MIMO capacity with channel uncertainty: does feedback help?

We investigate ergodic capacities and optimal transmitter strategies in Rayleigh fading multiple input multiple output (MIMO) channels with spatial correlation, when there exist channel uncertainties arising from the combined effect of channel estimation error and limited feedback. We consider both covariance feedback and instantaneous feedback, and formulate optimization problems that determine the capacities and optimal transmitter designs for both cases. In the high SNR regime, the optimal solutions have simple closed form formulas that involve inverting the channel covariance and waterfilling over instantaneous channel gains. Numerical results show that instantaneous feedback gives large capacity gain at low SNR and is also helpful at high SNR. Covariance feedback, on the other hand, seems to give little gain at mid SNR, but is almost as good as instantaneous feedback at high SNR under a reasonable channel estimation quality.