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

### Other

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

City | Vancouver, BC |

Period | 5/26/13 → 5/31/13 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Signal Processing
- Software
- Electrical and Electronic Engineering

### Cite this

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

**Space-time coherence and its exact null distribution.** / Klausner, Nick; Azimi-Sadjadi, Mahmood; Scharf, Louis; Cochran, Douglas.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings.*, 6638393, pp. 3919-3923, 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013, Vancouver, BC, Canada, 5/26/13. https://doi.org/10.1109/ICASSP.2013.6638393

}

TY - GEN

T1 - Space-time coherence and its exact null distribution

AU - Klausner, Nick

AU - Azimi-Sadjadi, Mahmood

AU - Scharf, Louis

AU - Cochran, Douglas

PY - 2013/10/18

Y1 - 2013/10/18

N2 - 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.

AB - 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.

KW - Generalized Likelihood Ratio Test

KW - Multichannel Coherence

KW - Multichannel Signal Detection

KW - Test for Block Independence

UR - http://www.scopus.com/inward/record.url?scp=84890468766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890468766&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2013.6638393

DO - 10.1109/ICASSP.2013.6638393

M3 - Conference contribution

SN - 9781479903566

SP - 3919

EP - 3923

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

ER -