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

Optimal transmitter designs obeying the water-filling principle are well-documented, and 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 develop in this paper optimal transmitter design based on the knowledge of mean values of the underlying channels. Applied to a multiple transmit-antenna paradigm, our optimal transmitter design turns out to be an eigen-beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the channel correlation matrix conditioned on channel mean, and with proper power loading across beams. The optimality pertains to minimizing a tight bound on the symbol error rate. 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.