On rate-optimal signalling for MIMO systems with mean and covariance feedback

A second-order approximation is derived for the ergodic capacity of a MIMO communication system in which the mean and covariance of the channel are known at transmitter. This approximation is then used to efficiently obtain an almost optimal input covariance. More specifically, the design of the input covariance matrix that optimizes the second-order approximation is cast as a convex optimization problem. Using the Karush-Kuhn-Tucker optimality conditions for that problem, an efficient algorithm is devised for obtaining second-order optimal input covariance matrices. Our design examples show that the resulting input covariances yield ergodic rates that are close to the ergodic capacity of the system.