Low-Complexity Joint Antenna Selection and Robust Multi-Group Multicast Beamforming for Massive MIMO

We consider low-complexity design for joint antenna selection and robust multi-group multicast beamforming in massive multiple-input multiple-output (MIMO) systems. Relying on the estimated channel covariance and assuming a limited number of antennas for transmission at the base station, we aim to minimize the transmit power subject to the worst-case signal-to-interference-plus-noise-ratio (SINR) guarantee and per selected antenna power budget. Converting the worst-case SINR constraints to a set of non-convex constraints, we propose a two-phase approach to solve the problem efficiently: the antenna selection phase, followed by the robust multicast beamforming generation phase. We propose an SINR-based approach for antenna selection, where the challenging mixed-integer problem is converted into an approximate joint optimization problem via a sequence of transformation, relaxation, and SINR approximation. We develop a fast two-layered alternating direction method of multipliers (ADMM)-based algorithm to compute an approximate solution. In particular, with our ADMM construction, we obtain semi-closed-form solutions for antenna selection and beamforming subproblems at each ADMM iteration for fast updates. To further reduce the computational complexity, we propose a signal-to-leakage-ratio (SLR)-based approach using the SLR constraints in the joint optimization problem. This allows us to develop a two-layered ADMM-based algorithm, which can compute a solution more efficiently due to the SLR structure. The robust multicast beamforming solution for the selected antennas is computed using the fast algorithm we developed recently. Simulation results show the effectiveness of our two proposed approximated approaches for antenna selection and the overall two-phase approach in both overall performance and substantially low computational complexity in a massive MIMO setting.