  We present two reduced-rank channel estimators for large-scale
multiple-input, multiple-output (MIMO) systems and analyze their mean square
error (MSE) performance. Taking advantage of the channel's transform domain
sparseness, the estimators yield outstanding performance and may offer
additional mean angle-of-arrival (AoA) information. It is shown that, for the
estimators to be effective, one has to select a proper predetermined unitary
basis (transform) and be able to determine the dominant channel rank and the
associated subspace. Further MSE analysis reveals the relations among the array
size, channel rank, signal-to-noise ratio (SNR), and the estimators'
performance. It provides rationales for the proposed rank determination and
mean AoA estimation algorithms as well.
  An angle alignment operation included in one of our channel models is proved
to be effective in further reducing the required rank, shifting the dominant
basis vectors' range (channel spectrum) and improving the estimator's
performance when a suitable basis is used. We also draw insightful analogies
among MIMO channel modeling, transform coding, parallel spatial search, and
receive beamforming. Computer experiment results are provided to examine the
numerical effects of various estimator parameters and the advantages of the
proposed channel estimators and rank determination method.
