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Multi-group multicast beamforming in wireless systems with large antennaarrays and massive audience is investigated in this paper. Multicastbeamforming design is a well-known non-convex quadratically constrainedquadratic programming (QCQP) problem. A conventional method to tackle thisproblem is to approximate it as a semi-definite programming problem viasemi-definite relaxation, whose performance, however, deteriorates considerablyas the number of per-group users goes large. A recent attempt is to applyconvex-concave procedure (CCP) to find a stationary solution by treating it asa difference of convex programming problem, whose complexity, however,increases dramatically as the problem size increases. In this paper, we proposea low-complexity high-performance algorithm for multi-group multicastbeamforming design in large-scale wireless systems by leveraging thealternating direction method of multipliers (ADMM) together with CCP. Inspecific, the original non-convex QCQP problem is first approximated as asequence of convex subproblems via CCP. Each convex subproblem is thenreformulated as a novel ADMM form. Our ADMM reformulation enables that eachupdating step is performed by solving multiple small-size subproblems withclosed-form solutions in parallel. Numerical results show that our fastalgorithm maintains the same favorable performance as state-of-the-artalgorithms but reduces the complexity by orders of magnitude.

ADMM-based Fast Algorithm for Multi-group Multicast Beamforming in Large-Scale Wireless Systems