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.
Bibliographical noteFunding 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: firstname.lastname@example.org; email@example.com).
© 2020 IEEE.
- Error probability
- Hypothesis testing
- Multivariate Gaussian noise