  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 estimation within reach. However, most existing channel
estimation work under the DD model has not 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 four-way
tensor, and thus the parameters can be effectively estimated via tensor
decomposition algorithms. To reduce computational complexity, we show that the
problem can be recast as a four-snapshot three-dimensional harmonic retrieval
problem, which can be solved using computationally efficient subspace methods.
On the theory side, we show that the DD channel with DP arrays is identifiable
under very mild conditions, leveraging identifiability of low-rank tensors.
Numerical simulations are employed to showcase the effectiveness of our
methods.
