Characterizing the Capacity for MIMO Wireless Channels with Non-zero Mean and Transmit Covariance

Transmit channel side information (Tx-CSI), particularly the mean and covariance, helps to increase MIMO wireless capacity. We formulate a dynamic Tx-CSI framework, using outdated channel measurements and channel statistics, to create an effective channel mean and covariance and establish the capacity expression given such Tx-CSI. We then derive the asymptotic capacity-optimal input signal at low SNRs and characterize the asymptotic capacity gains due to Tx-CSI at low and high SNRs. The optimal input signal and the capacity gain in general depend on the relative number of transmit and receive antennas. For systems with equal or fewer transmit than receive antennas, we study a lower bound on the capacity. For systems with more transmit than receive antennas, we characterize the conditions for mode dropping at high SNRs, using simplified channel models. Numerical examples are provided to show the impacts of channel parameters on the optimal input signal and the capacity gain with Tx-CSI.