Rate of MIMO systems with CSI at transmitter and receiver from pilot-aided estimation

We consider realistic multiple input multiple output antenna systems operating over spatially colored channels with instantaneous, albeit imperfect, channel state information at the receiver and only covariance knowledge available at the transmitter. We focus on pilot-aided channel estimation in which the receiver uses minimum mean square error channel estimation. For such a setup, our goal is then to design both the pilot and data sequences optimally to maximize the information rates achievable over the channel. We first demonstrate that the estimation error cannot be modeled as additive white Gaussian noise. We adopt a lower bound on channel capacity with imperfect channel knowledge and show that an optimum design leads to a matching of the eigenspaces of the pilots and of the data to the eigenspace of the channel. Furthermore, the ranks of the pilot and data covariance matrices need to be equal, and the optimal training duration need only equal the above rank. The assignment of powers to the different modes of transmission can then be obtained numerically. The paper, in essence, extends the results in the literature that assume perfect channel knowledge at the receiver, and shows that fully exploiting covariance knowledge leads to a visible improvement in capacity when compared to schemes that assume no channel knowledge, whatsoever, at the transmitter.