  Channel estimation has long been deemed as one of the most critical problems
in three-dimensional (3D) massive multiple-input multiple-output (MIMO), which
is recognized as the leading technology that enables 3D spatial signal
processing in the fifth-generation (5G) wireless communications and beyond.
Recently, by exploring the angular channel model and tensor decompositions, the
accuracy of single-user channel estimation for 3D massive MIMO communications
has been significantly improved given a limited number of pilot signals.
However, these existing approaches cannot be straightforwardly extended to the
multi-user channel estimation task, where the base station (BS) aims at
acquiring the channels of multiple users at the same time. The difficulty is
that the coupling among multiple users' channels makes the channel estimation
deviate from widely-used tensor decompositions. It gives a non-standard tensor
decomposition format that has not been well tackled. To overcome this
challenge, besides directly fitting the new tensor model for channel estimation
to the wireless data via block coordinate descent (BCD) method, which is prone
to the overfitting of noises or requires regularization parameter tuning, we
further propose a novel tuning-free channel estimation algorithm that can
automatically control the channel model complexity and thus effectively avoid
the overfitting. Numerical results are presented to demonstrate the excellent
performance of the proposed algorithm in terms of both estimation accuracy and
overfitting avoidance.
