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This study deals with the problem of adaptive radar detection when a limited number of training data, due to environmental heterogeneity, is present. Suppose that some a priori spectral models for the interference in the cell under test and a lower bound on the power spectral density (PSD) of the white disturbance term are available. Hence, generalised likelihood ratio test-based detection algorithms have been devised. At the design stage, the basic idea is to model the actual interference inverse covariance as a combination of the available a priori models and to account for the available lower bound on the PSD. At the analysis stage, the capabilities of the new techniques have been shown to detect targets when few training data are available as well as their superiority with respect to conventional adaptive techniques based on the sample covariance matrix.

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, it is shown that the new class of distribution-free estimators shares a shrinkage-type form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. At the analysis stage, the effectiveness of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) also in comparison with some existing counterparts. © 2017 IEEE.

This paper deals with the problem of testing the equality of $M$ covariance matrices. We first identify a suitable group of transformations leaving the problem invariant and obtain the corresponding maximal invariant statistic. Then, the Generalized Likelihood Ratio Test (GLRT) is recalled and explicit expressions for Rao, Wald, Gradient, and Durbin tests are provided. Also, equivalences among them and with other well-known tests proposed in open literature (mostly for the real-valued case) are analyzed and compared. Finally, the application of the proposed framework to the relevant signal processing application of multipass Coherent Change Detection (CCD) in polarimetric synthetic aperture radar is demonstrated both on simulated and on live data.

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes., Comment: submitted for journal publication

We deal with the robust design of multiple-input multiple-output (MIMO) waveform covariance matrices that optimize the worst case (over steering mismatches) transmit beampattern assuming either the peak sidelobe level (PSL) or the integrated sidelobe level (ISL) as figure of merit. To this end, we model the uncertainty set associated with each steering vector through two double-sided, potentially non-convex, quadratic constraints. In addition, we force two suitable constraints on the optimization variable. The former accounts for the width of the mainbeam, whereas the latter is either a uniform or a relaxed elemental power requirement allowing to control the amount of transmitted power. We prove that both the mentioned waveform covariance designs lead to non-convex optimization problems which remarkably share some hidden convexity properties. Hence, we devise polynomial time procedures aimed at synthesizing the desired optimal MIMO waveform covariance matrices. Finally, at the analysis stage, we assess the performance of the proposed techniques showing their capability to ensuring improved worst case performance than some counterparts available in open literature.

This letter deals with the problem of adaptive detection in Gaussian disturbance with unknown but persymmetric structured covariance matrix. A partially-homogeneous environment is considered at the design stage, and a receiver based on the generalized likelihood ratio test (GLRT) is derived. At the analysis stage, the performance of the new receiver is assessed, also in comparison with the unstructured GLRT, showing that the a-priori information on the covariance structure can lead to a noticeable performance improvement.

We deal with the robust design of the Multiple-Input Multiple-Output (MIMO) waveform covariance matrix optimizing the worst case (over steering mismatches) transmit beampattern Peak Sidelobe Level (PSL). To this end, we model the uncertainty set associated with each steering vector through two double-sided, potentially non-convex, quadratic constraints. Additionally, we force two suitable constraints on the optimization variable. The former accounts for the width of the mainbeam, whereas the latter is either a uniform or a relaxed elemental power requirement allowing to control the amount of transmitted power. We prove that the mentioned design leads to a non-convex optimization problem which remarkably shares some hidden convexity. Hence, we devise a polynomial time procedure aimed at synthesizing an optimal MIMO waveform covariance. Finally, at the analysis stage, we assess the performance of the proposed design technique showing that it ensures an improved worst case performance than some counterparts available in open literature.

Coherent multipolarization synthetic aperture radar (SAR) change detection exploiting data collected from $N$ multiple polarimetric channels is addressed in this letter. The problem is formulated as a binary hypothesis testing problem, and a special block-diagonal structure for the polarimetric covariance matrix is forced to design a detector based on the generalized likelihood ratio test (GLRT) criterion. It is shown that the structured decision rule ensures the constant false alarm rate property with respect to the unknown disturbance covariance. Results on both simulated and real high-resolution SAR data show the effectiveness of the considered decision rule and its superiority against the traditional unstructured GLRT in some scenarios of practical interest.

We deal with the problem of polarimetric detection of distributed targets in compound-Gaussian clutter with unknown covariance matrix. Since no uniformly most powerful (UMP) detector exists for the problem at hand, we devise and assess two classes of suboptimum receivers. The former contains two detectors, designed according to the Wald and the generalized likelihood ratio tests, which resort to secondary data, free of signal components and with the same covariance structure of the cells under test, for estimating the clutter spectral properties. The latter contains a detector which achieves adaptivity without exploiting the training set. All the decision rules ensure the constant false alarm rate (CFAR) property with respect to the texture statistics but they are not theoretically CFAR with respect to the disturbance covariance matrix. Finally, we present simulation results, based also on real clutter data, showing that the Wald test receiver achieves in general a better detection performance and a stronger robustness than its counterparts.

in this paper we address polarimetric adaptive detection of targets embedded in compound-Gaussian clutter with unknown covariance matrix. To this end we assume that a set of secondary data, free of signal components and with the same covariance structure of the cell under test, is available. We resort to a design procedure based upon the generalized likelihood ratio test (GLRT): first we derive the GLRT assuming that the textures are known, then we plug into the derived test suitable estimates of these parameters. Remarkably, the newly proposed detector has the constant false alarm rate (CFAR) property with respect to the texture statistical characterization. Moreover, even though it does not ensure the CFAR property with respect to the clutter covariance matrix, a sensitivity analysis shows that the probability of false alarm is only slightly affected by variations in the clutter correlation properties. Finally, the performance assessment, conducted via Monte Carlo simulations, confirms the capability of the receiver to operate in real radar scenarios. (C) 2002 Elsevier Science B.V. All rights reserved.

In this correspondence we prove two interesting properties of the fast maximum likelihood (FML) covariance matrix estimator proposed in [1] under the assumption of zero-mean complex circular Gaussian training data sharing the same covariance matrix. The new properties represent optimality claims regardless of the statistical characterization of the data and, in particular, of the multivariate Gaussian assumption for the observables. The optimality is proved with respect to two cost functions involving either the Frobenius or the spectral norm of an Hermitian matrix.

In this paper we deal with the problem of detecting extended targets embedded in Gaussian interference with structured covariance matrix. We model the target echo from each range bin as a deterministic signal with an unknown scaling factor that accounts for the target response. We also exploit some a-priori knowledge about the operating environment at the design stage. Specifically, we assume that inverse disturbance covariance matrix belongs to a set described through a family of unitary invariant convex functions. Hence, we derive a class of Generalized Likelihood Ratio Tests (GLRT's) for the resulting hypothesis test. At the analysis stage, we assess the performance of some detectors, lying in the aforementioned class, in terms of Detection Probability (PD). The results highlight that the better the covariance uncertainty characterization, the better the detection performance. © 2013 IEEE.

This paper deals with the problem of adaptive radar detection when a limited number of training data, due to environmental heterogeneity, is present. We suppose that some a-priori spectral models for the interference in the cell under test are available and determine Generalized Likelihood Ratio Test (GLRT) based detection algorithms. The basic idea is to model the actual interference inverse covariance as a combination of the available a-priori models and to account for this special structure when a receiver is synthesized. At the analysis stage, we show the capabilities of the new techniques to detect targets when a few training data are available as well as their superiority with respect to conventional adaptive techniques based on the sample covariance matrix.

In this paper we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the Maximum Likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e. the sum of a positive semidefinite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of detection capability of an Adaptive Matched Filter (AMF) receiver with the proposed estimator in place of the sample covariance matrix, for a spatial processing. The results show that the AMF with the structured constrained covariance matrix estimator can achieve higher Detection Probabilities (PD), than some counterparts available in open literature. © 2012 IEEE.

In this paper, we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the maximum likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e., the sum of a positive semi-definite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of achievable signal-to-interference-plus-noise ratio (SINR) both for a spatial and a Doppler processing. The results show that interesting SINR improvements, with respect to some existing covariance matrix estimation techniques, can be achieved. © 2012 IEEE.

In this paper we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the Maximum Likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e. the sum of a positive semi-definite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of achievable Signal to Interference plus Noise Ratio (SINR) for a spatial processing. The results show that interesting SINR improvements, with respect to other existing covariance matrix estimation techniques, can be achieved. © 2012 IEEE.

This paper deals with the problem of estimating the disturbance covariance matrix when a limited number of training data, due to environmental heterogeneity, is present. To this end, we suppose that some a-priori spectral models for the the disturbance in the cell under test are available and determine the Maximum Likelihood (ML) estimate of the actual inverse covariance (and hence of the covariance itself) as a suitable combination of the a-priori models. At the analysis stage, we show the capabilities of the new technique to track the actual clutter Power Spectral Density (PSD) and its superiority with respect to adaptive techniques based on the sample covariance matrix.

In this paper, we address the problem of adaptive detection in homogeneous Gaussian interference, with unknown covariance matrix, after reduction by invariance. Starting from a maximal invariant statistic, which contains all the information for the synthesis of an invariant detector, we devise the Rao test, generalized likelihood ratio test (GLRT), and Durbin test. Moreover, we compare their decision statistics with those of the receivers designed according to the same criteria from the raw data (i.e., before reduction by invariance). We prove that the GLRT in the original data space is statistically equivalent to the GLRT designed after reduction by invariance (under a very mild assumption) and coincide with the conditional uniformly most powerful invariant (C-UMPI) test, obtained conditioning on an ancillary part of the maximal invariant statistic. As to the Rao and Durbin criteria, when they are applied after reduction by invariance, lead to detectors different from the counterparts devised in the raw data domain. At the analysis stage, the performance of the receivers devised in the invariant domain is analyzed in comparison with that of the counterparts synthesized from the original observations.

The authors consider the problem of knowledge-aided covariance matrix estimation and its application to adaptive radar detection. The authors assume that an a priori (knowledge-based) estimate of the disturbance covariance M, derived from a physical scattering model of the terrain and/or of the environment, is available. Hence, starting from a set of secondary data, the authors evaluate the maximum likelihood (ML) estimate of M assuming that it lies in a suitable neighbourhood of the a priori estimate and formulate this ML estimation in terms of a convex optimisation problem which falls within the class of MAXDET problems. Both the cases of unstructured and structured disturbance covariance are considered. At the analysis stage, the authors assess the performance of the new knowledge-aided covariance estimators both in terms of estimation error and detection probability achievable by a class of adaptive detectors. The results highlight that, if the a priori knowledge is reliable, satisfactory levels of performance can be achieved with considerably less training data than those exploited by conventional algorithms.

In this paper we consider the issue of adaptive transmission and detection for MIMO radars operating under clutter with unknown covariance. In particular, we show that the availability of a set of secondary data allows defining constant-false-alarm rate (CFAR) receivers starting upon a family of previously known non-adaptive structures. We also show that, if the clutter correlation remains constant in several scans, an adaptive waveform selection procedure can also be implemented. The results show that the adaptive transmit/receive structures perform satisfactorily in comparison to their non-adaptive counterparts, the loss being in the order of 2-3 dB's for customary values of the system parameters.

This paper considers the problem of Multiple-Input Multiple-Output (MIMO) radars employing space-time coding to achieve diversity. To this end, after briefly outlining the model of the received echo, a suitable detection structure is derived, and its performance is expressed in closed-form as a function of the clutter statistical properties and of the space-time code matrix. Interestingly, this receiver requires prior knowledge of the clutter covariance, but the detection threshold is functionally independent thereof. At the transmitter design stage, we give two criteria for code construction: the former is based on the classical Chernoff bound, the latter is instead an information-theoretic criterion. Interestingly, the two criteria lead to the same condition for code optimality, which in turn specializes, under the assumption of uncorrelated clutter and square code matrix, in some well known full-rate space-time codes. A thorough performance assessment is also given, so as to establish the optimum achievable performance for MIMO radar systems.

We design three statistical tests to ascertain whether radar data comply with the hypotheses of multivariate Gaussianity, spatial homogeneity, and covariance persymmetry, respectively. For the first issue we develop a statistical procedure based on quadratic distributional distances, which exploits the representation of Gaussian vectors in generalized spherical coordinates. As to the spatial homogeneity we propose a technique, based on the Kolmogorov-Smirnov (KS) test, relying on the properties of quadratic forms constructed from Gaussian vectors and Wishart distributed matrices. Finally, in order to analyze the persymmetry property of the disturbance covariance matrix, we design a testing procedure based on the generalized likelihood ratio test (GLRT). We thus apply the new tests to L-band experimentally measured clutter data, collected by the MIT Lincoln Laboratory Phase One radar, at the Katahdin Hill site. The results show that the multivariate Gaussian hypothesis for the considered data file is reasonable. On the contrary the assumption of spatial homogeneity can be done only within small clutter regions which, in general, exhibit also a persymmetric covariance matrix.

In this paper we design two statistical tests to ascertain whether radar data comply with the hypotheses of multivariate Gaussianity and covariance persymmetry. For the first issue we develop a statistical procedure based on quadratic distributional distances, which exploits the representation of Gaussian vectors in generalized spherical coordinates. Moreover, in order to analyze the persymmetry property of the disturbance covariance matrix, we design a testing procedure based on the generalized likelihood ratio test. We thus apply the new tests to L-Band experimentally measured clutter data, collected by the MIT Lincoln Laboratory Phase One radar, at the Katahdin Hill site.

This paper deals with the problem of estimating the covariance structure of a compound-Gaussian process and of its application to adaptive radar detection in clutter-dominated disturbance. The proposed estimator exploits the persymmetry property typical of Toeplitz covariance matrices and is based on secondary data, free of signal components, and with the same covariance structure of the cell under test. We prove that, plugging the proposed covariance estimator into the normalized matched filter (NMF) [E. Conte, M. Lops, and G. Ricci, 1995], leads to an adaptive detector which, irrespective of the shape of the clutter power spectral density (psd), ensures the constant false alarm rate (CFAR) property with respect to both the clutter covariance matrix as well as the statistics of the texture. Finally, we show that this adaptive receiver has an acceptable loss with respect to its non-adaptive counterpart and outperforms the previously proposed CFAR adaptive NMF (ANMF) [E. Conte, A de Maio, and G. Ricci, 2002].

We present the problem of polarization diversity detection in compound-Gaussian clutter with unknown covariance matrix. To this end we assume that a set of secondary data, free of signal components and with the same covariance structure of the cell under test, is available. Due to the lack of a uniformly most powerful (UMP) detector we resort to a design procedure based upon the Rao and the Wald tests. Specifically we first derive the Rao and the Wald tests assuming that the covariance matrix is known, and then we substitute into the derived decision rules a suitable estimate of the clutter covariance. Interestingly, the newly proposed detectors share the constant false alarm rate (CFAR) property with respect to the texture statistical characterization. Moreover simulation results have shown that the Wald test based detector ensures a performance level higher than the Rao test. We have also conducted a further performance analysis, in the presence of real clutter data and in comparison with the previously proposed generalized likelihood ratio test (GLRT) based receivers, which highlights that, in general, the Wald test receiver outperforms its counterparts. Finally, since the newly proposed decision rules as well as the previously designed GLRTs do not ensure the CFAR property with respect to the clutter covariance matrix, we have developed a sensitivity analysis on the probability of false alarm (P/sub fa/), based on simulated clutter with covariance matrix estimated from real radar data. The results have shown that (P/sub fa/) is only slightly affected by variations in the clutter correlation properties and hence the CFARness is substantially achieved.

This paper deals with the problem of coherent radar detection of targets embedded in clutter modeled as a compound-Gaussian process. We first provide a survey on clutter mitigation techniques with a particular emphasis on adaptive detection schemes ensuring the constant false-alarm rate (CFAR) property with respect to all of the clutter parameters. Thus, we propose a novel decision rule based on a recursive covariance estimator, which exploits the persymmetry property of the clutter covariance matrix. Remarkably, the devised receiver is fully CFAR in that its threshold can be set independently of the clutter distribution as well as of its covariance, even if the environment is highly heterogeneous; namely, the disturbance distributional parameters vary from cell to cell. At the analysis stage, we compare the performance of the novel detector with some classical radar receivers such as that of Kelly and the adaptive matched filter both in the presence of simulated as well as on real radar data, which statistical analysis has shown to be compatible with the compound-Gaussian model. The results show that the new receiving structure generally provides higher detection performance than the others and, for a fluctuating target, it uniformly outperforms the counterparts. We also provide a discussion on the CFAR behavior of the analyzed receivers as well as on their computational complexity.

In this paper we address estimation of the structured covariance matrix of a Gaussian process. To this end we assume that the aforementioned quantity is the sum of a positive semidefinite hermitian and persymmetric term, which accounts for the interference, plus a matrix proportional to the identity and representative of the internal noise covariance. Under these constraints we devise the maximum likelihood estimator of the overall disturbance covariance matrix and remarkably show that exploiting persymmetry, in conjunction with the others structural covariance informations, can lead to a significant reduction in the number of training data required for ensuring satisfactory performances. (C) 2002 Elsevier Science B.V. All rights reserved.

This paper deals with the problem of detecting a signal known up to a scaling factor in the presence of Gaussian disturbance with unknown covariance matrix. We focus on scenarios where the number of secondary data which share the same covariance of the data under test is very limited. Thus, we propose a modified version of the adaptive matched filter (AMF) and of the adaptive cosine/coherence estimator (ACE) which can be applied even if the sample covariance matrix is rank deficient. Even though these detectors do not ensure the constant false alarm rate (CFAR) property with respect to the covariance matrix of the disturbance, a sensitivity analysis has shown that the threshold setting is very robust with respect to possible discrepancies between the design and the operating conditions. Finally, numerical results highlight that the proposed receivers outperform the conventional AMF and ACE in low sample situations. (C) 2002 Elsevier Science B.V. All rights reserved.

The design of knowledge-based adaptive algorithms has been dealt with for the cancellation of heterogeneous clutter. To this end, the application of the recursive least squares (RLS) technique has been revisited for the rejection of unwanted clutter, and modified RLS filtering procedures have been devised accounting for the spatial variation of the clutter power as well as of the disturbance covariance persymmetry property. Then the authors introduce the concept of knowledge-based RLS and explain how the a priori knowledge about the radar operating environment can be adopted for improving the system performance. Finally, the authors assess the benefits resulting from the use of knowledge-based processing both on simulated and on measured clutter data collected by the McMaster IPIX radar in November 1993.

In this paper we deal with the problem of polarization diversity detection in compound-Gaussian clutter with unknown covariance matrix. To this end we assume that a set of secondary data, free of signal components and with the same covariance structure of the cell under test, is available. Due to the lack of a uniformly most powerful (UMP) detector, we resort to a design procedure based upon the Rao test and the Wald test. Specifically, we first derive the Rao and the Wald tests assuming that the covariance matrix is known, and then we plug into the derived decision rules a suitable estimate of the clutter covariance. Interestingly, the newly proposed detectors share the constant false alarm rate (CFAR) property with respect to the texture statistical characterization. Moreover simulation results have shown that the Wald based detector ensures a performance level higher than the Rao test. We have also conducted a further performance analysis, in the presence of real radar data and in comparison with the previously proposed generalized likelihood ratio test (GLRT) based receivers, which highlights that in general the Wald test receiver outperforms its counterparts. Finally, since the newly proposed decision rules as well as the previously designed GLRTs do not ensure the CFAR property with respect to the clutter covariance matrix, we have conducted a sensitivity analysis on the probability of false alarm (P/sub fa/), based on simulated clutter with covariance matrix estimated from real radar data. The results have shown that P/sub fa/ is only slightly affected by variations in the clutter correlation properties and hence the CFARness is substantially achieved.