A Unifying Framework for Adaptive Radar Detection in Homogeneous plus Structured Interference-Part II: Detectors Design

This paper deals with the problem of adaptive multidimensional/multichannel signal detection in homogeneous Gaussian disturbance with unknown covariance matrix and structured (unknown) deterministic interference. The aforementioned problem extends the well-known Generalized Multivariate Analysis of Variance (GMANOVA) tackled in the open literature. In a companion paper, we have obtained the Maximal Invariant Statistic (MIS) for the problem under consideration, as an enabling tool for the design of suitable detectors which possess the Constant False-Alarm Rate (CFAR) property. Herein, we focus on the development of several theoretically-founded detectors for the problem under consideration. First, all the considered detectors are shown to be function of the MIS, thus proving their CFARness property. Secondly, coincidence or statistical equivalence among some of them in such a general signal model is proved. Thirdly, strong connections to well-known simpler scenarios found in adaptive detection literature are established. Finally, simulation results are provided for a comparison of the proposed receivers.Comment: Submitted for journal publicatio

A novel approach to robust radar detection of range-spread targets

This paper proposes a novel approach to robust radar detection of range-spread targets embedded in Gaussian noise with unknown covariance matrix. The idea is to model the useful target echo in each range cell as the sum of a coherent signal plus a random component that makes the signal-plus-noise hypothesis more plausible in presence of mismatches. Moreover, an unknown power of the random components, to be estimated from the observables, is inserted to optimize the performance when the mismatch is absent. The generalized likelihood ratio test (GLRT) for the problem at hand is considered. In addition, a new parametric detector that encompasses the GLRT as a special case is also introduced and assessed. The performance assessment shows the effectiveness of the idea also in comparison to natural competitors.Comment: 28 pages, 8 figure

On Time-Reversal Imaging by Statistical Testing

This letter is focused on the design and analysis of computational wideband time-reversal imaging algorithms, designed to be adaptive with respect to the noise levels pertaining to the frequencies being employed for scene probing. These algorithms are based on the concept of cell-by-cell processing and are obtained as theoretically-founded decision statistics for testing the hypothesis of single-scatterer presence (absence) at a specific location. These statistics are also validated in comparison with the maximal invariant statistic for the proposed problem.Comment: Reduced form accepted in IEEE Signal Processing Letter

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

Asymptotic robustness of Kelly's GLRT and Adaptive Matched Filter detector under model misspecification

A fundamental assumption underling any Hypothesis Testing (HT) problem is that the available data follow the parametric model assumed to derive the test statistic. Nevertheless, a perfect match between the true and the assumed data models cannot be achieved in many practical applications. In all these cases, it is advisable to use a robust decision test, i.e. a test whose statistic preserves (at least asymptotically) the same probability density function (pdf) for a suitable set of possible input data models under the null hypothesis. Building upon the seminal work of Kent (1982), in this paper we investigate the impact of the model mismatch in a recurring HT problem in radar signal processing applications: testing the mean of a set of Complex Elliptically Symmetric (CES) distributed random vectors under a possible misspecified, Gaussian data model. In particular, by using this general misspecified framework, a new look to two popular detectors, the Kelly's Generalized Likelihood Ration Test (GLRT) and the Adaptive Matched Filter (AMF), is provided and their robustness properties investigated.Comment: ISI World Statistics Congress 2017 (ISI2017), Marrakech, Morocco, 16-21 July 201

Foundational principles for large scale inference: Illustrations through correlation mining

When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset is often variable-rich but sample-starved: a regime where the number $n$ of acquired samples (statistical replicates) is far fewer than the number $p$ of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for "Big Data." Sample complexity however has received relatively less attention, especially in the setting when the sample size $n$ is fixed, and the dimension $p$ grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. We demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks