Reduced-rank Space-time Adaptive Processing Research Articles

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.

A Single-Dataset-Based Pre-Processing Joint Domain Localized Algorithm for Clutter-Suppression in Shipborne High-Frequency Surface-Wave Radar.

Due to the motion of the platform, the spectrum of first-order sea clutter will widen and mask low-velocity targets such as ships in shipborne high-frequency surface-wave radar (HFSWR). Limited by the quantity of qualified training samples, the performance of the generally used clutter-suppression method, space–time adaptive processing (STAP) degrades in shipborne HFSWR. To deal with this problem, an innovative training sample acquisition method is proposed, in the area of joint domain localized (JDL) reduced-rank STAP. In this clutter-suppression method, based on a single range of cell data, the unscented transformation is introduced as a preprocessing step to obtain adequate homogeneous secondary data and roughly estimated clutter covariance matrix (CCM). The accurate CCM is calculated by integrating the approximate CCM of different range of cells. Compared with existing clutter-suppression algorithms for shipborne HFSWR, the proposed approach has a better signal-to-clutter-plus-noise ratio (SCNR) improvement tested by real data.

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.

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.

Reduced-Rank STAP for Slow-Moving Target Detection by Antenna-Pulse Selection

Space-time adaptive processing (STAP) is an effective strategy for clutter suppression in airborne radar systems. Limited training data, high computational load and the heterogeneity of training data constitute the main challenges in STAP. In this letter, we propose a new detection strategy based on selecting an optimum subset of antenna-pulse pairs associated with maximum separation between the target and the clutter trajectory. The proposed strategy reduces redundancy while addressing the above three interlinked challenges for detecting slow-moving targets especially in heterogeneous cases. An iterative Min-Max algorithm is proposed to solve the antenna-pulse selection problem, which is NP-hard combinatorial optimization. Extensive simulation results confirm the effectiveness of the proposed strategy.

Fast reduced-rank STAP algorithm based on Gram–Schmidt orthogonalisation for airborne radar

In the reduced-rank space-time adaptive processing (STAP) methods, especially the principal component (PC) analysis STAP method, a set of dominant eigenvectors must be obtained by singular value decomposition of the space-time covariance matrix. Therefore, it is very difficult to be applied in practical system due to the intense computational complexity. In order to reduce the computational burden, a fast reduced-rank STAP algorithm based on Gram–Schmidt (GS) orthogonalisation is proposed in this article. In the proposed GS-PC STAP method, the clutter subspace is reconstructed by the GS orthogonalisation of training samples. Then, the STAP adaptive weight vector is calculated by orthogonally projecting the quiescent weight vector into clutter subspace, which can hold fast convergence measure of effectiveness (MOE) and require less computational complexity by compared with the conventional PC method. Based on the simulated data and multichannel airborne radar measurements data, the corresponding convergence MOE and the clutter suppression performances are verified in the article.

Reduced-rank STAP for target detection in heterogeneous environments

In an airborne radar context, heterogeneous situations are a serious concern for space-time adaptive processing (STAP), where the required secondary training data have to be target free and homogeneous with the tested data. Consequently, the performance of these detectors is severely impacted when facing a heavily heterogeneous environment. Single data-set algorithms such as the maximum likelihood estimation detector (MLED) algorithm, based on the amplitude and phase estimation (APES) method, have proved their efficiency in overcoming this problem by only working on primary data. However, restricting the estimation domain solely to the primary data often implies an inaccurate estimation of the covariance matrix. In this paper, we demonstrate that we can use reduced-rank STAP on the single data-set APES method to increase the performance of the STAP processing. We also introduce an algorithm that reduces the computational cost of the standard subspace-based algorithms based on eigenvalue decomposition. The results on realistic data show that reduced-rank methods outperform traditional single data-set methods in detection and in clutter rejection.

An improved reduced-rank STAP interference suppression method in design of GNSS receivers

In this paper, we address the problem of interference cancellation in global positioning system (GPS) receiver using an adaptive reduced-rank space-time adaptive processing (STAP) interference suppression method based on multistage nested Wiener filter (MSNWF). This improved adaptive reduced-rank method is based on the improved Gerschgorin radii algorithm. First, the cross-correlations between the desired signals of the adjacent stages of MSNWF are directly used to calculate the Gerschgorin radii instead of employing the eigenvalue decomposition of the covariance matrix. Then, a heuristic decision rule based on Gerschgorin disk estimator (GDE) is employed to estimate the rank of interference subspace. Thus optimal rank can be adaptively selected without increasing the computation. Analysis and results of the experiment show that the proposed method further reduces the computation of STAP and enhances its real-time property with the interference suppression performance unaffected.

Time-varying space–time autoregressive filtering algorithm for space–time adaptive processing

This study introduces a new type of space-time autoregressive (STAR) filtering algorithm for space-time adaptive processing (STAP) operating in a clutter environment that is not strictly stationary in slow time. The original STAR approach based on stationary autoregressive (AR) model, despite enjoying a fast convergence rate, suffers significant performance degradation when dealing with non-stationary clutter processes. To remedy this, the new proposed algorithm invokes a -relaxed- AR model, that is, the time-varying autoregressive (TVAR) model, and is called time-varying space-time autoregressive (TV-STAR) filtering. The authors demonstrate that, for stationary case, the two filters have identical output signal-to-interference plus noise ratio (SINR) with known interference covariance, but the convergence rate of TV-STAR is somewhat inferior to STAR with finite sample support. However, in the non-stationary case, the STAR filter totally fails because of -model-mismatch- whereas TV-STAR exhibits a commensurate performance with respect to the stationary case. Meanwhile, TV-STAR is shown to offer a favourable convergence rate over reduced-rank STAP techniques such as eigencanceler method in both cases. Simulated data as well as two sets of measured airborne radar data are used to demonstrate the performance of TV-STAR algorithm.

Reduced-Rank STAP Algorithms using Joint Iterative Optimization of Filters

We develop a reduced-rank space-time adaptive processing (STAP) method based on joint iterative optimization of filters (JOINT) for airborne radar applications. The proposed method consists of a bank of full-rank adaptive filters, which forms the projection matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe the proposed method for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. Adaptive algorithms including the stochastic gradient (SG), the recursive least square (RLS), and their hybrid algorithms are derived for the efficient implementation of the JOINT STAP method. The computational complexity analysis of the proposed algorithms is shown in terms of the number of multiplications and additions per snapshot. Furthermore, the convexity analysis of the proposed method is carried out. Simulations for a clutter-plus-jamming suppression application show that the proposed STAP algorithm outperforms the state-of-the-art reduced-rank schemes in convergence and tracking at significantly lower complexity.

Reduced-rank space-time adaptive interference suppression for navigation systems based on QR decomposition and approximations of basis functions

This paper presents a novel reduced-rank space–time adaptive processing (STAP) algorithm for interference suppression in global positioning system (GPS) receivers with low computational complexity for protection against the multipath and jamming interferences. The proposed STAP algorithm is based on the least-squares (LS) criterion to jointly optimize a projection matrix, which is used for dimensionality reduction, and the reduced-rank filter. The main novelties are the design of the projection matrix based on approximations of basis functions, the pattern matching between the projection matrix and the received data, and the derivation of a QR decomposition-based reduced-rank recursive LS algorithm for practical implementations. The proposed scheme works on an instantaneous basis, i.e. at each time instant, the most suitable pattern and the rank of the projection matrix are selected to reduce the dimensionality of the received data aiming at minimizing the squared error, while using an improved search algorithm to save the effort in finding the best projection matrix. Simulation results in a GPS system show that compared to existing reduced-rank and full-rank algorithms, the proposed algorithm has a much lower computational complexity, and remarkably better performance for interference suppression. Copyright © 2011 John Wiley & Sons, Ltd.

Reduced-Rank STAP Schemes for Airborne Radar Based on Switched Joint Interpolation, Decimation and Filtering Algorithm

In this paper, we propose a reduced-rank space-time adaptive processing (STAP) technique for airborne phased array radar applications. The proposed STAP method performs dimensionality reduction by using a reduced-rank switched joint interpolation, decimation and filtering algorithm (RR-SJIDF). In this scheme, a multiple-processing-branch (MPB) framework, which contains a set of jointly optimized interpolation, decimation and filtering units, is proposed to adaptively process the observations and suppress jammers and clutter. The output is switched to the branch with the best performance according to the minimum variance criterion. In order to design the decimation unit, we present an optimal decimation scheme and a low-complexity decimation scheme. We also develop two adaptive implementations for the proposed scheme, one based on a recursive least squares (RLS) algorithm and the other on a constrained conjugate gradient (CCG) algorithm. The proposed adaptive algorithms are tested with simulated radar data. The simulation results show that the proposed RR-SJIDF STAP schemes with both the RLS and the CCG algorithms converge at a very fast speed and provide a considerable SINR improvement over the state-of-the-art reduced-rank schemes.

Reduced-rank space-time adaptive processing using a modified projection approximation subspace tracking deflation approach

The projection approximation subspace tracking deflation (PASTd) algorithm is investigated in the context of the reduced-rank space-time adaptive processing (RR-STAP), where a recursive approach is employed to estimate the clutter subspace. Instead of a direct use of the classic PASTd algorithm in the RR-STAP, which suffers from a slow convergence rate because of the sequential tracking of multiple clutter eigenvectors, a modified PASTd adapted to the STAP is presented. In comparison with the conventional eigenvalue decomposition approach, the presented algorithm is computationally much more efficient and is also able to achieve comparable convergence effectiveness. The presented methodology is validated by the Monte Carlo simulation.

A STAP overview

This tutorial provides a brief overview of space-time adaptive processing (STAP) for radar applications. We discuss space-time signal diversity and various forms of the adaptive processor, including reduced-dimension and reduced-rank STAP approaches. Additionally, we describe the space-time properties of ground clutter and noise-jamming, as well as essential STAP performance metrics. We conclude this tutorial with an overview of some current STAP topics: space-based radar, bistatic STAP, knowledge-aided STAP, multi-channel synthetic aperture radar and non-sidelooking array configurations.

A study of Reduced-Rank stap

This paper starts with the discussion of the principle of Reduced-Rank (RR) Space-Time Adaptive Processing (STAP). It is followed by a dedication of the upper bound performance of all eigen-based RR methods provided by Cross Spectral Method (CSM) under the condition of a given processor rank and an identical secondary sample size. A performance comparison between two RR STAP processors with prefixed structure and CSM is performed by the means of simulations. It is shown that the performance of time pre-filtering followed by jointly localized STAP structure (i.e. 3DT-SAP) is very close to the upper bound and thereby it is an effective RR approach.

Reduced-rank STAP performance analysis

The space-time radar problem is well suited to the application of techniques that take advantage of the low-rank property of the space-time covariance matrix. It is shown that reduced-rank (RR) methods outperform full-rank space-time adaptive processing (STAP) when the space-time covariance matrix is estimated from a data set with limited support. The utility of RR methods is demonstrated by theoretical analysis, simulations and analysis of real data. It is shown that RR processing has two opposite effects on the performance: increased statistical stability which tends to improve performance, and introduction of a bias which lowers the signal-to-noise ratio (SNR). A method for evaluating the theoretical conditioned SNR for fixed RR transforms is also presented. It Is shown that while best performance is obtained using data-dependent transforms, the loss incurred by the application of fixed transforms (such as the discrete cosine transform) may be relatively small. The main advantage of fixed transforms is the availability of efficient computational procedures for their implementation. These findings suggest that RR methods could facilitate the development of practical, real-time STAP technology.

Optimal and adaptive reduced-rank STAP

This paper is concerned with issues and techniques associated with the development of both optimal and adaptive (data dependent) reduced-rank signal processing architectures. Adaptive algorithms for 1D beamforming, 2D space-time adaptive processing (STAP), and 3D STAP for joint hot and cold clutter mitigation are surveyed. The following concepts are then introduced for the first time (other than workshop and conference records) and evaluated in a signal-dependent versus signal independent context: (1) the adaptive processing region-of-convergence as a function of sample support and rank, (2) a new variant of the cross-spectral metric (CSM) that retains dominant mode estimation in the direct-form processor (DFP) structure, and (3) the robustness of the proposed methods to the subspace leakage problem arising in many real-world applications. A comprehensive performance comparison is conducted both analytically and via Monte Carlo simulation which clearly demonstrates the superior theoretical compression performance of signal-dependent rank-reduction, its broader region-of-convergence, and its inherent robustness to subspace leakage.