Joint Estimation of Clustered User Activity and Correlated Channels with Unknown Covariance in mMTC

This paper considers joint user identification and channel estimation (JUICE) in grant-free access with a \emph{clustered} user activity pattern. In particular, we address the JUICE in massive machine-type communications (mMTC) network under correlated Rayleigh fading channels with unknown channel covariance matrices. We formulate the JUICE problem as a maximum \emph{a posteriori} probability (MAP) problem with properly chosen priors to incorporate the partial knowledge of the UEs' clustered activity and the unknown covariance matrices. We derive a computationally-efficient algorithm based on alternating direction method of multipliers (ADMM) to solve the MAP problem iteratively via a sequence of closed-form updates. Numerical results highlight the significant improvements brought by the proposed approach in terms of channel estimation and activity detection performances for clustered user activity patterns.