Distribution-free detection under complex elliptically symmetric clutter distribution

Esa Ollila, David Tyler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Scopus citations

Abstract

We study the constant false alarm rate matched subspace detector (CFAR MSD) of a signal observed under additive noise following a complex elliptically symmetric (CES) distribution which include the class of compound-Gaussian (CG) distributions as special cases. We prove that the detector is distribution-free under the null (signal free) hypothesis and derive simple expressions for the probability of detection assuming CG-distributed clutter. The derived theoretical results are then illustrated by contrasting them with the performance of a practical adaptive detector which estimates the shape matrix (normalized clutter covariance matrix) from the set of secondary data using complex Tyler's M-estimator of scatter under small sample lengths. We also prove that the complex Tyler's M-estimator is the maximum likelihood estimator (MLE) of the shape matrix under the assumption that the secondary data are independent random vectors from a possibly different CES distributions but which share the same shape matrix parameter.

Original languageEnglish (US)
Title of host publication2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012
Pages413-416
Number of pages4
DOIs
StatePublished - Oct 12 2012
Event2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012 - Hoboken, NJ, United States
Duration: Jun 17 2012Jun 20 2012

Publication series

NameProceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
ISSN (Electronic)2151-870X

Other

Other2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012
CountryUnited States
CityHoboken, NJ
Period6/17/126/20/12

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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  • Cite this

    Ollila, E., & Tyler, D. (2012). Distribution-free detection under complex elliptically symmetric clutter distribution. In 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012 (pp. 413-416). [6250525] (Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop). https://doi.org/10.1109/SAM.2012.6250525