Sparse Bayesian Learning for the Time-Varying Massive MIMO Channels: Acquisition and Tracking

The low-rank property of the channel covariances can be adopted to reduce the overhead of the channel training in massive MIMO systems. In this paper, with the help of the virtual channel representation, we apply such property to both time-division duplex and frequency-division duplex systems, where the time-varying channel scenarios are considered. First, we formulate the dynamic massive MIMO channel as one sparse signal model. Then, an expectation maximization-based sparse Bayesian learning framework is developed to learn the model parameters of the sparse virtual channel. Specifically, the Kalman filter (KF) and the Rauch-Tung-Striebel smoother are utilized to track the model parameters of the uplink (UL) spatial sparse channel in the expectation step. During the maximization step, a fixed-point theorem-based algorithm and a low-complex searching method are constructed to recover the temporal varying characteristics and the spatial signatures, respectively. With the angle reciprocity, we recover the downlink (DL) model parameters from the UL ones. After that, the KF with the reduced dimension is adopt to fully exploit the channel temporal correlations to enhance the DL/UL virtual channel tracking accuracy. A monitoring scheme is also designed to detect the change of model parameters and trigger the relearning process. Finally, we demonstrate the efficacy of the proposed schemes through the numerical simulations.