On the distribution of indefinite quadratic forms in gaussian random variables

Tareq Y. Ai-Naffouri, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

54 Scopus citations

Abstract

In this work, we propose a transparent approach to evaluating the CDF of indefinite quadratic forms in Gaussian random variables and ratios of such forms. This quantity appears in the analysis of different receivers in communication systems and in various applications in signal processing. Instead of attem pting to find the pdf of this quantity as is the case in many papers in literature, we focus on finding the CDF. The basic trick that we implement is to replace inequalities that appear in the CDF calculations with the unit step function and replace the latter with its Fourier transform. This produces a multi-dimensional integral that can be evaluated using complex integration. We show how our approach extends to nonzero mean Gaussian real/com plex vectors and to the joint distribution of indefinite quadratic forms.

Original languageEnglish (US)
Title of host publication2009 IEEE International Symposium on Information Theory, ISIT 2009
Pages1744-1748
Number of pages5
DOIs
StatePublished - Nov 19 2009
Event2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of
Duration: Jun 28 2009Jul 3 2009

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8102

Other

Other2009 IEEE International Symposium on Information Theory, ISIT 2009
CountryKorea, Republic of
CitySeoul
Period06/28/0907/3/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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