Optimal downlink beamforming for statistical CSI with robustness to estimation errors

We consider the problem of worst-case robust downlink beamforming in a multiuser Multiple-input-single-output (MISO) network with statistical channel state information (CSI) that is erroneous. In previous beamforming techniques, robustness is usually incorporated by employing generic error models, in which the mismatch between the presumed and the true instantaneous channel vectors, or the corresponding channel covariance matrices, is bounded by the Frobenius norm. A shortcoming of these methods is that these strongly rely on the assumption that the exact noise variance of the terminals and bounds on the channel mismatch are available. If this assumption is violated, then the beamforming approach may result in either insufficient robustness or overly conservative solutions. This assumption is particularly difficult as different sources of CSI error are generally not considered. In our proposed robust approach, we consider CSI mismatch from estimation errors in the noise power and the channel plus noise covariance matrix. Addressing both estimation errors separately allows us to derive meaningful threshold values for the uncertainty sets. In contrast to previous robust approaches based on Frobenius norm, we propose to use confidence intervals with given confidence levels to model the uncertainty sets. The simulation results verify the effectiveness of the proposed techniques.