  Channel estimation is challenging for hybrid millimeter wave (mmWave)
large-scale antenna arrays which are promising in 5G/B5G applications. The
challenges are associated with angular resolution losses resulting from hybrid
front-ends, beam squinting, and susceptibility to the receiver noises. Based on
tensor signal processing, this paper presents a novel multi-dimensional
approach to channel parameter estimation with large-scale mmWave hybrid uniform
circular cylindrical arrays (UCyAs) which are compact in size and immune to
mutual coupling but known to suffer from infinite-dimensional array responses
and intractability. We design a new resolution-preserving hybrid beamformer and
a low-complexity beam squinting suppression method, and reveal the existence of
shift-invariance relations in the tensor models of received array signals at
the UCyA. Exploiting these relations, we propose a new tensor-based subspace
estimation algorithm to suppress the receiver noises in all dimensions (time,
frequency, and space). The algorithm can accurately estimate the channel
parameters from both coherent and incoherent signals. Corroborated by the
Cram\'{e}r-Rao lower bound (CRLB), simulation results show that the proposed
algorithm is able to achieve substantially higher estimation accuracy than
existing matrix-based techniques, with a comparable computational complexity.
