Large system analysis of beamforming for MIMO systems with limited training

We consider multiple-input multiple-output (MIMO) systems exploiting the full diversity order of a MIMO fading channel via optimal beamforming and combining. Specifically, an analytical characterization of the transient regime of a training-based MIMO system over arbitrarily correlated channels is presented. No channel state information is assumed to be available at either the transmitter or the receiver side, so that the design of the optimal transmit and receive beamformers is necessarily based on a finite collection of samples observed during a training phase. The focus is on practical scenarios where the length of the training sequence is comparable in magnitude to the system size. In these situations, the performance of the MIMO system can be expected to suffer from a considerable degradation. In order to characterize the actual performance under the previous realistic conditions, a large-system performance analysis is proposed that builds upon some new results on the convergence of the eigenvectors of large information-plus-noise covariance matrices.