  This paper provides a solution for the activity detection and channel
estimation problem in grant-free access with correlated device activity
patterns. In particular, we consider a machine-type communications (MTC)
network operating in event-triggered traffic mode, where the devices are
distributed over clusters with an activity behaviour that exhibits both
intra-cluster and inner-cluster sparsity patterns. Furthermore, to model the
network's intra-cluster and inner-cluster sparsity, we propose a structured
sparsity-inducing spike-and-slab prior which provides a flexible approach to
encode the prior information about the correlated sparse activity pattern.
Furthermore, we drive a Bayesian inference scheme based on the expectation
propagation (EP) framework to solve the JUICE problem. Numerical results
highlight the significant gains obtained by the proposed structured
sparsity-inducing spike-and-slab prior in terms of both user identification
accuracy and channel estimation performance.
