Centralized and Decentralized Active User Detection and Channel Estimation in mMTC

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.