Radar Space-time Adaptive Processing Research Articles

Expected likelihood approach for determining constraints in covariance estimation

Recent covariance estimation methods for radar space-time adaptive processing exploit practical constraints such as the rank of clutter subspace and the condition number of disturbance covariance to estimate accurate covariance even when training is not generous. While rank and condition number are very effective constraints, often practical nonidealities make it difficult to know them precisely using physical models. Therefore, we propose a method to determine constraints in covariance estimation for radar space-time adaptive processing via an expected likelihood approach. We analyze three cases of constraints: 1) a rank constraint, 2) both rank and noise power constraints, and 3) a condition number constraint. In each case, we formulate precise constraint determination as an optimization problem. For each of the three cases, we derive new analytical results which allow for computationally efficient, practical ways of determining these constraints with formal proofs. Through experimental results from a simulation model and the KASSPER data set, we show that the estimator with optimal constraints obtained by the expected likelihood approach outperforms state-of-the-art alternatives.

Joint Design of Transmit Waveforms and Receive Filters for MIMO Radar Space-Time Adaptive Processing

This paper considers the joint design of transmit waveforms and receive filters for airborne multiple-input-multiple-output (MIMO) radar systems. The aim is to maximize the output signal-to-interference-plus-noise ratio (SINR) such that we can achieve enhanced detection performance for a slow-moving target that might be obscured by clutter and jamming. We devise a cyclic algorithm to tackle the non-convex joint design problem. Considering practical implementation issues, we extend the algorithm to deal with constrained designs (i.e., the design of waveforms under a constant-envelope constraint and a similarity constraint, respectively). The convergence of all the devised algorithms is guaranteed. We provide several numerical examples to demonstrate the effectiveness of the proposed algorithms.

Space-Time Adaptive Processing With Vertical Frequency Diverse Array for Range-Ambiguous Clutter Suppression

A high-pulse-repetition-frequency (PRF) radar can handle the high Doppler frequencies of clutter echoes received by a fast-moving airborne radar. However, high-PRF radar causes range ambiguity. In addition, the clutter is range dependent when the airborne radar works in a forward-looking geometry. The range ambiguity and range dependence will lead to severe performance degradation of the traditional space-time adaptive processing (STAP) methods. In this paper, a vertical frequency diverse array (FDA), which applies frequency diversity in the vertical of a planar array, is explored to circumvent the range ambiguity problem in STAP radar. A range-ambiguous clutter suppression approach is devised, which consists of vertical spatial frequency compensation and pre-STAP filtering. In the vertical-FDA radar, the vertical spatial frequency depends not only on the depression angle but also on the slant range. By using this characteristic, the range-ambiguous clutter can be separated in the vertical spatial frequency domain, and then, clutter suppression is achieved for each separated range region. As a result, both problems of range ambiguity and range dependence are solved. Simulation results are provided to demonstrate the effectiveness of the proposed method.

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.

An Efficient Adaptive Angle-Doppler Compensation Approach for Non-Sidelooking Airborne Radar STAP.

In this study, the effects of non-sidelooking airborne radar clutter dispersion on space-time adaptive processing (STAP) is considered, and an efficient adaptive angle-Doppler compensation (EAADC) approach is proposed to improve the clutter suppression performance. In order to reduce the computational complexity, the reduced-dimension sparse reconstruction (RDSR) technique is introduced into the angle-Doppler spectrum estimation to extract the required parameters for compensating the clutter spectral center misalignment. Simulation results to demonstrate the effectiveness of the proposed algorithm are presented.

Overview of Space-Time Adaptive Processing for Airborne Multiple-Input Multiple-Output Radar

Multiple-Input Multiple-Output (MIMO) radar is an emerging radar system that is of great interest to military and academic organizations due to its advantages and extensive applications. The main purpose of Space-Time Adaptive Processing (STAP) is to suppress ground clutter and realize Ground Moving Target Indication (GMTI). Nowadays, STAP technology has been extended to MIMO radar systems, and MIMO radar STAP has quickly become a hot research topic in international radar fields. This paper provides a detailed description of the extension and significant meaning of MIMO-STAP, and gives an overview of the current research status of clutter modeling, analysis of clutter Degree Of Freedom (DOF), reduced-dimension (reduced-rank) processing, simultaneous suppression of clutter plus jamming, non-homogeneous environment processing, and so on. The future perspective for the development of MIMO-STAP technology is also discussed.

Improving EFA-STAP performance using persymmetric covariance matrix estimation

This paper deals with the estimation of the clutter covariance matrix in airborne radar space-time adaptive processing (STAP). Based on the persymmetry property, a novel STAP method, referred to as persymmetric extended factored processing (Per-EFA), is derived, which can make a more intensive use of the secondary data and improve the STAP performance in training-limited scenarios. Simulation results demonstrate the effectiveness of this method.

Space-Time-Range Adaptive Processing for Airborne Radar Systems

Conventional phased-array space-time adaptive processing (STAP) radar combines angle and Doppler domains to realize clutter suppression. However, it suffers from severe performance degradation in electronic countermeasures scenarios, especially in the presence of mainbeam deceptive jamming. In this paper, a multiple-input multiple-output (MIMO) STAP radar is studied with a frequency diverse array (FDA) acting as the transmit array, which is referred to as FDA-MIMO STAP radar. FDA can provide controllable degrees of freedom in both range and angle domains. As a result, in FDA-MIMO STAP radar, the target can be discriminated from the clutter and jamming in joint range-angle-Doppler domains. By combining the range, angle and Doppler domains in FDA-MIMO STAP radar, a space-time-range adaptive processing method is proposed based on subspace projection technique. Simulation results demonstrate the effectiveness of the proposed approach in suppressing the clutter and jamming.

Student research highlight estimation of structured covariance matrices for radar STAP

Radar systems using multiple antenna elements that coherently process multiple pulses offer significant benefits, such as overcoming the directivity and resolution limits of a single sensor. Specifically, joint adaptive processing in the spatial and temporal domains called space-time adaptive processing (STAP) creates an ability to suppress interference signals, while simultaneously preserving gain on the desired signal. For STAP implementation, the interference statistics, in particular, the covariance matrix of the disturbance or interference, must be estimated from target-free training data. Therefore, the disturbance covariance estimation plays a pivotal role in radar target detection for radar STAP.

Computationally efficient toeplitz approximation of structured covariance under a rank constraint

Disturbance covariance estimation is a centrally important problem in radar space-time adaptive processing (STAP). Because training is invariably scarce, estimators that exploit inherent structure and physical radar constraints are needed in practice. This paper develops a new computationally efficient estimator that obtains a Toeplitz approximation of the structured interference covariance under a rank constraint. Previous work has shown that exact maximum likelihood (ML) estimation of Toeplitz covariance matrix has no closed-form solution, and most versions of this problem result in iterative estimators that are computationally expensive. Our proposed solution focuses on a computationally efficient approximation and involves a cascade of two closed-form solutions. First, we obtain the rank-constrained ML estimator whose merits have recently been established firmly for radar STAP. The central contribution of this paper is the rank-preserving Toeplitz approximation, which we demonstrate can be modeled as an equality-constrained quadratic program and also admits a closed form. Extensive performance evaluation on both simulated and knowledge-aided sensor signal processing and expert reasoning data confirms that the proposed estimator yields unbeatable performance for radar STAP under the previously stated conditions of rank and Toeplitz constraints.

Rank-Constrained Maximum Likelihood Estimation of Structured Covariance Matrices

This paper develops and analyzes the performance of a structured covariance matrix estimate for the important practical problem of radar space-time adaptive processing in the face of severely limited training data. Traditional maximum likelihood (ML) estimators are effective when training data are abundant, but they lead to poor estimates, degraded false alarm rates, and detection loss in the realistic regime of limited training. The problem is exacerbated by recent advances, which have led to high-dimensionalof the observations arising from increased antenna elements, as well as higher temporal resolution (time epochs and finally=). This work addresses the problem by incorporating constraints in the ML estimation problem obtained from the geometry and physics of the airborne phased array radar scenario. In particular, we exploit the structure of the disturbance covariance and, importantly, knowledge of the clutter rank to derive a new rank-constrained maximum likelihood (RCML) estimator of clutter and disturbance covariance. We demonstrate that despite the presence of the challenging rank constraint, the estimation can be transformed to a convex problem and derive closed-form expressions for the estimated covariance matrix. Performance analysis using the knowledge-aided sensor signal processing and expert reasoning data set (where ground truth covariance is made available) shows that the proposed estimator outperforms state-of-the-art alternatives in the sense of a higher normalized signal-to-interference and noise ratio. Crucially, the RCML estimator excels for low training, including the notoriously difficult regime of K≤N training samples.

On Clutter Sparsity Analysis in Space–Time Adaptive Processing Airborne Radar

To have a further understanding of the recently developed space-time adaptive processing (STAP) methods based on sparse representation (SR-STAP), this letter details the clutter sparsity observed by STAP radar systems. First, we review the principle and discuss the existing problems about clutter sparsity of the SR-STAP-type algorithms. Then, a theoretical analysis on clutter sparsity for a side-looking uniform linear array with constant pulse repetition frequency, constant velocity, and no crab is performed. Some important conclusions are obtained, and simulations are used to validate the correctness of them.

Local degrees of freedom of clutter for airborne space–time adaptive processing radar with subarrays

Space–time adaptive processing (STAP) is an advanced technique for airborne radar to mitigate clutter and detect moving targets effectively. Based on adaptive radar theory, the degrees-of-freedom of a STAP processor should be larger than that of a clutter. In this study, the local degrees-of-freedom (LDOF) of clutter for reduced-dimensional STAP (RD-STAP) methods with subarray configurations are studied. The LDOF formulas are proposed and verified by simulations. With these formulas, the LDOFs of clutter will collapse under certain radar configurations, which are favourable for clutter mitigation. Therefore these formulas could be used as guidance for STAP radar to choose appropriate system parameters and processing methods.

Three-dimensional reduced-dimension transformation for MIMO radar space–time adaptive processing

In this paper, a spatial–temporal filter with three-dimensional (3D) cascaded configuration is proposed for multi-input multi-output (MIMO) radar space–time adaptive processing (STAP) based on reduced-dimension transformation. The 3D weight vector which is decomposed into the Kronecker product of transmitting, receiving and temporal weight vectors can be efficiently obtained by the proposed tri-iterative algorithm (TRIA). It is shown that the proposed approach can significantly reduce the computational burden and training-data requirement. The effectiveness of the proposed algorithm is demonstrated via the numerical experiments as compared with the other methods.

Geometry-Induced Range-Dependence Compensation for Bistatic STAP with Conformal Arrays

Radar space-time adaptive processing (STAP) is a well-suited technique to detect slow-moving targets in the presence of a strong interference background. We consider STAP for a radar operating in a bistatic radar configuration and collecting returns with a conformal antenna array (CAA). The statistics of the secondary data snapshots used to estimate the optimum weight vector are not identically distributed with respect to range, thus preventing the STAP processor from achieving its optimum performance. The compensation of the range-dependence (RD) requires the knowledge of the locus of the clutter signature. We use a new RANSAC-based method for estimating this locus or, equivalently, the flight configuration parameters. Based on this knowledge, we perform an RD compensation of the snapshots to obtain an accurate estimate of the clutter covariance matrix. End-to-end performance analysis in terms of signal-to-inference-plus-noise ratio loss shows that our method yields promising performance.

Taylor series expansions for airborne radar space-time adaptive processing

Space-time adaptive processing (STAP) for range-dependent clutter rejection in airborne radar is considered. Indeed, radar antenna architectures or configurations that are different from the conventional uniform linear antenna array (ULA) and side-looking (SL) configuration have consequences on the clutter properties. The authors here investigate the use of Taylor series expansions (TSEs) of the space–time covariance matrix in the classical sample matrix inversion (SMI) STAP method in order to mitigate the range non-stationarity of the clutter and they compare it to the derivative-based updating (DBU) already proposed in the literature. The authors also propose a new algorithm based on a TSE of the clutter plus noise subspace in conjunction with the eigencanceler-based (EC) STAP, which improves the performance in term of signal-to-interference plus noise ratio (SINR) loss, compared to the DBU method. In this study, the particular cases of a ULA and a uniform circularly curved antenna (UCCA) array in SL and non-SL monostatic configurations as well as a ULA in some bistatic configurations are considered for the test and the comparison of the presented algorithms.

Sensitivity of MIMO STAP Radar with Waveform Diversity

Space-time adaptive processing (STAP) is an effective method adopted in airborne radar to suppress ground clutter. Multiple-input multiple-output (MIMO) radar is a new radar concept and has superiority over conventional radars. Recent proposals have been applying STAP in MIMO configuration to the improvement of the performance of conventional radars. As waveforms transmitted by MIMO radar can be correlated or uncorrelated with each other, this article develops a unified signal model incorporating waveforms for STAP in MIMO radar with waveform diversity. Through this framework, STAP performances are expressed as functions of the waveform covariance matrix (WCM). Then, effects of waveforms can be investigated. The sensitivity, i.e., the maximum range detectable, is shown to be proportional to the maximum eigenvalue of WCM. Both theoretical studies and numerical simulation examples illustrate the waveform effects on the sensitivity of MIMO STAP radar, based on which we can make better trade-off between waveforms to achieve optimal system performance.

Code Design for Radar STAP via Optimization Theory

In this paper, we deal with the problem of constrained code optimization for radar space-time adaptive processing (STAP) in the presence of colored Gaussian disturbance. At the design stage, we devise a code design algorithm complying with the following optimality criterion: maximization of the detection performance under a control on the regions of achievable values for the temporal and spatial Doppler estimation accuracy, and on the degree of similarity with a pre-fixed radar code. The resulting quadratic optimization problem is solved resorting to a convex relaxation that belongs to the semidefinite program (SDP) class. An optimal solution of the initial problem is then constructed through a suitable rank-one decomposition of an optimal solution of the relaxed one. At the analysis stage, we assess the performance of the new algorithm both on simulated data and on the standard challenging the Knowledge-Aided Sensor Signal Processing and Expert Reasoning (KASSPER) datacube.

Foundation for mitigating range dependence in radar space-time adaptive processing

The problem of detecting slow-moving targets using a space-time adaptive processing (STAP) radar is addressed. The determination of the optimum interference-rejection weights at each range is based on snapshots at neighbouring ranges. However, in virtually all bistatic configurations or/and when using conformal antenna arrays (CAA), snapshot statistics are range dependent, which results in poor detection performance. To address this issue, a foundation for range-dependence compensation in STAP in the case of Gaussian interference and noise is proposed. The realistic case where received snapshots are the only source of information for mitigating the range dependence is considered. To illustrate the usefulness of the proposed foundation, this foundation is used to design a method to adaptively compensate for range dependence in a challenging situation, that is, for a radar using a CAA and operating in a bistatic configuration.

Handling partially calibrated conformal antenna arrays in range–dependence compensation for airborne bistatic space–time adaptive processing radar

The authors consider space-time adaptive processing (STAP) when the radar returns are recorded by a conformal antenna array (CAA). The statistics of the secondary data snapshots used to estimate the optimum weight vector are not identically distributed with respect to range, thus preventing the customary STAP processor from achieving its optimum performance. The compensation of the range dependence of the secondary data requires precise knowledge of the array response for any direction of arrival (DOA), and, thus, of the spatial steering vectors (SVs). The authors propose a novel registration-based range-dependence compensation algorithm that gives an accurate estimate of the interference-plus-noise covariance matrix under the hypotheses that calibrated spatial SVs are available only for a small set of DOAs, and that the errors in the model giving the true spatial SV for each DOA are DOA dependent. The performance in terms of signal-to-interference-plus-noise ratio loss is promising.