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On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables
 

Summary: On the Distribution of Indefinite Quadratic Forms in
Gaussian Random Variables
Tareq Y. Al-Naffouri
Department of Electrical Engineering
King Fahd University of Petroleum & Minerals
Dhahran, Saudi Arabia
Email: naffouri@kfupm.edu.sa
Babak Hassibi
Department of Electrical Engineering
California Institute of Technology
Pasadena, CA
Email: hassibi@systems.caltech.edu
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

  

Source: Al-Naffouri, Tareq Y. - Electrical Engineering Department, King Fahd University of Petroleum and Minerals

 

Collections: Engineering