Block-Sparse Channel Estimation in Massive MIMO Systems by Expectation Propagation

We consider downlink channel estimation in massive multiple input multiple output (MIMO) systems using a Bayesian compressive sensing (BCS) approach. BCS exploits the sparse structure of the channel in the angular domain in order to reduce the pilot overhead. Due to limited local scattering, the massive MIMO channel has a block-sparse representation in the angular domain. Thus, we use a conditionally independent and identically distributed spike-and-slab prior to model the sparse vector coefficients representing the channel and a Markov prior to model its support. An expectation propagation (EP) algorithm is developed to approximate the intractable joint posterior distribution on the sparse vector and its support with a distribution from an exponential family. The unknown model parameters which are required by EP, are estimated using the expectation maximization (EM) algorithm. The proposed combination of EM and EP algorithms is reminiscent of variational EM and is referred to as EM-EP. The approximated distribution is then used for estimating the massive MIMO channel. Simulation results show that our proposed EM-EP algorithm outperforms several recently-proposed algorithms in channel estimation.