Gradient of Error Probability of [Formula Omitted]-ary Hypothesis Testing Problems Under Multivariate Gaussian Noise

This letter considers an [Formula Omitted]-ary hypothesis testing problem on an [Formula Omitted]-dimensional random vector perturbed by the addition of Gaussian noise. A novel expression for the gradient of the error probability, with respect to the covariance matrix of the noise, is derived and sh...

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Bibliographic Details
Published inIEEE signal processing letters Vol. 27; p. 1909
Main Authors Jeong, Minoh, Dytso, Alex, Cardone, Martina
Format Journal Article
LanguageEnglish
Published New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.01.2020
Subjects
Covariance matrix
Hypotheses
Hypothesis testing
Mathematical analysis
Matrix algebra
Matrix methods
Noise
Random noise
Random variables
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Summary:This letter considers an [Formula Omitted]-ary hypothesis testing problem on an [Formula Omitted]-dimensional random vector perturbed by the addition of Gaussian noise. A novel expression for the gradient of the error probability, with respect to the covariance matrix of the noise, is derived and shown to be a function of the cross-covariance matrix between the noise matrix (i.e., the matrix obtained by multiplying the noise vector by its transpose) and Bernoulli random variables associated with the correctness event.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2020.3031487