Optimal structure and efficient algorithm for max-min fair multi-group multicast beamforming
In this thesis, we consider the max-min fair (MMF) multi-group multicast beamforming design to maximize the minimum signal-to-interference-plus-noise ratio (SINR) subject to transmit power limit. We obtain the optimal multicast beamforming solution structure for an arbitrary system configuration. We show that the optimal MMF solution has a weighted minimum mean square error (MMSE) filter structure and a similar structure to that of the quality-of-service (QoS) problem. Directly using the optimal beamforming structure, we propose two algorithms by either direct method via successive convex approximation (SCA), or solving the QoS problem iteratively. For massive MIMO systems, we propose an efficient MMF multicast beamforming design based on the optimal solution structure. The semi-definite relaxation (SDR) method and an SCA-based method are applied to solve the problem with low-complexity. Simulation results show that our proposed methods that used optimal beamforming structure achieve near-optimal performance. Additionally, they have relatively low computational complexity compared with the conventional direct SDR method for large-scale antennas or user-per-group. Our proposed efficient methods show comparable performance to the optimal beamforming structure methods but with significantly lower computational complexity for massive MIMO systems.