### 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 language | English (US) |
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Title of host publication | 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012 |

Pages | 413-416 |

Number of pages | 4 |

DOIs | |

State | Published - Oct 12 2012 |

Event | 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012 - Hoboken, NJ, United States Duration: Jun 17 2012 → Jun 20 2012 |

### Publication series

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

### Other

Other | 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012 |
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Country | United States |

City | Hoboken, NJ |

Period | 6/17/12 → 6/20/12 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*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