compound-Gaussian Clutter Research Articles

Adaptive MIMO Radar Design and Detection in Compound-Gaussian Clutter

Multiple-input multiple-output (MIMO) radars with widely separated transmitters and receivers are useful to discriminate a target from clutter using the spatial diversity of the scatterers in the illuminated scene. We consider the detection of targets in compound-Gaussian clutter, describing heavy-tailed clutter distributions fitting high-resolution and/or low-grazing-angle radars in the presence of sea or foliage clutter. First we introduce a data model using the inverse gamma distribution to represent the clutter texture. Then we apply the parameter-expanded expectation-maximization (PX-EM) algorithm to estimate the clutter texture and speckle as well as the target parameters. We develop a statistical decision test using these estimates and demonstrate its statistical characteristics. Based on the statistical characteristics of this test, we propose an algorithm to adaptively distribute the transmitted energy among the transmitters and maximize the detection performance. We demonstrate the advantages of the MIMO setup and adaptive energy allocation in target detection in the presence of compound-Gaussian clutter using Monte Carlo (MC) simulations.

The Rao and Wald Tests Designed for Distributed Targets with Polarization MIMO Radar in Compound-Gaussian Clutter

In high resolution radars, the distributed target is usually modeled as a few isolated points referred to multiple dominant scattering centers, while the clutter is a compound-Gaussian model. Additionally, the polarimetric diversity can be exploited to enhance detection performance. Motivated by extending the detection problem of multiple-input multiple-output (MIMO) radar to such cases, this paper mainly addresses distributed targets detection problem with polarization MIMO radar against a compound-Gaussian clutter dominated scenario with unknown covariance matrix. The adaptive detectors based on Rao and Wald criteria are studied, and a two-step design procedure is adopted. Specifically, the Rao and Wald tests are derived by assuming a known covariance matrix, and then a suitable estimation of the covariance matrix based on the secondary data is inserted into the derived detectors to make them fully adaptive. Some numerical results are presented together with a polarization generalized likelihood ratio test (GLRT), showing that the derived detectors provide excellent detection performance in spiky clutter for distributed targets, and that the polarimetric diversity can be exploited to improve detection performance. Overall, the Wald test performs the best.

Rao and Wald tests design of polarimetric multiple-input multiple-output radar in compound-Gaussian clutter

In high–resolution radars or at low gazing angles, the clutter is more satisfied in the compound-Gaussian model. Meanwhile, the polarisation diversity can be exploited to enhance the detection performance. Motivated by extending the detection problem of multiple-input multiple-output radar to such cases, this study mainly addresses the adaptive detectors design with an unknown covariance matrix based on Rao and Wald criterions. The two-step design strategy is adopted. Three estimation strategies of covariance with secondary data, such as sampled covariance matrix (SCM), normalised sampled covariance matrix (NSCM) and fixed point estimation (FPE) matrix, are introduced to make derived receivers fully adaptive. A thorough performance assessment is given by several numerical examples, the results of which show that Rao and Wald tests can provide good detection performance in even spikier clutter, and the polarimetric diversity can also be exploited to improve the detection performance. Meanwhile, the FPE strategy is more suitable to implement the adaptive detection algorithms, and the adaptive loss is completely acceptable in practical applications.

PERFORMANCE OF THE ADAPTIVE NORMALIZED MATCHED FILTER DETECTOR IN COMPOUND-GAUSSIAN CLUTTER WITH INVERSE GAMMA TEXTURE MODEL

In the present paper, we deal with the performance analysis of the Adaptive Normalized Matched Filter (ANMF) detector in compound-Gaussian clutter with inverse gamma texture model and unknown covariance matrix. First, the maximum likelihood estimate (MLE) of the covariance matrix for this clutter model is derived. The MLE is then plugged into the ANMF test and compared to the well known normalized sample covariance matrix estimate (NSCM) and the approximate maximum likelihood estimate (AML). The performance in terms of CFAR behavior and detection probability is evaluated in the presence of simulated clutter and real sea clutter data, which is collected by the McMaster IPIX radar.

Radar detection based on compound-Gaussian model with inverse gamma texture

The coherent radar detection against a background of compound-Gaussian clutter with inverse gamma texture is studied and three detectors: One-step generalised likelihood ratio test (1S-GLRT), maximum a posteriori GLRT (MAP-GLRT) and two-step GLRT (2S-GLRT) are proposed. The detectors have the same structure with their test statistics and modified thresholds, respectively, related to the scale and the shape parameters of the texture, which can also be formulated in a matched filter (MF) form. Subsequently, the performance assessments are given by their probability of detection and probability of false alarm. The authors find that the probability of false alarm is dependent on the shape parameter, meaning the detectors have no CFAR property. When the shape parameter and the number of the integrated radar pulses satisfy certain condition, it has no relation with the shape parameter and then the detectors have CFAR property. Finally, simulation results show that: (i) 1S-GLRT and MAP-GLRT have the same performance for fixed probability of false alarm and 2S-GLRT bears slightly bad performance; (ii) the performance of 1S-GLRT is much closer to the adaptive coherence estimator (ACE) and is better than that of the Kelly GLRT and (iii) the 1S-GLRT is robust when parameter estimation errors exist.

AR-model-based adaptive detection of range-spread targets in compound Gaussian clutter

In this paper, we consider the problem of adaptive detection for range-spread targets with known Doppler and unknown complex amplitude in compound Gaussian clutter. The speckle component of the clutter is modeled as an autoregressive (AR) process. By using the generalized likelihood ratio test (GLRT) approach, we will first estimate the AR parameters and the unknown complex amplitude, and then propose an adaptive AR-based GLR detector. The performance assessments are presented too. The computer simulations show that the proposed detector, without a priori information of the covariance matrix, has the same asymptotical performances as the two-step GLR-based detector with known covariance matrix.

Multiple-input multiple-output radar detectors design in non-Gaussian clutter

This study mainly deals with the problem of multiple-input multiple-output (MIMO) radar in compound-Gaussian clutter-dominated scenario with unknown covariance matrix. The general MIMO model, with widely separated sub-arrays and co-located antennas at each sub-array, is adopted. First, the signal model is developed to compound-Gaussian clutter, and then, the generalised likelihood rate test (GLRT) and Rao detectors are derived with known covariance matrix. To make the detectors fully adaptive, the secondary with signal-free data is collected to estimate the covariance. A thorough performance assessment is also given, which considers the sense with co-located antennas configuration of transmitters and receivers array. Via several numerical examples, it is shown that the derived GLRT and Rao detectors can provide excellent detection performance in spikier clutter compared with the detector, which is derived by Jian Li in Gaussian clutter. To this end, the Rao detector outperforms best.

Performance analysis of GLRT-based adaptive detector for distributed targets in compound-Gaussian clutter

The problem of adaptive detection for spatially distributed targets in compound-Gaussian clutter is studied. We first derive the optimum NP detector and suboptimum two-step GLRT detector. For the two-step detection strategy, we also introduce three covariance matrix estimation strategies and evaluate their CFAR properties and complexity issues. Next, the numerical results are presented by means of Monte Carlo simulation strategy. In particular, the simulation results highlight that the performance loss due to adaptively estimating the texture is negligible, and that the loss due to adaptively estimating covariance matrix largely depends on the estimation algorithm, the number of the secondary data vectors and the number of the scatterers.

Adaptive polarimetry design for a target in compound-Gaussian clutter

We develop optimal adaptive design of radar waveform polarizations for a target in compound-Gaussian clutter. We present maximum likelihood estimates of the target's scattering matrix and clutter parameters using a parameter-expanded expectation-maximization (PX-EM) algorithm. We compute the Cramér–Rao bound (CRB) on the target's scattering matrix. To design the polarization, we propose an algorithm that minimizes a CRB function. We propose also suboptimal versions of this algorithm and illustrate the performance as well as compare our algorithm with numerical examples.

Performance of the adaptive generalised matched subspace constant false alarm rate detector in non-Gaussian noise: an experimental analysis

The authors deal with the performance analysis of an adaptive version of the generalised matched subspace detector (GMSD) in compound-Gaussian clutter with unknown covariance matrix. The original GMSD was proposed to detect subspace signals in compound-Gaussian noise with known covariance matrix and ensures the constant false alarm rate (CFAR) property. In real situations, this assumption is unrealistic, which means that the covariance matrix must be estimated from training data. The authors use a robust estimate of the covariance matrix called the fixed-point estimate, recently proposed in the literature. The performance of the obtained adaptive detector, in terms of CFAR behaviour and probability of detection, is evaluated in the presence of real sea clutter data, collected by the McMaster IPIX radar.

Adaptive subspace detection of range-distributed target in compound-Gaussian clutter

This paper deals with high-resolution radar (HRR) adaptive detection of range-distributed target embedded in compound-Gaussian clutter which is modeled as a spherically invariant random process (SIRP). Using multiple dominant scattering (MDS) model of range-distributed target, we justify that range-distributed target can be modeled as a subspace random signal. The unknown deterministic parameters are replaced by their ML estimates and then the nonadaptive detector is proposed. A closed-form expression for the probability of false alarm of the nonadaptive detector is derived and it ensures CFAR property with respect to the unknown statistics of the clutter texture component. Moreover, an adaptive detector is obtained relying on a two-step GLRT-based design procedure. Performances of these proposed detectors are assessed through Monte Carlo simulations and are shown to have better detection performance compared with existing similar detector.

Maximum likelihood estimation for compound-gaussian clutter with inverse gamma texture

The inverse gamma distributed texture is important for modeling compound-Gaussian clutter (e.g. for sea reflections), due to the simplicity of estimating its parameters. We develop maximum-likelihood (ML) and method of fractional moments (MoFM) estimates to find the parameters of this distribution. We compute the Cramer-Rao bounds (CRBs) on the estimate variances and present numerical examples. We also show examples demonstrating the applicability of our methods to real lake-clutter data. Our results illustrate that, as expected, the ML estimates are asymptotically efficient, and also that the real lake-clutter data can be very well modeled by the inverse gamma distributed texture compound-Gaussian model.

Maximum Likelihood Estimation of Compound-Gaussian Clutter and Target Parameters

Compound-Gaussian models are used in radar signal processing to describe heavy-tailed clutter distributions. The important problems in compound-Gaussian clutter modeling are choosing the texture distribution, and estimating its parameters. Many texture distributions have been studied, and their parameters are typically estimated using statistically suboptimal approaches. We develop maximum likelihood (ML) methods for jointly estimating the target and clutter parameters in compound-Gaussian clutter using radar array measurements. In particular, we estimate i) the complex target amplitudes, ii) a spatial and temporal covariance matrix of the speckle component, and iii) texture distribution parameters. Parameter-expanded expectation-maximization (PX-EM) algorithms are developed to compute the ML estimates of the unknown parameters. We also derived the Cramer-Rao bounds (CRBs) and related bounds for these parameters. We first derive general CRB expressions under an arbitrary texture model then simplify them for specific texture distributions. We consider the widely used gamma texture model, and propose an inverse-gamma texture model, leading to a complex multivariate t clutter distribution and closed-form expressions of the CRB. We study the performance of the proposed methods via numerical simulations

A GLRT for multichannel radar detection in the presence of both compound Gaussian clutter and additive white Gaussian noise

Motivated by multichannel radar detection applications in the presence of both white Gaussian noise and Gaussian clutter with unknown power, we develop maximum likelihood parameter estimates for the disturbance process. Both cases with known and unknown white noise variance are treated. As the estimators do not admit closed-form solutions, numerical iterative procedures are developed that are guaranteed to at least converge to the local maximum. The developed estimates allow us to construct a generalized likelihood ratio test (GLRT) for the detection of a signal with constant but unknown amplitude. This GLRT has important applications in multichannel radar detection involving both white Gaussian noise and spherically invariant random process clutter and is shown to have better detection performance and CFAR property compared with existing statistics.

Polarization diversity detection of distributed targets in compound-gaussian clutter

We deal with the problem of polarimetric detection of compound-Gaussian clutter with unknown distributed targets in 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.

Polarization diversity detection in compound-gaussian clutter

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.

Exploiting persymmetry for CFAR detection in compound-gaussian clutter

Presented here is 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, leads to an adaptive detector which, irrespective of the shape of the clutter power spectral density, ensures the constant false alarm rate 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 nonadaptive counterpart and outperforms the previously proposed CFAR adaptive NMF (ANMF).

Polarimetric adaptive detection in non-Gaussian noise

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.

Vector subspace detection in compound-Gaussian clutter. Part II: performance analysis

For pt. I see ibid., vol. 38, no. 4, p. 1295 (2002). In this second part we deal with the problem of detecting subspace random signals against correlated non-Gaussian clutter modeled by the compound-Gaussian distribution. In the first part of the paper, we derived the optimum Neyman-Pearson (NP) detector, the generalized likelihood ratio test (GLRT), and a constant false-alarm rate (CFAR) detector; we also provided some interesting interpretations of them. In this second part, these detectors are tested against both simulated data and measured high resolution sea clutter data to investigate the dependence of their performance on the various clutter and signal parameters. Numerical examples concern a space-time adaptive processing (STAP) scenario and a ground-based surveillance radar system scenario.

Vector subspace detection in compound-Gaussian clutter. Part I: survey and new results

Deals with the problem of detecting subspace random signals against correlated non-Gaussian clutter exploiting different degrees of knowledge on target and clutter statistical characteristics. The clutter process is modeled by the compound-Gaussian distribution. In the first part of the paper, the optimum Neyman-Pearson (NP) detector, the generalized likelihood ratio test (GLRT), and a constant false-alarm rate (CFAR) detector are sequentially derived both for the Gaussian and the compound-Gaussian scenarios. Different interpretations of the various detectors are provided to highlight the relationships and the differences among them. In particular, we show how the GLRT detector may be recast into an estimator-correlator form and into another form, namely a generalized whitening-matched filter (GWMF), which is the GLRT detector against Gaussian disturbance, compared with a data-dependent threshold. In the second part of this paper, the proposed detectors are tested against both simulated data and measured high resolution sea clutter data to investigate the dependence of their performance on the various clutter and signal parameters.