Joint Activity Detection and Channel Estimation for MIMO Grant-Free Random Access through Bayesian Learning

Massive machine-type communications (mMTC) are anticipated to be supported by grant-free random access (GF-RA) and multiple-input multiple-output (MIMO) techniques. Compressed sensing (CS) is extensively advocated to accommodate massive connectivity due to bursty data transmission. In this paper, we formulate the joint activity detection and channel estimation for the MIMO-enabled GF-RA system as a block single measurement vector (SMV) problem. First, the hierarchical block sparse Bayesian learning (BSBL) framework is developed to solve this problem, where the potential block sparse properties induced by multiantenna reception are exploited by assigning the structured hyperprior. Then, by integrating the generalized approximate message passing (GAMP) approach into the BSBL formulation to effectively approximate the posterior distribution, we propose a computationally efficient Bayesian learning algorithm named GAMP-BSBL. Fortunately, the proposed Bayesian algorithms enable automatic learning of block sparse solutions without requiring noise level and user sparsity ratio as explicit conditions. Simulation results show that the proposed algorithms provide improved performance gains as compared with the standard CS methods.