Sparse Bayesian learning-based channel estimation in millimeter wave hybrid MIMO systems

This paper develops a novel sparse Bayesian learning (SBL)-based multiple-input multiple-output (MIMO) channel estimation technique for hybrid millimeter wave (mmWave) wireless systems by exploiting spatial sparsity in the wireless channels arising from the highly directional nature of propagation. The spatially sparse MIMO channel is modeled in terms of the basis array response matrices corresponding to the quantized directional cosines at the transmit and receive antenna arrays followed by the development of an expectation maximization (EM)-based sparse Bayesian learning (SBL) channel estimation approach. Subsequently, an enhanced variant of the SBL scheme is proposed based on hard thresholding the associated hyperparameter estimates, which is observed to significantly improve the accuracy of channel estimation. The Bayesian Cramér-Rao bound (BCRB) is also derived to benchmark the accuracy of the proposed SBL-based channel estimation schemes. Finally, simulation results are presented to illustrate the performance improvement achieved in comparison to the existing state-of-the-art orthogonal matching pursuit (OMP)-based sparse mmWave channel estimation scheme.