An alternating iterative hybrid beamforming method for millimeter wave large-scale antenna arrays

With the growth of the scale of antenna arrays, the full digital beamformer, which requires one dedicated radio frequency (RF) chain per antenna element, is costly and of power consumption. The hybrid beamformer, which offloads part of the beamformer to the analog domain via phase shifters, is an alternative to the full digital beamformer for large-scale antenna arrays. The whole hybrid beamformer is equivalent to the product of a reduced digital beamformer and an analog beamformer. Whereas, the analog beamformer subjects to a constant modulus constraint, because the phase shifters can only control the phase of signals. Due to the non-convex constant modulus constraint, the global optimal hybrid beamformer is infeasible. Therefore, a novel alternating iterative hybrid beamforming algorithm is proposed in this paper. The algorithm divided the analog beamforming matrix and digital beamforming matrix into column blocks and row blocks respectively, only one column of the analog beamforming matrix and one row of the digital beamforming matrix are updated in each processing cycle. The optimal column of the analog beamforming matrix is obtained by the partial derivative of the phase angle of the entries of the analog beamforming matrix, and the corresponding row of the reduced digital beamforming matrix is computed by the least square method. All of the columns of the analog beamforming matrix and rows of the digital beamforming matrix are updated one by one, meanwhile, the residual error of the hybrid beamformer is reduced gradually. Simulation results show that the proposed approach achieves higher achievable data rate compared with the previous works.