Efficient Single-Group Multicast Beamforming: A Determinantal Point Process Approach

The problem of single-group multicast beamforming (SMBF) is well-known NP-hard. It motivates the pursuit of computationally efficient near-optimal solutions. Due to multicasting, the multicast group is bottlenecked by the user(s) with the minimum received signal-to-noise ratio (SNR). This paper proposes to solve the SMBF problem in two steps: i) select the bottlenecking users by a machine learning approach based on determinantal point process (DPP); and ii) design the beamformer for the selected users. The DPP model jointly considers the magnitudes and directions of users' channel vectors, and thus enables an efficient selection of the bottlenecking users. The beamformer is specifically designed for the selected users by applying the QR algorithm, which facilitates the computation by leveraging channel orthogonalization. Numerical results demonstrate the superiority of the proposed algorithm in terms of the performance-complexity compromise.