An improved adaptive sidelobe blanker

We propose a two-stage detector consisting of a subspace detector followed by the whitened adaptive beamformer orthogonal rejection test. The performance analysis shows that it possesses the constant false alarm rate property with respect to the unknown covariance matrix of the noise and that it can guarantee a wider range of directivity values with respect to previously proposed two-stage detectors. The probability of false alarm and the probability of detection (for both matched and mismatched signals) have been evaluated by means of numerical integration techniques

An ABORT-like detector with improved mismatched signals rejection capabilities

In this paper, we present a GLRT-based adaptive detection algorithm for extended targets with improved rejection capabilities of mismatched signals. We assume that a set of secondary data is available and that noise returns in primary and secondary data share the same statistical characterization. To increase the selectivity of the detector, similarly to the ABORT formulation, we modify the hypothesis testing problem at hand introducing fictitious signals under the null hypothesis. Such unwanted signals are supposed to be orthogonal to the nominal steering vector in the whitened observation space. The performance assessment, carried out by Monte Carlo simulation, shows that the proposed dectector ensures better rejection capabilities of mismatched signals than existing ones, at the price of a certain loss in terms of detection of matched signals

Adaptive detection in nonhomogeneous environments using the generalized eigenrelation

This letter considers adaptive detection of a signal in a nonhomogeneous environment, more precisely under a covariance mismatch between the test vector and the training samples, due to an interference that is not accounted for by the training samples, e.g., a sidelobe target or an undernulled interference. We assume that the covariance matrices of the test vector and the training samples verify the so-called generalized eigenrelation. Under this assumption, we derive the generalized likelihood ratio test and show that it coincides with Kelly’s detector

GLRT-Based Direction Detectors in Homogeneous Noise and Subspace Interference

In this paper, we derive and assess decision schemes to discriminate, resorting to an array of sensors, between the H0 hypothesis that data under test contain disturbance only (i.e., noise plus interference) and the H1 hypothesis that they also contain signal components along a direction which is a priori unknown but constrained to belong to a given subspace of the observables. The disturbance is modeled in terms of complex normal random vectors plus deterministic interference assumed to belong to a known subspace. We assume that a set of noise-only (secondary) data is available, which possess the same statistical characterization of noise in the cells under test. At the design stage, we resort to either the plain generalized-likelihood ratio test (GLRT) or the two-step GLRT-based design procedure. The performance analysis, conducted resorting to simulated data, shows that the one-step GLRT performs better than the detector relying on the two-step design procedure when the number of secondary data is comparable to the number of sensors; moreover, it outperforms a one-step GLRT-based subspace detector when the dimension of the signal subspace is sufficiently high

Theoretical performance analysis of the W-ABORT detector

In a recent paper we introduced a modification of the adaptive beaniformer orthogonal rejection test (ABORT) for adaptive detection of signals in unknown noise, by supposing under the null hypothesis the presence of signals orthogonal to the nominal steering vector in the whitened observation space. We will refer to this new receiver as the whitened adaptive beamformer orthogonal rejection test (W-ABORT). Through Monte Carlo simulations this new detector was shown to provide better rejection capabilities of mismatched (e.g., sidelobe) signals than existing ones, like ABORT or the adaptive coherence estimator (ACE), but at the price of a certain loss in terms of detection of matched (i.e., mainlobe) signals. The aim of this paper is to provide a theoretical validation of this fact. We consider both the case of distributed targets and point-like targets. We provide a statistical characterization of the W-ABORT test statistic, under the null hypothesis, and for matched and mismatched signals under the alternative hypothesis. For distributed targets, the probability of false alarm and the probability of detection can only be expressed in terms of multi-dimensional integrals, and are thus very complicated to obtain; in contrast, for point-like targets, such probabilities can be easily calculated by numerical integration techniques. The theoretical expressions derived herein corroborate the simulation results obtained previously

Detection in the presence of surprise or undernulled interference

We consider the problem of detecting a signal of interest in the presence of colored noise, in the case of a covariance mismatch between the test cell and the training samples. More precisely, we consider a situation where an interfering signal (e.g., a sidelobe target or an undernulled interference) is present in the test cell and not in the secondary data. We show that the adaptive coherence estimator (ACE) is the generalized likelihood ratio test for such a problem, which may explain the previously observed fact that theACE has excellent sidelobe rejection capability, at the price of low mainlobe target sensitivity

Detection of a signal in linear subspace with bounded mismatch

We consider the problem of detecting a signal of interest in a background of noise with unknown covariance matrix, taking into account a possible mismatch between the actual steering vector and the presumed one. We assume that the former belongs to a known linear subspace, up to a fraction of its energy. When the subspace of interest consists of the presumed steering vector, this amounts to assuming that the angle between the actual steering vector and the presumed steering vector is upper bounded. Within this framework, we derive the generalized likelihood ratio test (GLRT). We show that it involves solving a minimization problem with the constraint that the signal of interest lies inside a cone. We present a computationally efficient algorithm to find the maximum likelihood estimator (MLE) based on the Lagrange multiplier technique. Numerical simulations illustrate the performance and the robustness of this new detector, and compare it with the adaptive coherence estimator which assumes that the steering vector lies entirely in a subspace

Adaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured plus Gaussian Interference Via Invariance

This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna. The problem is solved via the Principle of Invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant. A maximal invariant statistic, which completely characterizes the class of invariant decision rules and significantly compresses the original data domain, as well as its statistical characterization are determined. Thus, the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules. At the analysis stage, the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions

A bayesian approach to adaptive detection in nonhomogeneous environments

We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter

Design of Robust Radar Detectors Through Random Perturbation of the Target Signature

The paper addresses the problem of designing radar detectors more robust than Kelly's detector to possible mismatches of the assumed target signature, but with no performance degradation under matched conditions. The idea is to model the received signal under the signal-plus-noise hypothesis by adding a random component, parameterized via a design covariance matrix, that makes the hypothesis more plausible in presence of mismatches. Moreover, an unknown power of such component, to be estimated from the observables, can lead to no performance loss, under matched conditions. Derivation of the (one-step) GLRT is provided for two choices of the design matrix, obtaining detectors with different complexity and behavior. A third parametric detector is also obtained by an ad-hoc generalization of one of such GLRTs. The analysis shows that the proposed approach can cover a range of different robustness levels that is not achievable by state-of-the-art with the same performance of Kelly's detector under matched conditions