Precoder design based on correlation matrices for MIMO systems

This paper presents a precoder design based only on the correlation matrices to avoid the need of perfect channel knowledge at the transmitter and receiver in practical MIMO systems. The structures for optimal linear precoders are derived for three criteria: minimum pairwise error probability, minimum mean squared-error, and maximum ergodic (mean) channel capacity. The minimum pairwise error probability and minimum mean squared-error criteria lead to the same optimum precoder structure. It is shown that, in general, the optimal linear transformations for the three criteria are the eigen-beamformers that transmit the signal along the eigenvectors of the transmit correlation matrix. Power loading across the eigen-beams is determined by considering the eigenvalues of both transmit and receive correlation matrices and can be viewed as a water-pouring policy. Simulation results show noticeable performance improvement over conventional systems, particularly when their transmit correlation matrix has low rank.