Transmit Directions and Optimality of Beamforming in MIMO-MAC with Partial CSI at the Transmitters

We consider a multi-input multi-output (MIMO) multiple access channel (MAC) where the receiver has the perfect channel state information (CSI), while the transmitters have partial CSI, which is in the form of either the covariance matrix of the channel or the mean matrix of the channel. We show that the transmit directions of each user are the eigenvectors of the channel covariance and mean feedback matrices in covariance and mean feedback models, respectively. Then, we find the conditions under which beamforming is optimal for all users. We observe through simulations that the region where beamforming is optimal for all users gets larger with the addition of new users to the system.