Beamforming with imperfect channel knowledge: performance degradation analysis based on perturbation theory

We analyses the performance degradation of beamforming due to imperfect channel knowledge based on eigenvector perturbation theory. Easily computable approximations are given for the average signal to noise ratio loss when an estimate of the channel is available. The performance degradation of imperfect beamforming is then later assessed for LMMSE channel estimation taking into consideration power constraints.