MTI methods suffer from the problems of insufficient training samples and low detection probability in a non-homogeneous clutter environment. To address these issues, this paper proposes a novel deep learning framework to improve target indication capability. First, combined with the problems of target indication caused by the non-homogeneous clutter, the clutter-plus-target training dataset was modeled by simulation, where various non-ideal factors, such as aircraft crabbing, array errors and internal clutter motion (ICM), were considered. The dataset considers various realistic situations, making the proposed method more robust. Then, a five-layer two-dimensional convolutional neural network (D2CNN) was designed and applied to learn the clutter and target characteristics distribution. The proposed D2CNN can predict the target with a high resolution to implement an end-to-end moving target indication (ETE-MTI) with a higher detection accuracy. In this D2CNN, the input was obtained by the clutter-plus-target angle-Doppler spectrum with a low-resolution estimated only by a few samples. The label was given by the target angle-Doppler spectrum with a high-resolution obtained by the target’s exact angle and Doppler. Thirdly, the proposed method used a few samples to improve the target indication and detection probability, which solved the problem of insufficient samples in the non-homogeneous clutter environments. To elaborate, the proposed method directly implements ETE-MTI without the support of the conventional STAP algorithm to suppress the clutter. The results verify the validity and the robustness of the proposed ETE-MTI with a few samples in the non-homogeneous and low signal-to-clutter ratio (SCR) environments.

The Study of the Possibility of Applying Parallel Programming to the Algorithms of Space-Time Adaptive Processing

The article presents the description, assumptions and subsequent steps of the space-time adaptive processing (STAP) algorithms used as a signal processing tool in radars. The possibilities of object detection using the Sample Matrix Inversion (SMI) and Data Domain Least Squares (DDLS) algorithms were compared and showned. The article shows the impact of the use of parallel programming on the computation time of both algorithms. The main aim of this study was to propose an efficient method for the real-time implementation of the STAP algorithm in airborne radar systems. The idea of using parallel programming in STAP, supported only by the preliminary research results presented above, gives a real chance for the casual implementation of the STAP algorithm in a radar operating in close to real time mode.

Adaptive Support-Driven Sparse Recovery STAP Method with Subspace Penalty

Detecting a moving target is an attractive topic in many fields, such as remote sensing. Space-time adaptive processing (STAP) plays a key role in detecting moving targets in strong clutter backgrounds for airborne early warning radar systems. However, STAP suffers serious clutter suppression performance loss when the number of training samples is insufficient due to the inhomogeneous clutter environment. In this article, an efficient sparse recovery STAP algorithm is proposed. First, inspired by the relationship between multiple sparse Bayesian learning (M-SBL) and subspace-based hybrid greedy algorithms, a new optimization objective function based on a subspace penalty is established. Second, the closed-form solution of each minimization step is obtained through the alternating minimization algorithm, which can guarantee the convergence of the algorithm. Finally, a restart strategy is used to adaptively update the support, which reduces the computational complexity. Simulation results show that the proposed algorithm has excellent performance in clutter suppression, convergence speed and running time with insufficient training samples.

A Novel Sparse Bayesian Space-Time Adaptive Processing Algorithm to Mitigate Off-Grid Effects

Space-time adaptive processing (STAP) algorithms based on sparse recovery (SR) have been researched because of their low requirement of training snapshots. However, once some portion of clutter is not located on the grids, i.e., off-grid problems, the performances of most SR-STAP algorithms degrade significantly. Reducing the grid interval can mitigate off-grid effects, but brings strong column coherence of the dictionary, heavy computational load, and heavy storage load. A sparse Bayesian learning approach is proposed to mitigate the off-grid effects in the paper. The algorithm employs an efficient sequential addition and deletion of dictionary atoms to estimate the clutter subspace, which means that strong column coherence has no effect on the performance of the proposed algorithm. Besides, the proposed algorithm does not require much computational load and storage load. Off-grid effects can be mitigated with the proposed algorithm when the grid-interval is sufficiently small. The excellent performance of the novel algorithm is demonstrated on the simulated data.

Robust Multiple-Measurement Sparsity-Aware STAP with Bayesian Variational Autoencoder

Due to the shortage of independent and identically distributed (i.i.d.) training samples, space−time adaptive processing (STAP) often suffers remarkable performance degradation in the heterogeneous clutter environment. Sparse recovery (SR) techniques have been introduced into STAP for the benefit of the drastically reduced training requirement, but they are incompletely robust for involving the tricky selection of hyper−parameters or the undesirable point estimation for parameters. Given this issue, we incorporate the Multiple−measurement Complex−valued Variational relevance vector machines (MCV) to model the space−time echoes and provide a Gibbs−sampling−based method to estimate posterior distributions of parameters accurately. However, the Gibbs sampler require quantities of iterations, as unattractive as traditional Bayesian type SR−STAP algorithms when the real−time processing is desired. To address this problem, we further develop the Bayesian Autoencoding MCV for STAP (BAMCV−STAP), which builds the generative model according to MCV and approximates posterior distributions of parameters with an inference network pre−trained off−line, to realize fast reconstruction of measurements. Experimental results on simulated and measured data demonstrate that BAMCV−STAP can achieve suboptimal clutter suppression in terms of the output signal to interference plus noise ratio (SINR) loss, as well as the attractive real−time processing property in terms of the convergence rate and computational loads.

An Efficient Sparse Bayesian Learning STAP Algorithm with Adaptive Laplace Prior

Space-time adaptive processing (STAP) encounters severe performance degradation with insufficient training samples in inhomogeneous environments. Sparse Bayesian learning (SBL) algorithms have attracted extensive attention because of their robust and self-regularizing nature. In this study, a computationally efficient SBL STAP algorithm with adaptive Laplace prior is developed. Firstly, a hierarchical Bayesian model with adaptive Laplace prior for complex-value space-time snapshots (CALM-SBL) is formulated. Laplace prior enforces the sparsity more heavily than Gaussian, which achieves a better reconstruction of the clutter plus noise covariance matrix (CNCM). However, similar to other SBL-based algorithms, a large degree of freedom will bring a heavy burden to the real-time processing system. To overcome this drawback, an efficient localized reduced-dimension sparse recovery-based space-time adaptive processing (LRDSR-STAP) framework is proposed in this paper. By using a set of deeply weighted Doppler filters and exploiting prior knowledge of the clutter ridge, a novel localized reduced-dimension dictionary is constructed, and the computational load can be considerably reduced. Numerical experiments validate that the proposed method achieves better performance with significantly reduced computational complexity in limited snapshots scenarios. It can be found that the proposed LRDSR-CALM-STAP algorithm has the potential to be implemented in practical real-time processing systems.

A Fast Space-Time Adaptive Processing Algorithm Based on Sparse Bayesian Learning for Airborne Radar.

Space-time adaptive processing (STAP) plays an essential role in clutter suppression and moving target detection in airborne radar systems. The main difficulty is that independent and identically distributed (i.i.d) training samples may not be sufficient to guarantee the performance in the heterogeneous clutter environment. Currently, most sparse recovery/representation (SR) techniques to reduce the requirement of training samples still suffer from high computational complexities. To remedy this problem, a fast group sparse Bayesian learning approach is proposed. Instead of employing all the dictionary atoms, the proposed algorithm identifies the support space of the data and then employs the support space in the sparse Bayesian learning (SBL) algorithm. Moreover, to extend the modified hierarchical model, which can only apply to real-valued signals, the real and imaginary components of the complex-valued signals are treated as two independent real-valued variables. The efficiency of the proposed algorithm is demonstrated both with the simulated and measured data.

Cascaded Least Square Algorithm for Strong Clutter Removal in Airborne Passive Radar

Owing to the continuous random and nonperiodic characteristics of the passive signal, the random range sidelobe coupling (RRSC) effects of the strong clutter (i.e., the direct path signal and the strong multipath signal) will exacerbate the performance of space-time adaptive processing (STAP) algorithm in airborne passive radar (APR). This article analyzes the influence of RRSC caused by strong clutter on detection range cell of interest and illustrates that strong clutter should be suppressed before applying the STAP algorithm. A cascaded least square (CLS) algorithm based on the directional dependence of clutter Doppler frequency is proposed for side-looking APR, where the first least square (LS) algorithm is performed to achieve the amplitude estimation of the Doppler-shift echo signal, and the channel amplitude and phase error correction factor can be obtained by the estimated amplitude information of the direct patch signal and the APR geometric configuration. The second LS is employed to further estimate the amplitude information of the strong clutter, and the resulting weight vector can be utilized for clutter cancelation. To make the CLS algorithm more practical, a batch version of the CLS (CLS-B) algorithm is proposed in this article. The advantage of the method is that it cannot only cancel clutter along the clutter ridge but also effectively prevent the suppression of targets falling in the clutter Doppler band. In addition, the proposed CLS algorithm performs well in the presence of the channel amplitude and phase error. A series of simulations are conducted to test the proposed algorithms.

A Novel Dimension-Reduced Space–Time Adaptive Processing Algorithm for Spaceborne Multichannel Surveillance Radar Systems Based on Spatial–Temporal 2-D Sliding Window

When an early warning radar installed in a spaceborne platform works in a down-looking mode to detect a low-altitude flying target, the severely broadened main-lobe clutter cannot be ignored, which will cause the deterioration of the moving target detection capability. To deal with this problem, a space–time adaptive processing (STAP) technique is proposed for effective clutter suppression based on the spatial–temporal 2-D joint filtering. However, the full-dimensional optimal STAP encounters the challenges of high computational complexity and large training sample requirement. Therefore, the dimension-reduced STAP technique becomes necessary. This article proposes a novel dimension-reduced STAP algorithm based on spatial–temporal 2-D sliding window processing. First, several sets of spatial–temporal data are obtained by using spatial–temporal 2-D sliding window. Then, for each set of data, the 2-D discrete Fourier transform is performed to transform the echo data into the angle-Doppler domain. Finally, jointly adaptive processing is performed to realize the clutter suppression. Compared with the conventional STAP algorithms, the improvements of this method over the existing methods are: 1) the proposed method requires fewer training samples due to the 2-D localization processing and 2) the proposed method can obtain the better clutter suppression performance with lower computational complexity. The feasibility and effectiveness of the proposed algorithm are verified by both simulated and real-measured multichannel surveillance radar data.

A General Framework for Slow and Weak Range-Spread Ground Moving Target Indication Using Airborne Multichannel High-Resolution Radar

Airborne multichannel high-resolution radar (HRR)-ground moving target indication (GMTI) is of great significance to wide-area surveillance, traffic monitoring and target recognition. The Aerospace Information Research Institute, Chinese Academy of Sciences, produced an advanced airborne digital array radar with high resolution and conducted an experiment with slow and weak cooperative moving targets in 2021. In this paper, an overall processing framework for target detection, parameter estimation and target tracking using this system is introduced. For HRR detection, the echo energy of targets is spread into multiple range units, so-called range-spread targets; thus, using detectors designed for point-like targets will severely degrade the detection performance, especially for slow and weak targets. To address the adaptive detection of such range-spread targets embedded in Gaussian clutter with an unknown covariance matrix, a novel two-step generalized space-time adaptive processing (GSTAP) algorithm is proposed, which offers an enhanced clutter suppression capability compared with natural competitors. Moreover, a tracking method is implemented in the range-Doppler domain to avoid track loss caused by azimuth relocation error and reject discrete false alarms. Both simulation and experimental results are presented to demonstrate the effectiveness of the proposed method and provide a paradigm for further research.

A Clutter Suppression Algorithm via Weighted ${\ell }_2{\rm{ - norm}}$ Penalty for Airborne Radar

In this letter, to improve the performance of the space-time adaptive processing (STAP) filter with finite training samples, a novel algorithm with multiple measurement vectors (MMV) based on sparse recovery (SR) is proposed. Compared with traditional SR STAP algorithms, we utilize the knowledge of Capon spectrum to design a weighted <inline-formula><tex-math notation="LaTeX">${\ell }_2{\rm{ - norm}}$</tex-math></inline-formula> penalty which can better approximate the original <inline-formula><tex-math notation="LaTeX">${\ell }_0{\rm{ - norm}}$</tex-math></inline-formula>. Besides, the proposed algorithm has fast convergence performance and closed-form analytic solution in each iteration. Simulation results demonstrate the effectiveness and great performance of the proposed method.

Multi-Task Learning STAP via Spatial Smoothness and Group Sparsity Regularizations

In practical applications, limited independent and identically distributed training snapshots brings a serious challenge in space-time adaptive processing (STAP), especially in the nonhomogeneous environments. Motivated by the significant spatial smoothness and sparsity commonality of weight vectors among related STAP tasks, we propose a novel STAP algorithm based on multi-task learning. In the proposed algorithm, the weight vectors corresponding to neighboring range bins of interest are kept consistent, and all weight vectors are constrained to share a common feature. Then, an alternating direction method of multipliers (ADMM) is used to solve the proposed algorithm, and the convergence of the algorithm is guaranteed. In addition, in case that the feature matrix is unknown or we want to learn a better feature matrix so that the associations among STAP tasks can be enhanced, we also provide an extension of the proposed algorithm to jointly optimize the feature matrix and weight matrix. Simulation results demonstrate the effectiveness of the proposed strategies.

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.