Abstract
We discuss the origin of the well-known integral form for the Gaussian Q-function. Although this form is originally attributed to Craig in his 1991 paper, it actually was inferred in previous communications theory references in the literature by Weinstein, and explicitly stated by Pawula, Rice and Roberts. Specifically, this form can be seen as a particular case of the general F-function, that is related to the distribution of the phase angle between two vectors perturbed by Gaussian noise. We show that the F-function includes as particular cases the one- and two-dimensional Gaussian Q-functions, and is connected with a class of confluent hypergeometric functions through the multivariate Φ 1 (n) function. This connection generalizes the existing relation between the Gaussian Q-functions and this family of hypergeometric functions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
