Non-robustness of statistics-based beamformer design in correlated MIMO channels

Recent attention on correlated multi-input multi-output systems has centered around the case of imperfect channel or statistical information at the transmitter. The focus of this work is on correlated channels with arbitrary antenna array geometry and spacings, a coherent receiver, and imperfect statistical knowledge at the transmitter. Leveraging a recently proposed channel modeling paradigm that exploits processing in the angular domain, we first elucidate the structure of the optimal schemes when 'genie-aided' perfect statistical information is available at the transmitter. In the low-SNR case, we then show that the beamforming scheme that is optimal when perfect statistical information is available does not degrade smoothly with imperfections in the statistical information. We then go on to show that there exists a certain low-complexity beamforming approach which, while being sub-optimal in the genie-aided case, is robust to statistical feedback as well as the dynamics of its evolution.