  We study the problem of downlink channel estimation in multi-user massive
multiple input multiple output (MIMO) systems. To this end, we consider a
Bayesian compressive sensing approach in which the clustered sparse structure
of the channel in the angular domain is employed to reduce the pilot overhead.
To capture the clustered structure, we employ a conditionally independent
identically distributed Bernoulli-Gaussian prior on the sparse vector
representing the channel, and a Markov prior on its support vector. An
expectation propagation (EP) algorithm is developed to approximate the
intractable joint distribution on the sparse vector and its support with a
distribution from an exponential family. The approximated distribution is then
used for direct estimation of the channel. The EP algorithm assumes that the
model parameters are known a priori. Since these parameters are unknown, we
estimate these parameters using the expectation maximization (EM) algorithm.
The combination of EM and EP referred to as EM-EP algorithm is reminiscent of
the variational EM approach. Simulation results show that the proposed EM-EP
algorithm outperforms several recently-proposed algorithms in the literature.
