  In this paper, we propose a channel tracking method for massive multi-input
and multi-output systems under both time-varying and spatial-varying
circumstance. Exploiting the characteristics of massive antenna array, a
spatial-temporal basis expansion model is designed to reduce the effective
dimensions of up-link and down-link channel, which decomposes channel state
information into the time-varying spatial information and gain information. We
firstly model the users movements as a one-order unknown Markov process, which
is blindly learned by the expectation and maximization (EM) approach. Then, the
up-link time varying spatial information can be blindly tracked by Taylor
series expansion of the steering vector, while the rest up-link channel gain
information can be trained by only a few pilot symbols. Due to angle
reciprocity (spatial reciprocity), the spatial information of the down-link
channel can be immediately obtained from the up-link counterpart, which greatly
reduces the complexity of down-link channel tracking. Various numerical results
are provided to demonstrate the effectiveness of the proposed method.
