On the Capacity of MIMO Systems with Magnitude Knowledge and Phase Uncertainty

In this work, we study different capacity formulations in multi-input multi-output channels where the transmitter is only informed with the magnitude of the complex channel matrix coefficients. Perfect channel knowledge is assumed at the receiver side. First, we give the expressions for the ergodic, compound, and outage capacities for our particular model of channel state information. Next, focusing on the compound formulation, we find that the optimal transmitter strategy consists in independent signaling through the transmit dimensions. Finally, we present some results on the optimal power allocation for the maximization of the outage mutual information for a simple MIMO system where the transmitter is equipped with only two antennas.