Extreme Eigenvalue Distributions of Finite Random Wishart Matrices with Application to Spectrum Sensing

We employ a unified framework to express the exact cumulative distribution functions (CDF's) and probability density functions (PDF's) of both the largest and smallest eigenvalues of central uncorrelated complex random Wishart matrices of arbitrary (finite) size. The resulting extreme eigenvalue distributions, which are put in simple closed-forms, are then applied to build a Hypothesis-Test to solve the Primary User (PU) detection problem (aka Spectrum Sensing), relevant to Cognitive Radio (CR) applications. The proposed scheme is shown to outperform all asymptotic approaches recently proposed, as consequence of the fact that the distributions of the extreme eigenvalues are closed-form and exact, for any given matrix size.