Ergodic capacity of a 2 × 2 MIMO system under phase uncertainty at the transmitter

In this paper, we find an expression for the ergodic capacity of a 2 × 2 multi-input multi-output (MIMO) flat fading channel for a particular case of partial channel state information at the transmitter: we focus our study on the case where the transmitter is informed just with the modulus of the channel matrix coefficients. First, we prove that a simple power allocation strategy between transmitting antennas is the optimal scheme, in the sense that is a capacity achieving architecture. Next, we derive an expression to calculate the optimal power assigned to each antenna, and find out that it can be expressed as a function of one of the roots of a fourth order polynomial. Finally, some conclusions are presented.