We consider a joint unicast and multi-group multicast beamforming problem for massive multiple-input multiple-output (MIMO) system with a large number of unicast users. We propose an alternating direction method of multipliers (ADMM)-based fast algorithm that efficiently obtains the beamforming solutions for unicast and multicast users to minimize the transmit power subject to quality-of-service constraints.Utilizing the optimal multicast beamforming structure obtained recently, we separate the original problem into unicast and multicast subproblems to be solved using the alternating optimization technique. We solved the unicast subproblem in closed-form by exploring the unicast beamforming structure, which reduces the computational complexity, substantially. For the multicast subproblem, we apply the successive convex approximation (SCA) method to solve it iteratively. Each SCA subproblem is then reformulated to the ADMM form, providing the closed-form update for the multicast subproblem. Simulation results show that the proposed algorithm achieves a near-optimal performance with low complexity for large-scale systems.

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