  We provide a maximum likelihood formulation for the blind estimation of
massive mmWave MIMO channels while taking into account their underlying sparse
structure. The main advantage of this approach is the fact that the overhead
due to pilot sequences can be reduced dramatically especially when operating at
low SNR per antenna. Thereby, the sparsity in the angular domain is exploited
as a key property to enable the unambiguous blind separation between user's
channels. On the other hand, as only the sparsity is assumed, the proposed
method is robust with respect to the statistical properties of the channel and
data and allows the estimation in rapidly time-varying scenarios and eventually
the separation of interfering users from adjacent base stations. Additionally,
a performance limit is derived based on the clairvoyant Cram\'er Rao lower
bound. Simulation results demonstrate that this maximum likelihood formulation
yields superior estimation accuracy with reasonable computational complexity
and limited model assumptions.
