A Learning Approach for Efficient Multicast Beamforming Based on Determinantal Point Process

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 provides an in-depth interpretation of the SMBF problem from the multicasting point of view and proposes to solve it 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. Moreover, for a specific channel model, the DPP model is only associated with network size and each takes a one-off training cost, thus can be used as a codebook. The proposed DPP-based subset selection is incorporated adaptively into two fast beamforming algorithms, i.e., the QR decomposition algorithm and the successive beamforming (SB) algorithm. They specifically design the beamformers for the selected users by leveraging channel orthogonalization therein. Numerical results demonstrate the superiority of the proposed QR-DPP and SB-DPP algorithms in terms of the performance-complexity compromise and their robustness to different scenarios.