We consider the problems of active user detection (AUD) and channel estimation (CE) in the uplink of massive machine type communication (mMTC) network. We propose a coupled prior sparse Bayesian learning algorithm that exploits the sporadic user activity and variable-sized block channel sparsity. We first design a novel coupled hierarchical Gaussian prior model which captures the variable size block-sparsity. We then derive its sub-optimal precision hyperparameter updates using majorization-minimization technique. We extensively investigate the proposed algorithm performance and show that it, due to its generic prior, outperforms the existing ones.

We consider the problem of estimating channel and detecting active users in the uplink of a massive machine type communication (mMTC) network. We propose a centralized coupled prior based sparse Bayesian learning (cCP-SBL) algorithm that exploits the sporadic user activity and variable-sized block mMTC channel sparsity in the virtual angular domain. To achieve this objective, we first design a generalized coupled hierarchical Gaussian prior which captures this variable-sized block sparsity. We then derive its sub-optimal precision hyperparameter updates using majorization minimization framework. We next design a decentralized CP-SBL (dCP-SBL) algorithm for the emerging base station architectures with multiple processing units. The dCP-SBL algorithm converts the centralized hyperparameter cCP-SBL updates to an equivalent optimization problem, and solves it decentrally using asynchronous alternating direction method of multipliers. We also theoretically analyze the convergence of the dCP-SBL algorithm. We show using extensive numerical investigations that the i) proposed cCP- and dCP-SBL algorithms outperform several existing state-of-the-art designs; and ii) dCP-SBL algorithm is robust to processing unit failures and has a lower time complexity than the cCP-SBL algorithm.