Design of multiple antenna coding schemes with channel feedback

We derive multiple antenna transmission strategies in the presence of limited channel information at the transmitter and the receiver. In, particular, we look at the cases of complete channel information, channel phase information and channel amplitude information at the transmitter. We highlight that transmission along the eigenvector of the channel corresponding to the maximum eigenvalue minimizes error probability, when complete channel information is available at the transmitter. In the case where only the channel phase information is available at the transmitter, we derive the beamformer which minimizes the error probability. We also show that, in the presence of channel amplitude information at the transmitter without any phase information, selection diversity at the transmitter is the best beamforming strategy. We evaluate the penalty in SNR incurred by the transmission schemes in the case of limited channel information compared to the case of complete channel information at the transmitter.