Multi-Group Multicast Beamforming by Superiorized Projections onto Convex Sets
Abstract
In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a semidefinite program in a real Hilbert space, which allows us to approximate a point in the feasible set by iteratively applying a bounded perturbation resilient fixed-point mapping. Inspired by the superiorization methodology, we use this mapping as a basic algorithm, and we add in each iteration a small perturbation with the intent to reduce the objective value and the distance to nonconvex rank-constraint sets. We prove that the sequence of perturbations is bounded, so the algorithm is guaranteed to converge to a feasible point of the relaxed semidefinite program. Simulations show that the proposed approach outperforms existing algorithms in terms of both computation time and approximation gap in many cases.
Cite
@article{arxiv.2102.11947,
title = {Multi-Group Multicast Beamforming by Superiorized Projections onto Convex Sets},
author = {Jochen Fink and Renato L. G. Cavalcante and Slawomir Stanczak},
journal= {arXiv preprint arXiv:2102.11947},
year = {2021}
}