On the Maximal Invariant Statistic for Adaptive Radar Detection in Partially-Homogeneous Disturbance with Persymmetric Covariance

This letter deals with the problem of adaptive signal detection in partially-homogeneous and persymmetric Gaussian disturbance within the framework of invariance theory. First, a suitable group of transformations leaving the problem invariant is introduced and the Maximal Invariant Statistic (MIS) is derived. Then, it is shown that the (Two-step) Generalized-Likelihood Ratio test, Rao and Wald tests can be all expressed in terms of the MIS, thus proving that they all ensure a Constant False-Alarm Rate (CFAR).Comment: submitted for journal publicatio

Exploiting persymmetry for low-rank Space Time Adaptive Processing

International audienceReducing the number of secondary data used to estimate the Covariance Matrix (CM) for Space Time Adaptive Processing (STAP) techniques is still an active research topic. Within this framework, the Low-Rank (LR) structure of the clutter is well-known and the corresponding LR STAP filters have been shown to exhibit a smaller Signal Interference plus Noise Ratio (SINR) loss than classical STAP filters, only 2r secondary data (where r is the clutter rank) instead of 2m (where m is the data size) are required to reach the classical 3 dB SNR loss. By using other features of the radar system, other properties of the CM can be exploited to further reduce the number of secondary data; this is the case for active systems using a symmetrically spaced linear array with constant pulse repetition interval, which results in a persymmetric structure of the noise CM. In this context, we propose to combine this property of the CM and the LR structure of the clutter to perform CM estimation. In this paper, the resulting STAP filter is shown, both theoretically and experimentally, to exhibit good performance with fewer secondary data; 3 dB SINR Loss is achieved with only r secondary data

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

Model Order Selection Rules For Covariance Structure Classification

The adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper. This represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties. The considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of Model Order Selection (MOS) is exploited to devise suitable decision rules. Several MOS techniques, such as the Akaike, Takeuchi, and Bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed. At the analysis stage, illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

Unit Circle Roots Based Sensor Array Signal Processing

As technology continues to rapidly evolve, the presence of sensor arrays and the algorithms processing the data they generate take an ever-increasing role in modern human life. From remote sensing to wireless communications, the importance of sensor signal processing cannot be understated. Capon\u27s pioneering work on minimum variance distortionless response (MVDR) beamforming forms the basis of many modern sensor array signal processing (SASP) algorithms. In 2004, Steinhardt and Guerci proved that the roots of the polynomial corresponding to the optimal MVDR beamformer must lie on the unit circle, but this result was limited to only the MVDR. This dissertation contains a new proof of the unit circle roots property which generalizes to other SASP algorithms. Motivated by this result, a unit circle roots constrained (UCRC) framework for SASP is established and includes MVDR as well as single-input single-output (SISO) and distributed multiple-input multiple-output (MIMO) radar moving target detection. Through extensive simulation examples, it will be shown that the UCRC-based SASP algorithms achieve higher output gains and detection probabilities than their non-UCRC counterparts. Additional robustness to signal contamination and limited secondary data will be shown for the UCRC-based beamforming and target detection applications, respectively

Adaptive Radar Detection in Heterogeneous Clutter-dominated Environments

In this paper, we propose a new solution for the detection problem of a coherent target in heterogeneous environments. Specifically, we first assume that clutter returns from different range bins share the same covariance structure but different power levels. This model meets the experimental evidence related to non-Gaussian and non-homogeneous scenarios. Then, unlike existing solutions that are based upon estimate and plug methods, we propose an approximation of the generalized likelihood ratio test where the maximizers of the likelihoods are obtained through an alternating estimation procedure. Remarkably, we also prove that such estimation procedure leads to an architecture possessing the constant false alarm rate (CFAR) when a specific initialization is used. The performance analysis, carried out on simulated as well as measured data and in comparison with suitable well-known competitors, highlights that the proposed architecture can overcome the CFAR competitors and exhibits a limited loss with respect to the other non-CFAR detectors

Learning Strategies for Radar Clutter Classification

In this paper, we address the problem of classifying clutter returns in order to partition them into statistically homogeneous subsets. The classification procedure relies on a model for the observables including latent variables that is solved by the expectation-maximization algorithm. The derivations are carried out by accounting for three different cases for the structure of the clutter covariance matrix. A preliminary performance analysis highlights that the proposed technique is a viable means to cluster clutter returns over the range.Comment: 12 pages, 13 figure