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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.
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