On the capacity of the Fading MIMO Broadcast Channel without channel information at the transmitter and imperfect estimation at the receivers

Consider a base station transmitting information over a downlink wireless communication channel, where the mobiles (the receivers) only dispose of a noisy estimate of the channel parameters, and these estimates are not available at the base station (the transmitter). In this paper, we examine the effects of imperfect channel estimation at the receivers and no channel knowledge at the transmitter on the capacity of the multiuser Fading MIMO Broadcast Channel. We derive the optimal Dirty-paper coding (DPC) scheme and its corresponding achievable rates with the assumption of Gaussian inputs. Our results, for uncorrelated Rayleigh fading, are particularly useful for a system designer to assess the amount of training data and the channel characteristics (e.g. SNR, fading process, number of antennas) to achieve target rates. We provide numerical results for a two-users MIMO Broadcast Channel with maximum-likehood (ML) channel estimation. These illustrate a practical trade-off between the amount of training and its impact to the multiuser interference cancellation performance. In particular, we observe the surprising result that a Broadcast Channel with a single transmitter and receiver antenna, and imperfect channel estimation at the receivers, does not need the knowledge of estimates at the transmitter to achieve large rates.