Capacity of a Gaussian MIMO channel with nonzero mean

We characterize the input covariance that maximizes the ergodic capacity of a flat-fading, multiple-input-multiple-output (MIMO) channel with additive white Gaussian noise, when the entries of the channel matrix are independent, circularly symmetric, complex Gaussian random variables of nonzero (and possibly different) means and identical variances. We show that the optimal transmit covariance must have the same eigenvectors as the squared mean channel, thereby reducing the computation of the optimal covariance to a simple convex optimization. This generalizes existing results for multiple-input-single-output (MISO) channels and MIMO channels restricted to have a mean of unit rank.