Precoding of orthogonal STBC with channel covariance feedback for minimum error probability

This paper develops the linear transformation (or precoding) of orthogonal space-time block codes (STBC) for minimizing probability of decoding error, when the channel covariance matrix is available at the transmitter. We build on recent work that stated the optimization problem without solving for the transformation. Specifically, we provide a closed-form solution for the multi-input single-output (MISO) systems, and a numerical solution for the multi-input multi-output (MIMO) systems. Our results confirm that eigen-beamforming is optimal at low SNR or highly correlated channels, and full diversity is optimal at high SNR or weakly correlated channels.