Optimal Multi-group Multicast Beamforming Structure

Min Dong, Qiqi Wang

Abstract: This paper considers the multi-group multicast beamforming optimization problem, of which the optimal solution has been unknown due to the non-convex and NP-hard nature. By exploring the successive convex approximation method and Lagrangian duality, we obtain the optimal multicast beamforming solution structure. We show that the optimal multicast beamforming has an MMSE filter structure based on a weighted sum of channel directions in the group and a weighted sum of channel covariance matrices. We also show that the inherent low-dimensional structure in the optimal solution benefits significantly the numerical computation, especially for systems with large antenna arrays. We propose algorithms to obtain the multicast beamforming solution based on the optimal structure. Simulation shows that our proposed algorithms achieve near-optimal performance with substantially low computational complexity that does not increase with the number of antennas and increase only mildly with the number of users.