Iterative methods for physical-layer multicast beamforming

In this paper, we derive an iterative method for physical-layer multicast beamforming based on alternating minimization. A salient feature of the proposed iterative method is that beams can be found using simple matrix-vector multiplications without resorting to any optimization solver. Thus, it becomes attractive for hardware-based implementations. Furthermore, since the complexity of the proposed method mainly depends on the number of users in a multicast group regardless of the number of antenna elements in an array, it has a computational advantage over successive convex approximation (SCA) methods and semidefinite relaxation (SDR) approaches with randomization when the number of antennas is larger than the number of users. Through simulations, we see that the proposed iterative method can perform better than the conventional method based on SDR with randomization, while its performance is slightly worse than that of SCA. For millimeter-wave (mm-wave) channels of limited scattering, the proposed iterative method is also applied to physical-layer multicast beamforming by hybrid beamformers in order to find a sparse solution.