On the optimality-range of beamforming for MIMO systems with covariance feedback

We study the optimal transmission strategy of a multiple-input multiple-output (MIMO) communication system with covariance feedback. We assume that the receiver has perfect channel state information while the transmitter knows only the channel covariance matrix. We consider the common down-link transmission model where the base station is un-obstructed while the mobile station is surrounded by local scatterer. Therefore the channel matrix is modeled with Gaussian complex random entries with independent identically distributed rows and correlated columns. For this transmission scenario the capacity achieving eigenvectors of the transmit covariance matrix are known [8]. The capacity achieving eigenvalues can not be computed easily. We analyze the optimal transmission strategy as a function of the transmit power. A MIMO system using only one eigenvalue performs beamforming. We derive a necessary and sufficient condition for when beamforming achieves capacity. The theoretical results are illustrated by numerical simulations.