Show simple item record

dc.contributor.authorAl-Naffouri, Tareq Y.
dc.contributor.authorMoinuddin, Muhammed
dc.contributor.authorAjeeb, Nizar
dc.contributor.authorHassibi, Babak
dc.contributor.authorMoustakas, Aris L.
dc.date.accessioned2016-11-03T13:21:51Z
dc.date.available2016-11-03T13:21:51Z
dc.date.issued2015-10-30
dc.identifier.citationAl-Naffouri TY, Moinuddin M, Ajeeb N, Hassibi B, Moustakas AL (2016) On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables. IEEE Transactions on Communications 64: 153–165. Available: http://dx.doi.org/10.1109/TCOMM.2015.2496592.
dc.identifier.issn0090-6778
dc.identifier.doi10.1109/TCOMM.2015.2496592
dc.identifier.urihttp://hdl.handle.net/10754/621649
dc.description.abstract© 2015 IEEE. In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-meansquare (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables.We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.
dc.description.sponsorshipThis publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. URF/1/2221-01.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.subjectCorrelated Gaussian random vectors
dc.subjectMulti-user diversity
dc.subjectWeighted norms of Gaussian variables
dc.subjectWireless communications
dc.titleOn the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.identifier.journalIEEE Transactions on Communications
dc.contributor.institutionDepartment of Electrical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
dc.contributor.institutionDepartment of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
dc.contributor.institutionCenter of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, Saudi Arabia
dc.contributor.institutionDepartment of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon
dc.contributor.institutionDepartment of Electrical Engineering, California Institute of Technology, Pasadena, CA, United States
dc.contributor.institutionDepartment of Physics, National Kapodistrian University of Athens, Panepistimiopolis, Athens, Greece
kaust.personAl-Naffouri, Tareq Y.
kaust.grant.numberURF/1/2221-01
kaust.acknowledged.supportUnitOffice of Sponsored Research (OSR)
dc.date.published-online2015-10-30
dc.date.published-print2016-01


This item appears in the following Collection(s)

Show simple item record