  Consider a random matrix whose variance profile is random. This random matrix
is ergodic in one channel realization if, for each column and row, the
empirical distribution of the squared magnitudes of elements therein converges
to a nonrandom distribution. In this paper, noncrossing partition theory is
employed to derive expressions for several asymptotic eigenvalue moments (AEM)
related quantities of a large Wishart-type random matrix $\bb H\bb H^\dag$ when
$\bb H$ has a random variance profile and is nonergodic in one channel
realization. It is known the empirical eigenvalue moments of $\bb H\bb H^\dag$
are dependent (or independent) on realizations of the variance profile of $\bb
H$ when $\bb H$ is nonergodic (or ergodic) in one channel realization. For
nonergodic $\bb H$, the AEM can be obtained by i) deriving the expression of
AEM in terms of the variance profile of $\bb H$, and then ii) averaging the
derived quantity over the ensemble of variance profiles. Since the AEM are
independent of the variance profile if $\bb H$ is ergodic, the expression
obtained in i) can also serve as the AEM formula for ergodic $\bb H$ when any
realization of variance profile is available.
