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Entropy 2016, 18(11), 381; doi:10.3390/e18110381

The Geometry of Signal Detection with Applications to Radar Signal Processing

School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
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Academic Editors: Arye Nehorai, Satyabrata Sen and Murat Akcakaya
Received: 30 August 2016 / Revised: 13 October 2016 / Accepted: 20 October 2016 / Published: 25 October 2016
(This article belongs to the Special Issue Radar and Information Theory)
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Abstract

The problem of hypothesis testing in the Neyman–Pearson formulation is considered from a geometric viewpoint. In particular, a concise geometric interpretation of deterministic and random signal detection in the philosophy of information geometry is presented. In such a framework, both hypotheses and detectors can be treated as geometrical objects on the statistical manifold of a parameterized family of probability distributions. Both the detector and detection performance are geometrically elucidated in terms of the Kullback–Leibler divergence. Compared to the likelihood ratio test, the geometric interpretation provides a consistent but more comprehensive means to understand and deal with signal detection problems in a rather convenient manner. Example of the geometry based detector in radar constant false alarm rate (CFAR) detection is presented, which shows its advantage over the classical processing method. View Full-Text
Keywords: hypothesis testing; signal detection; information geometry; likelihood ratio test; Neyman–Pearson detection; matrix CFAR detector hypothesis testing; signal detection; information geometry; likelihood ratio test; Neyman–Pearson detection; matrix CFAR detector
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Cheng, Y.; Hua, X.; Wang, H.; Qin, Y.; Li, X. The Geometry of Signal Detection with Applications to Radar Signal Processing. Entropy 2016, 18, 381.

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