Deterministic Annealing for Hybrid Beamforming Design in Multi-Cell MU-MIMO Systems

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.