Space-time Adaptive Processing Filter Research Articles

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.

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.

Joint design of transmit beamspace and reduced‐dimension receiver filter for MIMO radar STAP

In this article, the problem of the transmit beamspace (TB) matrix design in multiple-input multiple-output (MIMO) radar is considered. To reduce the computational burden and to focus the energy within optimal spatial sector, a joint design method of the TB matrix and a reduced-dimension space-time adaptive processing (STAP) filter is proposed based on the maximum signal-to-clutter-plus-noise ratio (SCNR). Firstly, the signal model of the reduced-dimension STAP for TB-based MIMO radar is established. Then, using the maximum SCNR as the design metric, the joint design model of the TB matrix and the reduced-dimension STAP filter is presented. Furthermore, the cyclic optimisation method is exploited to deal with the non-convex joint design problem with the energy constraint. Finally, simulation experiments demonstrate the joint design method of the TB matrix and the STAP filter not only has better output SCNR performance but also owns lower computational burden when compared with the other existing methods.

Data‐dependent reduced‐dimension STAP

Space-time adaptive processing (STAP) is supposed to be a key technique for detection of slow-moving targets in airborne radar applications. To overcome the difficulties of obtaining lots of independent and identical distributed secondary data samples, many sub-optimal STAP algorithms are proposed such as reduced-dimension STAP, reduced-rank STAP, or the sparse-recovery-based STAP. In this study, based on the observation that the STAP filter weight is sparse, a novel clutter-dependent reduced-dimension STAP is proposed. In the proposed approach, the sparse feature of the weight vector in the angular-Doppler domain is utilised to design the reduced-dimension transform matrix. Simulation results show that the output signal-to-interference-plus-noise ratio loss is just 3 dB with only one secondary data sample in the extremely heterogeneous clutter environments.

A Novel Two-Level Nested STAP Strategy for Clutter Suppression in Airborne Radar

Nested arrays have been studied recently in array signal processing field because of their closed-form expressions for the sensor locations and achievable degrees of freedom (DOFs). In this paper, the concept of nesting is further extended to space-time adaptive processing (STAP). Different from the traditional uniform-STAP method that calculates the clutter plus noise covariance matrix (CNCM) and performs the STAP filter direct using the data snapshots collected from the uniform linear array (ULA) and the transmitting pulses with uniform pulse repetition interval (PRI), we present a new optimum two-level nested STAP (O2LN-STAP) strategy which employs an optimum two-level nested array (O2LNA) and an optimum two-level nested PRI (O2LN-PRI) to exploit the enhanced DOFs embedded in the space-time O2LN structure. Similar to the difference coarray perspective, we first construct a virtual space-time snapshot from the direct covariance matrix of the received signals. Then, a new CNCM estimation corresponding to the virtual space-time snapshot can be computed by the spatial-temporal smoothing technique for STAP filter. Furthermore, the comparative simulations and analyses with the traditional uniform-STAP and the recently reported coprime-STAP are carried out to verify the effectiveness of the O2LN-STAP approach.

A Fast Iterative Three-Dimensional Joint Domain Localized Method in Airborne MIMO Radar

In general, space–time adaptive processing (STAP) can achieve excellent clutter suppression and moving target detection performance in the airborne multiple-input multiple-output (MIMO) radar for the increasing system degrees of freedom. However, the performance improvement is accompanied by the dramatic increase in computational cost and training sample demanding. Though reduced-dimensional STAP can alleviate these problems, its performance will still be heavily degraded for insufficient training sample support, which will frequently be met in the airborne MIMO radar. Hence, in this work, by utilizing the special structure of the MIMO radar signal, the STAP filter coefficients of the conventional joint domain localized processing method are constrained as the Kronecker product form so that the computational cost and training sample demanding are further reduced. Then, the tri-iterative algorithm is applied to find the desired solution. Simulation results demonstrate the effectiveness of the proposed method.

Deterministic-aided single dataset STAP method based on sparse recovery in heterogeneous clutter environments

Traditional space-time adaptive processing (STAP) usually needs many independent and identically distributed (i.i.d) training datasets for estimating clutter covariance matrix (CCM). But this requirement is hardly satisfied in the heterogeneous clutter environments, which lead to an inaccurate estimation of CCM and accordingly degrade the performance of STAP significantly. To improve the performance of STAP in heterogeneous environments, a novel deterministic-aided (DA) single dataset STAP method based on sparse recovery technique (SR) is proposed in this paper. This presented algorithm exploits the property that the clutter components of side-looking airborne or spaceborne radar are distributed along the clutter ridge to estimate the CCM of the cell under test (CUT) without any secondary training data. The new method only uses a single CUT data to acquire a high-resolution angle-Doppler power spectrum using sparse recovery (SR) approach and then employs a new adaptive deterministic-aided generalized inner product (GIP) algorithm to recognize and select the clutter components in the CUT angle-Doppler power spectrum automatically. Subsequently, the CCM, which is used to construct the weights of STAP filter, can be effectively estimated by the selected clutter components to fulfill the final STAP filter processing. Simulation results verify the effectiveness of the proposed detection method.

Space–time adaptive processing by enforcing sparse constraint on beam‐Doppler patterns

In this Letter, the author proposes a novel space–time adaptive processing (STAP) algorithm by enforcing sparse constraint on the beam-Doppler patterns for clutter mitigation when the number of training data is limited. By exploiting the sparsity of the beam-Doppler patterns of the STAP filter, the proposed algorithm formulates the filter design as a mixed l 2-norm and l 1-norm minimisation problem. Moreover, the proposed algorithm develops an adaptive approach to update the regularisation parameter. Simulation results illustrate that the proposed algorithm outperforms the traditional STAP algorithms in a limited sample support.

Thinned knowledge‐aided STAP by exploiting structural covariance matrix

The authors propose a thinned knowledge-aided space–time adaptive processing (STAP) scheme based on structural prior information of the clutter covariance matrix (CCM). Due to the low-rank Toeplitz-block-Toeplitz structure of the CCM, the CCM can be expressed by a series of basis matrices on the clutter ridge. In contrast to the expression based on the Vandermonde decomposition of the CCM, this expression can avoid searching of the clutter subspace. This expression also allows reducing the dimension of STAP and estimating the CCM with compressed data. Based on this expression, the authors derive a closed-form CCM estimate using a modified generalised least squares (GLS) method, and the proposed estimator is unbiased, consistent and more asymptotically efficient than the conventional GLS method. We derive the average signal-to-clutter-noise ratio loss (SCNRL) of the STAP filter using the proposed CCM estimates. Exploiting the prior structural information of the CCM can enhance the STAP performance with a limited sample size, and a lower compression rate can achieve more improvement. Finally, a unified framework is proposed for covariance estimation and SCNRL analysis when structural information of the CCM is exploited. Simulations also validate these results.

Clutter suppression algorithm based on fast converging sparse Bayesian learning for airborne radar

Adapting the space-time adaptive processing (STAP) filter with finite number of secondary data is of particular interest for airborne phased-array radar clutter suppression. Sparse representation (SR) technique has been introduced into the STAP framework for the benefit of drastically reduced training requirement. However, most SR algorithms need the fine tuning of one or more user parameters, which affect the final results significantly. Sparse Bayesian learning (SBL) and multiple sparse Bayesian learning (M-SBL) are robust and user parameter free approaches, but they converge quite slowly. To remedy this limitation, a fast converging SBL (FCSBL) approach is proposed based on Bayesian inference along with a simple approximation term, then, it is extended to the multiple measurement vector case, and the resulting approach is termed as M-FCSBL. To improve the performance of STAP in finite secondary data situation, the M-FCSBL is utilized to estimate the clutter plus noise covariance matrix (CCM) from a limited number of secondary data, and then the resulting CCM is adopted to devise the STAP filter and suppress the clutter. Numerical experiments with both simulated and Mountain-Top data are carried out. It is shown that the proposed algorithm has superior clutter suppression performance in finite secondary data situation.

Space time adaptive processing algorithm for multiple‐input–multiple‐output radar based on Nyström method

In this study, a new space-time adaptive processing (STAP) algorithm based on Nystrom (Nystrom-STAP) method is proposed to adaptively suppress the clutter and jammer in multiple-input-multiple-output (MIMO) radar system. The proposed method can reduce the number of training data and computation complexity with less performance loss. In the algorithm, by exploiting the low-rank characteristic with Nystrom extension strategy and column sampling technique, the Nystrom-based covariance estimator is obtained to approximate the clutter subspace with high accuracy, and it only need small clutter homogenous training data support. Then, combining block-diagonal feature of the jammer covariance matrix and the low-rank property of clutter subspace, the STAP filter can be formed by the inversions of low dimension matrices, which has less computation complexity. In order to further improve the convergence performance of the proposed method, with the help of adaptive displaced phase centre array technique, the reduced-rank Nystrom approaches are proposed. Simulation results demonstrate that the proposed methods exhibit better signal-to-interference-plus-noise ratio and probability of detection performance than conventional STAP algorithms with fewer training data and lower computation complexity.

L 1 ‐regularised joint iterative optimisation space‐time adaptive processing algorithm

In this study, two novel joint iterative optimisation space-time adaptive processing (STAP) algorithms are proposed based on L 1-regularised for airborne radar. Both of them are implemented in generalised sidelobe canceller (GSC) architecture. When the rank of the interference covariance matrix is far fewer than the system degrees of freedom, the STAP filter weight will be sparse. In this case, a sparse constraint is further imposed to the minimum variance criterion of GSC. To solve this optimisation problem, a joint iterative recursive least squares (RLS) algorithm (L 1-JI-RLS) and a joint iterative least mean square (LMS) algorithm (L 1-JI-LMS), both of which are based on L 1-regularised, are proposed. The L 1-JI-RLS algorithm achieves the minimum output power by adjusting the penalty parameter and filter weight adaptively, while the L 1-JI-LMS algorithm does it by adjusting the penalty parameter, step and filter weight adaptively. The computational complexity of the L 1-JI-LMS algorithm is far lower than the conventional and some sparse STAP algorithms. Monte Carlo experiments validate that both the L 1-JI-RLS and L 1-JI-LMS algorithms outperform other L 1-based and reduced-rank STAP algorithms, such as a faster convergence rate, improved output signal-to-interference-plus-noise-ratio and target detection performance.

Waveform Design for Radar STAP in Signal Dependent Interference

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, non-convex optimization problem, Nevertheless, it is however shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of: a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP but the primary bottleneck is the computational complexity of the algorithms.

Exploiting persymmetry for low-rank Space Time Adaptive Processing

Reducing the number of secondary data used to estimate the Covariance Matrix (CM) for Space Time Adaptive Processing (STAP) techniques is still an active research topic. Within this framework, the Low-Rank (LR) structure of the clutter is well-known and the corresponding LR STAP filters have been shown to exhibit a smaller Signal Interference plus Noise Ratio (SINR) loss than classical STAP filters, only 2r secondary data (where r is the clutter rank) instead of 2m (where m is the data size) are required to reach the classical 3dB SNR loss. By using other features of the radar system, other properties of the CM can be exploited to further reduce the number of secondary data; this is the case for active systems using a symmetrically spaced linear array with constant pulse repetition interval, which results in a persymmetric structure of the noise CM. In this context, we propose to combine this property of the CM and the LR structure of the clutter to perform CM estimation. In this paper, the resulting STAP filter is shown, both theoretically and experimentally, to exhibit good performance with fewer secondary data; 3dB SINR Loss is achieved with only r secondary data.

Adaptive clutter suppression based on iterative adaptive approach for airborne radar

To improve the performance of the recently developed weighted least-squares-based iterative adaptive approach (IAA) in space–time adaptive processing (STAP) for weak or slow targets detection, we propose a novel IAA scheme to adaptively suppress the ground clutter by using the secondary training data (STD). Especially, we use the IAA to estimate the clutter plus noise covariance matrix from a very small number of STD. The resulting clutter plus noise covariance matrix can be utilized to form the STAP filter and then suppress the clutter. To reduce the computational complexity of the IAA, we exploit the sparsity of large clutter components in the angle-Doppler image and develop a modified IAA algorithm employing a soft-thresholding to adaptively determine the entries of each iteration that should be updated. Simulation results show that our proposed scheme outperforms the conventional IAA scheme over weak or slow targets detection and the modified IAA algorithm exhibits a comparable or even a better performance than the IAA algorithm but a lower computational complexity.

$L_1$-Regularized STAP Algorithms With a Generalized Sidelobe Canceler Architecture for Airborne Radar

In this paper, we propose novel l1-regularized space-time adaptive processing (STAP) algorithms with a generalized sidelobe canceler architecture for airborne radar applications. The proposed methods suppose that a number of samples at the output of the blocking process are not needed for sidelobe canceling, which leads to the sparsity of the STAP filter weight vector. The core idea is to impose a sparse regularization (l1-norm type) to the minimum variance criterion. By solving this optimization problem, an l1-regularized recursive least squares (l1-based RLS) adaptive algorithm is developed. We also discuss the SINR steady-state performance and the penalty parameter setting of the proposed algorithm. To adaptively set the penalty parameter, two switched schemes are proposed for l1-based RLS algorithms. The computational complexity analysis shows that the proposed algorithms have the same complexity level as the conventional RLS algorithm (O((NM)2)), where NM is the filter weight vector length), but a significantly lower complexity level than the loaded sample covariance matrix inversion algorithm (O((NM)3)) and the compressive sensing STAP algorithm (O((NsNd)3), where N8Nd >; NM is the angle-Doppler plane size). The simulation results show that the proposed STAP algorithms converge rapidly and provide a SINR improvement using a small number of snapshots.

Doppler compensation in forward-looking STAP radar

For air- and spaceborne MTI radar the clutter Doppler frequency depends on range for all array geometries other than linear sidelooking. This applies particularly to forward-looking arrays. The range dependence of the clutter Doppler causes specific problems in clutter rejection through STAP (space–time adaptive processing) techniques. One aspect is the lack of training data required for adapting the STAP filter. Another aspect is that the STAP filter becomes range dependent. A technique for compensating for the range dependence is proposed. The efficiency of the method is verified by use of clutter data measured with the multichannel radar AER II (airborne experimental radar).