Low-Complexity Minimum Energy Beamforming in Directional Networking

We study the problem of finding the minimum energy beamforming that satisfies the users' signal-to-noise ratio requirements. Traditional transform based beamforming uses heuristics to determine the radiation pattern first, and then calculates the beamforming vector. Recent optimization based beamforming optimizes the beamforming vector directly and greatly outperforms the transform based beamforming. However, optimization based beamforming has prohibitively high complexity due to the semidefinite programming to be solved. In this paper, we propose to solve the optimal beamforming problem by the alternating direction method of multipliers (ADMM). We can achieve near optimal performance while greatly reducing the computational complexity. Simulations demonstrate the advantages of our proposed algorithm over transform based beamforming in terms of performance (e.g., 4 dB reduction in transmit power), and over optimization based beamforming in terms of computation time (e.g., 10 times reduction in computation time).