Premium
Some Bounds on the Distribution of Certain Quadratic Forms in Normal Random Variables
Author(s) -
Gao Hongsheng,
Smith Peter
Publication year - 1998
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00008
Subject(s) - mathematics , diagonal , hermitian matrix , combinatorics , transpose , independent and identically distributed random variables , random variable , diagonal matrix , positive definite matrix , matrix (chemical analysis) , quadratic equation , constant (computer programming) , identity matrix , distribution (mathematics) , identity (music) , mathematical analysis , pure mathematics , statistics , eigenvalues and eigenvectors , geometry , physics , materials science , quantum mechanics , computer science , acoustics , composite material , programming language
The paper derives bounds on the distribution of the quadratic forms Z = y H ( X Γ X H ) −1 y and W = y H (σ 2 I + X Γ X H ) −1 y , where the elements of the M × 1 vector y and the M × N matrix X are independent identically distributed (i.i.d.) complex zero mean Normal variables, Γ is some N × N diagonal matrix with positive diagonal elements, I , is the identity, σ 2 is a constant and H denotes the Hermitian transpose. The bounds are convenient for numerical work and appear to be tight for small values of M . This work has applications in digital mobile radio for a specific channel where M antennas are used to receive a signal with N interferers. Some of these applications in radio communication systems are discussed.