Impact of Channel Estimation Errors on Single Stream MIMO Beamforming

In single stream MIMO communication systems, the beamforming or precoding vectors are chosen as the singular vectors corresponding to the largest singular value of the MIMO channel matrix, in order to maximize the received signal to noise ratio (SNR). In practical scenarios, beamforming vectors are chosen based on the estimated channel matrix corrupted by estimation errors. In this letter, we analytically obtain lower bounds on the received SNR and the corresponding channel capacity, under this mismatched beamforming. We apply our bounds to millimeter wave beamforming systems and show that they are tight in moderate to high SNR regimes.