The problem of finding the vector of an adaptive filter for stationary interference with a Toepli... more The problem of finding the vector of an adaptive filter for stationary interference with a Toeplitz correlation matrix is considered, and an existence theorem for a Toeplitz solution is proved. The theorem is then used to derive lower bounds on the improvement in noise cancellation obtained by using a priori information about the Toeplitz structure of the correlation matrix. We indicate constructive methods of obtaining adaptive solutions consistent with these bounds.
Recent experimental studies of bi-static dual polarised sea-clutter returns have demonstrated tha... more Recent experimental studies of bi-static dual polarised sea-clutter returns have demonstrated that for widely separated receive sites, there is little correspondence between clutter ‘spiking’ events. This suggests that a multi-static polarimetric radar network with appropriately separated nodes has the potential for significant detection performance improvement when compared to a traditional mono-static radar. In this study, we demonstrate the improved detection performance using different detection schemes which non-coherently fuse the data processed from the different radar nodes. In a real radar system, there is always Gaussian noise present and hence the limiting effect of additive Gaussian noise is also quantified through accurate simulation of the sea-clutter.
We consider the problem of estimating the direction of arrival of a signal embedded in K-distribu... more We consider the problem of estimating the direction of arrival of a signal embedded in K-distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information matrix (FIM) for complex elliptically distributed data, we provide a simple expression of the FIM with the two data sets framework. In the specific case of K-distributed noise, we show that, under certain conditions, the FIM for the deterministic part of the model can be unbounded, while the FIM for the covariance part of the model is always bounded. In the general case of elliptical distributions, we provide a sufficient condition for unboundedness of the FIM. Accurate approximations of the FIM for K-distributed noise are also derived when it is bounded. Additionally, the maximum likelihood estimator of the signal DoA and an approximated version are derived, assuming known covariance matrix: the latter is then estimated from secondary data using a c...
2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013
ABSTRACT Recently it has been proposed that two-dimensional (2D) oversampled received arrays coul... more ABSTRACT Recently it has been proposed that two-dimensional (2D) oversampled received arrays could be used to provide signal-to-external noise ratio (SENR) gains for over-the-horizon radar applications which are strongly externally noise limited. These array configurations can be used to exploit superdirective adaptive beamforming techniques. A key element of the superdirective adaptive beamforming process is the estimation of the array spatial noise covariance matrix. In this paper we propose a parametric covariance modeling technique called aperture varying autoregressive (AVAR) covariance modeling that captures the 2D spatial correlation structure of high-frequency (HF) background noise sampled by an oversampled 2D receive array. The use of this covariance modeling technique can significantly reduce the computational requirements for the inversion of large spatial covariance matrices. Additional gains are achieved via reduced sample support requirements for an N-element 2D receive array. In this paper we introduce 2D aperture varying autoregressive models AVAR(m,l) that are spatially non-stationary generalizations of traditional autoregressive AR(m) or AR (m,l) techniques. While traditional AR techniques model covariance structure as toeplitz or toeplitz-block-toeplitz, these new AVAR models enforce a banded or doubly banded inverse covariance structure which is more general. The introduced AVAR methods are closely coupled to the oversampled array architecture which in the presence of nearly homogeneous external noise exhibits spatial correlation most strongly amongst closely spaced elements. Therefore the use of these AVAR methods effectively restricts the adaptive beamforming to gains achievable through superdirective beamforming.
IET International Conference on Radar Systems (Radar 2012), 2012
ABSTRACT This work addresses the problem of spatial compressive sensing (SCS) DOA estimation perf... more ABSTRACT This work addresses the problem of spatial compressive sensing (SCS) DOA estimation performance evaluation by exploiting an estimation-theoretic method known as expected likelihood (EL). This work provides a novel application of the EL method to mitigate two bias sources present in the SCS DOA estimation approach due to discretization of the azimuth bearing space and L1-regularization.
2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009
ABSTRACT Performance of maximum-likelihood estimation (MLE) is analysed in the so-called threshol... more ABSTRACT Performance of maximum-likelihood estimation (MLE) is analysed in the so-called threshold region. Here, due to insufficient training sample volume and/or signal-to-noise ratio, the actual MLE performance degrades considerably with respect to the Cramer-Rao bound, because of the onset of severely erroneous estimates ("outliers"). Recently, for a limited number of training samples comparable with the observation (antenna) dimension, an improved (with respect to MLE) G-estimate of covariance matrix eigenvalues and eigenvectors have been derived by Mestre, using tools from the random matrix theory. We use these G-estimates to form the "G-likelihood function" and compare the threshold performance of the conventional ML and G-ML DOA estimation.
The synchronous interference cancellation problem is addressed when training and working interval... more The synchronous interference cancellation problem is addressed when training and working intervals are available that contain the desired signal and completely overlapping interference. A maximum-likelihood (ML) approach is applied for estimation of the structured covariance matrices over both training and working intervals for a Gaussian data model. It is shown that the efficiency of the ML solution is close to the efficiency of the least-squares (LS) estimator, which means that the conventional training-based LS algorithm practically cannot be improved upon in the class of second-order semiblind techniques under the synchronous interference scenario.
IEEE Transactions on Aerospace and Electronic Systems, 2000
ABSTRACT In over-the-horizon radar (OTHR) the need to preferentially select propagation mode aris... more ABSTRACT In over-the-horizon radar (OTHR) the need to preferentially select propagation mode arises when one or more modes are perturbed by ionospheric disturbances. Due to mixed-mode propagation and range-elevation coupling, such control is only implementable using noncausal beamforming via MIMO radar architectures. We introduce three key principles that govern mode-selective multiple-input multiple-output (MIMO) OTHR design. Numerical examples illustrate the high potential efficiency of mode-selective MIMO OTHR, while field trials support the introduced main principles.
The problem of finding the vector of an adaptive filter for stationary interference with a Toepli... more The problem of finding the vector of an adaptive filter for stationary interference with a Toeplitz correlation matrix is considered, and an existence theorem for a Toeplitz solution is proved. The theorem is then used to derive lower bounds on the improvement in noise cancellation obtained by using a priori information about the Toeplitz structure of the correlation matrix. We indicate constructive methods of obtaining adaptive solutions consistent with these bounds.
Recent experimental studies of bi-static dual polarised sea-clutter returns have demonstrated tha... more Recent experimental studies of bi-static dual polarised sea-clutter returns have demonstrated that for widely separated receive sites, there is little correspondence between clutter ‘spiking’ events. This suggests that a multi-static polarimetric radar network with appropriately separated nodes has the potential for significant detection performance improvement when compared to a traditional mono-static radar. In this study, we demonstrate the improved detection performance using different detection schemes which non-coherently fuse the data processed from the different radar nodes. In a real radar system, there is always Gaussian noise present and hence the limiting effect of additive Gaussian noise is also quantified through accurate simulation of the sea-clutter.
We consider the problem of estimating the direction of arrival of a signal embedded in K-distribu... more We consider the problem of estimating the direction of arrival of a signal embedded in K-distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information matrix (FIM) for complex elliptically distributed data, we provide a simple expression of the FIM with the two data sets framework. In the specific case of K-distributed noise, we show that, under certain conditions, the FIM for the deterministic part of the model can be unbounded, while the FIM for the covariance part of the model is always bounded. In the general case of elliptical distributions, we provide a sufficient condition for unboundedness of the FIM. Accurate approximations of the FIM for K-distributed noise are also derived when it is bounded. Additionally, the maximum likelihood estimator of the signal DoA and an approximated version are derived, assuming known covariance matrix: the latter is then estimated from secondary data using a c...
2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013
ABSTRACT Recently it has been proposed that two-dimensional (2D) oversampled received arrays coul... more ABSTRACT Recently it has been proposed that two-dimensional (2D) oversampled received arrays could be used to provide signal-to-external noise ratio (SENR) gains for over-the-horizon radar applications which are strongly externally noise limited. These array configurations can be used to exploit superdirective adaptive beamforming techniques. A key element of the superdirective adaptive beamforming process is the estimation of the array spatial noise covariance matrix. In this paper we propose a parametric covariance modeling technique called aperture varying autoregressive (AVAR) covariance modeling that captures the 2D spatial correlation structure of high-frequency (HF) background noise sampled by an oversampled 2D receive array. The use of this covariance modeling technique can significantly reduce the computational requirements for the inversion of large spatial covariance matrices. Additional gains are achieved via reduced sample support requirements for an N-element 2D receive array. In this paper we introduce 2D aperture varying autoregressive models AVAR(m,l) that are spatially non-stationary generalizations of traditional autoregressive AR(m) or AR (m,l) techniques. While traditional AR techniques model covariance structure as toeplitz or toeplitz-block-toeplitz, these new AVAR models enforce a banded or doubly banded inverse covariance structure which is more general. The introduced AVAR methods are closely coupled to the oversampled array architecture which in the presence of nearly homogeneous external noise exhibits spatial correlation most strongly amongst closely spaced elements. Therefore the use of these AVAR methods effectively restricts the adaptive beamforming to gains achievable through superdirective beamforming.
IET International Conference on Radar Systems (Radar 2012), 2012
ABSTRACT This work addresses the problem of spatial compressive sensing (SCS) DOA estimation perf... more ABSTRACT This work addresses the problem of spatial compressive sensing (SCS) DOA estimation performance evaluation by exploiting an estimation-theoretic method known as expected likelihood (EL). This work provides a novel application of the EL method to mitigate two bias sources present in the SCS DOA estimation approach due to discretization of the azimuth bearing space and L1-regularization.
2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009
ABSTRACT Performance of maximum-likelihood estimation (MLE) is analysed in the so-called threshol... more ABSTRACT Performance of maximum-likelihood estimation (MLE) is analysed in the so-called threshold region. Here, due to insufficient training sample volume and/or signal-to-noise ratio, the actual MLE performance degrades considerably with respect to the Cramer-Rao bound, because of the onset of severely erroneous estimates ("outliers"). Recently, for a limited number of training samples comparable with the observation (antenna) dimension, an improved (with respect to MLE) G-estimate of covariance matrix eigenvalues and eigenvectors have been derived by Mestre, using tools from the random matrix theory. We use these G-estimates to form the "G-likelihood function" and compare the threshold performance of the conventional ML and G-ML DOA estimation.
The synchronous interference cancellation problem is addressed when training and working interval... more The synchronous interference cancellation problem is addressed when training and working intervals are available that contain the desired signal and completely overlapping interference. A maximum-likelihood (ML) approach is applied for estimation of the structured covariance matrices over both training and working intervals for a Gaussian data model. It is shown that the efficiency of the ML solution is close to the efficiency of the least-squares (LS) estimator, which means that the conventional training-based LS algorithm practically cannot be improved upon in the class of second-order semiblind techniques under the synchronous interference scenario.
IEEE Transactions on Aerospace and Electronic Systems, 2000
ABSTRACT In over-the-horizon radar (OTHR) the need to preferentially select propagation mode aris... more ABSTRACT In over-the-horizon radar (OTHR) the need to preferentially select propagation mode arises when one or more modes are perturbed by ionospheric disturbances. Due to mixed-mode propagation and range-elevation coupling, such control is only implementable using noncausal beamforming via MIMO radar architectures. We introduce three key principles that govern mode-selective multiple-input multiple-output (MIMO) OTHR design. Numerical examples illustrate the high potential efficiency of mode-selective MIMO OTHR, while field trials support the introduced main principles.
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Papers by yuri abramovich