Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback

Optimal transmitter designs obeying the water-filling principle are well-documented; they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter. Because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems, we design, in this paper, an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels. Our optimal transmitter design turns out to be an eigen-beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams. The optimality pertains to minimizing an upper bound on the symbol error rate, which leads to better performance than maximizing the expected signal-to-noise ratio (SNR) at the receiver. Coupled with orthogonal space-time block codes, two-directional eigen-beamforming emerges as a more attractive choice than conventional one-directional beamforming with uniformly improved performance, without rate reduction, and without essential increase in complexity. With multiple receive antennas and reasonably good feedback quality, the two-directional eigen-beamformer is also capable of achieving the best possible performance in a large range of transmit-power-to-noise ratios, without a rate penalty.