On the Amount of Downlink Training in Correlated Massive MIMO Channels

In this paper, we study the effect of downlink (DL) training on the achievable sum rate of multiuser massive MIMO channels with spatial correlations, and derive sufficient conditions of the DL channel estimation error covariance matrices that maintain the full multiplexing gain at high data signal-to-noise-ratios (SNRs). Given the derived conditions, a simple asymptotic upper bound on the average sum rate loss due to channel estimation is obtained. We derive, in closed-form, training sequences of limited duration that satisfy these conditions. The training duration is variable and increases with the data SNR, while the sequences lie in a subspace spanned by a variable number of user spatial covariance matrices' eigenvectors. We additionally study the problem of sequence codebook design and find solutions to this problem for uniform linear and rectangular arrays using asymptotic results. For the aforementioned training structure, the designed codebooks are observed numerically to be near-optimal for a moderate number of base station antennas. Due to their ability to identify a sufficient limited number of channel directions to train, the proposed solutions can substantially reduce DL training overheads while providing achievable rates that are comparable with the rates achieved with perfect channel state information.