Fast Algorithm for Joint Unicast and Multicast Beamforming for Large-Scale Massive MIMO

We consider the problem of joint unicast and multi-group multicast beamforming design for large-scale massive multiple-input multiple-output (MIMO) systems, with a potentially large number of unicast users. Focusing on minimizing the total transmit power subject to quality-of-service constraints, we propose an alternating direction method of multipliers (ADMM)-based fast algorithm to efficiently obtain the beamforming solutions for both unicast and multicast users. Exploiting the optimal beamforming structure obtained recently for multi-group multicast beamforming, we decompose the original problem into two subproblems for the unicast and multicast users and solve them using the alternating optimization technique. We obtain the solution to the unicast subproblem in closed form by exploring the unicast beamforming structure, thereby substantially reducing the computational complexity of the overall algorithm. We solve the multicast subproblem by approximating the non-convex constraints with a sequence of convex constraints using the successive convex approximation. Each convex subproblem is then reformulated into an ADMM form, which enables us to derive a closed-form update for the multicast subproblem. Simulation results show that our proposed algorithm achieves a near-optimal performance at a very low complexity for large-scale systems.