### Abstract

Summary form only given, as follows. The generalized coherence (GC) estimate, a recently introduced detection statistic that forms the basis of a nonparametric test for a common but unknown signal on several noisy channels, is shown to be geometric in nature. This perspective is used to show that the GC estimate is the unique function of M ≥ 2 complex sample sequences having a desirable set of properties. Its distribution function is derived under the H_{0} assumption that the sample sequences representing filtered data from M noisy channels are drawn from independent Gaussian processes. This is accomplished by exploiting the interpretation of the MSC estimate as the volume of a polytope in (real) 2M-dimensional space. The properties and performance of the GC estimate as a detection statistic are also discussed. Detection thresholds corresponding to different false alarm probabilities are derived for various numbers of channels and sequence lengths. The performance of the GC detector as a function of the signal-to-noise ratios on the noisy channels is evaluated by simulation, and the results are compared with performance data for other multiple-channel detection schemes.

Original language | English (US) |
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Title of host publication | 1990 IEEE Int Symp Inf Theor |

Place of Publication | Piscataway, NJ, United States |

Publisher | Publ by IEEE |

Pages | 164 |

Number of pages | 1 |

State | Published - 1990 |

Event | 1990 IEEE International Symposium on Information Theory - San Diego, CA, USA Duration: Jan 14 1990 → Jan 19 1990 |

### Other

Other | 1990 IEEE International Symposium on Information Theory |
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City | San Diego, CA, USA |

Period | 1/14/90 → 1/19/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*1990 IEEE Int Symp Inf Theor*(pp. 164). Piscataway, NJ, United States: Publ by IEEE.

**A geometrical approach to multiple-channel detection.** / Cochran, Douglas; Gish, Herbert.

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

*1990 IEEE Int Symp Inf Theor.*Publ by IEEE, Piscataway, NJ, United States, pp. 164, 1990 IEEE International Symposium on Information Theory, San Diego, CA, USA, 1/14/90.

}

TY - GEN

T1 - A geometrical approach to multiple-channel detection

AU - Cochran, Douglas

AU - Gish, Herbert

PY - 1990

Y1 - 1990

N2 - Summary form only given, as follows. The generalized coherence (GC) estimate, a recently introduced detection statistic that forms the basis of a nonparametric test for a common but unknown signal on several noisy channels, is shown to be geometric in nature. This perspective is used to show that the GC estimate is the unique function of M ≥ 2 complex sample sequences having a desirable set of properties. Its distribution function is derived under the H0 assumption that the sample sequences representing filtered data from M noisy channels are drawn from independent Gaussian processes. This is accomplished by exploiting the interpretation of the MSC estimate as the volume of a polytope in (real) 2M-dimensional space. The properties and performance of the GC estimate as a detection statistic are also discussed. Detection thresholds corresponding to different false alarm probabilities are derived for various numbers of channels and sequence lengths. The performance of the GC detector as a function of the signal-to-noise ratios on the noisy channels is evaluated by simulation, and the results are compared with performance data for other multiple-channel detection schemes.

AB - Summary form only given, as follows. The generalized coherence (GC) estimate, a recently introduced detection statistic that forms the basis of a nonparametric test for a common but unknown signal on several noisy channels, is shown to be geometric in nature. This perspective is used to show that the GC estimate is the unique function of M ≥ 2 complex sample sequences having a desirable set of properties. Its distribution function is derived under the H0 assumption that the sample sequences representing filtered data from M noisy channels are drawn from independent Gaussian processes. This is accomplished by exploiting the interpretation of the MSC estimate as the volume of a polytope in (real) 2M-dimensional space. The properties and performance of the GC estimate as a detection statistic are also discussed. Detection thresholds corresponding to different false alarm probabilities are derived for various numbers of channels and sequence lengths. The performance of the GC detector as a function of the signal-to-noise ratios on the noisy channels is evaluated by simulation, and the results are compared with performance data for other multiple-channel detection schemes.

UR - http://www.scopus.com/inward/record.url?scp=0025626590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025626590&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025626590

SP - 164

BT - 1990 IEEE Int Symp Inf Theor

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -