A geometric approach to multiple-channel signal detection

The paper introduces the generalized coherence (GC) estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels. The GC estimate is developed as a natural generalization of the magnitude-squared coherence (MSC) estimate-a w...

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Bibliographic Details
Published in:IEEE transactions on signal processing 1995-09, Vol.43 (9), p.2049-2057
Main Authors: Cochran, D., Gish, H., Sinno, D.
Format: Article
Language:English
Subjects:
Applied sciences
Biosensors
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Gaussian noise
Geology
Information, signal and communications theory
Probability
Signal and communications theory
Signal detection
Signal to noise ratio
Signal, noise
Statistical distributions
Statistics
Telecommunications and information theory
Testing
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Summary:The paper introduces the generalized coherence (GC) estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels. The GC estimate is developed as a natural generalization of the magnitude-squared coherence (MSC) estimate-a widely used statistic for nonparametric detection of a common signal on two noisy channels. The geometrical nature of the GC estimate is exploited to derive its distribution under the H/sub 0/ hypothesis that the data channels contain independent white Gaussian noise sequences. Detection thresholds corresponding to a range of false alarm probabilities are calculated from this distribution. The relationship of the H/sub 0/ distribution of the GC estimate to that of the determinant of a complex Wishart-distributed matrix is noted. The detection performance of the three-channel GC estimate is evaluated by simulation using a white Gaussian signal sequence in white Gaussian noise. Its performance is compared with that of the multiple coherence (MC) estimate, another nonparametric multiple-channel detection statistic. The GC approach is found to provide better detection performance than the MC approach in terms of the minimum signal-to-noise ratio on all data channels necessary to achieve desired combinations of detection and false alarm probabilities.< >
ISSN:1053-587X
1941-0476
DOI:10.1109/78.414766