  This paper proposes hybrid beamforming designs for millimeter-wave (mmWave)
multiple-input multiple-output (MIMO) backhaul systems equipped with uniform
planar arrays (UPAs) of dual-polarization antennas at both the transmit and
receive base stations. The proposed beamforming designs are to near-optimally
solve optimization problems taking the dual-polarization UPA structure into
account. Based on the solutions of optimization problems, this paper shows it
is possible to generate the optimal dual-polarization beamformer from the
optimal single-polarization beamformer sharing the same optimality. As specific
examples, squared error and magnitude of inner product are considered
respectively for optimization criteria. To optimize proposed beamformers,
partial channel information is needed, and the use of low overhead pilot
sequences is also proposed to figure out the required information. Simulation
results verify that the resulting beamformers have the most uniform gain (with
the squared error criterion) or the highest average gain (with the magnitude of
inner product criterion) in the covering region with the UPA of
dual-polarization antennas.
