  The 3GPP suggests to combine dual polarized (DP) antenna arrays with the
double directional (DD) channel model for downlink channel estimation. This
combination strikes a good balance between high-capacity communications and
parsimonious channel modeling, and also brings limited feedback schemes for
downlink channel state information within reach---since such channel can be
fully characterized by several key parameters. However, most existing channel
estimation work under the DD model has not yet considered DP arrays, perhaps
because of the complex array manifold and the resulting difficulty in algorithm
design. In this paper, we first reveal that the DD channel with DP arrays at
the transmitter and receiver can be naturally modeled as a low-rank tensor, and
thus the key parameters of the channel can be effectively estimated via tensor
decomposition algorithms.
  On the theory side, we show that the DD-DP parameters are identifiable under
very mild conditions, by leveraging identifiability of low-rank tensors.
Furthermore, a compressed tensor decomposition algorithm is developed for
alleviating the downlink training overhead. We show that, by using judiciously
designed pilot structure, the channel parameters are still guaranteed to be
identified via the compressed tensor decomposition formulation even when the
size of the pilot sequence is much smaller than what is needed for conventional
channel identification methods, such as linear least squares and matched
filtering.
  Numerical simulations are presented to showcase the effectiveness of the
proposed methods.
