Multigroup multicast with application-layer coding: Beamforming for maximum weighted sum rate

In a multicast scenario, the performance is usually determined, and therefore limited, by the weakest link present in the system. With multiple co-channel multicast groups, the problem is further exacerbated due to interference from other transmissions. In this work we investigate an alternative communication scheme, in which additional coding at the application layer is used, spanning over a number of channel realizations. Aiming at maximization of the weighted sum of rates achieved in each group, we show that the optimal transmission strategy depends only on the current channel realization, which, assuming multiple antennas at the base station, allows for formulation of an interesting transmit beamforming problem. In order to find the solution of the problem, we show that the utility-based power control framework, developed for a network consisting of a number of point-to-point wireless links, can be generalized to the case of multigroup multicast. Building upon this framework, we propose iterative beamforming algorithms which can be applied in scenarios both with and without additional coding at the application layer. Numerical experiments are included in the paper to demonstrate the performance of the proposed algorithms.