  Bilayer intelligent omni-surface (BIOS) has recently attracted increasing
attention due to its capability of independent beamforming on both reflection
and refraction sides. However, its specific bilayer structure makes the channel
estimation problem more challenging than the conventional intelligent
reflecting surface (IRS) or intelligent omni-surface (IOS). In this paper, we
investigate the channel estimation problem in the BIOS-assisted multi-user
multiple-input multiple-output system. We find that in contrast to the IRS or
IOS, where the forms of the cascaded channels of all user equipments (UEs) are
the same, in the BIOS, those of the UEs on the reflection side are different
from those on the refraction side, which is referred to as the heterogeneous
channel property. By exploiting it along with the two-timescale and sparsity
properties of channels and applying the manifold optimization method, we
propose an efficient channel estimation scheme to reduce the training overhead
in the BIOS-assisted system. Moreover, we investigate the joint optimization of
base station digital beamforming and BIOS passive analog beamforming.
Simulation results show that the proposed estimation scheme can significantly
reduce the training overhead with competitive estimation quality, and thus
keeps the performance advantage of BIOS over IRS and IOS with imperfect channel
state information.
