Sparse Bayesian Learning (SBL)-Based Frequency-Selective Channel Estimation for Millimeter Wave Hybrid MIMO Systems

This work develops a novel sparse Bayesian learning (SBL)-based channel estimation technique for frequency-selective millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. Towards this end, the concatenated frequency-selective MIMO channel matrix is represented in terms of the beamspace channel vector employing suitable transmit and receive array response dictionary matrices. Subsequently, a multiple measurement vector (MMV) model is developed for estimation of the sparse beamspace channel vector considering the block transmission of zero-padded training frames. The unique aspects of the proposed scheme are that it exploits the group-sparsity inherent in the equivalent beamspace channel vector of the frequency-selective mmWave MIMO channel and also considers the effect of correlated noise in the equivalent system model due to RF-combining. This feature, coupled with the improved ability of SBL for sparse signal recovery, leads to a significantly enhanced performance of the proposed scheme in comparison to the orthogonal matching pursuit (OMP) technique proposed recently. Bayesian Cramér-Rao bounds (BCRBs) are also derived to characterize the estimation performance. Simulation results are presented to demonstrate the improved performance of the proposed SBL-based channel estimation technique in comparison to the existing scheme and also a performance close to the various benchmarks.