Limited feedback space-time coding in correlated MIMO channels

Space-time codes have been designed over the last decade to enhance the reliability of open-loop fading wireless systems. However, recent technological advances have enabled the possibility of low-rate feedback from the receiver to the transmitter. The focus of this work is on the implications of this feedback in a point-to-point MIMO system with a coherent receiver and a general model for spatial correlation that is known at the transmitter. We assume that B bits of quantized channel information are available at the transmitter. Coding over space-time is then studied by considering the family of linear dispersion (LD) codes that meets an additional orthogonal condition, which leads to a decoding complexity comparable to orthogonal space-time block codes (OSTBC). Our results show that, when B is small, a space-time coding scheme that is equivalent to beamforming and does not code across time is optimal in a weak sense in that it maximizes the average received SNR. As B increases, this weak optimality transitions to optimality in a strong sense characterized by the maximization of the average mutual information. Hence, from a system designer's perspective, our work suggests that beamforming may not only be attractive from a low-complexity viewpoint, but also from an information-theoretic viewpoint.