  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 eigenvalues of a Wishart matrix. In order to
carry out this calculation, we need the marginal pdf of an arbitrary subset of
the ordered eigenvalues. In this letter, we derive an upper bound to the
marginal pdf of the eigenvalues. 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. We 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. After a standard bounding procedure in a Pairwise Error Probability
(PEP) analysis, by applying the marginal pdf to the calculation of the
expectation, the diversity order for a number of MIMO systems can be obtained
in a simple manner. Simulation results that support the analysis are presented.
