The ADMM-based beamforming design with per-antenna power constraints

In this paper, we consider the uplink transmission of a system with one multi-antenna base station (BS) and multiple single antenna user equipments (UEs), which forms a virtual multiple-input multiple-output (MIMO) system. To investigate the capacity maximization problem under per-antenna power constraints, the alternating direction method of multipliers (ADMM) is exploited to obtain the optimal solution. Compared with the semi-definite programming (SDP) algorithm, the proposed ADMM-based algorithm can significantly reduce the computational complexity. In addition, a complexity analysis is presented to show that when the number of antennas becomes larger, the proposed algorithm has a much lower complexity. Simulation results also illustrate that with the lower signal-to-noise-ratio (SNR), the proposed algorithm achieves a little less capacity performance than the SDP algorithm, which is tolerable. Whereas the two algorithm achieve the nearly identical capacity with the higher SNR. Thus, the proposed ADMM-based algorithm provides a more efficient method with the lower computational complexity, which can replace the SDP algorithm to obtain nearly the same capacity performance for wireless communication systems especially with very large antennas.