Low-Complexity Channel Estimation in Correlated Massive MIMO Channels

In this paper, we propose low-complexity channel estimation schemes in spatially correlated massive MIMO channels. Minimum-mean-square-error (MMSE) estimators at the user(s) and optimized downlink (DL) training sequences that exploit channel correlations are standard used techniques. To keep the training overheads acceptable, only the case with less observations (training sequences) than the length of the channel vector is considered. Though the standard least squares (LS) estimator is not defined in this case, we show in the singleuser case that with optimized training sequences, the MMSE estimator is alternatively given by a simpler expression that is reminiscent of the LS estimator at high signal-to-noise-ratio (SNR). In the multiuser case, LS-like estimators simplify the channel estimation sum MSE function and allow obtaining training solutions in closed-form, thereby avoiding existing iterative procedures. The simplified formulation further allows deriving a novel result on the minimum training duration that drives the channel estimation sum MSE to zero as the SNR goes to infinity in multiuser scenarios with spatially correlated channels. The obtained training duration depends on two crucial factors: the ranks of the spatial covariance matrices, and the overlap between their range spaces. The proposed solution results in comparable estimation and sum rate performance to existing solutions in the medium and high SNR regime while substantially reducing the computational complexity at both sides of the link.