Channel estimation using variational Bayesian learning for multi-user mmWave MIMO systems

This paper presents a novel variational Bayesian learning-based channel estimation scheme for hybrid pre-coding-employed wideband multiuser millimetre wave multiple-input multiple-output communication systems. We first propose a frequency variational Bayesian algorithm, which leverages common sparsity of different sub-carriers in the frequency domain. The algorithm shares all the information of the support sets from the measurement matrices, significantly improving channel estimation accuracy. To enhance robustness of the frequency variational Bayesian algorithm, we develop a hierarchical Gaussian prior channel model, which employs an identify-and-reject strategy to deal with random outliers imposed by hardware impairments. A support selection frequency variational Bayesian channel estimation algorithm is also proposed, which adaptively selects support sets from the measurement matrices. As a result, the overall computational complexity can be reduced. Validated by the Bayesian Cramér-Rao bound, simulation results show that, both frequency variational Bayesian and support selection-frequency variational Bayesian algorithms can achieve higher channel estimation accuracy than existing methods. Furthermore, compared with frequency variational Bayesian, support selection-frequency variational Bayesian requires significantly lower computational complexity, and hence, it is more practical for channel estimation applications.