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On the distribution of indefinite quadratic forms in Gaussian random variables

Al-Naffouri, Tareq Y. and Hassibi, Babak (2009) On the distribution of indefinite quadratic forms in Gaussian random variables. In: IEEE International Symposium on Information Theory, 2009. ISIT 2009. IEEE , Piscataway, NJ, pp. 1744-1748. ISBN 978-1-4244-4312-3. https://resolver.caltech.edu/CaltechAUTHORS:20150204-073234311

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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 attempting 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/complex vectors and to the joint distribution of indefinite quadratic forms.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2009.5205261DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5205261PublisherArticle
ORCID:
AuthorORCID
Al-Naffouri, Tareq Y.0000-0001-6955-4720
Additional Information:© 2009 IEEE. The work of T. Y. Al-Naffouri was supported by the Fulbright Scholar Program and by a research grant from King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.
Funders:
Funding AgencyGrant Number
Fulbright Scholar ProgramUNSPECIFIED
King Fahd University of Petroleum and Minerals (KFUPM)UNSPECIFIED
Record Number:CaltechAUTHORS:20150204-073234311
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150204-073234311
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54348
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:05 Feb 2015 00:29
Last Modified:09 Mar 2020 13:18

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