Optimizing Training-Based Transmission for Correlated MIMO Systems with Hybrid Feedback

In this paper, we consider multiple-input multiple-output (MIMO) communication systems with combined channel covariance feedback (CCF) and channel gain feedback (CGF), hereafter called hybrid CCF-CGF systems. Using an ergodic capacity lower bound as the figure of merit, we investigate the optimal training and data transmission strategies as well as the optimal transmit resource allocation. We prove that the optimal structure for data transmission follows a water-filling solution according to the estimated channel gains, rotated and truncated into the trained eigen-directions. We analytically find the range of the optimal training length. Through numerical evaluations we also show that a closed-form solution of the training power allocation achieves near optimal performance. Finally, we show that the capacity of hybrid CCF-CGF systems can be significantly increased by adding extra transmit antennas without increasing the training resources or feedback overhead.