Multi-Group Multicast Beamforming by Superiorized Projections onto Convex Sets

TL;DR

This paper introduces an iterative superiorized projection method for multi-group multicast beamforming, effectively solving a nonconvex optimization problem with improved efficiency and accuracy over existing algorithms.

Contribution

It develops a novel superiorization-based iterative algorithm for nonconvex multicast beamforming, combining convex relaxation with perturbation techniques for better convergence.

Findings

Outperforms existing algorithms in computation time

Achieves smaller approximation gaps in simulations

Guarantees convergence to feasible solutions

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.