Exact Minimum Eigenvalue Distribution of a Correlated Complex Non-Central Wishart Matrix

We derive the exact cumulative distribution function (c.d.f.) of the minimum eigenvalue of a correlated complex non-central Wishart matrix. This result is in the form of a simple infinite series with fast convergence, and applies for the important case where the non-centrality matrix has rank one. Simplified asymptotic expressions for the c.d.f. are given for large matrix dimensions, as well as first-order expansions around the origin. The eigenvalue distributions in this paper have various important applications to multiple-input multiple-output (MIMO) communication systems, as well other scientific areas such as econometrics and multivariate statistics.