Precoder Design Based on Correlation Matrices for MIMO Systems

This paper presents a general framework for precoder designs for MIMO systems using partial channel knowledge on the transmit and receive correlation matrices at the transmitter. It is shown that the optimal linear precoder for any uncoded and coded MIMO system based on the MMSE or ergodic capacity criterion, or for an orthogonal ST coded MIMO system based on the minimum PEP criterion, is an eigen-beamformer that transmits the signal along eigenvectors of the transmit correlation matrix. Based on the eigen-values of both the transmit and receive correlation matrices, power loading across the eigen-beams is determined by water-pouring policy. Individual effects of the transmit and receive correlation matrices on the system performance are investigated. Simulation results show noticeable performance improvement over MIMO systems without precoder, particularly when the transmit correlation matrix has low rank