Exact Statistical Characterization of $2\times 2$ Gram Matrices with Arbitrary Variance Profile

Nicolas Auguin, David Morales-Jimenez, Matthew McKay

This paper is concerned with the statistical properties of the Gram matrix $\mathbf{W}=\mathbf{H}{\mathbf{H}}^{†}$, where $\mathbf{H}$ is a $2\times 2$ complex central Gaussian ma…