An Upper Bound to the Marginal PDF of the Ordered Eigenvalues of Wishart Matrices
Diversity analysis of a number of Multiple-Input Multiple-Output (MIMO) applications requires the calculation of the expectation of a function whose variables are the ordered multiple eigen-values of a Wishart matrix. In order to carry out this calculation, the authors need the marginal pdf of an arbitrary subset of the ordered eigen-values. In this paper, they derive an upper bound to the marginal pdf of the eigen-values. The derivation is based on the multiple integration of the well-known joint pdf, which is very complicated due to the exponential factors of the joint pdf. They suggest an alternative function that provides simpler calculation of the multiple integration. As a result, the marginal pdf is shown to be bounded by a multivariate polynomial with a given degree.