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[show abstract]
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ABSTRACT: We characterize a sequence of M interference observations by a time-varying autoregressive model of order m (TVAR(m)). We recently demonstrated that the maximum-likelihood (ML) TVAR(m) covariance matrix estimate (CME) of Gaussian data is the Dym-Gohberg transformation of the sample (direct data) covariance matrix averaged over the T independent training samples (snapshots), provided that T > m. Here we investigate the efficiency of adaptive filters and adaptive detectors based on this CME which (for m ¿ M) permits a significant reduction in training sample support compared with the traditional sample matrix inversion (SMI) method that requires T ¿ M samples. We analyze truly TVAR(m) or AR(m) (autoregressive) interferences, focusing on the signal-to-noise-ratio (SNR) loss factors in these adaptive filters and adaptive detectors that are due to the finite-sample support T, and the accuracy of false-alarm threshold calculation. We compare the performance of diagonally loaded adaptive matched filter (LAMF) and TVAR(m) adaptive detectors, and find that, even for TVAR(m) interferences, the question of which detector is better strongly depends on the eigenspectrum of the interference covariance matrix. When properly applied, both detectors are significantly better than the adaptive matched filter (AMF) detector (that uses the conventional sample CME with more than M training samples).
IEEE Transactions on Aerospace and Electronic Systems 02/2010; · 1.10 Impact Factor
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[show abstract]
[hide abstract]
ABSTRACT: The well-known problem of adaptive signal detection in background interference is addressed for situations where only a small number of training data samples are available. Since all known constant false-alarm rate (CFAR) adaptive detectors such as the traditional generalized likelihood-ratio test (GLRT), adaptive matched filter (AMF), and adaptive coherence estimator (ACE) detectors use the generic maximum-likelihood (ML) sample covariance matrix estimate (CME), the sample support necessary for accurate detection must significantly exceed the adaptive system (e.g., antenna array) dimension M, and so is often impractically large. For scenarios with a limited number m of dominant covariance matrix eigenvalues, more efficient diagonally loaded CMEs are available, whose required sample support is comparable to m (rather than M) for efficient interference mitigation. Since detectors that adopt these and other CMEs that use some a~priori information are not strictly CFAR, here we consider a "two-stage" adaptive detection scheme that optimally partitions the total sample support T into two sets: T_CME data samples are used to design the adaptive filter (beamformer), and the remaining T_CFAR samples are used to calculate the adaptive scalar false-alarm threshold. We present a comparative analysis of the detection performance of "one-stage" CFAR and "two-stage" adaptive detectors.
IEEE Transactions on Aerospace and Electronic Systems 02/2010; · 1.10 Impact Factor
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ABSTRACT: Even for the simple rank-one plane-wave model, the accurate maximum-likelihood (ML) solution of the detection-estimation problem is infeasible, mainly because the multivariate likelihood function is non-convex and multi-extremal. For this reason, a number of "ML-proxy" routines have been developed that, in some important practical cases, approach the efficiency of the ML performance benchmark (Cramer-Rao bound, CRB), for sufficiently large sample volume T and/or signal-to-noise ratio (SNR).
Signals, Systems and Computers, 2009 Conference Record of the Forty-Third Asilomar Conference on; 12/2009
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ABSTRACT: We analyse an iterative adaptive multiple-input-multiple-output (MIMO) radar receiver in the situation where a K L-variate adaptive transmit-receive beamformer is structured as the Kronecker product of a K-variate (transmit) and an L-variate (receive) beamformer. We present results for the special case of two clutter propagation modes separated in elevation angle, where the direction-of-departure (DoD) of one mode and the direction-of-arrival (DoA) of the other mode coincide with that of a target. We introduce the analytical condition of convergence and signal-to-interference-plus-noise ratio (SINR) loss factor for a given training sample volume under a number of assumptions for a sample-matrix inversion (SMI)-based iterative algorithm, and demonstrate that the diagonally loaded SMI algorithm can provide significant improvement in the convergence rate of the iterative "Kronecker MIMO receiver".
Radar Conference, 2009. EuRAD 2009. European; 11/2009
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[hide abstract]
ABSTRACT: We introduce an iterative adaptive multiple-input-multiple-output (MIMO) radar receiver that is useful when the KL-variate adaptive transmit-receive beamformer is structured as the Kronecker product of a K-variate transmit and an L-variate receive beamformer. We consider the case of two clutter propagation modes with different elevation angles, and where the direction-of-departure (DoD) of one mode and the direction-of-arrival (DoA) of the other mode coincide with that of a target. For an example simulation scenario, we demonstrate that our iterative adaptive ldquoKronecker receiverrdquo achieves high performance.
Image and Signal Processing and Analysis, 2009. ISPA 2009. Proceedings of 6th International Symposium on; 10/2009
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ABSTRACT: In a series of two papers, a new class of parametric models for two-dimensional multivariate (matrix-valued, space-time) adaptive processing is introduced. This class is based on the maximum-entropy extension and/or completion of partially specified matrix-valued Hermitian covariance matrices in both the space and time dimensions. This first paper considers the more restricted class of Toeplitz Hermitian covariance matrices that model stationary clutter. If the clutter is stationary only in time then we deal with a Toeplitz-block matrix, whereas clutter that is stationary in time and space is described by a Toeplitz-block-Toeplitz matrix. We first derive exact expressions for this new class of 2-D models that act as approximations for the unknown true covariance matrix. Second, we propose suboptimal (but computationally simpler) relaxed 2-D time-varying autoregressive models (ldquorelaxationsrdquo) that directly use the non-Toeplitz Hermitian sample covariance matrix. The high efficiency of these parametric models is illustrated by simulation results using true ground-clutter covariance matrices provided by the DARPA KASSPER Dataset 1, which is a trusted phenomenological airborne radar model, and a complementary AFRL dataset.
IEEE Transactions on Signal Processing 12/2008; · 2.63 Impact Factor
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[show abstract]
[hide abstract]
ABSTRACT: In a series of two papers, a new class of parametric models for two-dimensional multivariate (matrix-valued, space-time) adaptive processing is introduced. This class is based on the maximum-entropy extension and/or completion of partially specified matrix-valued Hermitian covariance matrices in both the space and time dimensions. The first paper considered the more restricted class of Hermitian Toeplitz-block covariance matrices that model stationary clutter. This second paper deals with the more general class of Hermitian-block covariance matrices that model nonstationary clutter. For our recently proposed 2-D time-varying autoregressive (TVAR) model, we derive optimal and computationally practical suboptimal methods for calculating such parametric models. The maximum-likelihood covariance matrix estimate for the 2-D TVAR model is also derived. The efficacy of the introduced models is illustrated by signal-to-interference-plus-noise ratio (SINR) degradation results obtained when applying the covariance matrix models to space-time adaptive processing filter design, compared with the true clutter covariance matrix provided by the DARPA KASSPER dataset.
IEEE Transactions on Signal Processing 12/2008; · 2.63 Impact Factor
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[hide abstract]
ABSTRACT: We continue our investigation into the new class of two-dimensional autoregressive relaxed models (ldquorelaxationsrdquo) for space-time adaptive processing (STAP) applications. Previously reported results on the DARPA KASSPER simulated dataset for airborne side-looking radar are now complemented by STAP performance analysis for all range bins and varying antenna-array errors. We discuss the variability of signal-to-interference-plus-noise ratio (SINR) performance associated with the changing terrain conditions across all 1000 KASSPER range bins, and more closely investigate the impact of antenna errors and training data inhomogeneity. Performance improvements due to the previously proposed regularisation of the parametric models are also demonstrated in more detail.
Radar, 2008 International Conference on; 10/2008
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ABSTRACT: In space-time adaptive processing (STAP) applications, temporally stationary clutter results in a Toeplitz-block clutter co- variance matrix. In the reduced-order parametric matched filter STAP technique, this covariance matrix is reconstructed from a small number of estimated parameters, resulting in a much more efficient use of training samples. This paper explores a computationally advantageous "relaxed" maximum entropy (Burg) reconstruction technique which does not restore a strict Toeplitz-block structure, but does preserve the Burg spectrum. Performance of the reconstructed covariance matrix model as a STAP filter is evaluated using the DARPA KASSPER dataset and compared with "proper" Toeplitz-block reconstruction.
Sensor Array and Multichannel Signal Processing Workshop, 2008. SAM 2008. 5th IEEE; 08/2008
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ABSTRACT: We analyze the performance of a recently described class of two-dimensional autoregressive parametric models for space-time adaptive processing (STAP) in airborne radars on the DARPA side-looking radar model known as KASSPER Dataset 1. We investigate the trade-offs between signal-to-interference-plus-noise ratio (SINR) degradation (with respect to the optimal clairvoyant receiver) due to the mismatch between the observed covariance matrix and its parametric model, and the degradation due to the limited training sample volume. The impact of ground-clutter inhomogeneity on parametric STAP performance is demonstrated, as well as the significant superiority of parametric STAP over the conventional loaded sample-matrix inversion (SMI) technique.
Radar Conference, 2008. RADAR '08. IEEE; 06/2008
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ABSTRACT: Adaptive signal detection for scenarios with a limited number of sources of interest and background interferers (less than the number of antenna elements) can be efficiently executed using diagonally loaded covariance matrix estimates, but the resultant detectors are not strictly constant false-alarm rate (CFAR). The loss of ldquoCFARnessrdquo means that the problem of adaptive interference mitigation and the problem of adaptive false-alarm threshold control must be treated separately, yet draw on the same collection of secondary training samples. Here we consider a ldquotwo-stagerdquo adaptive detection scheme that optimally partitions the total sample support T into two sets: T<sub>CME</sub> data samples are used to design the adaptive filter (beamformer), then the remaining T<sub>CFAR</sub> samples are used to calculate the adaptive scalar false-alarm threshold. We present a comparative analysis of the detection performance of ldquoone-stagerdquo CFAR and ldquotwo-stagerdquo adaptive detectors.
Radar Conference, 2008. RADAR '08. IEEE; 06/2008
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ABSTRACT: A new method for interference mitigation which efficiently combines continuous-wave (CW) external-noise mitigation with transient and impulsive-noise mitigation in high-frequency over-the-horizon (HF OTH) radars is proposed in this paper. The efficiency of the method is demonstrated on real data collected by the JORN and SECAR HF OTH radars.
Radar Conference, 2008. RADAR '08. IEEE; 06/2008
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ABSTRACT: We introduce a new class of parametric models for two-dimensional (space-time) adaptive processing for (slow-time) stationary multivariate interference (clutter). This class is based on maximum-entropy (ME) extensions (completions) of partially specified block- Toeplitz covariance matrices. We derive exact solutions for the ME extensions and also provide computationally advantageous suboptimal solutions for efficient STAP filter design. The efficiency of the proposed parametric models is illustrated by an airborne radar scenario provided by the DARPA KASSPER dataset.
Signals, Systems and Computers, 2007. ACSSC 2007. Conference Record of the Forty-First Asilomar Conference on; 12/2007
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ABSTRACT: The well-known general problem of signal detection in background interference is addressed for situations where a certain statistical description of the interference is unavailable, but is replaced by the observation of some secondary (training) data that contains only the interference. For the broad class of interferences that have a large separation between signal-and noise-subspace eigenvalues, we demonstrate that adaptive detectors which use a diagonally loaded sample covariance matrix or a fast maximum likelihood (FML) estimate have significantly better detection performance than the traditional generalized likelihood ratio test (GLRT) and adaptive matched filter (AMI') detection techniques, which use a maximum likelihood (ML) covariance matrix estimate. To devise a theoretical framework that can generate similarly efficient detectors, two major modifications are proposed for Kelly's traditional GLRT and AMF detection techniques. First, a two-set GLRT decision rule takes advantage of an a priori assignment of different functions to the primary and secondary data, unlike the Kelly rule that was derived without this. Second, instead of ML estimates of the missing parameters in both GLRT and AMF detectors, we adopt expected likelihood (EL) estimates that have a likelihood within the range of most probable values generated by the actual interference covariance matrix. A Gaussian model of fluctuating target signal and interference is used in this study. We demonstrate that, even under the most favorable loaded sample-matrix inversion (LSMI) conditions, the theoretically derived EL-GLRT and FL-AMF techniques (where the loading factor is chosen from the training data using the EL matching principle) gives the same detection performance as the loaded AMF technique with a proper a priori data-invariant loading factor. For the least favorable conditions, our EL-AMF method is still superior to the standard AMF detector, and may be interpreted as an intelligent (data-dep-
endent) method for selecting the loading factor.
IEEE Transactions on Aerospace and Electronic Systems 08/2007; · 1.10 Impact Factor
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[show abstract]
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ABSTRACT: For a set of T independent observations of the same N-variate correlated Gaussian process, we derive a method of estimating the order of an autoregressive (AR) model of this process, regardless of its stationary or time-varying nature. We also derive a test to discriminate between stationary AR models of order m,AR(m), and time-varying autoregressive models of order m,TVAR(m). We demonstrate that within this technique the number T of independent identically distributed data samples required for order estimation and discrimination just exceeds the maximum possible order m<sub>max</sub>, which in many cases is significantly fewer than the dimension of the problem N
IEEE Transactions on Signal Processing 07/2007; · 2.63 Impact Factor
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[hide abstract]
ABSTRACT: Instead of a "hard" decision on ignoring "outlier" training samples in constructing the covariance matrix estimate, we propose a "softer" method that reduces the impact of such abnormal data samples on adaptive filter performance. Specifically, we introduce a diagonally loaded covariance matrix estimate that is normalised by a generalised inner product (GIP), which is more robust against outliers. We demonstrate the efficiency of this technique on high-frequency (HF) over-the-horizon radar (OTHR) data
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on; 05/2007 · 4.63 Impact Factor
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[show abstract]
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ABSTRACT: We consider the adaptive radar problem where the properties of the (nonstationary) clutter signals can be estimated using multiple observations of radar returns from a number of sufficiently homogeneous range/azimuth resolution cells. We derive a method for approximating an arbitrary Hermitian covariance matrix by a time-varying autoregressive model of order m, TVAR(m), that is based on the Dym-Gohberg band-matrix extension technique which gives the unique TVAR(m) model for any nondegenerate covariance matrix. We demonstrate that the Dym-Gohberg transformation of the sample covariance matrix gives the maximum-likelihood (ML) estimate of the TVAR(m) covariance matrix. We introduce an example of TVAR(m) clutter modeling for high-frequency over-the-horizon radar that demonstrates its practical importance
IEEE Transactions on Signal Processing 05/2007; · 2.63 Impact Factor
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[show abstract]
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ABSTRACT: The problem of estimating the number of independent Gaussian sources and their parameters impinging upon an antenna array is addressed for scenarios that are problematic for standard techniques, namely, under "threshold conditions" (where subspace techniques such as MUSIC experience an abrupt and dramatic performance breakdown). We propose an antenna geometry-invariant method that adopts the generalized-likelihood-ratio test (GLRT) methodology, supported by a maximum-likelihood-ratio lower-bound analysis that allows erroneous solutions ("outliers") to be found and rectified. Detection-estimation performance in both uniform circular and linear antenna arrays is shown to be significantly improved compared with conventional techniques but limited by the performance-breakdown phenomenon that is intrinsic to all such maximum-likelihood (ML) techniques
IEEE Transactions on Signal Processing 02/2007; · 2.63 Impact Factor
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[show abstract]
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ABSTRACT: For a set of T independent N-variate Gaussian training samples (T < N), we derive a test for discriminating between stationary autoregressive models of order m, AR(m), and time-varying autoregressive models of order m, TVAR(m)
Sensor Array and Multichannel Processing, 2006. Fourth IEEE Workshop on; 08/2006
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[show abstract]
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ABSTRACT: We introduce a new generalized likelihood-ratio test (GLRT) framework for adaptive detection that differs from Kelly's standard method (E.J. Kelly, 1986) in two main aspects. First, the separate functions of the primary and secondary data are respected, with a single set of interference estimates for both hypotheses being searched to optimize the detection performance. Second, instead of the traditional maximum likelihood (ML) principle, we propose to search for a set of estimates that generates statistically the same likelihood as the unknown true parameters. We present results for a typical example scenario that demonstrates considerable detection performance improvement.
Computational Advances in Multi-Sensor Adaptive Processing, 2005 1st IEEE International Workshop on; 01/2006
