A Maximum Entropy Characterization of Spatially Correlated MIMO Wireless Channels

We investigate the problem of establishing the joint probability distribution of the entries of a multiple-input multiple-output (MIMO) spatially correlated flat-fading channel, when little or no information about the channel properties are available. We show that the entropy of a random positive semidefinite matrix is maximized by the Wishart distribution. We subsequently obtain the maximum entropy distribution of the MIMO transfer matrix by establishing its distribution conditioned on the covariance, and by later marginalizing over the covariance matrix. The obtained distribution is isotropic, and is described analytically as a function of the Frobenius norm of the channel matrix.