On a Mutual Information and a Capacity Bound Gap of Pilot-Aided MIMO Channels

For single-user MIMO channels with partial re ceiver CSI, we study the difference between a lower bound and two alternative upper bounds of the mutual information achieved with Gaussian codebooks. These differences are termed bound gaps Δ and δ, respectively. The latter may serve to derive a capacity bound gap. In contrast to previous studies, we assume that the channel estimation error statistics are not given a priori, but depend on the parameters of a training routine, in which a pilot sequence is transmitted, and where the channel realization is linearly estimated. Under these conditions, we successively determine analytic upper and lower bounds on the mutual information bound gap Δ. We further study the asymptotic behavior of said bound gaps for high SNR and a large number of antennas. This allows us to prove, for example, that for MISO channels and a certain class of semicorrelated MIMO channels, when the training and transmit power levels are equal, the capacity is approached to within min(N_T, N_R) bits by the capacity bounds, where N_T and N_R stand for the number of transmit and receive antennas, respectively.