 
Summary: An Upper Bound to the Marginal PDF of the
Ordered Eigenvalues of Wishart Matrices and Its
Application to MIMO Diversity Analysis
Hong Ju Park and Ender Ayanoglu
Center for Pervasive Communications and Computing
Department of Electrical Engineering and Computer Science
University of California, Irvine
Email: hjpark@uci.edu, ayanoglu@uci.edu
AbstractDiversity analysis of a number of multipleinput
multipleoutput (MIMO) applications requires the calculation of
the expectation of a function whose variables are the ordered
multiple eigenvalues of the Wishart matrices. To solve this, we
need the marginal pdf of an arbitrary subset of the ordered
eigenvalues. The marginal pdf shown in the literature is useful
in numerical analysis, but not beneficial to diversity analysis.
In this paper, we derive an upper bound to the marginal pdf
of the eigenvalues. The derivation is based on the multiple
integration of the wellknown joint pdf, which is very complicated
due to the exponential factors of the joint pdf. We suggest
an alternative function that provides simpler calculation of the
