### Abstract

This paper considers the problem of testing for the independence among multiple (≥ 2) random vectors with each random vector representing a time series captured at one sensor. Implementing the Generalized Likelihood Ratio Test involves testing the null hypothesis that the composite covariance matrix of the channels is block-diagonal through the use of a generalized Hadamard ratio. Using the theory of linear prediction and its connection with Gram determinants, it is shown that this generalized Hadamard ratio can be written as a product of scalars which are independently drawn from a beta distribution under the null hypothesis. This result is useful from a Monte Carlo analysis standpoint in that it is much more computationally efficient to form a product of scalar beta random variables than it is to compute the determinant of complex Wishart matrices.

Original language | English (US) |
---|---|

Title of host publication | 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings |

Pages | 3919-3923 |

Number of pages | 5 |

DOIs | |

State | Published - Oct 18 2013 |

Event | 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada Duration: May 26 2013 → May 31 2013 |

### Publication series

Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
---|---|

ISSN (Print) | 1520-6149 |

### Other

Other | 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 |
---|---|

Country | Canada |

City | Vancouver, BC |

Period | 5/26/13 → 5/31/13 |

### Keywords

- Generalized Likelihood Ratio Test
- Multichannel Coherence
- Multichannel Signal Detection
- Test for Block Independence

### ASJC Scopus subject areas

- Software
- Signal Processing
- Electrical and Electronic Engineering

## Fingerprint Dive into the research topics of 'Space-time coherence and its exact null distribution'. Together they form a unique fingerprint.

## Cite this

*2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings*(pp. 3919-3923). [6638393] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2013.6638393