Optimality of beamforming in fading MIMO with noisy channel estimation

In this paper, we consider a single user block fading communication system where both the transmitter and receiver have multiple antennas. A transmission block is divided into training and data transmission phases. The channel estimation at the receiver is noisy. The transmitter has long term statistics of the estimated channel in the form of a covariance matrix. The general problem is to find optimum transmit covariance matrix under these channel state information (CSI) assumptions. Beamforming strategy is optimum when the optimum transmit covariance matrix is unit rank. Previous works find conditions under which beamforming is optimal when the receiver has instantaneous and full CSI. Here, we consider noisy CSI at the receiver and introduce a condition over channel covariance matrix, block length and the transmit power constraint, where beamforming is always the optimum transmission strategy. We show through simulations that beamforming is optimal for a larger set of parameters when block duration is short and when SNR is low. An interesting result we observe through simulations is that beamforming is always optimal when transmission block is at most three symbols long. This means that when block fading becomes faster, beamforming becomes optimal almost always regardless of number of antennas or other parameters.