Multiple-measurement vector based implementation for single-measurement vector sparse Bayesian learning with reduced complexity

•Complexity reduced MMV based implementation for SMV sparse Bayesian learning (SBL) is proposed.•Optimal solution for the MMV formulation is shown to be the same with the SMV formulation.•Two suboptimal solutions based on multitask Bayesian compressive sensing and simultaneous SBL are proposed.•Maximal ratio combining is applied to exploit deterministic correlation to improve estimation performance.

Sparse Bayesian learning (SBL) has high computational complexity associated with matrix inversion in each iteration. In this paper, we investigate complexity reduced multiple-measurement vector (MMV) based implementation for single-measurement vector SBL problems. For problems with special structured sensing matrices, we propose two sub-optimal SBL schemes with significantly reduced complexity and slight estimation performance degradation, by exploiting the deterministic correlation in the converted MMV model explicitly. Two application scenarios on channel estimation in multicarrier systems and direction of arrival estimation are presented. Simulation results validate the effectiveness of the schemes.