ADMM-Based Fast Algorithm for Multi-Group Multicast Beamforming in Large-Scale Wireless Systems

• Published in: IEEE transactions on communications Vol. 65; no. 6; pp. 2685 - 2698
• Main Authors: Chen, Erkai, Tao, Meixia
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Alternating direction method of multipliers (ADMM); Antenna arrays; Approximation algorithms; Array signal processing; Beamforming; Complexity; Computational geometry; convex-concave procedure (CCP); Convexity; large-scale optimization; Multicasting; non-convex quadratically constrained quadratic programming (QCQP); Physical layer multicasting; Programming; Quadratic programming; Quality of service; Semidefinite programming; State of the art; Transmitters; Wireless communication
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2017.2679708

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.