Random Matrix Transforms and Applications via Non-Asymptotic Eigenanalysis

This work introduces an effective approach to derive the marginal density distribution of an unordered eigenvalue for finite-dimensional random matrices of Wishart and F type, based on which we give several examples of closed-form and series expressions for the Shannon and eta transforms of random matrices with nonzero mean and/or dependent entries. The newly obtained results allow for a compact non-asymptotic characterization of MIMO and multiuser vector channels in terms of both ergodic capacity and minimum mean square error (MMSE). In addition, the derived marginal density distributions can be of interest on their own in other fields of applied statistics