Gradient of error probability of m-ary hypothesis testing problems under multivariate gaussian noise

Minoh Jeong, Alex Dytso, Martina Cardone

Research output: Contribution to journalArticlepeer-review


This letter considers an M-ary hypothesis testing problem on an n-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.

Original languageEnglish (US)
Article number9226081
Pages (from-to)1909-1913
Number of pages5
JournalIEEE Signal Processing Letters
StatePublished - 2020

Bibliographical note

Funding Information:
Manuscript received August 11, 2020; revised September 25, 2020; accepted October 10, 2020. Date of publication October 15, 2020; date of current version November 4, 2020. The work of M. Jeong and M. Cardone was supported in part by the U.S. National Science Foundation under Grant CCF-1849757. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jun Liu (Corresponding author: Minoh Jeong.) Minoh Jeong and Martina Cardone are with the Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55404 USA (e-mail:;

Publisher Copyright:
© 2020 IEEE.


  • Error probability
  • Gradient
  • Hypothesis testing
  • Multivariate Gaussian noise


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