Joint AMP-SBL Algorithms for Device Activity Detection and Channel Estimation in Massive MIMO mMTC Systems

We consider the problem of detecting active devices and estimating their channels in the uplink of a massive machine type communication (mMTC) network. The base station (BS) in this mMTC system is equipped with massive multiple input multiple output (mMIMO) technology, and the channels across its antennas are correlated, an aspect ignored by most of the existing mMTC works. We propose three Bayesian learning algorithms which exploit channel spatial correlation, and comprehensively outperform several existing state-of-the-art algorithms, which do not exploit it. The proposed algorithms perform better in terms of the normalized mean squared error, activity error rate, and spectral efficiency (SE). The first correlated vector approximate message passing (AMP) algorithm has the best performance, but fails when the BS does not have knowledge of channel large scale fading and device activity probability. The second block sparse Bayesian learning (B-SBL) algorithm overcomes these limitations, but has a high complexity. The third combined AMP-BSBL algorithm retains the advantages of B-SBL, but with a much reduced complexity. We show that all three channel estimators can be represented as plug-in linear minimum mean squared estimators. This crucially helps us in deriving a common lower bound on the SE of mMIMO mMTC systems.