Low-Complexity ADMM-Based Multicast Beamforming in Cell-Free Massive MIMO Systems

TL;DR

This paper introduces an ADMM-based algorithm for multicast beamforming in cell-free massive MIMO systems, achieving near-optimal solutions with lower complexity and better scalability than existing methods.

Contribution

It proposes a novel ADMM framework with an iterative elimination strategy to efficiently solve non-convex multicast beamforming problems in massive MIMO networks.

Findings

Achieves near-global optimal beamforming solutions.

Reduces computational complexity compared to SDP and randomization.

Scales favorably with system size and number of antennas.

Abstract

The growing demand for efficient delivery of common content to multiple user equipments (UEs) has motivated significant research in physical-layer multicasting. By exploiting the beamforming capabilities of massive MIMO, multicasting provides a spectrum-efficient solution that avoids unnecessary intra-group interference. A key challenge, however, is solving the max-min fair (MMF) and quality-of-service (QoS) multicast beamforming optimization problems, which are NP-hard due to the non-convex structure and the requirement for rank-1 solutions. Traditional approaches based on semidefinite relaxation (SDR) followed by randomization exhibit poor scalability with system size, while state-of-the-art successive convex approximation (SCA) methods only guarantee convergence to stationary points. In this paper, we propose an alternating direction method of multipliers (ADMM)-based framework for MMF and QoS multicast beamforming in cell-free massive MIMO networks. The algorithm leverages SDR but incorporates a novel iterative elimination strategy within the ADMM updates to efficiently obtain near-global optimal rank-1 beamforming solutions with reduced computational complexity compared to standard SDP solvers and randomization methods. Numerical evaluations demonstrate that the proposed ADMM-based procedure not only achieves superior spectral efficiency but also scales favorably with the number of antennas and UEs compared to state-of-the-art SCA-based algorithms, making it a practical tool for next-generation multicast systems.