Multiuser Downlink Hybrid Analog-Digital Beamforming with Individual SINR Constraints

This paper deals with the problem of multiuser transmit hybrid analog-digital beamforming. Precisely, we tackle the problem of transmit power minimization under minimum signal-to-noise-plus-interference ratio (SINR) constraints. While the all-digital beamforming solution has been extensively studied in the recent years, little is known about the hybrid analog-digital optimization. This latter design is known to be a non-convex NP-hard problem as the analog part entails the optimization of a quadratically constraint quadratic program with several equality constraints. In order to solve this problem, we propose an alternating optimization with a successive convex approximation procedure. The conceived scheme is able to consider an arbitrary sub-array connectivity matrix (i.e. localized, interleaved, fully-connected,...). Through numerical simulations it is observed that the proposed framework yields to an efficient solution in few iterations providing a substantial gain compared to current heuristic approaches.