paper

An Efficient Global Algorithm for Single-Group Multicast Beamforming

arXiv:1702.01974 · doi:10.1109/TSP.2017.2699640

Abstract

Consider the single-group multicast beamforming problem, where multiple users receive the same data stream simultaneously from a single transmitter. The problem is NP-hard and all existing algorithms for the problem either find suboptimal approximate or local stationary solutions. In this paper, we propose an efficient branch-and-bound algorithm for the problem that is guaranteed to find its global solution. To the best of our knowledge, our proposed algorithm is the first tailored global algorithm for the single-group multicast beamforming problem. Simulation results show that our proposed algorithm is computationally efficient (albeit its theoretical worst-case iteration complexity is exponential with respect to the number of receivers) and it significantly outperforms a state-of-the-art general-purpose global optimization solver called Baron. Our proposed algorithm provides an important benchmark for performance evaluation of existing algorithms for the same problem. By using it as the benchmark, we show that two state-of-the-art algorithms, semidefinite relaxation algorithm and successive linear approximation algorithm, work well when the problem dimension (i.e., the number of antennas at the transmitter and the number of receivers) is small but their performance deteriorates quickly as the problem dimension increases.

The paper has been accepted for publication in IEEE Transactions on Signal Processing. The paper has 14 pages in double-column format.The MATLAB codes of the proposed argument cut relaxation based branch-and-bound (ACR-BB) algorithm in the paper for solving the single-group multicast beamforming problem are available at https://www.dropbox.com/s/safrgm97emdgyl9/ARC-BB.rar?dl=0

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