  This paper develops efficient channel estimation techniques for
millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems
under practical hardware limitations, including an arbitrary array geometry and
a hybrid hardware structure. Taking on an angle-based approach, this work
adopts a generalized array manifold separation approach via Jacobi-Anger
approximation, which transforms a non-ideal, non-uniform array manifold into a
virtual array domain with a desired uniform geometric structure to facilitate
super-resolution angle estimation and channel acquisition. Accordingly,
structure-based optimization techniques are developed to effectively estimate
both the channel covariance and the instantaneous channel state information
(CSI) within a short sensing time. In particular, the difference in
time-variation of channel path angles and path gains is capitalized to design a
two-step CSI estimation scheme that can quickly sense fading channels.
Theoretical results are provided on the fundamental limits of the proposed
technique in terms of sample efficiency. For computational efficiency, a fast
iterative algorithm is developed via the alternating direction method of
multipliers. Other related issues such as spurious-peak cancellation in
nonuniform linear arrays and extensions to higher-dimensional cases are also
discussed. Simulations testify the effectiveness of the proposed approaches in
hybrid mmWave massive MIMO systems with arbitrary arrays.
