A Parallel Low Complexity Zero-Forcing Beamformer Design for Multiuser MIMO Systems Via a Regularized Dual Decomposition Method

Zero-forcing beamforming under per-antenna power constraint (PAPC) is considered in this paper, and the objective is to maximize the minimum user information rate. A parallel low complexity zero-forcing beamformer design is proposed in this paper for MU-MIMO systems by introducing a regularized dual decomposition method. The idea of this method is to solve the problem via solving its dual problem. Since the dual objective is not differentiable, a Tikhonov regularization is introduced. The regularized problem can be solved by using a gradient-based method in a parallel manner. Moreover, the optimal solution of the Lagrangian is in a closed form. The smoothness properties of the regularized dual function are investigated. We also estimate the error bound between the optimal function value of the primal problem and that of the regularized dual problem. Corresponding convergence analysis and convergence rate of the proposed algorithm are established. Computational complexity analysis is carried out to compare the complexity of the proposed method with that of state-of-the-art interior point method. Simulation results are provided to show the effectiveness of the proposed method.