### Abstract

Extreme Value Theory (EVT) is used to analyze the peak sidelobe level distribution for array element positions with arbitrary probability distributions. Computations are discussed in the context of linear antenna arrays using electromagnetic energy. The results also apply to planar arrays of random elements that can be transformed into linear arrays. For sparse arrays with small number of elements, Gaussian approximations to the beampattern distribution at a particular angle introduce inaccuracies to the probability calculations. EVT is applied without making these Gaussian approximations. It is shown that the peak sidelobe level distribution converges weakly to a Gumbel distribution in the limit of a large number of beampattern samples. This result is for both sparse and dense arrays of randomly placed antennas over a large aperture. The definition of a large aperture in this context is ambiguous, but a possible rule-of-thumb is that it is at least a wavelength.

Original language | English (US) |
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Title of host publication | IEEE National Radar Conference - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1671-1676 |

Number of pages | 6 |

Volume | 2015-June |

Edition | June |

DOIs | |

State | Published - Jun 22 2015 |

Event | 2015 IEEE International Radar Conference, RadarCon 2015 - Arlington, United States Duration: May 10 2015 → May 15 2015 |

### Other

Other | 2015 IEEE International Radar Conference, RadarCon 2015 |
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Country | United States |

City | Arlington |

Period | 5/10/15 → 5/15/15 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*IEEE National Radar Conference - Proceedings*(June ed., Vol. 2015-June, pp. 1671-1676). [7131267] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/RADAR.2015.7131267