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

Abstract

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

Multicast Multigroup Precoding and User Scheduling for Frame-Based Satellite Communications

“…When advancing to multigroup multicast systems, however, the service levels between different groups can be adjusted towards achieving some other optimization goal. The sum rate maximization (max SR) problem in the multigroup multicast context was initially considered in [15] under SPC. Therein, a heuristic iterative algorithm based on the principle of decoupling the beamforming design and the power allocation problem was proposed.…”

“…When advancing to multicasting assumptions, the structure of the problem becomes even more involved, as already explained [11]. Consequently, the present work builds upon the heuristic methods of [15], [16].…”

“…The novelty of the SR lies in the PACs, i.e. (7) instead of the conventional SPC proposed in [15]. Therein, to solve the elaborate max SR under a SPC problem, the decoupling of the precoder calculation and the power loading over these vectors was considered.…”

“…To the end of solving the novel SR problem, a heuristic algorithm is proposed herein. Different than in [15], the new algorithm calculates the perantenna power constrained precoders by utilizing recent results [13]. Also, modified sub-gradient optimization methods are proposed to take into account the PACs.…”

“…Nonetheless, when multigroup multicasting is considered, the cost function C SR = N t k=1 log (1 + min i∈G k {SINR i }) . is no longer differentiable due to the min i∈G k operation and one has to adhere to subgradient solutions [15]. What is more, as in detail explained in [15], the cost function needs to be continuously differentiable, strictly increasing, with a log-convex inverse function.…”