Learning to Beamform in Multi -Group Multicast with Imperfect CSI

Consider the max-min fair multi-group multicast beamforming problem in wireless networks, where the users with the same request are partitioned into a multicast group and served by the same beam from a multi-antenna base station (BS). The problem is non-convex and generally NP-hard. Due the channel estimation error, the perfect channel state information (CSI) is usually unavailable. The existing optimization-based methods either need the statistic information of estimation error or a time-consuming sample average approximation. In this paper, we propose a graph neural network (GNN) based structure, called multi-group multicast GNN (MMGNN), to learn an efficient robust multicast beamforming strategy based on the estimated channel without any statistic information. Benefiting from the wireless topology based network structure, MMGNN not only captures the interactions between users naturally but also can model the vital property of multicast transmission that the multicast rate is determined by the worst user in each multicast group. Moreover, by sharing the parameters across different users, MMGNN exhibits a pretty good scalability to different numbers of users and guarantees the permutation equivalence about the users. Numerical results show that MMGNN outper-forms a fully connected neural network and a widely used sample approximation based algorithm.