Distributed Optimization for Coordinated Beamforming in Multicell Multigroup Multicast Systems: Power Minimization and SINR Balancing

Abstract

This paper considers coordinated multicast beamforming in a multi-cell\nmultigroup multiple-input single-output system. Each base station (BS) serves\nmultiple groups of users by forming a single beam with common information per\ngroup. We propose centralized and distributed beamforming algorithms for two\ndifferent optimization targets. The first objective is to minimize the total\ntransmission power of all the BSs while guaranteeing the user-specific minimum\nquality-of-service targets. The semidefinite relaxation (SDR) method is used to\napproximate the non-convex multicast problem as a semidefinite program (SDP),\nwhich is solvable via centralized processing. Subsequently, two alternative\ndistributed methods are proposed. The first approach turns the SDP into a\ntwo-level optimization via primal decomposition. At the higher level,\ninter-cell interference powers are optimized for fixed beamformers while the\nlower level locally optimizes the beamformers by minimizing BS-specific\ntransmit powers for the given inter-cell interference constraints. The second\ndistributed solution is enabled via an alternating direction method of\nmultipliers, where the inter-cell interference optimization is divided into a\nlocal and a global optimization by forcing the equality via consistency\nconstraints. We further propose a centralized and a simple distributed\nbeamforming design for the signal-to-interference-plus-noise ratio (SINR)\nbalancing problem in which the minimum SINR among the users is maximized with\ngiven per-BS power constraints. This problem is solved via the bisection method\nas a series of SDP feasibility problems. The simulation results show the\nsuperiority of the proposed coordinated beamforming algorithms over traditional\nnon-coordinated transmission schemes, and illustrate the fast convergence of\nthe distributed methods.\n