Low-Complexity ADMM-Based Algorithm for Robust Multi-Group Multicast Beamforming in Large-Scale Systems

• Published in: IEEE transactions on signal processing Vol. 70; pp. 2046 - 2061
• Main Authors: Mohamadi, Niloofar, Dong, Min, ShahbazPanahi, Shahram
• Format: Journal Article
• Language: English
• Published: New York IEEE 2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; alternating direction method of multipliers (ADMM); Array signal processing; Beamforming; Closed form solutions; Complexity; Convergence; Covariance matrix; Exact solutions; Interference; Iterative algorithms; Iterative methods; large-scale systems; low-complexity; Multicast algorithms; Multicasting; Optimization; Optimization techniques; Quality of service; Robust multicast beamforming; Robustness; Signal processing algorithms; Signal to noise ratio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2022.3160004

We design an efficient robust multi-group multicast beamforming scheme for massive multiple-input multiple-output (MIMO) systems. Assuming only estimates of the channel covariance matrices are available at the base station with a bounded error, we formulate the robust quality-of-service (QoS) problem, which is to minimize the transmit power subject to the worst-case minimum signal-to-interference-plus-noise-ratio (SINR) guarantee. We directly solve the worst-case SINR problem and convert the robust QoS constraint into a number of non-convex constraints. Based on the recent convergence result of the alternating direction method of multipliers (ADMM) for non-convex problems, we develop an ADMM-based fast algorithm to directly tackle the reformulated non-convex problem with a convergence guarantee. The algorithm contains two layers of ADMM procedures. We design the outer-layer ADMM to decompose the problem into three convex subproblems and solve them alternatingly. We further develop an inner-layer consensus-ADMM-based algorithm to efficiently solve one subproblem. By exploring each subproblem structure and developing the special optimization techniques, we obtain closed-form or semi-closed-form solutions to each subproblem. These results lead to a fast iterative algorithm, which is guaranteed to converge to a stationary point of the original robust QoS problem. Simulation shows that our proposed algorithm provides a favorable performance compared with existing alternative methods with magnitudes of computational complexity reduction.