Optimum transmit architecture of a MIMO system under modulus channel knowledge at the transmitter

In this paper, we study the ergodic capacity of a multiple input multiple output (MIMO) uncorrelated flat fading channel with perfect channel state information at the receiver and partial channel state information at the transmitter. We focus our attention on the case where the transmitter is informed only with the modulus of the channel matrix coefficients. First, we prove that a simple power allocation strategy among transmitting antennas is the optimal scheme, in the sense that is a capacity achieving architecture. Next, for the particular case where only two antennas are used at each communication end, we derive closed form expressions for the ergodic capacity and the optimal power assigned to each antenna.