  On the time-varying channel estimation, the traditional downlink (DL) channel
restoration schemes usually require the reconstruction for the covariance of
downlink process noise vector, which is dependent on DL channel covariance
matrix (CCM). However, the acquisition of the CCM leads to unacceptable
overhead in massive MIMO systems. To tackle this problem, in this paper, we
propose a novel scheme for the DL channel tracking. First, with the help of
virtual channel representation (VCR), we build a dynamic uplink (UL) massive
MIMO channel model with the consideration of off-grid refinement. Then, a
coordinate-wise maximization based expectation maximization (EM) algorithm is
adopted for capturing the model parameters, including the spatial signatures,
the time-correlation factors, the off-grid bias, the channel power, and the
noise power. Thanks to the angle reciprocity, the spatial signatures,
timecorrelation factors and off-grid bias of the DL channel model can be
reconstructed with the knowledge of UL ones. However, the other two kinds of
model parameters are closely related with the carrier frequency, which cannot
be perfectly inferred from the UL ones. Instead of relearning the DL model
parameters with dedicated training, we resort to the optimal Bayesian Kalman
filter (OBKF) method to accurately track the DL channel with the partially
prior knowledge. At the same time, the model parameters will be gradually
restored. Specially, the factor-graph and the Metropolis Hastings MCMC are
utilized within the OBKF framework. Finally, numerical results are provided to
demonstrate the efficiency of our proposed scheme.
