On the Capacity of Linear Vector Gaussian Channels with Magnitude Knowledge and Phase Uncertainty

We are interested in studying different capacity formulations in linear vector Gaussian channels where the transmitter is only informed with the magnitude of the complex channel matrix coefficients and the receiver has perfect channel knowledge. Initially, we give the general 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 a new result on the power allocation for the maximization of the outage mutual information