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Consider a random matrix whose variance profile is random. This random matrixis ergodic in one channel realization if, for each column and row, theempirical distribution of the squared magnitudes of elements therein convergesto a nonrandom distribution. In this paper, noncrossing partition theory isemployed 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 channelrealization. It is known the empirical eigenvalue moments of $\bb H\bb H^\dag$are dependent (or independent) on realizations of the variance profile of $\bbH$ when $\bb H$ is nonergodic (or ergodic) in one channel realization. Fornonergodic $\bb H$, the AEM can be obtained by i) deriving the expression ofAEM in terms of the variance profile of $\bb H$, and then ii) averaging thederived quantity over the ensemble of variance profiles. Since the AEM areindependent of the variance profile if $\bb H$ is ergodic, the expressionobtained in i) can also serve as the AEM formula for ergodic $\bb H$ when anyrealization of variance profile is available.

Asymptotic Eigenvalue Moments of Wishart-Type Random Matrix Without Ergodicity in One Channel Realization