Multi-Layer Sparse Bayesian Learning for mmWave Channel Estimation

Millimeter wave (mmWave) communications has been considered one of the key techniques for the future generations of wireless systems due to the large mmWave bandwidth available. In mmWave systems, channel state information (CSI) is critical for the design of the precoder and combiner for operations respectively at transmitter and receiver. In this article, we motivate to design the low-complexity and high-accuracy channel estimation methods for the mmWave systems employing orthogonal frequency division multiplexing (OFDM) signaling and hybrid transmitter/receiver beamforming. Specifically, a multi-layer sparse Bayesian learning (SBL) channel estimator is proposed to both improve the performance of channel estimation and reduce the complexity of signal processing, when compared with a range of related channel estimators, including the orthogonal matching pursuit (OMP)-, approximate message passing (AMP)- and conventional SBL-assisted channel estimators. The proposed multi-layer SBL estimator is compared with these legacy channel estimators, when impacts from different perspectives are considered. Furthermore, the Bayesian Cramer-Rao Bound of channel estimation is analyzed and evaluated. Our studies and simulation results show that the proposed multi-layer SBL estimator is capable of achieving better performance than the benchmark estimators considered. Specifically, when compared with the traditional SBL estimator, the proposed multi-layer SBL estimator is capable of achieving a lower mean-square error (MSE), while simultaneously, requiring only about 1/10 of the computational complexity of the traditional SBL estimator.