LPA-SD: An Efficient First-Order Method for Single-Group Multicast Beamforming

In this work, we develop a new first-order method called linear programming-assisted sub gradient descent (LPA-SD) for solving the single-group multicast beamforming (SGMB) problem. As the SGMB problem is NP-hard, most existing methods focus on finding a good sub-optimal solution. Our objective is to maximize the minimum signal-to-noise ratio (SNR) subject to a given transmit power. We then propose a first-order descent algorithm on the unit sphere to solve the SGMB problem efficiently. We prove that our algorithm converges to a critical point. Our numerical results further demonstrate our algorithm outperforms the state-of-the-art method for the SGMB problem with a much faster computational speed and a better SNR, especially when the number of users or antennas is large.