  We consider the problem of downlink channel estimation for millimeter wave
(mmWave) MIMO-OFDM systems, where both the base station (BS) and the mobile
station (MS) employ large antenna arrays for directional precoding/beamforming.
Hybrid analog and digital beamforming structures are employed in order to offer
a compromise between hardware complexity and system performance. Different from
most existing studies that are concerned with narrowband channels, we consider
estimation of wideband mmWave channels with frequency selectivity, which is
more appropriate for mmWave MIMO-OFDM systems. By exploiting the sparse
scattering nature of mmWave channels, we propose a CANDECOMP/PARAFAC (CP)
decomposition-based method for channel parameter estimation (including angles
of arrival/departure, time delays, and fading coefficients). In our proposed
method, the received signal at the BS is expressed as a third-order tensor. We
show that the tensor has the form of a low-rank CP decomposition, and the
channel parameters can be estimated from the associated factor matrices. Our
analysis reveals that the uniqueness of the CP decomposition can be guaranteed
even when the size of the tensor is small. Hence the proposed method has the
potential to achieve substantial training overhead reduction. We also develop
Cramer-Rao bound (CRB) results for channel parameters, and compare our proposed
method with a compressed sensing-based method. Simulation results show that the
proposed method attains mean square errors that are very close to their
associated CRBs, and presents a clear advantage over the compressed
sensing-based method in terms of both estimation accuracy and computational
complexity.
