We report the similarity between the Nakagami-m fading distribution and the three Gaussian ensembles of random matrix theory. We provide a brief review of random matrix theory and wireless fading. We show that the Nakagami-m distribution serves as mapping between the three ensembles. The statistics of the wireless fading amplitude, as modeled by Nakagami-m distribution, provide a rare example of a classically chaotic system that exhibits a transition between the Gaussian orthogonal, Gaussian unitary, and Gaussian symplectic ensembles of random matrix theory.