On the distribution of indefinite quadratic forms in Gaussian random variables
- Creators
- Al-Naffouri, Tareq Y.
- Hassibi, Babak
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.
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.Attached Files
Published - 05205261.pdf
Files
Name | Size | Download all |
---|---|---|
md5:65547ecf3bd8ee71f53ba2c1e863389d
|
779.5 kB | Preview Download |
Additional details
- Eprint ID
- 54348
- DOI
- 10.1109/ISIT.2009.5205261
- Resolver ID
- CaltechAUTHORS:20150204-073234311
- Fulbright Scholar Program
- King Fahd University of Petroleum and Minerals (KFUPM)
- Created
-
2015-02-05Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field