Is Transmit Beamforming Robust?

Transmit beamforming is a simple strategy that uses only one spatial direction in a multiple-input multiple-output (MIMO) channel. Due to its simplicity, beamforming is usually seen sensitive to inaccuracies of the channel state information at the transmitter (CSIT). In this paper, we investigate the robustness of beamforming with respect to the worst-case CSIT. Our result shows that beamforming is actually robust, in the sense that it achieves the maximum received signal-to-noise ratio (SNR) in the worst channel within an elliptical uncertainty region defined by the weighted spectral norm. This result implies that beamforming has the ability to combat against the imperfectness of CSIT, especially when channel dimensions or channel uncertainty are small.