Optimal signal design for estimation of correlated MIMO channels

Optimal estimation of multi-input multi-output correlated channels using pilot signals is considered, assuming knowledge of the second order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the recently proposed virtual channel representation for uniform linear arrays, which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in correlated channels. However, the analysis can be generalized to other known channel models. We show that optimal signaling is in block form corresponding to beams transmitted in successive time intervals along the transmit virtual angles, with powers determined by water filling arguments based on the optimization criteria. The block length depends on the channel correlation and decreases with SNR. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.