ADMM-based Fast Algorithm for Multi-group Multicast Beamforming in Large-Scale Wireless Systems

TL;DR

This paper introduces a fast, low-complexity ADMM-based algorithm for multi-group multicast beamforming in large-scale wireless systems, outperforming existing methods in efficiency while maintaining high performance.

Contribution

The paper proposes a novel ADMM combined with CCP approach that significantly reduces computational complexity in large-scale multicast beamforming problems.

Findings

Reduces complexity by orders of magnitude compared to state-of-the-art methods.

Maintains comparable performance to existing algorithms.

Enables parallel processing of small subproblems with closed-form solutions.

Abstract

Multi-group multicast beamforming in wireless systems with large antenna arrays and massive audience is investigated in this paper. Multicast beamforming design is a well-known non-convex quadratically constrained quadratic programming (QCQP) problem. A conventional method to tackle this problem is to approximate it as a semi-definite programming problem via semi-definite relaxation, whose performance, however, deteriorates considerably as the number of per-group users goes large. A recent attempt is to apply convex-concave procedure (CCP) to find a stationary solution by treating it as a difference of convex programming problem, whose complexity, however, increases dramatically as the problem size increases. In this paper, we propose a low-complexity high-performance algorithm for multi-group multicast beamforming design in large-scale wireless systems by leveraging the alternating direction method of multipliers (ADMM) together with CCP. In specific, the original non-convex QCQP problem is first approximated as a sequence of convex subproblems via CCP. Each convex subproblem is then reformulated as a novel ADMM form. Our ADMM reformulation enables that each updating step is performed by solving multiple small-size subproblems with closed-form solutions in parallel. Numerical results show that our fast algorithm maintains the same favorable performance as state-of-the-art algorithms but reduces the complexity by orders of magnitude.