  To glean the benefits offered by massive multi-input multi-output (MIMO)
systems, channel state information must be accurately acquired. Despite the
high accuracy, the computational complexity of classical linear minimum mean
squared error (MMSE) estimator becomes prohibitively high in the context of
massive MIMO, while the other low-complexity methods degrade the estimation
accuracy seriously. In this paper, we develop a novel rank-1 subspace channel
estimator to approximate the maximum likelihood (ML) estimator, which
outperforms the linear MMSE estimator, but incurs a surprisingly low
computational complexity. Our method first acquires the highly accurate
angle-of-arrival (AoA) information via a constructed space-embedding matrix and
the rank-1 subspace method. Then, it adopts the post-reception beamforming to
acquire the unbiased estimate of channel gains. Furthermore, a fast method is
designed to implement our new estimator. Theoretical analysis shows that the
extra gain achieved by our method over the linear MMSE estimator grows
according to the rule of O($\log_{10}M$), while its computational complexity is
linearly scalable to the number of antennas $M$. Numerical simulations also
validate the theoretical results. Our new method substantially extends the
accuracy-complexity region and constitutes a promising channel estimation
solution to the emerging massive MIMO communications.
