© 1991-2012 IEEE. We study the maximum likelihood problem for the blind estimation of massive mmWave MIMO channels while taking into account their underlying sparse structure, the temporal shifts across antennas in the broadband regime, and ultimately one-bit quantization at the receiver. The sparsity in the angular domain is exploited as a key property to enable the unambiguous blind separation between user's channels. The main advantage of this approach is the fact that the overhead due to pilot sequences can be dramatically reduced especially when operating at low SNR per antenna. In addition, as sparsity is the only assumption made about the channel, the proposed method is robust with respect to the statistical properties of the channel and data and allows the channel estimation and the separation of interfering users from adjacent base stations to be performed in rapidly time-varying scenarios. For the case of one-bit receivers, a blind channel estimation is proposed that relies on the expectation maximization algorithm. Additionally, performance limits are derived based on the Clairvoyant Cramer-Rao lower bound. Simulation results demonstrate that this maximum likelihood formulation yields superior estimation accuracy in the narrowband as well as the wideband regime with reasonable computational complexity and limited model assumptions.