Abstract—This work deals with hybrid beamforming (HBF)
for the MIMO Interfering Broadcast Channel (IBC), i.e. the
Multi-Input Multi-Output (MIMO) Multi-User (MU) Multi-Cell
downlink channel. HBF is a low complexity alternative to fully
digital precoding in Massive MIMO systems. Hybrid architectures
involve a combination of digital and analog processing that
enables both beamforming and multiplexing gains. We consider
BF design by maximizing the Weighted Sum Rate (WSR) for
the case of Perfect Channel State Information at the Transmitter
(CSIT).We optimize the WSR using minorization and alternating
optimization, the result of which is observed to converge fast. We
furthermore propose a deterministic annealing based approach
to avoid issues of local optima that plague phase shifter constrained
analog beamformers. Simulation results indicate that
the proposed deterministic annealing based approach performs
significantly better than state of the art Weighted Sum Mean
Squared Error (WSMSE) or WSR based solutions. We also
propose a closed form solution for the analog BF in case the
number of RF chains equals or exceeds the total number of
multipath components and the antenna array responses are
phasors.