On optimal training and beamforming in uncorrelated MIMO systems with feedback

This paper studies the design and analysis of optimal training-based beamforming in uncorrelated multiple-input multiple-output (MIMO) channels with known Gaussian statistics. First, given the response of the MIMO channel to a finite sequence of training vectors, the beamforming vector which maximizes the average received signal-to-noise ratio (SNR) over all channel realizations is found. Secondly, the question of what consists of optimal training for a given amount of training is addressed. Upper and lower bounds for the maximum achievable SNR using beamforming are established. Furthermore, optimal training sequences are conjectured to satisfy the Welch bound. The conjecture is supported by the evidence that such sequences achieve close to the upper bound with moderate to large amount of trainings.