Fast First-Order Algorithm for Large-Scale Max-Min Fair Multi-Group Multicast Beamforming

TL;DR

This paper introduces a fast, first-order algorithm based on projected subgradient methods for large-scale max-min fair multi-group multicast beamforming, significantly reducing computational complexity while maintaining near-optimal performance.

Contribution

It develops a novel PSA-based approach that directly solves a weakly convex reformulation of the MMF problem, avoiding iterative inverse problem solutions.

Findings

Achieves near-optimal beamforming performance.

Reduces computational complexity compared to existing methods.

Converges to a near-stationary point within finite iterations.

Abstract

We propose a first-order fast algorithm for the weighted max-min fair (MMF) multi-group multicast beamforming problem in large-scale systems. Utilizing the optimal multicast beamforming structure obtained recently, we convert the nonconvex MMF problem into a min-max weight minimization problem and show that it is a weakly convex problem. We propose using the projected subgradient algorithm (PSA) to solve the problem directly, instead of the conventional method that requires iteratively solving its inverse problem. We show that PSA for our problem has closed-form updates and thus is computationally cheap. Furthermore, PSA converges to a near-stationary point of our problem within finite time. Simulation results show that our PSA-based algorithm offers near-optimal performance with considerably lower computational complexity than existing methods for large-scale systems.