  In this paper, we propose a novel channel estimation algorithm based on the
Least Square Estimation (LSE) and Sparse Message Passing algorithm (SMP), which
is of special interest for Millimeter Wave (mmWave) systems, since this
algorithm can leverage the inherent sparseness of the mmWave channel. Our
proposed algorithm will iteratively detect exact the location and the value of
non-zero entries of sparse channel vector without its prior knowledge of
distribution. The SMP is used to detect exact the location of non-zero entries
of the channel vector, while the LSE is used for estimating its value at each
iteration. Then, the analysis of the Cramer-Rao Lower Bound (CRLB) of our
proposed algorithm is given. Numerical experiments show that our proposed
algorithm has much better performance than the existing sparse estimators (e.g.
LASSO), especially when mmWave systems have massive antennas at both the
transmitters and receivers. In addition, we also find that our proposed
algorithm converges to the CRLB of the genie-aided estimation of sparse
channels in just a few turbo iterations.
